THE U N I V E R S I T Y OF M I C H I G A N COLLEGE OF ENGINEERING Department of Electrical Engineering Space Physics Research Laboratory Scientific Report THEORY AND DATA PROCESSING FOR THE PITOT TECIHNIQUE OF UPPER ATMOSPHERE MEASUREMENT Prepared on behalf of the project by R. J. Cittadini R. W. Simmons G. T. Poole ORA Project 03632 under contract with: NATIONAL AERONAUTICS AND SPACE ADMINISTRATION GODDARD SPACE FLIGHT CETER CONTRACT NO. NAS5-21147 GREENBELT, MARYLAND administered through: OFFICE OF RESEARCH ADMINISTRATION ANN ARBOR April 1970

TABLE OF CONTENTS Page LIST OF FIGURES iv LIST OF SYMBOLS v 1. INTRODUCTION 1 2. CALCULATION OF ATMOSPHERIC DENSITY 2 2.1. Continuum Flow Region 2 2.2, Free Molecular Flow Region 3 2, 3 Transition Flow 5 3, ATMOSPHERIC PRESSURE AND TEMPERATURE CALCULATION 9 3 51. o Pressure Calculation 9 3,2, Temperature Calculation 11 4, ASPECT DETERMINATION 12 4,1. Angle Between the Probe and the Earth's Magnetic Field Vector 12 4,2, Angle Between the Probe and the Sun (Moon) Vector 14 4,,3 Orientation of the Probe in Space 15 )44 4 n o' I f.fttck y' 4.5~ Special Case: Precession Cone Method 17 5. PROCESSING OF FLIGHT DATA 24 5. Ground Support Requirementts 24 5o1,1. Tracking 24 5,1o2. Telemetry 24 5,2, Data. Conditioning, Analog to Digital Conversion 32 5,35 Processing of Aspect Data 32 5530lo Angle between the rocket vector and the geomagnetic field vector 32 5.3,2, Angle of attack 34 5.4, Processing of Gauge Output Data 44 5.5. Obtaining Final Data 68 6. REFERENCES 71 iii

LIST OF FIGURES Figure Page 1. Correction factor which accounts for the effect of gas-wall collisions within the gauge antechamber versus angle of attack. 6 2, Pitot probe gauge and antechamber geometry. 7 35 Transition number versus p. 8 4. Relationship between LB and 0 for dV/dt = 0. 14 5. Sun-axis coordinate system. 16 6. Angular-momentum-axis coordinate system. 18 7, Determination of precession period. 19 8. DOVAP trajectory information format. 27 9. Telemetry format, 28 10. Oscillograph record format, summary, 29 11, Oscillograph record format, data. 30 120 Oscillograph record format, aspect, 51 13. MOP abbreviated flow chart. 36 14, MOP output format. 37 15, Pitot Aspect Program output format. 41 16. Timing functions and gauge output versus time, 47 17. Analog oscillograph record of flight data. 48 18, PITOT abbreviated flow chart, 49 19. PITOT output format, 59 20. FLOP abbreviated flow chart. 64 21, FLOP output format, iv

LIST OF SYMBOLS a local speed of sound in the undisturbed region of the gas flow b instrument sensitivity factor (a constant) B geomagnetic field vector BD distorted geomagnetic field vector BM component of BD along the axis of the magnetometer sensor c output bias voltage (a constant) d characteristic dimension of the probe g gravitational acceleration g0 standard sea level gravitational acceleration h geometric altitude H geopotential altitude k Boltzmann's constant K transition number K(M) function of Mach number (defined in Equation (5)) Kn Knudsen number ~, m, n direction cosines in the X, Y, Z directions, respectively L angular momentum vector L1 unit vector parallel to the angular momentum vector m molecular mass M Mach number of the probe M magnetometer vector (a unit vector along the magnetometer sensor axis) p atmospheric pressure v

P. impact pressure behind the shock wave created by the blunt nose 1 of the probe r radius of the earth 0 R gas constant R rocket vector (a unit vector along the longitudinal axis of the probe) S speed ratio, vG/U S sun (or moon) vector S speed ratio, v/u o T temperature of the gas in the undisturbed region of the flow, atmospheric temperature T. internal temperature of the gauge u most probable thermal speed of a molecule v speed of flight of the probe v velocity vector VG velocity component along the gauge orifice axis V magnetometer voltage output X,Y,Z cartesian coordinate axes a angle of attack of the probe P projection of ~ on the XY plane y ratio of specific heats of a gas correction factor which accounts for the effect of gas-wall collisions within the antechamber 9 angle between B and M X molecular mean free path B angle between R and B vi

precession cone half angle p atmospheric density P1 atmospheric density calculated by using continuum flow theory P2 P coscY Pfmf atmospheric density calculated by using free molecular flow theory a angle between R and S 0 angle between S and B w spin rate of the probe

1. INTRODUCTION The pitot probe, as well as its predecessor the pitot static probe, is a rocket-borne instrumentation system designed for the purpose of measuring atmospheric density, temperature, and pressure in the region of the earth's atmosphere between 30 and 120 km (Ainsworth, Fox, and LaGow, 1961; Horvath, Simmons, and Brace, 1962). The technique utilizes a' straightforward application of pressure sensing technology to obtain a measurement of the pressure at the stagnation point of a suitably designed rocket nose cone (Handy, 1970). The interpretation of this impact pressure data in terms of atmospheric density follows from basic aerodynamic theory (Simmons, 1964). The following sections review the theory and present the procedures necessary for the reduction and presentation of data acquired through the implementation of the pitot technique by investigators at the Space Physics Research Laboratory (SPRL) of The University of Michigan. The theory which forms the basis of the pitot measurement is presented in terms of the equations used in the reduction of the data and is treated separately from the detailed processing of the actual numerical data. In the sections pertaining to the processing of the data, emphasis is placed upon the acquisition and applicatior of auxiliary data, necessary for obtaining the final atmospheric density profile. The design and implementation of the pitot probe system in conjunction with available analog to digital data conditioning equipment has resulted in the achievement of nearly 100% automatic processing of these data, A detailed account of the software and procedures used along with sample outputs from the various phases of the processing of a recent data set are given. 1

2. CALCULATION OF ATMOSPHERIC DENSITY By measuring the impact pressure at the tip of a suitably designed rocket probe, atmospheric density can be calculated by means of equations appropriate to the fluid flow regime being encountered. A detailed discussion of the flow theories, the derivation of pertinent equations, and a statement of the involved assumptions is given by Simmons (1964). Because of the wide range of atmospheric density covered by the pitot probe, there is a large variation in the mean free path of the atmospheric particles and in the characteristics of the flow field surrounding the probe. At low altitudes, compressible, nonviscous fluid flow theory adequately describes the flow field around the probe, and at high altitudes, particle theory or free molecular flow theory applies. 2.1. CONTINUUM FLOW REGION In that portion of the atmosphere where the mean free path, A, of the molecules is much smaller than a characteristic dimension, d, of the probe, the flow behaves us a continuum. With the Knudsen number defined as Kn = /d, (1) the condition for continuum flow is that Kn << 1. In the case of the pitot probe, the characteristic length, d, corresponds to the diameter of the blunt nose of the probe, Atmospheric density is found from the impact pressure measurement by using the following equation, derived from the well-known Rayleigh supersonic pitot tube formula, P. P1 = 1 (2) _2 + T (y + 1)2 M2 7(i-l) 2y ( L47 M2 - 2y + 2J where Pi = atmospheric density for continuum flow, Pi = impact pressure behind the shock wave created by the blunt nose of the probe, v = speed of flight of the probe, 2

y = ratio of specific heats of the gas, and M = Mach number of the probe, defined as V v M = - - (3) where a = local speed of sound in the undisturbed region of the flow, R = gas constant, k/m, where k = Boltzmann's constant and m = molecular mass of the specie considered, T = temperature of the gas in the undisturbed region of the flow (atmospheric temperature). To obtain P1 in units of kg/m3, Equation (2) can be written 133.3218 P. with the gauge pressure, P, given in torr and velocity from the trajectory in m/sec. The function of Mach number, 1 K(Z) + -- Z (= + 1)2 M2;+ -1 K( M74) M2 — 2y +2 cannot be evaluated exactly because M requires a knowledge of T (Equation (3)), which is one of the atmospheric parameters unknown at the time of measurement. However, in the region of measurement, because of the weak dependence of K(M) upon M, K(M) can be approximated to an uncertainty of less than 1% by K(M1), where M1 is calculated by using the Standard Atmosphere speed of sound in Equation (3). 2,2, FREE MOLECULAR FLOW REGION As the probe reaches higher altitudes, A increases as the atmospheric density decreases, When the mean free path of the molecules is much larger than the characteristic length of the probe, the flow is free molecular flow, The condition for free molecular flow is that Kn >> 1. The equation linking atmospheric density, p, and impact pressure, Pi,, in the free molecular flow region is P. = 1 (6) R.3Jo F(S) 5

where T. = internal temperature of the gauge, S = speed ratio, v /u where vG = velocity component along the gauge orifice axis, defined as VG = v cosa (7) where a = angle of attack of the probe (see the section on probe aspect), = most probable thermal speed of a molecule, and - 2kT u = m. (8) The function F(S), defined as S2 F(S) = e + SF [1 + erf S] (9) can be approximated quite accurately for S > 1.5 by F(S) 2jTS S (10) By substituting Equations (7) and (10) into Equation (6), we obtain P p = (11) \2qRT. v cosa If we now let P2 = p cosc, (12) we can write 3.1263 P. P2 = (13) Ti v Equation (13) gives pa in kg/m3 for air provided that P. is given in torr, T. in ~K, and v in m/sec.

In the free molecular flow region, a correction for the geometry of the gauge and antechamber is necessary (Pearl, 1970). The correction factor, Ar, is a function of the angle of attack of the probe, a, and of the speed ratio, So = v/u. Figure 1 shows r(a,So) versus a for the pitot probe geometry shown in Figure 2. The speed ratio can be written as a function of Mach number: S fTM (14) It was mentioned earlier that we do not know M, and therefore we approximate S by using M1* Atmospheric density in the free molecular flow region is then given by (15) Pfmf =a cosa 2 3. TRANSITION FLOW Neither continuum nor free molecular flow exists in the region where Kn - 1, the transition fl'ow region. To date, there is no satisfactory theoretical approach that would allow us to calculate atmospheric density easily in this region. In looking for a means of using the impact pressures measured in the transition zone to calculate atmospheric density, a numerical model was derived by using actual pitot probe data and extrapolated experimental data from Wainwright and Rogers (1966), A transition number, K, has been obtained for the particular pitot probe geometry shown in Figure 2 and is presented in Figure 5, The atmospheric density in the transition region is approximated by using the following formula. P =pi 1 (16) where Pi = density according to the continuum flow theory (Equation (4)), and Pfmf = density according to the free molecular flow theory, (Equation (15)). An iterative procedure is necessary for the calculation of p since K is a strong function of p. 5

So = 3.6 1.10 1.08 2.6 2.0 1.5 106 0 IL tO 1.0 4 - z 0 I — 01.02 w LtJ 0 0 _1.00 w F0 w 98 So 6 3. 2.8.96 2.6 2.0 1.5.94.92 0 10 20 30 40 50 60 70 80 90 100 ANGLE OF ATTACK r (DEGREES) Figure 1. Correction factor which accounts for the effect of gas-wall collisions within the gauge antechamber versus angle of attack. 6

KNIFE EDGE ORIFICE HEMISPHERICAL NOSE TIP BAFFLE GAUGE BODY ANTECHAMBER HOT FILAMENT IONIZATION GAUGE VIAIZATIO- en \ RADIOACTIVE IONIZATION GAUGE Figure 2. Pitot probe gauge and antechamber geometry.

I I I I I I' I i'1 1.0.9.8 7.7 W.6 z.5 z 00 0 4 ().3 z:.2 lo08 i0-7 1-6 10-5 10-4 DENSITY (KG/M3) Figure 3. Transition number versus p.

3, ATMOSPHERIC PRESSURE AND TEMPERATURE CALCULATION In the preceding section, the necessary equations for obtaining atmospheric density are given. From this density, atmospheric pressure and temperature may be obtained. The following paragraphs describe in detail the method used. 3.1. PRESSURE CALCULATION Pressure is calculated by means of the hydrostatic equation: dp -pg (17) dh where p = atmospheric pressure, p = atmospheric density, h = geometric altitude, and g = gravitational acceleration. We assume that the'density can be represented locally as an exponential of geopotential altitude of the type p(Hi) p(Hi) expf-C(Hi - Hi)) (18) 1 1 i-l 1 where H denotes geopotential altitude, i is a positive integer, and Hi 1 > Hi > H By rearranging Equation (18), in (Hi) - in p(Hi_) c (=(19) H -H. i-1 i By integrating Equation (17), h Ap. = - f p(h) g(h) dh. (20) hi From the definition of geopotential altitude, g dh = g dH (21)

where go = standard sea level gravitational acceleration, If we use the approximati on g o go _ 0 h2 (22) g (r + h)2 where r0 = radius of the earth, we arrive at r h r + h ~ 0 If we express Equation (20) in terms of geopotential altitude, we obtain H1 Ap. = gf / p(H) dH (24) H. By substituting Equation (18) into Equation (24), APi = g p(Hi) fH1 expf- C(H - H )] dH = [p(H ) p(Hi)]' i H-il i 1*. 1 (25) Then by substituting for C as given by Equation (19) and by reverting to geometric altitude, r2(h -h) H. -H 0 i-lH i (26) i (r +h )(r +h) (2 we arrive at (h hi) p(h )- p(h ) 2 i-l 1 i 1 (27) APi o o (ro + h)(r + h ) ~n (h (27) 0 1-1 0 1 i-l Therefore, the change in atmospheric pressure between altitudes h, and h is given by n n n (h h.) p(h.) p(h.) p, r2 - 1 1 (28) i1li o o i=l (r + h (. h ) (rn P(hi ) - n P(hi) 10

Thus, n P = P i + 7 Ap (29) n 1 i i where P1 = atmospheric pressure at altitude hl. From Equation (29) and the equation of state of an ideal gas, p = pRT, (3o) we obtain n plkT1 = + Ap (31) n m i i where Pi (determined from the impact measurement described previously) and T1 are the density and temperature at a reference altitude hlo. Since T1 is not available, it is approximated by using the Standard Atmosphere temperature at the reference altitude. The numerical integration for APn, Equation (28), is carried from high altitude downward. As the integration proceeds, the summation term in Equation (31) increases rapidly and Pn quickly becomes insensitive to T1, the assumed reference temperature0 3 2. TEMPERATURE CALCULATION From Equations (30) and (31) we can write 1 n T = [p[kT1 + m i pi ] (32) n kp i n 11

40 ASPECT DETERMINATION It is evident from Equation (7) (Section 2.2) that knowledge of the angle of attack of the probe is necessary for the calculation of atmospheric density. The angle of attack of the probe changes with altitude. At low altitudes the main aerodynamic forces acting upon the probe are largely due to high atmospheric density and to the high speed of the probe0 The angle of attack is essentially zero because of the influence of the restoring moments generated by aerodynamic forces acting on the fins, Throughout this portion of the flight, the spin rate is high and the angle of the precession cone is negligible. When the probe reaches an altitude at which the restoring moments become vanishingly small, the precession cone increases0 How large this cone becomes depends on the flight configuration of the probe, In those cases in which the precession cone angle is very noticeable, the angle of attack can become significant long before the probe gets close to the peak of its trajectory, The angle of attack is determined if the orientations in space of the pitot probe and of the'Velocity vector, v, are known, Velocity vector orientation is readily obtained from the trajectory information, The orientation of the pitot probe is calculated from data supplied by a magnetic sensor (magnetometer) and an optical sensor (sun or moon sensor), 4.1, ANGLE BETWEEN THE PROBE AND THE EARTH'S MAGNETIC FIELD VECTOR As part of its instrumentation the pitot probe carries a magnetometer whose output is used to determine the angle between the probe and the geomagnetic field vector, The cylindrical sensor of the magnetometer assembly is mounted with its axis normal to the longitudinal axis of the probe. Magnetometer output is a voltage proportional to the component of the geomagnetic field parallel to the axis of the sensor, V = b(BoM) + c = b(B cosO) + c (33) where V = magnetometer voltage output, b = instrument sensitivity factor (a constant), B = geomagnetic field vector, = magnetometer vector (a unit vector along the axis of the sensor of the magnetometer), c = output bias voltage (a constant), and O = angle between ~ and A. 12

3. ATMOSPHERIC PRESSURE AND TEMPERATURE CALCULATION In the preceding section, the necessary equations for obtaining atmospheric density are given. From this density, atmospheric pressure and temperature may be obtained. The following paragraphs describe in detail the method used. 3.1. PRESSURE CALCULATION Pressure is calculated by means of the hydrostatic equation: dp -pg (17) where p = atmospheric pressure, p = atmospheric density, h = geometric altitude, and g = gravitational acceleration. We assume that the density can be represented locally as an exponential of geopotential altitude of the type p(H ) p(Hi) exp[-C(H1 Hi)) (18) where H denotes geopotential altitude, i is a positive integer, and H, > H. > H i-1 i - n By rearranging Equation (18), in p(Hi) - n P(H_ ) C = (19) H - (1 By integrating Equation (17), h. Ap. = - f p(h) g(h) dh. (20) hi From the definition of geopotential altitude, g dh -= g dH (21) 9

where go = standard sea level gravitational acceleration, If we use the approximati on r2 - 0 (22) gO (rO + h)2 (22 where r~ = radius of the earth, we arrive at r h H = (23) r + h (2 o If we express Equation (20) in terms of geopotential altitude, we obtain H 1 p. g f -p(H) dH (24) H. By substituting Equation (18) into Equation (24), H. g Api= g~ p(H) JH exp(- C(H - H.)} dH - [p(H ) - p(H) i-l 1 C i-1 (25) Then by substituting for C as given by Equation (19) and by reverting to geometric altitude, r2(h. - hi) X ~ -I 1 (26) i i (r +h )(r +h) ( 0 i-1 0 1 we arrive at (h. -h ) p(h ) - p(h) AP 9 r (27) Pi = g o (r + h.')(r + hi) n p(hi ) - Qn P(hi) Therefore, the change in atmospheric pressure between altitudes hi and h is given by n n (h. - hi.) P(hi) - p(hi) Z p. = gr2 1-1 1 (28) i i ~ il (r + hi )(r + h.) Qn P(hi ) - n P(hi) 10

Let us now define a vector R, called the rocket vector, a unit vector along the pitot probe longitudinal axis~ We adopt a cartesian coordinate system defined by unit vectors i, j, and 1 such that ~ is parallel to R, and impose the following restrictions: (1) the probe's spin rate, C, is much higher than its precession rate, (2) the spin rate varies very slowly with time, that is, it is nearly constant during a spin period, and (3) B stays constant during a spin period. lA + Let t = 0 be the instant at which 1 is parallel to M, and we can now write R = k (34) M = ((coswt) i + (sincwt) j, and (35) +3 B +AB ( 36) x y z By substituting Equations (34), (35), and (36) into Equation (33), we obtain V = b(B cosot + B sinct) + c (37) The magnetometer output is shown in Figure 17 in Section 503o At a maximum or minimum, dV/dt = 0, and (R x M)~B = dt 0 (38) Since none of the three vectors is zero, they must be coplanar when dV/dt = Go If we call IB the angle between the rocket vector and the magnetic field vector, we have the situation depicted in Figure 4 for V = V X and for V = V Using Equation (33), we can write an equation for the voltage difference, AV, between maximum and minimum in magnetometer outputs AV = VMAx - VMIN = (b B[cos( - iB)] + c] - (b B[cos(2 +B)] + c 2b B sing B B (39) 15

FdV=o [4tV =o Figure 4. Relationship between LB and 0 for dV/dt = O. By means of Equation (39), B can be calculated from the measured AV provided that b and B are known. The quantity 2b represents a calibration constant. The value of B can be obtained from a geomagnetic field model. Assuming that the distortion caused by the probe in the magnetic field seen by the magnetometer sensor is negligible, we can say that B is known. As mentioned before, at low altitudes the angle of attack of the probe is negligible and R and v can be considered to have the same orientation in space. Hendricks, and Jensen, 1965), at low altitudes ILB vB B arc cos V=V(40) From the value of ~B calculated at low altitudes, the value of the calibration constant 2b can be determined, 2b V= (41) B sinB where LB is given by Equation (40)anA an and AV is taken at the same altitude at which B was calculated. Equation (39) is used to calculate AB for that portion of that b and are known. Thelquantity 2b representis of interest. 4.2. ANGLE BETWEEN Tbe obtainE PROBE A g THE SUN (MOON) VEC TOR Let us define a vector ca lld the sun (moon) vector, ar s a u nit vector 14

having the direction of the line joining the center of the probe and the center of the sun (moon), The angle a between the rocket vector and the sun (moon) vector is given by the output of the optical sensor. The measurement is direct and will not be treated in detail. The position of the sun (moon) can be obtained from the ephemeris. 4,30 ORIENTATION OF THE PROBE IN SPACE Once the angle LB between the rocket vector and the geomagnetic field vector, and the angle a between the rocket vector and the sun (moon) vector are known, the orientation of the probe can be calculated, The angle 0 between the sun vector and the geomagnetic field vector is given by S-B cost SB (42) Now we introduce, for the sake of simplicity, a right-handed cartesian coorA dinate system in which the Z axis is defined by a unit vector k parallel to the sun (moon) vector S, and the X axis is contained in the plane determined by the vectors B and S (see Figure 5), This coordinate system is called the sun-axis coordinate system. The loci of possible positions of R with respect to B determine a cone with its axis parallel to B and with a, cone angle of 2~B. The loci of possible positions of R with respect to S determine another cone with its axis parallel to S and a cone angle of 2ao The intersection of the two cones gives the possible positions of the R vector in space. The following equations can be written in the sun-axis coordinate system: S = +o. (43) B sini + cos4. (44) B R = R i + R j + R. (45) x y z R-S = cosa = R z R'B B = cost = sin~ R + cos$ R (46) R2 + R2 + R2 = 1 o x y z 15

O3J 0 0 H-UI cIC(I (D CI r~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~

From the system of equations numbered (46), the following solutions are obtained: COSIB - cost cosa R:9 (47) x sins R = + 1 - (R2 + R2), and (48) y - x z R = cos (49) z Equations (47), (48), and (49) give the direction cosines of the rocket vector R, In the most general case, there are two solutions for the vector Ro The choice of one of the solutions should be based on the physics of the problem. 4, 4 ANGLE OF ATTACK The rocket vector is then converted from the sun-axis coordinate system to the launch pad coordinate system, a cartesian coordinate system with positive Y north, positive X east, and positive Z perpendicular to the earth's tangent plane at the site. Calculation of the angle of attack is straightforward. v-R cos = (- 0) v 4~50 SPECIAL CASE: PRECESSION CONE METHOD When the flight configuration of the probe is such that significant precession takes place, another method can be used to solve the aspect problem and to determine the angle of attack. It is believed that, in general, the probe causes some distortion in the geomagnetic field; hence, the magnetometer sensor does not sense the geomagnetic field vector B, but rather a somewhat distorted geomagnetic field vector, BID The alternate method has the advantage of obtaining the geomagnetic field vector from flight data without having to resort to geomagnetic field models, thereby resulting in what is believed to be improved accuracy, The probe precesses about the total angular momentum vector L which remains unchanged when there are no exterior moments acting on the probe, For the sake of simplicity, we use a unit vector L1 parallel to L, We then define a right-handed cartesian coordinate system which we call the angular-momentumaxis coordinate system, The Z axis is defined by a unit vector k parallel to the angular momentum vector L of the probe, The Y axis, defined by a vector j, 17

is such that the YZ plane contains the sun vector S. The X axis completes the right-handed system (see Figure 6). PRECESSION CONE __________~~~~ Y Figure 6. Angular-momentum-axis coordinate system. Consider a precession period at the apogee of the trajectory for a given probe. A precession period is easily distinguished in the magnetometer output or by plotting the optical sensor output (see Figure 7). Let 25 be the angle of the precession cone. The rocket vector R describes in time a cone with its axis parallel to L1 and a cone half angle ~. The angle 5 can be calculated easily from optical (sun or moon) sensor data (see Figure 7). 2E; = C _ a-. (51) MAX MIN The angle between the rocket vector R and the distorted geomagnetic field vector BD varies during a. precession period from a. minimum, LBB, to a maximum, BM, such that MIN MAX - + a~. (52) BMAX BMIN 18

61 BM MAGNETIC FIELD STRENGTH o- ANGLE TO THE SUN (MOON) FROM MAGNETOMETER OUTPUT (MILLIGAUSS) _ MAX — "N- I - _- _ t - H ~ ~ ----— ~cK-2 BM MIN (Dl L.MIN CD H' r D II 96 ct - 0X I CD 0 iJo a emI

The component of BD along the axis of the magnetometer sensor is denoted as BM. Magnetometer output given in volts can be converted to magnetic flux density in milligauss through the calibration data supplied by the manufacturer o BDsin BMI = B, and (53) ) BMIN MMIN BDsin MA (54) Solving the system of Equations (52), (53), and (54) for BD and ItB yields B MIN MMIN B = arc sin,and (55) MIN B B - B cos 2~ B cos 2+| )+ B+ (56) D -j sin 2~IN The quantity ED is determined quite accurately at apogee where all the intervening quantities can be measured without much error because of the large precession half cone angle,o Because the geomagnetic field strength varies with altitude above the earth's surface, the values of BD at different altitudes can be approximated by applying to BD, as calculated by Equation (56), the same percentage variation with altitude suffered by B as given in the geomagnetic field model, In this case, we have used only the rate of decay in the field from the geomagnetic field model, as opposed to using the geomagnetic field vector (direction, magnitude, and their rates of change) from the model as required in the method described in Section 4t.l At apogee the following equations can be written (see Figure 6): L1 S cos( MIN+ ) (57) By L1 = cos(CBIa + i ) B' (58) B B- + D (58) DMIND (L1 x S)@(L1 x BDL =MIN + )1][sin(GB + )1]} x(1 B L1)( SCB B OL1)( S i~1) * (59) 20

The angle y (see Figure 6) is the projection on the XY plane of the angle $ between the sun vector S and the distorted geomagnetic field vector BD. The angle y can be calculated (see Figure 7) by means of the following relationship: _ 3 2.2 (60) t3 - tl Combining Equations (57), (58), and (59), we obtain S*B+ = B~ cosy[sin(aM + )][sin(BI + + f[cos(E + ) cos( + ) MIN D D MIN B+ BMiN MIN (61) The general equation RB B B = + B (62) D D B D B can be written in a different form when the probe is in the low-altitude region. At low altitudes, where the aerodynamic restoring moments are the controlling factor in the orientation of the probe, the velocity vector v and the rocket vector R can be considered to be coincident. Equation (62) then becomes v-B vB cost- + rB z B-' / (63) D D CB v D K)[ j J The previous equations can then be grouped into systems of equations that would allow us to obtain the orientation of the rocket vector R. In order to find the orientation of BD we use Equations (61) and (63) and add the condition which must be satisfied by the direction cosines of a vector in a cartesian coordinate system. The following system results. S+B SBD = S B + S B + S BD = fcos7[sin( + )][sin(( + D MIN + {[cos(BMi + )][cos(aM + I)] (64) MIN vB- = v B +vB +vB + Ll (p5] and (65) VBD Q D2 m Dm n Dn _LDn 21

B +3 +3 = 1, (66) Di Dm Dn The subscripts ~, m, and n denote direction cosines of the subscripted quantity in the X, Y, and Z directions, respectively. The solution of the system of Equations (64), (65), and (66) gives the direction cosines BDI, BDm, and BDn of the distorted geomagnetic field vector BDo In Equation (65), BM and BD should be given for the same low altitude at which v~, vm, and vn are taken. Although the orientation of the geomagnetic field vector changes with altitude, the change in the region of interest (between 70 and 140 km) is so small that it can be neglected, On these grounds we disregard any variation in BD~, BDm, and BDn with altitude, In order to find the orientation of the rocket vector, we resort to the following system of equations. Notice that the following equations apply to any point along the trajectory. They are not restricted to near apogee conditions like Equations (61) and (64) or to low altitudes like Equations (63) and (65). RS = RS + R S + R S = cos, (67) R m m m n n BD_ = RmB m3 +R 2 = + -1 (i), and (68) R2 + R2 + R2 = 1 (69) R m n Solution of the system constituted by Equations (67), (68), and (69) provides the direction cosines RR, Rm, and Rn of the rocket vector for the time and altitude corresponding to the values of a, BM, and BD used in Equations (67) and (68), Once the rocket vector R is known along the trajectory, the angle of attack can be calculated by means of Equation (50). Note that although the equations were derived for the sake of simplicity by using the angular-momentumaxis coordinate system, any other coordinate system can be used, for example, the launch pad coordinate system. The systems of Equations (64), (65), and (66), and (67), (68), and (69) are of the following type: a X + a Y + a Z = K1, x y z b X + b Y + b Z = K2 X y z X2 + y2 + Z2 = 1 J (70) 22

and the general solution is of the following form: - (C K - C K ) + ((C K - C K )- [(c + 2 +C 2 )(K2 + K2- C ) ]}1/2 zx z xY zx z zY y xy yz zx z y yz X = + C + C2 xy yz zx (71) (C K - C K ) + ((C K - C K )2 _ [(C2 + C2 + 2 )(K2 + K2 - c2 )11/2 yz z xy x - yz z xy x xy yz zx z x zx (C2 + C2 + C ) xy yz zx (72) Z= + (- X2 _y2)1/2 () where x x K = Klb - K2ay, K = Klb - K2a, z z z and C = a b - a b xy x y y x C = a. b - a b yz y z z y C = ab - ab ZX Z X X Z 23

5, PROCESSING OF FLIGHT DATA 5 o1 o GROUIND SUPPORT REQUIREMENTS Because of the automated data processing techniques used in the reduction of pitot data, the following modest ground support requirements must be met for each flight~ Failure to fulfill these requirements can result in a degradation of the overall quality of the final data as well as jeopardize the automatic data processing procedures, 5 o 1lo Tracking The complete time history of the position and velocity of the probe during flight may be obtained from either radar or DOVAP (Doppler Velocity and Position) tracking. The fully processed tracking (trajectory) data may be supplied in the form of either a digital magnetic tape or punched tape decks along with a formatted listing of the contents of either. These data should be presented in either common metric or English units and should include the geometric position and velocity of the probe referred to a launch pad coordinate system versus time. Figure 8 illustrates the required punched card format (two decks: one for velocity data and one for position data)o The required magnetic tape format is 7-track, BCD mode recorded at 556 BPI with even longitudinal parity. The information contained must include, at least, that which is shown in Figure 8. It is common, however, to provide more information than that specified for the card decks, Upon receipt, this information is read into and stored on a disc file at The University of Michigan Computing Center for future use as input to the main processing programs. 5.1.2. Telemetry Since the pitot probe utilizes an IRIG FM/FM telemetry system, the range must provide an appropriate telemetry receiving station for acquiring and recording the data from the probe in flight. In addition, the station must provide a source of range timing suitable for both magnetic and strip chart or oscillograph recording, and a source of 100 kHz to be used for magnetic tape wow and flutter compensations. Range timing should be a modulated carrier BCD type. Usable codes are: NASA 36 Bit, AMR D5, IRIG A and IRIG B for both tape and oscillograph recording; and NASA 28 Bit for oscillograph recordings only. Figure 9 shows a typical telemetry format for the pitot probe As stated previously, the pitot probe data are processed automatically using the SPRL Data Conditioning System (Caldwell, 1966), and The University of 24

Michigan Computing Center's IBM 360/67. For this reason, the quality and format of the analog magnetic tape is of primary importance and a few words regarding this format are in order. The SPRL Data Conditioning System is primarily an FM/FM Analog to Digital conversion facility. Included in the equipment of this system is an analog instrumentation recorder which is used to play back the analog tape. The data output of the recorder is then demodulated and the individual data channels are digitized and recorded in digital form on an IBM compatible magnetic tape. The analog recorder is of the low band direct record type and is capable of processing 7-track, 1/2 in, wide direct recorded magnetic tapes at speeds of 60 or 30 ips. The tape drive is capable of the other standard lower tape speeds, but proper equalization electronics are not available~ For this low band recorder (Range Commanders Council, 1966) the frequency response at 60 ips is 100-120,000 Hz while at 50 ips it is 50-60,000 Hz. At 30 ips the maximum "flat" frequency response (-3 db) is 60 kHz; above 60 kHz the nonlinearity in response can introduce severe cross-talk and distortion in the telemetry signals of higher frequency. In addition, the tape speed (wow and flutter) compensation hardware of the Data Conditioning System will accept ornly 100 kAz reference signals. If only VCO frequencies lower than 60 kHz are used in a telemetry video, it is still desirable to record a 100 kHz reference signal, for it has been found that if the signal is strong, enough of it can be recovered at 30 ips for use by the compensation discriminator. However, when maximum VCO frequencies exceed 60 kHz, as is the general case with the pitot probe, a tape speed of 60 ips is mandatory0 Recording levels should be adjusted to give 1%o (or less) third-harmonic distortion. Tracks 2 and 4 of the magnetic tape should not carry signals with strong 100-500 Hz components (such as voice) because of the cross-talk characteristics of magnetic tape recorders, A suggested use for tracks 2 and 4 is that of back-up data. Tracks 1, 3, 5, and 7 should carry the most valuable signals and those with the most critical time relationships because these tracks are all in the same head stack, and at 60 ips the time delay between head stacks is 25 msec, Taking into consideration the preceding observations, the following magnetic tape format should be requested, This format insures high data quality and compatibility witlh automatic processing procedures, Recording Mode: Direct Tape Speed: 60 ips Tape Width: 1/2 in, Tape Thickness: At least 1 mil Head Format: IRIG Recording Levels: Normal (see above) 25

TRACK INFORMATION REMARKS 1 NASA 36 Bit Time Code 100 pps/1 kHz 2 Rx #A Video Backup 3 Diversity Combiner #A Video Primary Data Track 4 Diversity Combiner #B Video Backup 5 100 kHz Ref. ONLY 6 Station Multiplex Reference 100 kHz NASA 36 Bit 70 kHz + 7o5% NASA 28 Bit 40 kHz + 7.5% Voice 52,5 kHz + 7o5% AGC A 10.5 kHz AGC B 7.35 kHz AGC C 5,4 kHz AGC D 3,9 kHz 7 Rx #D Video Backup Note: Record 100 kHz and time code at maximum level. The paper oscillograph record requirements are straightforward and are of secondary importance to the data processing techniques used for the pitot probe, Figures 10, 11, and 12 show typical oscillograph record formats required for visual analysis. 26

GMT TIME vx v v vt.x ~ y z y Day Hr Min Sec (m/sec) (m/sec) (m/sec) (m/sec):3;'4,0.! C 5O. 019;?47 7 -15 E: 12-67. 7 139L:' 1 80000000 0000000008 0 000OO OOOOOOOOOO00OOOO OOOOOO0 0O0000OO OOO OOOOOOOOOOOOOOOOO06 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 05 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65-66 67 68 69 7071 72 73 74 75 76 77 76 79 8 111111111111111111111 1 111111 111111111 111111 11111111111111 11111 111 111 1 111 1111111111111 1 22 2222 222222222222222222222 222222222222222222222 2222222222 22222222222222222 3 333333333333333333 33333333333 3333-33333 333333 33 3333333 33 3333333333333333 444 4444444444444444444444444 4 44444444 4 4 4444444444444 4444444444444444444444444 5555555555555 5555 5555555555555555555555 55555555555555555555555555555555555555 66-6 6 6 6 6 6 6 6 6 6 6 6 6666666666666666666666666666 66666666 66 6666666 66666666666666666666 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 777 7 77777777777777777 1 7777777777777777777777777777 88888888888888 8 888888 88888888888 8 8 8 888888 8 8 88888888 88888888 88888888888888888 9 9 9 9 9 9 9 9 9 9 9 9 9 9999999999 999999999 99999999999999999999999999 999999999999999999 1 2 3 4 5 6 7 8 9 1011 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 Z: 53 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 HACKETT M 5081 GMT TIME. X Y Z Lat Long Alt Day Hr Min Sec (meters) (meters) (meters) (deg) (deg) (meters): -. S. 0- 1:9,-:n,._ 5;.,;:.. " E.? r,'' 7' i 5,7 7' 0oooo00o 0000 0 OODOOOOO 000000000000000000 0000800800 0OOOO0000OOOOOOO0 00000 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24'5 26 27 28 29 30 31 32 33 34 35 36 37.38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 8 111111111111111 111111111111111111 11111111111111111111111111111111111111111111 2222 22222222222222222222222222222222 222222 22 22 22222222222222 222 222222222 2222 3 33333333333 333333333333 3333333333 333333333 333 3 333333333 333333333333 3 444 44444444444444444444444444444 4444 4 4 4 4 4 4 4 4 44444 4 444444444 44444444 44 555555555 5 55555555555 5 5555555555 5 5 55555 5 5 5 5 5 5 5 5 5 555555555555555 5 5 5 555555555 55 555 666666666666666666666666 66666666666666666666666666666666666666 77 7 77777777777 7777777777777777777777777777777 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 7 717 7 7 7 7 7 7 7 7 7 77 7 7 77 7 7 77777777 888888888888 8 8 8 8 8 8 88888 888 888 88888 8 8888888888 88888 88868888 8 88888888888 8 9999999999999999 9999999999 9999S99999999999999999999999999 99999999999999999999 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 "~.3 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60 61 62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79 80 HACKETT M 5081 Figure 8. DOVAP trajectory information format. 27

NOSE CONE PRIMARY TM 244.3 RF LINK TOTAL DEVIATION 155 KHZ DESCRIPTION IRIG CHANNEL NO. CENTER FREQ FREQ DCR LP FILTER FREQ FILTER TYPE GAGE 18 70 kHz 7-1/2 % 1050 CD DUAL COLLECTOR RADIOACTIVE FREE RUN SAMPLE TIME 152 SEC | SEGMENT WIDTH IONIZATIONR OR RANGE CHANGE FORCED SAMPLE GA6E LAUNPH ~SGAGE INFORM & PURPOSE SUPPLY Rsi Rs THERM I G 1 GAGE THERM 3.7 V 5.003 0 K 30 K 2 0 VOLT REF +.004 3 5 VOLT REF. 003 4 2.5 VOLT REF 2.503 5 RANGE INDICATE 4.5 V DATA GAGE OUTPUT DESCRIPTION IRIG CHANNEL NO CENTER FREQ FREQ DEVILP FILTER FREQ FILTER TYPE GAGE U IT 52.5 kHz - I/2 % 790 CD HOT FILAMENT _ IONIZATION COMMUTATOR FREE RUN SAMPLE TIME 5 SEC ISEGMENT WIDTH GAGE OR RAECHANGE FORCED SAMPL msc TO %G INFORM & PURPOSE lI.ffi SUPPLY Rs R | THERM I +28 BAT. REF. 4.3 V BATT.-. 33 K 5.1K 2 0 VOLT REF +.004 3 5 VOLT REF. 5.003 * 4 2.5 VOLT REF 2.503 5 RANGE INDICATE 3.5 V DATA GAGE OUTPUT DESCRIPTION IRIG CHANNEL NO.CENTER FREQIFREQ DEVILP FILTER FREQ FILTER TYPE 13 14.5 kHz?11/2 % 220 CD MAgNETOMETER FREE RUN SAMPLE TIME 14.5 SEC SEGMENT WIDTH COMMUTATOR msec TO G INFORM S PURPOSE ~AOriC s SUPPLY Ris Rs; THERM I 4 THERM 4.9 V 5.003 1.8S I MEG 2 0 VOLT REF +.004 3 5 VOLT REF 5.003 4 3 THERM 4.9V 5.003 3.3 K 300 K 5 2 THERM 4.9 V 5.003 3.3 K 300 K DATA MAG. OUTPUT DESCRIPTION IRIG CHANNEL NO.CENTER FRE FREQ DEVLP FILTER FREQ FILTER TYPE SOLAR ASPECT 15 30 kHz 7. 1/2 % 450 CD Figure 9. Telemetry format. 28

ROCKET 14.362 AGC I 30kHz/45OHCfj 14.5kHz/220OHz CD 5325kHz/790OHz CD 70kHz 1O50 H CD UPPER UPPER IUPPER UPPER UPPE R E I EN CENTER CENTE R CENTER CENTER LOWER LOWER LOWER LOWER LOWER 2" 3",lc i 0 ] L l: L z _, "- -I 3 3A "1 AGC ASPECT MAGNETOMETER DATA 2 DATA 1 STATIC STATIC STATIC STATIC NASA REFERENCE REFERENCE REFERENCE REFERENCE NASA 28 BIT 28 BIT GENERAL: ALL CHANNELS ARE 7Z % REALTIME FLIGHT DATA FINAL FLIGHT DATA PAPER SPEED I ips I Ips TAPE SPEED COMPENSATION USED ON ALL PLAYBACKS PAPER PERMANENT WIMB PERMANENT WIMI STATION CALIBRATE AT THE BEGINNING AND END OF EACH RECORD SOURCE REALTIME PLAYBACK TIME -30 SEC TO LOS -60 SEC TO LOS NO.OF RECORDS I PER FLIGHT 3 COPIES PER FLIGHT ENGINEER -PO DRAFTSMAN MLN SPACE PHYSICS RESEARCH LABORATORY NASA 14.362 SUMMARY DEPARTMENT OF ELECTRICAL ENGINEERING FLIGHT RECRD3-14-69 UNIVERSITY OF MICHIGAN I I 27-e ANN ARBOR, MICHIGAN B- E 1420 DATE Figure 10. Oscillograph record format, summary.

ROCKET I14.362 30 kHz/450 Hz CD 52.5 kHz/790 Hz CD 70 kHzA050Hz CD UPPER UPPER UPPER 7: 1 I~ CENTER CENTER CENTER LOWER LOWER LOWER 0 I V2Z' —-- 4" - 4" ASPECT DATA 2 DATA 1 STATIC STATIC NASA NASA ENASA 36 BIT REFERENCE REFERENCE 36 BIT GENERAL: ALL CHANNELS ARE 74 % FINAL FLIGHT DATA PAPER SPEED 10 Ips TAPE SPEED COMPENSATION USED ON ALL PLAYBACKS PAPER PERMANENT STATION CALIBRATE AT THE BEGINNING AND END OF EACH RECORD SOURCE PLAYBACK TIME -30 SEC TO LOS NO. OF RECORDS I PER TEST ENGINEER P0H DRAFTSMAN MLH SPACE PHYSICS RESEARCH LABORATORY NASA 14.362 DATA 3-14-6| DEPARTMENT OF ELECTRICAL ENGINEERING FLIGHT RECORD 2 10-3-66 UNIVERSITY OF MICHIGAN 9-27-6 ANN ARBOR, MICHIGAN B-E 1421 DATE Figure 11. Oscillograph record format, data.

K&E 19 1153 6-67ROCKET {14.362 | AGC | 30kHz/450Hz CD | 14.5kHz/220Hz CD | 70kHz/lO5OHz CO. I |UPPER UPPER UPPER. " 1~3 1 ICENTER CENTER CENTER CENTER IOWER LOWER LOWER LOWER 1- I im MAa —, 3,, H-~ N AGC ASPECT MAGNETOMETER GAGE 1 NASA STATIC STATIC STATIC NASA 36 BIT REFERENCE REFERENCE REFERENCE 36 BIT GENERAL: ALL CHANNELS ARE 7Z % FINAL FLIGHT DATA PAPER SPEED 10 Ips TAPE SPEED COMPENSATION USED ON ALL PLAYBACKS PA PER | PERMANENT STATION CALIBRATE AT THE- EGINNING AND END OF EACH RECORD SOURCE PLAYBACK TIME -30 SEC TO LOS NO. OF RECORDS I PER TEST ENGINEER POH DRAFTSMAN MLH SPACE PHYSICS RESEARCH LABORATORY NASA 14.3620 ASPECT DEPARTMENT OF ELECTRICAL ENGINEERING FLIGHT RECORD 3 UNIVERSITY OF MICHIGAN L -s ANN ARbOR MICHIGAN B-E 1422 DATE Figure 12. Oscillograph record format, aspect.

5.2o DATA CONDITIONING, ANALOG TO DIGITAL CONVERSION When the magnetic tape containing analog telemetry data is received at SPRL, it is processed in the Data Conditioning System of the laboratory. The discriminators in the system are set so that the upper band edge produces an output of -8V and the lower band edge produces a +8V output. The 12-bit successive approximation A/D converter has a resolution of plus or minus half the least significant bit, or + 2.4 mV referred to a -1OV to +10V full scale signal. Channel-to-channel spacing can be adjusted between 57~3 and 500 isec; 57.3 psec is the spacing used for pitot probe data, Three channels are sampled in every pitot probe flight. Multiplexer scans are triggered by an external signal which is commonly either the 100 kHz reference signal recorded on the tape or the BCD time code carrier. For the pitot probe, the reference signal is divided so as to provide a sampling rate of 100 samples per sec per channel when the data are sampled The overall data sampling rate capability of the system is 13 kHz, and for pitot probe data the overall sampling rate is 300 samples/seco The 100 kHz reference is also used to compensate for tape wow and flutter, The BCD time code can be sampled without missing a data sample, and the sampling is done eithei~ on external command signal or at the beginning of each digital tape record, The second procedure is standard when pitot probe data are processed, The BCD time code carrier normally used is one kHz, providing one msec time resolution, During normal processing of pitot probe data, the time taken is that corresponding to the first data sample in each record. Each record of data contains 334 samples per channel, As the converter digitizes one data record, the record is accumulated in one buffer of the PDP-8 computer of the Data Conditioning System until the buffer (with a capacity of 1028 words) is filled, Then the following data record starts filling the second buffer while the first buffer is written onto the digital magnetic tape, The recorded digital tape is a standard seven-track magnetic tape recorded in binary mode at 556 characters/in. 553o PROCESSING OF ASPECT DATA 5,3,1, Angle Between the Rocket Vector and the Geomagnetic Field Vector Throughout the upleg portion of the flight, measurements of the voltage difference AV in the magnetometer output and the OV and 5V calibrations from the magnetometer channel are made at 1-sec intervals, Of these data, the first 20 or 30 sec are selected as calibration data for calculation of the calibration constant, A computer program called MOP (Magnetometer Orientation Program) is used for the calculations, and was written for the IBM 360/670 Inputs to MOP are these: 32

(1) launch site coordinates, (2) height of the launch site above the mean radius of the earth, (3) time from launch and magnetometer data (AV and channel calibrations), and (4) trajectory information (velocity components and altitude versus time). The program includes subroutines which generate the geomagnetic field model (Breckenridge, 1965). The generation is achieved by means of Legendre polynomials using Gaussian-normalized coefficients derived from spherical harmonics analysis. A calibration constant is calculated (see Equations (40) and (41)) for every second of calibration data. These calibration constants are averaged into one which is then used to calculate the angle between the rocket vector and the geomagnetic field vector (see Equation (39))o An abbreviated flow chart for MOP is given in Fi-gure 13. Output from the program (see Figure 14) follow: Calibration information: (1) time from launch (TIME) in sec (2) altitude (ALTITUDE) in km (3) angle between the geomagnetic field vector ancd the velocity vector (UNTGLE) in deg (4) elevation of the geomagnetic field vector (EL B) in deg (5) azimuth of the geomagnetic field vector (AZ B) in deg (6) elevation of the velocity vector (EL TRAJ) in deg (7) azii iluth of the velocity (AZ TRAJ) in deg (8) calibration constant (CAL COUNST) Other inf ormation: (1) relation between voltage and magnetic field (Average Calibration Constant) (2) time from launch (TIME) in sec (3) altitude (ALTILTUDE) in km 33

(4) angle between the geomagnetic field vector and the rocket vector, NAB (ANGLE 2) in deg (5) supplement to LB (ANGLE 1) in deg (6) elevation of the geomagnetic field vector (EL B) in deg (7) azimuth of the geomagnetic field vector (AZ B) in deg (8) elevation of the velocity vector (EL TRAJ) in deg (9) zenith of the velocity vector (ZEN TRAJ) in deg (10) azimuth of the velocity vector (AZ TRAJ) in deg 5.3.2. Angle of Attack Once the angle LOB between the rocket vector and the geomagnetic field vector, and the angle a between the sun (moon) vector and the rocket vector are known, the angle of attack is calculated by a computer program called Pitot Aspect Program. The program is written for the IBM 360/67. Inputs to the program are (1) GMT launch time in hr, min, and sec (2) latitude and longitude of the launch site in deg (3) apparent right ascension of the sun (moon) in hr (4) apparent sidereal time in hr (5) declination of the sun (moon) in deg (6) time from launch (7) angle between the rocket vector and sun (moon) vector in deg (8) angle between the rocket vector and geomagnetic field vector in deg The first five are used for the purpose of defining the sun vector. The last three are given at 1-sec intervals over the region of interest. The program calculates the rocket vector from Equations (47), (48), and (49), and the angle of attack from Equation (50), There are two possible solutions for the rocket vector and for the angle of attack, Output from the program (see Figure 15) are 34

(1) zenith angle of the sun (moon) in deg (2) azimuth of the sun (moon) in deg (3) time from launch (TIME) in sec (4) zenith angle of the rocket vector (ZENITH) in deg First (5) azimuth of the rocket vector (AZIMUTH) in deg Solution (6) angle of attack (ALPHA) in deg (7) cosine of the angle of attack (COS ALPHA) (8) zenith angle of the rocket vector (ZENITH) in deg Second (9) azimuth angle of the rocket vector (AZIMUTH) in deg Solution 10) angle of attack (ALPHA) in deg (11) cosine of the angle of attack (COS ALPHA) (12) zenith angle of the velocity vector (VEL ZEN) in deg (13) azimuth angle of the velocity vector (VEL AZ) in deg

READ FLIGHT ID NFCAL (NUMBER HF FLIGHT CALIBRATES) NDAT (NUMBER HF DATA POINTS) NTEAJ (NUMBER OF TRAJECTORY CARDS) ITH, ITM, TD (HOURS, MINUTES, SECONDS OF LAUNCH TIME GMT) DELTAT (TIME CORRECTION) ALTL (ALTITUDE OF LAUNCH SITE ABOVE EARTH MEAN RADIUS) SW (ALTITUDE UNITS) DLAT (LATITUDE OF LAUNCH SITE) Y DLONG (LONGITUDE HF LAUNCH SITE) I>NFCAI; A DA/N]CA DDTERMINE NUMBER OF CARDDE LT IN V C 1 TOBE PROCESSED NMC D NFCAL + NDAT F N ~~~~~~~~~~NNFCAI+ DREAD VELOCITY TRAJECTORY I a I+1 ~~~~~~~~~~~KH (HOUR) ( IINDAHE HF MADNHTHEHTHH THT)KM (MINUTE) I A A I = O ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~SEC (SECOND) HAJ EDDHXDOT (X COMPONENT) DDPT YDOT (Y COMPONENT) >M ZDOT (ZCOMPONENT)' I = F READ ALTITUDE TRAJECTORY KH (HOUR) KM (MINUTE) INTERPOLATE IN VELOCITY I>Mc SEC (SECOND) TRAJECTORY FOR VX,VY,VZ N lTALT (ALTITUDE) AT TIME DTIM(I) CALL FIELD1(DLAT,DLN, L(),EBVB STHE= DELTAV(I)=EDVI FigureT15.EMOPAabbreviatedAflowCchart. READ CALIBRATION DATA CALL FIELD1(DAT,DLONG,ALT(l),BE,BNBV,B) HT2=10H DFTIM (FLIGHT TIMrE) INTERPOLATE IN ALTITUDE TH = ARCOS((VX-BE+VY-BN-VZ-BVT)/(V-B)) GVO (ZERO VOLT CALIBRATE) TRAJECTORY FOR ALT(I) DA = DELTAV(I)/(B-SIN(TH) ) GVMIN (MINIMUM OF MAGNETOMETER OUTPUT) AT TIME DTIM(I) AS = AS + DA W G~~~~~~IGMAX (MAXIMUM OF MAGNETOMETER OUTPUT) PRINT REUT GV5 (FIVE VOLT CALIBRATE) TMI ATIHT,HT2DPAZ EENAT PRINT CALIBRATION DATA DTIM(I),ALT(l),TH,DDIP,AZB,ELT,AZT,DA CORRECT TIME DTIM(I) = DFTIM + DELTAT VMIN = 5.0/(GV5-GVO) + (GVMIN-GVO) VMAX = 5.0/(GV5-GVO) + (GVMAX-GVO) DELTAV(1) = VMAX-VMIN Figgmre 13. MOP abbreviated f low chart.

CALIBRATION INFORMATION TIME ALTITUDE ANGLE EL B AZ B FL TRAJ AZ TRAJ CAL CONST 20.1-85 11.401 158. 959 -69. 821 351.526 77. 240 95.100 4.8707 21.185 11.787 158.756 -69.821 351. 527 76.801 94.906 4.5386 22.185 12. 160 158.897 -69.820 351.528 76.681 95.782 4.6515 23. 185 12.556 160.279 -69.820.351. 529 77.501 101.074 4.8752 24.185 13.113 162.058 -69.819 351.530 78.587 108.840 5.5362 25.185 13.851 163.044 -69.818 351.532 79.029 113.830 5.8502 26.185 14.787 163.497 -69.817 351.534 79.225 116.273 6.0616 27.185 15.958 163.826 -69.816 351.537 79.437 118.162 6.4003 28.185 17.414 164.019 -69.815 351.541 79.466 119.256 6.5895 29. 185 19.064 164.225 -69.8 13 351. 545 79.3-93 120. 349 6.7895 30.185 20.708 164.329 -69.81 1 351.550 79.329 120.877 6.9503 31.185 22. 327 164.369 -69. 809 351. 554 79. 258 121.045 7.0289 32.185 23.924 164.421 -69.808 351.558 79.217 121. 307 6.8337 33.185 25.501 1.64. 334 -69.806 351.56? 79. 280 120. 896 6.8465 34.1 85 27.060 164.367 -69.80.5 351. 566 79.237 121. 054 69221 35.185 28. 602 164.434 -69.803 351.570 79.150 121.359 6.7324 36.185 3Q.128 164.405 -69. 801 351.573 79.085 121.159 6.7812 37.185 31.640 164.372 -69.800 351. 577 79.045 120.964 6.7725 38.185 33.138 164.354 -69.798 351.581 79.029 120.870 6.7143 39.185 34.623 164.332 -69.797 351.585 78.970 120.724 6.5425 Figure 14. MOP output format.

MAGNETOMETER DATA REDUCTION FOR NASA 14.*386 FROM THE INFLIGHT CALIBRATION THE FOLLOWiNG RELATION BETWEE~4 LAUNCH TIIME 72299.815 VOLTAGE AND MAGNETIC FIELD HAS BEEN DETERMINED LATITUDE 37. 840~ ________ _______ _______ ________ _______ _______ _______LONGITUDE -75.480 P-P VOLTAGE= 6.214382. *MAG.F IEL D*S IN(fANGL E) TIME ALTITUDE ANGLEI ANGLE2 EL B AZ B. EL TRAJ ZEN TRAJ AZ TRAJ 40.'185 36.095 17.259 162.741 -69.795 351.589 78.825 11.175 120.823 41.185 37.555 ~~17.272 162.728 -69.794 351.592 78.797 11.203 120.637 42.185 39.005 17.140 162.860 -69.792 351.596 78.740 11.260 120.501 43.185 40.444 16.715 163.285 -69.791 3.6078.549 11.451 120.566 44.185 41.872 16.436 163.564 -69.789 351.603 78.414 11.586 120.421, 45.185 43.288 16.302 163.698 -69.7.88 351.607 78.571 11.429 120.322 46.185 44.697 15.296 164.704 -69.786 351.610 78.612 11.388 120.634 47.185 46.095 15.505 164.495 -69.785 351.614 78.315 -11.685 120.757 48.185 47.483 15.370 164.630 -69.783 351.617 78.320 11.680 120.589 49.185 48.861 14.944 165.056 -69.782.351.621 78.238 11.762 120.788 50.185 50.229 15.831 164.169 -69.780 351.624 78.087 11.913 120.488 51.185 51.587 16.429 163.571 -69.779 351.628 78.058 11.942 120.412 52.185 52.935 15.414 164.586 -69.778 351.631 77.937 12.063 121.057 53.185 54.273 14.111 165.889 -69.776 351.634 77.830 12.170 121.536 54.185 55.602 14.558 165.442 -69.775 351.638 77.851. 12.149 120.616 ~55.185 56.921 15.i886 164.114 -69.773 351.641 77.711 12.289 120.977 56.185 58.230 17.373 162.627 -69.7 351.644 774812.i512 1287 57.185 59.529 18.12A 161.872 -69.771 351.647 77.448 12.552 121.263 58. 185 60.818 17.248 162.752 -69.770.351. 651 77.413 12.587 121.289 OD -~~~~59.185 62.098 16.077 163.923 -69.768 351.654 77.323 12.677 121.387 60.185 63.368 14.764 165.236 -69.767 351.657 77.228 12.772 121.318 61.185 64.628 14.236 165.764 -69.766 351.660 77.129 12.871 121.307 62.185 65.879 1.4.392 16 5. 60 8 -69.764 351.663 77.018 12.982 121.380 63.185 67.120 15.286 164.714 -69.,763 351.666 76.925 13.075 121.375 64.185 68.352 16.779 163.221 -6,9.762 351.669 76.807 13.193 121.465 65.185 69.573 17.836 162.164 -69.760 351.672 76.727 13.273 121.387 66.185 70.785 18.750 161.250 -69.759 351.676 76.671 13.329 121.339 67.185 71.988 19.518 160.482 -69,758 351.678 76.565 13.435 121.416 68.185 73.181 19.530 160.470 -69.757 351.681 76.466 13.534 121.384 69.185 74.365 19.391 160.609 -69.756 351.684 76.368 13.632 121.333 7.0.185 75.540 18.948 161.052 -69-.754 351.687 76.286 13.714 121.278 71.185 76.705.18.204 161.796 -69.753 351.690 76.178 13.822 121.32172.185 77.860. 17.914 162.086 -69.752 351.693 76.066 ~ 13.934 121.366 -73.185 79.006 16.873 163. 127 -69.751 351.696 75.957 14.043 121.350 74.185 80.142 16.434 163.566 -69.750, 351.698 75.841 14.159 121.350 75.185 81.269 16.063 ~~~163.937 -69.748 351.701 757614.264 121.282 76.185 82.386 16.072 163.928 -69.747 351.704 75.616 14.384 121.'254 77.185 83.494 16.230 163.770 -69.746 351.707 75.465 14.5351234 78.185 84.591 16.538 163.462 -69.745 35-1.709 75.321 14.679 121.433 79.185 85.679 16.846 163.154 -69.744 351.712 75.191 14.809 121.424 80-185 86.758 -17.305 162.695 -69.743 351.715 75.075 14.925 121.471 81.185- 87.827 17.916 162.084 -69.742 351.718 74.972 15.028. 121.578 82.185 88.886 18.681 161.319 -69.741 351.720 74.858 15.142 121.550 83.185 89.936 19.'603 160.397 -69.740 351.723 74.712 15.288 121.590 84.185 90.976 20.224 159.776 -69.738 351.725 74.557 15.443 121.664 Figure 14. (Continued~)

85.185 92. 007 21. 002 158.998 -69.737 351.728 74.499 15.501 121.496 86.185 93.028 21.785 [58. 215 -69. 736 351.730 74.381 15.619 121.480 87.185 94 040 22.573 157. 42T -69. 735 351.733 74,206 15. 794 1 21.539 88.185 95.043 23.250 156. 750 -69.734 351.735 74.095. 15.905 121.453 89.185. 96.036 23.892 - 156. 108 -69. 733 351.738 73.961 16.039 121.499 90.185 97.019 24.696 155.304 -69.732 351.740 73.848 16,152 121.529 91.185; 97.993 25 1865 154.814 -69.731 351.742 73.707 16,293 121.523 92.185 98.958 25.679 154.321 -69.730 351.745 73.535 16.465 121.553 93.185 99.91'3 26.335 153.665 -69.729 351.747 73.413 16.587 121.5B2 94.185 100.859 26.671 153. 329 -69. 728 351.749 73.279 16.721 121.590 95.185 101.795 26.8647 153.153 -69.727 351.751 73.104 16.896 121.631 96,185 102.721 27. 023 152.977 -69.726 351.754 72.913 17.087 121.722 97.185 103. 638 27.036 152.964 -69.725 351.756 72.750 17.250 121.878 98.185 104.545 27.212 152. 788 -69.725 351.758 72.648 17.352 122.001 99.185 105.443 - 27.063 152.937 -69.724 351.760 72.517 17.483 121.999 100.-185 106. 32 26.913 153.087 -69.723 351.762 72.398 17.602 122.161 101.185 107.211 26.926 153.074 -69.722 351.765 72.249 17.751 122.228 102.185 108.081 26.614 153e 386 -69. 721 351. 767 72.093 17.907 122.166 103.185 108.941 26.303 153.697 -69.720 351.769 7T1o935 18.065 122.291 104.185 109.792 25.508 15-4.492 -69.719 ~ 351.771 7i.752 18,248 122.332 105.185 110.633 25.198 154.802 -69.718 351. 773 7!. 566 18.434 122.270 106.185 111.465 24. 409 155.591 -69.718 351.775 71.335 18.665 122.395 107o18;5 112 ~ 288 23.942 156.058 -69.717 351.777 7!. 168 18._832 122.372 108. 185 113.101 23.318 156.682 -69.716 35 1. 779 71. 059.18.941 122.264 109.185.113.905 22. 696 157. 304 -69.715 351.781 70.884 19. 1 16 122. 361 110 185 114.700 21.762 158 238 -69.714 351.783 70.685 19.315 122.340 111 185 115.485 21.746 158.854 -69.713 351.785 70.461 19.539 122.300 112 185 1 6-.261 20.531 159. 469 -69.713 351.787 70.236 19,764 122.345 113.185 117~027 19.764 160.236 -69.712 351,7908 69. 815 2 198594 _ 122.320 114.185 117.784 18. 999 161.001 -692711 351.790 69.4815 20185 12226349 115.185 118.532 18.237 161.763 -69.710 351.792 69.582 20, 418 122.264 116.185 1 19.270 17.449 162.551 -69.710 351. 794 69. 408 20. 592 12 2.235 117.185 120. 000 17,150 162.850 - 69.709 351.796 69. 204 20.796 122.$29 118.185 120.720 16.852 163.148 -69. 708 351.797 68. 973 21.027 122.216 119.185 121.430 16.402 163.598 -69.707 351.799 68,748 21.252 122.046 120.185 122. 131 16.408 163. 592 -69.70i 351.801 68.497 21.503 1221037 121.185 122.823 16.262 163.738 -69.706 351.802 68.224 21.776 122.12 8 122. 185 123. 50b 16.115 163.885 -69.705 351.804 67.992 22.008 122.195 123.185 124. 179 160 730 163. 270 -69. 705 351 806 67.728 22,272 122. 218 124.185 124.843 16.735 163.265 -69.704 351. 807 67. 372 22.628 122.183 125. 185 125.497 17.046 162.954 -69.703 351.809 67T,041 22.959 122.156 126 185 126.141 17.818 162.182 -69.703 351,810 66.754 23.246 122.087 127. 185 126.777 18.439 161. 561 -69.702 351.812 66.462 23.538 121 987 128.185 127.403 18.908 161.0 92 -69.701 351.813 66.180 23.820 122.040 129.185 128.019 19.689 160.311 -69.701 351.815 65.856 24.144 122.041 130.185 128.626 20.388 159.612 -69.700 351.816 65.472 24.528 121.993 131.185 129.224 21.179 158.821 -69.700 351.818 65.112 24.888 122.135 132.185 129.812 22.134.157.866 -69.699 351.819 64.779 25.221 122.188 133.185 130.391 22.777 157.223 -69.698 351.821 64.453 25.547 122.022 134.185 130.961 23.103 156.897 -69.698 351.822 64.077 25.923 122.008 135.185 131. 522 23.911 156.089 -69.697 351.823 63,;671 26.329 122.066 136.185 132.073 24.563 155.437 -69.697 351.824 63.306 26.694 122.037 137.185 132.614 - 25.056 154.944 -69.696 351. 826 62.930 27.070 121.875 138.185 133. 146 25.0551 154.49 69,696 351.827 62.529 27.471 121.763 139.185 133.670 26.049 153.951 -69.695 351.828 62.157 27.843 121.826 140.185 134.183 26.220 153.780 -69o694 351o830 61.755 28.245 121o871 141.185 134. 688 26.556 153.444 -69.694 351.831 61.356 28. 644 121.955 142.185 135.183 26.728 153.272 -69.693 351.832 60.926 29.074 122.035 143.185 135. 669 27.065 152.935 -69.693 351.833 60.435 29.565 1210986 144.185 136.146 26 5928 153,072 -69.693 351.834 59.862 30.138 l21.944 Figure 14. (Continued)

145,,185 136. 613.'2t,3,~~'.~*::15.6 "''9.-354:'1 158 1 6 53*065' -69a&92 -.351..835: 30... 1232.063 146.185. 137.070 153.:223'35 j 836 58.925 3II. 075 1 z 2. 09 147.185 137. 511984 153.'216 -69.69.::. ". 3~J~1.83'7 58.4.36' 31[',566'.' 1226695 1~4 8. 1 8~5 ~ 137.9 58 27.284i~ 1.716 -69.;691::~~- 35b19 57.896 32. 10!1221232 149.185 138.388 27.621 152379 -695690 351: 8,~ 0.27'1 32,7 29 122.305 150.185 ~ 138,809'27.6128 1252.372_ -- 69.690 351.841f 56. 606~;~ ~ 33,3696 - I89 122.287 151.185 139.220 27.634 152.366'69.689 351.842 55.959 34.041 122.658 152.185 139.621 27.474 152.526 -69.689 351.843 55.341 36.659 -122.689 153.185 140,013 27.646 152.354 -69. 689 35I.844 54.680 12 2'. 696 154.185 140. 396 27.486 152.514 -69.688 351.844 53.882 36. 118' 122.7T57, 155.185 140.769 26.66 6 153,334 -69 688 351,845 53. 136 36 864 122.822 156.185 141.133 26.343 153.657 -69.687 351.846 52. 487 37.513 122.725 157.185 141.487 25. 857 154. 143 -69.687 351.847 51.786 38.214 122.654 158.185 141.832 25.508 154.492 -69.687 351,. 848 51o040 38.960 122.811 159.185 142.168 24. 859 155.141 -69.686 351.849 50.196 39. 804 122.731 160'185 142.494 24.052 155.948 -69.686 351. 849 49.264 40.736 12 2.666 161.185 142.811 23.088 156.912 -69.686 351I. 850 48.'325 41.675 122.801,162. 185 143. 118 22. 291 157. 709 -69.685 351.851 47.273 42.727 122.701 163.185 143.416 21.497 158o503 -69. 685 351. 852 46.339 43.661 122.504 164.185 -143. 704 20.392 159. 608 -69 ~685 351,.S852 45.399 44. 601 12 2573 165o185.49821. 160.549 -.69.685 351.853 44.425 45.575 12 2.692 166.185 144o252 18.359 161.641 -69.684 351.854 43.358 46.642 1'2 2.702 167.185 144.512 17.274 162.726 -69.684 351. 854 42.140 47.860 12 2.662 168.185 144.761 16.503 163. 497 -69. 684 351.855 40.884 49.116 122.588 169.185 145.001 15o581 164. 419 -69.684 351.855 39.709 50. 291. 122. 622 170.185 145.233 14.510 165.490 -69.683 351.856 38.556 51.444 122.623 I171.185 145.454 14.206 165. 794 -69.683 351. 856. 37.350 52.650 122.601 172.185 145.666 13.423 166. 577 -69.683 351.857 36.193 53. 807 122. 710 173.185 145.869 12.969 167.031 -69.683 351.857 35.038 54.962 122.73' 7 174.1185 146.-063 12.819 167.181 -69. 683 351. 858 33. 844 56.156 122.712 175.185 146. 248 12. 820 167.180 -69.682 351.858 32.732 57.268 122.831 0 176o185 146.424 13.125 166. 875 -69. 682 351. 859 31.624 58.376 12 2.967 177.185 146. 591 13,734 i66. 266 -69. 682 351-859 30. 335 59.665 123. 66 178.185 146.750 14.344 165 656 -69.682 351.859 28.984 61.016 123.367 179.185- 146.899 14.957 165.043 -69.682 351. 860 2 7. 569 62.43 1 12 3.296 180.185 147. 039 15.725 164.275 -69.'682 351.860 26.181 63.819 123.333 181.185 147.170 16.650 163. 350 - -69.681 351.860 24.809 65.191 123.499 182.185 147.293 17.890' r 162.110 -69.681 351.861 23.202 66.798 123.513 183.185 147. 406 18.670 161.330 -69.681 351.861 21.663 68. 337 123.588 184.185 147.510 19. 768 160.232 -69.68 1 351. 861 20.105 69.895 123. 892 185.185 147.605 20.873 159.127 -69.681 351 h861 18.300 71.700 123.997 186.185 147. 691 21. 668 158. 332 -69.681 351. 862 16.441 73.559 123.987 187.185 147.767 22.307 157. 693 -69.681 351. 862 14.599 75.401 123.923 188.185 147.835 23.270 156.730 -69.681 351.862 12.734 77.266 123.759 189.185 147.892 24.403 155.597 -69.681 351.862 10.858 79.142 123.697 190.185 147.941 25.055 154.945 -69.681 351.8'62 8. 867 81.'133 123.626 191. 185 147. 980 25.711 154.289 -69.681 351.862 6.808 83. 19i 123.666 192.185 148.009 26.040 153.960 -69.681 351. 862 4.771 85.229 12 3. 7.82 193.185 148.0 29 26.701 153. 299 -69. 681 351.863 2. 805 87.195 12 362 8 194.185 148.040 2-7.03 3 152.967 -6,?.680 351.863. 0.824 89. 176 1Z3. 429 195.18-5 148.04 1 27,532 _ —.66.6...... 51.863 -!.2_6 9 Figure 14. (Concluded)

,.~131-AR PN$,I~:W~N 7FN I TH AMGi F 7=',. R &7'! MtJTH 2~8.1 ~... P ITf].T A gPF. CT r-fiR'NASA 1'4.'~Sh ~ TIME ZENITH AZIMUTH ALPHA COS ALPHA - ZENITH AZIMUTH ALPHA' COS ALPHA VEL ZEN'VEL AZ 40+0,'?R.R.. 1~,4_ 7 1'R. 1,"'L, g5 072 g.,7 ~14.1 _2~-R O.gg'R7g ]'1,.:5 170.4' 41'0 30.9 139.4 20.5 0.93655 5.6 12~1.6 5.7 0.99505 11'.3 120.Z 42.() 28.7 1.34.9 18.0 0.9513] 8._& — 11Z~,_8. 2.9 0..99874 11,,~' 12_.0,1 43.0 29.5 1.37.0 18.7 0.9/+727 7.5 118.1 4.1 0.99746 1[o5 I20or ~. 44.0' 29.9 __lq9.? 19.2 0.-9444~ 6.6 124~.__. 5.1 ____0__.~00, 11,7 120.0 45.0 30.5 141.3 20.1 0.93885 5.7 132.1 6.2 0.99420 11.6 11.9.9 AF..~ 98.5 ]%R.R ___17- q 0.95146 R 0 127.1 3-8 0.99786 11..5 120.1 47.0 28.3 138.8 17.5 0.95350 8.1 127.41 3.8 0,99775 11.8 IZO.2 __ 48,0 2_~03 141. 3 18.8 0.94689 6-8 134.3 5~.5 0~99546 11.8 120.1 49.0 29o6 143.2 19.2 0,94457 605 142.0 6.4 0.99386 11.9 120.2 50.0, 29;l L41.0 18.3 0.94927 7.1 __133.7 5.4 Q.99555 12.0 120.0 51.0 29.5 138.7 18.5 0.94855 7.0 I23.6 5.1 0.99605 12. I 119.9 52.O.... 28-q..... I 39.9 17.8 0.95201 7.4 * 130~ ] 5-0 0.996! 5 12.2 120.4 53.0 28.3 143.0 17.5 0.95373 7.7 141.7 508 0,99495 12.3 120,,9 54.0 29 5 144.6 18.9 0.94586 _____6_._5 l_~uP.1 7.2 0.99_2_13 12 3: 120.2 55.0 29.7 142.2 18.7 0.94720 6.4 137.5 6.6 O. 99339 12.4 120.3 56.0 31.0 139,5 19.4 __Q~94308 5.5 12I;!....L.] 0.99222 12.6 121.1 57.0 31.1 137.1 19.2 0.94435 6.1 110.6 6.8 0.99294 12.7 12008._ 38.~. q].? lgR.~ - ]9.4'. 0.94=J29 5.6,, ]lR-~J 7...:~ 0_99218 l-?-? 120.7 59.0 30.5 140.7 18.9 0.94586 5.7 129 2 7.2 0.99208 12.8 120.8 60,0 29.2 142.3 ]7.8 ~0.9591_3 6.8 138.5_~~ 7 O. qP=tlO __ 12-9 _120..7 61.0 28.6 143.0 17.2 0,95513 7.4 141.7 6.6 0.993.30 13.0 120.7 62.0 28.6 142.6 17.0 0.956] 8 1.5 14Q.iL.....6_.=5 0.99347 13.1 120. L 63.0 28.8 141.4 17.1 0.95604 7.3 135.5 605 0.99367 13.2 120,,8 64.'0 29.8 ]39.5 ]7.6 0.953] % 6.6 126.? 6.8 oo 99300 1F..4 120.8 65.0 31.3 137.6 18.8 0.94674 5.8 111.3 708 0.99075 1_'3.4 [20.8..56.0 31.6 135 9'18.9_~ 0_,,_9_._4._63_0 6.,_IL.... 103..0_ ____7_,,9__: —__0_,L9_9048 ~ 13_~5.. 120.7 67.0 31.8 134.8 1.8.9 0.94625 fi,4 ~98.3 8~0 0.99016 13.6 120.8 68,,0 31-6 ~ 1'34_,_0 18,5 Q,94857 6.9 97.6 7.8 0,9_9.073 1.3.7!20,7 _ 69.0 31.3 133.7 18.1 0.95062 7.2 98.6 7.6 0.99119 13.8 120,7 7O-O ~ 30.9 1'3~~-9 17.6 0.95318 7.4 101.7 7'.] 0.99192 13.9 120.6 71.0 29.9 134.1 16.6 0.95853 8.0 107.6 6.5 0.99365 14.0 120.6 72.0 31.2 ~ 13'5.2 17.8 0.9_5197 6.7 103..5 _. 8.0 0.99035 14~.L 120.7 73.0 28.7 1.35.1 15.3 0.96467 8.6 115.5 5,7 0.99507 14,.2 120.7. 74,,0 27.6 134.8 14.1 -____0.97008 9__.6_ 118.8_____ _.__~_t'[___ 0.99659' 14.3 120.7. 75,,0 27.0 134.4 13.4 0.97279 10.2 119.5 4,3 0.99721 14.5 120.6 76,.0?6.5 13.3-5 12.7 0.97540 ]0.8 ] 19,.0 3,8 0,99781 14,.6 120~.b 77.0 26.2 132.7 12.2 0.97736 11.3 118o.3 3.5 0,,998.12 14.7 120.6 78.0 26.2 1'31.7 __11.9 0,,97843 11.5 116.7 3,.5 0,,99818 14.9 120.'I 79.0 26.0 i30.4. 11.4 0.98018 12ol 115.3 3.2 0,,99845 15.0 120.7 80,0 2.5.7 128,9 t0.9 0,98182 12.7 _11Lb 3__~}_ __Q_.__99_9_8_~5L. L5_,_1_= 120.7 81.0 25.8 127.2 10.8 0.98242 13.2 111.1 3.i 0.99849 15.2 120.8 82.0 26.6' 126.4 1l,.4 0.98027 12.9 107.~. ~.I 0.997.46 15,4. 120,,8 8.3.0 26.9 125.0 11. 5 0.97981 13.2 104,4 4.6 0,,99671 15.5 120,,9 84.0 27.6 123._ 8 ___ 11.9 0.9'7834 13.3 100. 9____ — ~_____~,.__9__9_5.i_3__ 15.7 IZO. 9 85.0 28.4 122.9 12,7 0.91547 13.3 96.7 6.5 0.99367 15.7 120,,8 8'6.0 29.1 __ —121.7' 13,3 0,97329!3.5'93.0 7.3 0,,99__1_.9_5 1.5__-8 IZO.7 87.0 29.6 120.3 13.6.0.97214 14.0 90.3 8.0 0.99015 16.0 120.8 ~ 88.0 30.? 119..,.4 14-1 0.9699'%' 14.3 87-:; _ 8,.9 fl. 98a07 16.1 120.7 89.0 30.8 118.6 14.6 0.96787 14.6 89-.6 9,.6 0.98597 16,.3 120.7 qO.O 30.9 117.4 146 0.96771 15.2 83.7 10.0 0.98486 16.4:120,.8 9-1.0 31.3 116.5 14.9 0.96652 15.6 82.1 10.5 0.98310 16.5 i20.8 Figure 15. Pitot aspect program output format.

9. 0 31.8 I11.1I 1522 0.96i,4919 158~80.2 111I 0.98113' 16o7 1.20.,8 9.3,0..32.. 0 I115. 5 15.4.0.9643-0 16.1I 79..2 11.-6 O' 97974 16o-8 120o-8 32 5 1 1 9.3 I S- 7 0-196287 1&. 2 ~77.7 12..1 0.,9779-7 170 1295.,0 32.6 1.15.0 1.5.6 0.96297.16. 3 77. 2 12,3 0.97705 17, 120.8 96.0 32.,7 11 4.7 " 15,6. 0.96314 16.5 7'6.8 12,-6 0.97603' 17.3'120.9 97.0 33.1 1'15, 3 15.8 0,962.20 16. 2 75. 3 13.0 0.9.7447 17o5 121,1 98.0 33. 5 1.1'5.8 16. 0 0,96105 l~q'7. 53.9 0T.0796 121.2 99.0' 33.6 ~~~~116. 3 1. 0 96316 73.6 13.5 0'.972'57 17.7' 2. IOn. O'- 3'3-R I117. I 1 16.1 0.96099 15,.?7 I 7' 6 13. 7 0-0971 59 17.9 2. 101.0.34. 0 118. 1 16. 0 0,69611I0 14.7 71.9 13.9 0.97088. 18.,0 121,4 10(2.0 34.1 11q.0 -1 6;0 0,,96130 14.2 71.-2 14..0 0.97019 18.2 121.4 103.0 34, 1 1 20.2- 15. 8 0..96213 135 71. 1 14. 1 0.96989 18.3 121.5 104.0 3'4. 0 12'1.0 15. 5 O. 96 360 13.0 71,-6 14, 1 0.-96997 18,,'5 t21.5 105.0.33. 8 12 2,,2 15.1, — 0.9.6'561 12.3 72. 8 13.9 0.97058 18.7 121.5 J1n6.o -:33.6 123.~ - 1 4. 7 0. 9673 8 I.I 73.8 13-.9'- 097055 18.9 121..6 102.0 33.3 124.4 14. 3 0,,96 909 11.2 75. 3 13.9 0.97086 19.01 121.6.1 08.0 3 3. _ 1 25.8 13.9 0.9 706 1 10.5 _77.4 1-.3.7 0,.971 52 19-2' 1215 109.01 32. 3 126. 5 13. 1 0. 97399 10.2,81.8 13.2 0.97359 19.4 121. 5 -110.0.31. 127.5 12.4. 0.97665 9. 9 85, 9 12.9 0.97487 19.6, 121.5 I111.0 31. 2 128.4 11.8 0,97898 9.6 89. 8 12. 6 0. 97575 19,,8 1L21.5 112.0 3. 19. 1 13. 9029.3 93.0 12.7 0.97573 20.0 121.5 1 13. 0 30-.2 130.3 10.6 0.98 28 7 9.3 98.0 12, 3 0.97711 20.2 121,5' 114. 0 29.7 1'31.1 10. 1 0.9 84-45 9,2 101.7 _ 122 _D, 97744 20. 5 121.5 1'15.0 29.1 131.c9 9. 5 0. 90638 9. 3 106.2 12.0 0.97832: 20.7.121,,4 I 1 6. 0 28.4 132. 3 8,71 0.98 843.9 7 110,4 11.5 097_9_88 20,9 1 21.-4 117.0 28. 0 133.0 8. 4 0. 98936 1.8 13.4 11.5 0.97995 21. 1 121. 5 I11q.O 2 7 - 1 3I'.6. a-?2 A.o8969 9g7! 1 5.2 11.7 0.97921 21.3 121.-4 119. 0 27. 2 133. 6 7.6 0.9,9126 10.2 117.2 11.4 0.98043 21. 5 121,2 -120.-0 26.6 1 33. 6. 8 09.9_2.8.7 1 0.8 117.9 11-0 0.98'163 21.8 1 21.2,. 121.0 26. 1 13 2.'4 6.0 0. 99448 I1. 5 118. 2 10. 6 0. 982-87 -22. 1 121.3 1 22.0 _ 2 5.7 131.7. 5.4 0. 99 558 12.0 118__.1_ 10'. 4_____.983 59 22.3 121.3 4~' ~ ~~~~~~123.0.2.5.4 130.6 4. 7 O~.. 9 6 69 12.5 117.2. 10ol 0.98438 22.6 121.4 I 24.13 25.0' 1 29.4 3- 9 0.99'771 1.. 1649.9 0. 98504 22-9 12'1.4 1 25.0 24.9.128. 1 3. 2 0. 99840 13.5 114.8 10.0 0.98496 23. 2 121,,3 I 26.0 25.? 1 27.0?,9.0, 9 9 B374- 1 3,7 112. 8 10.2 0.98408 23. 5 121.3 12'7. 0 2 5. 7 126. 0 2.8 0.99884 1.3.6 109. 7 10.8.0.98215 23. 8 121,2 I21283 2.6.3 12 5.0 2. 7 0,,99 889 1 3.. 6 106, 11.5 0.980__0_2_ 24,1. 121oZ_ 1.29.0 26.9 12-4.0. 7 0. 9988 8'1.3.6 103. 6 12. 2 0. 97757..4 121.2 1 30. 2 7.2 12 2. 6 2 5 0.99905 1 3.9 100.9 1 2.6 0. 97577 24, 8 121.2 1 31,0' 27..9 121.6 2. 7 0. 99890 14. 1 9 7,.6 13,4 0.97258 25.2 121.3 13. 28. 7 120.0 3, 2 0.99844 14,0 93.9 14. 5 0-96818 25.5 121.4 1 33.0 29. 1 119. 7 3.3 0. 99830 14.,5 91.6 15.0 0.96'602 25.9 121.2 -134.0 29.7. 118,~9 3,.7 Q,99'797 14. 7 88..9 15.8 0.96236 26. 2 121.2_ 135.0 29. 9 117. 5 3. 7 0.99792 15.3 87'.7 16.1 0.96076 26.6 12 1'.2 __16O 3. 1 1 6.8 4. 1 0. 99 745 I 5.15 85.-1 169.9 a 0.95669 77.0 121.2 1 37.0 3 0. 6 115.6 4.2 0. 99'733 16. 1 84.4 17. 2 0.95547 27.4 12. -1 48,8 O -30. 7 11 4. 5 4.-3 0.99723 16.7 84. 0 17.4 0. 954,38. - 27,.8 1271.0 1 39.0 31.1 114. 3 4. 4 0. 99702 16.7 82.4 18.1 0.95048 28.2 121.0 -140. 0'1.1 114. 4 4.6- 0.99683. 17. 2 82.4 18. 3 0. 94934 28.6 1 21.1 141.0 31.,3 1 1'3.0 - 4,.7 0. 99663.17.4 8,1.7 18.8 0.94672 29,,0 121.1 -1 42-0 341 -.4.112. 7 4.8 -O -q 65 ~ 17. 6 Al.2 19.2,0-9441 5 19.4 - 1 21.2 143. 0 31. 9 113. 2 4.[6 0.99681 17.3 79.5 20. 2 - 0.93841 29.09 121.2 -144.0'32:4 1'13,,8 4. 4 0. 99712 I7. 0 77.8 21.2 0.93216, 30~.4 121o21 45. 0 33.0 114.8 4.0 0.99755 16.4 75.7 - 22. 4 0. 92450 31.0 121.2 -146. 0 343.4 115;.3 3. 8 0.99784 16.1. 74,.3 23. 3 O. 91 867 31,,4 121-.3 147.0 33.9 I116.2 3. 5 0. 99818 15.7 72.3 24.3 0.91106 31.9 121.3 -148. 0 34.6. 117.4:1..1 0.99864' 15.1 -9 5 -9193- 1149.0 35.0O 118. 3 2. 6 0. 99893.'14.6 68,0 ~ 26.8 0.89294 33.0 121..5 -150.0 35.3 119. 2 2. 2 0.009217 14. 1 66.2 079.843365 3. 2..151.0 35. 8 120. 3 1. 7 0.99954 13,6 63.9 29,2. O. 87276.34.3 121.8 Fiue15. (Continued)

]592.0 36. 1.1 21. I2 0. 99977 13.0 62.3' 30. 3 0.86377 35.0 2 1 53. 0 3 6. 5 12 2. 4 0. 9 0.99987 1.2.4 - 60. 1 31. 5 0. 853.04. 35.6. 121. 1194_0 B`,6 7 12;;'g 7 ]..99F 1].7 5R.1 32.-7 0.R841 27,6.. 4 122 155.0 36.8 1201.8 0.99950 II. 0 57. 2 33.8 0.83131 3. 2. 1 1;6, ~ 6, 8 124.2 2. A o. 99,9834 ]0.. 56.-3'34.7 0. 8271 7 37.8 1 22 I 57.0 3'7.0' 1.27.9 4. 0 O. 99759 9. 3 54.0 35.9 0.80987 38.5 121. I 58.0C 3.9 2~4. ] 09 97 8.4 54. 6 36. 9 0. 7998993. 2. 1 59.0 37.0 13 11. 4 6. 6'0,99337 7.3 50. 5 38. 3 0.7.8475 40. 1 122. 1~ ~ ~ ~ ~~3.]i 90 1I A19 0 h.I 49.2 1A9.'S 0.-771 1,5 41.0 1 2. I161.0 3 6.E- 1 34. 7 9. 6 0.98603 5. 3 5 0. 9 40. 5 0. 76038 42.0 122. I!?.0 3 6. I 136,.? 1. g 0. 98 09'~ 4.3i 55.4 41.4 0.,740,75 43,.0.122. 1 63.0 35. 5 137.4 13. 0 0. 974.36 3. 6 64.6 42. 1 0.74228 4+3.9 121. 64,64.0 34. 7 1B38.-4 1 4.6 0.9136 751 5 ~.3 4O. 42. 5 0774. 2. 16-S5.0 3 3 9 139.6 16o 4 O0. 95 955 3. 1 98.5 43.1 0.73064 45.9 122. r) ~ ~~~~~~~~~~~~~~~~~~'.'? 1140-.7 1 A~ ~ 59 43. 7 0. 72243 46.g9 12'2. 1 67. 0 ~32.4 141. 7 20.!I 0. 9393.4 3.8 128.5 44.3 0.71514 48. 1 122. I3Y 0 I1. ]4?.4 2 2 - 2. )9259]I 4. 7. 368 44. 8 0. 70978 49.4 12. 1 69. 0 3.0. 2 142. 9 24. 2 0.g91 222 5. 8' 140.2 45. 1.0.7064'1 50.5 1 21 1 70.0 2 9.2 1 43.1 2 6. I O. 99788 6.-9 141.9 45.3 0.70349 51. 7 12._ 1 71.0.2P..3 143.2 28. 0 0. 8 8329 7. 8 142. 4 45.7 0.69862 52.9 1 21 I 77. 0 2 7. 4 142.9 29. 6 C,.g6 g3f 8.6 141 -6 46,.0 ~0,.69453 54. 1 - 122, 1 73.0 26.4 142. 3 31. 4 0. 85 3 52 9.7 140.3 46.1 0.69316 55.2 122.! 74.0 2 5.5 t 4,1. 2. 3, I]1 0, 83 809 10. 6 138. 2 46. 3 0. 69079 56o4 1.22 1 75. 0 24. 7 1,39. 9 34. 6 0. 82 3 58 ll.5 135. 9 46, 5 0. 68868 57. 6 122. 1 76-.0 9 4. 13.9 35.6 O.] 29 1 1. 8 _ _133. 6 47.1 0. 68053 58,.7 2. 1 77. 0 24. 5 137,.2 365. 6 0. 80293 1.2.0 130. 8 48. 1 0.66820 59.9 1 22 17 7g. q?4.7 14,5. a 37. 5 f0. 79360 1 017-8 49I 0-61696,- 1 79.0 24.5 13~3. 5 3 8. 7 0.78000 12. 5 124. 1 50.2 0.64074 62.7 122. t310. 0 24+.6 131. 4 3q. 8 0.76 816 I?__.9 120.4 51. 2 0- 62696 64. 1 122, 129.2 40.6 0.7593 7 ]~~~~~~~~~~~13-.1 11-6.0 52.4 0.60980 6. 2. ~ -~ 18;',0;;'5,~~~~~~~~~29.5 1 27.0 41.6 0.747859 1 3.4 III1.7 ___53-9 0. 58957 67.0 1 2,. 1 83.0O 2 6.0 1I25. 0 42. 6 O..73 536. 13.8' 107.7 55.3 0. 56902 6-8. 6 12~. 2 7,-0 1?~.46 4.-3 1 0. 7 29(',1 3,.7 1 07.8 67.4 0-..53'91 3 70.-1 I12. 1,~,5. 0 2 27.7 12 2.]1 44.2 0. 7172 5 ]m3. 9 98. 7 59. 4 0.5.0976 71.9.123.'lR6S 2,0?79 1209.2 4' 45.9 ~. 69649 ] 4.6 9 6.4A 60.8 0.-48719} 73 7 1 2,. 1 87.0 28.9! 19.S 4,6.8 0. 68453 14. 6 92, 5 63. 2 0,45101 75.6 123. I PI33,0 2. 6 1 183 48. 0 0.,6 692 1 1 5.0 8'9.1 65. 2 0. 41878 77.4 1 23 1 89.0 30.5 117. 7 49. 0 0. 6561c 15.1 85,4 67.6 0.3,813 5 79,.3 123. 1.0 3'1,4 I 1 17.?.'01 0.64n84' 15.?2 82. 0 70. 0 0, 341-95 8.1 23. 191 0 32 2 1.17'3 5 1. 3 0. 62 512 15.1 78. 7 7 2.8 0.29641 83.3 123, 1 CO.0 32,~7 17, ( 52. 9 0, 6030,3 159.3 76,.9 7540O 0.25866 85.4 123. 1 93. 0 3 3. 5 1!7. 2 54. 1 0.5,9650 15. 1 73. 9 77.6 0.21426 87.4 123. 194.0':-34, 2' 1 1'7.6' 55.3 0, 560861 14___9.... 71.2 _ 80.2 0.17025 89. 3. 123Figure 15. (Concluded)

5.4. PROCESSING OF GAUGE OUTPUT DATA Figure 16 is a drawing of the timing functions and gauge outputs versus flight time for the two ionization gauges of the pitot probe. Gauge 1 provides the data for the early part of the flight and gauge 2 becomes the main gauge in the high altitude portion of the flight. Gauge output data are as shown in Figure 17, The calibration sequence, composed of five segments (see Figure 8), includes (1) thermistor output (2) OV reference (3) 5V reference nominal values (real values are used) (4) 2o5V reference range indicator The data formats are essential to the automatic processing of the data. The above mentioned information, along with the gauge output data, is contained in one channel for each gauge. During the flight, a calibration sequence occurs automatically whenever there is a range change. This feature has been included in order to place the calibrations and housekeeping data where the data are lost because of range switches, When the gauge stops changing range, a calibration sequence occurs every 15 sec (nominal) as commanded by an internal free run timer. The data from both gauges are processed in exactly the same way by means of a main program called PITOT, which has been written for the IBM 360/670 The procedure for processing data from a gauge is as follows, First, the program is supplied with the following input data: (1) trajectory information (stored in disc file), (2) gauge output data from the digital magnetic tape, (3) gauge calibration table, and (4) angle of attack versus flight time9 Tables included in the program are (1) speed of sound from the U, S. Standard Atmosphere, 1962, (2) geometry correction factor ~(a,S), and (3) transition number K(p)o 44

The program reads every data point from the digital tape after which a scan is performed which looks for a calibration sequence. When a calibration sequence is recognized by the program, a second order polynomial is fit through the three points. The data points between two calibration sequences are calibrated in terms of voltage with the aid of the fit polynomial. This procedure is repeated until all the data points are in the form of a calibrated voltage. At this point an impact pressure is associated to each data point by means of a calibration table lookup. This pressure is corrected for gauge temperature (gauge 1 only) which is a function of the gauge thermistor output included in the calibration sequence (Simmons, 1964). The time interval corresponding to 250 meters in altitude is obtained from trajectory information. For this time interval, which varies along the trajectory, a straight line least squares fit of impact pressure versus time is computed. Impact pressure is then determined at the time of interest, which corresponds to an even quarter km point. Mach number is then approximated by using velocity information from the trajectory data and the speed of sound is obtained from the U. S. Standard Atmosphere, 1962. Values of 1P- and P2 are calculated by using Equations (4) - y _ and (13), respectively. For those times which are included within the table of angle of attack versus time given, the program will obtain an angle of attack by interpolation, The velocity ratio S is calculated from the approximated Mach number. The geometry correction factor ~ is calculated by double entry interpolation in the geometry correction factor tables. After 1 and coso are obtained, they are applied to P2 (see Equation (15)), and atmospheric density is obtained according to the free molecular flow theory, At this point atmospheric density has been computed according to continuum flow theory, Pi, and according to free molecular flow theory, Pfmf. Atmospheric density in the transition region is then calculated by using Equation (16). An iterative procedure is used in thi.s computation, An abbreviated flow chart for PITOT is given in. Figure 18. The printed output of the program has the format shown in Figure 19, and includes (1) time from launch (TIME) in sec (2) altitude (ALTITUDE) in km (5) velocity (VELOCITY) in m/sec (4) impact pressure corrected for gauge temperature (PRESSURE) in ramrHg (5) atmospheric density according to continuum flow theory (RHO 1) in kg/mr3

(6) P2 according to Equation (13) (RHO 2) in kg/m3 (7) angle of attack of the probe (ALPHA) in deg (8) geometry and angle of attack correction factor 1/q cosoy (CORR) (9) atmospheric density according to free molecular flow theory (RH02*CORR) in kg/m3 (10) transition number (K) (11) atmospheric density

K&~ 19 1S53 4-6e "B T ~ ~ ~ ~ ~ ~~T T T T T T T T T I I I I i ~ 4I41 -.3~~~~~~~ I I1 I I j I o.. I ~ * I T +~~~~~~ o R7 R6 R5 I R4 R3 R2 RI 04 I I-I W~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ T T I I I! " ~I~~ f t f I, t i $-r T - J- J- t CL i I R 0 I I I. T P I I I rI i I I ~ ~~~~~~~~~~~~~~~~~~~~~ 12~~~.& O 20 30 40 50 60 o 0 100 110 120 30 0 T ~ N~ I II I~ ~ ~ ~~R S R I i I R6 Rm R4 R3 R2 RI + T i t 4- 4 T T I t T T T T + I~~~~~~ 4j,I_,, i- - I I I I I I ~~~~~~~~II I I I I I I I IO_6~I + ENGINEER I DRATSMAN MI w 0i IIj8 I R SPACE R PHYSIC RESEARCH LABORA TIMING FUNCTIONS R RAGT I I,II I L. J ~.. I/IL 0 I~~~~~~~~~w04 z~~~~~~~~~~~~~~~~~~~~~~~~~~~~ 6868 DEPARTMENT OF ELECTRICAL ENGINEERING I0-3-8 F. ELECTRICAL PITOGT PROSE 14.386 UNIVERSITY OF MICHIGAN ANN ARBOR, MICHIGAN BE 1426 Figure 16. Timing functions and gauge output versus time.

TIME CODE (NASA 36 BIT) SUN SENSOR rill~ ~ ~ ~ i I~~~~~~~~~~~~~~~~~~~~W Uiiii iLi MAGNETOMETER rv C L. GAUGE THERMISTOR RANGE'INDICATOR GAUGE I (RANGE 6) 212 X AL. GAUGE I (RANGE 7) V9AL. Figure 17. Analog oscillograph record of flight data.

READ FLIGHT ID, LAUNCH TIME INTEPLT I TO FILE, CHANNEL =sii GDATA (T,U TA T = TIR C T1 TSTRT, TSTOP (START AND STOP TIMES) S 407 VS, VO, VM (MEASURED 5,0,2.5 V CALIBRATE LEVELSI RVSTEA, RDELV (RANGE INDICATE REFERENCE AUD STEP) VT L (GAGE THERMISTOR OUTPUT AT CALIBRATION) (OUTPUT ALTITUDE INTERVAL) INTERPOLATE IN ALTITUDE TPJECTORY NTERPOLATE IN ALTITUDE FOR ALTT = ALTIirUDE (T) I TRAJECTORY FOR T TIME (ALT) RDEL f 50 XM CALL SETBUF TO ATSTARTTIRE READ AND CHECK TAPE FILE LABEL ISTOP DETCERTITPREUR OF CHANNELS AND SAMPLING RATE N IE RE Y READ VOLTAGE PRESSURE CALIBRATION CURVES INTERPOLATE IN VELOCITY TRAJECTORY IIIT 0 ~ FOR VEL VELOCITY (T) DL Y T1 =T-VEL/(2AH) RO READ TIMIE CORRECTIONS AND a'S 30 T = T+VEL/(2AH) RO TA~~~~T UaS O a ZERO SUMS FOR LEAST SQUARES STRAIGHT LINE OF TIME,PRESS CALL SDATA TO INITIALIZE CALIBRATION ROUTINE FigureIM 18.AIVL PITOT abreiae flwcat 407N CLLGDAA (IMPRS> AND RHO SN FIND ALT FIRST MULTIPLE OFAH>LTUDRO R z 0 / I ~~~AT START TIME CAL GAT (TMEPRSS PRINT T,ALTT,VEL,P,RHO1,RH022,a,l/ECETA' COS ta)],CAH2KR-~ -C cn~~CAL GDATA (T,P) TO CAL~L GDATA (TIMEPRESS) TO ACCUMULATE SUMS FOR.READ DATA POINT READ DATA POINT > T2 LEAST SQUARES FIT \O ~~~~CALIBRATE IF VS 34 0 CALIBRATE IF VS:, 0 CONVERT TO PRESSURE IF RDELV 0 CONVERT TO PRESSURE IF RDELV 0 EVALUATE P FROM LEAST SQUARES FITT T< Y AT TIME T ALTT = ALT TSTRT 407 129 IPRIT CAIBRAION EQUECE SMMARY l SO Figgnure 18. PITOT abbreviated f low chart.

SPACE PHYSICS RESEARCH LABCRATORY THE UNIVERSITY OF MICHIGAN ANN ARBOR, MICHIGAN l1346.11 DECEMBER.18,196 NASA 114.386:GAGE I F LAUNC'H TIME: 20=: 4:59.815 Z INPUT FILE 1 CHANNEL INDEX 1 ) TAPE' I: SPRL NASA.14,386 12/12/69 8020 F' OB Q CALIBRATE LEVELS: 5.003 0.004 2.503 VTtCAL: 3.700 RANGE 1 INDICATE: 0.500 S:'t-EP BETWEEN RANGES: 0.500 Fv~r,5-,. RANGE:, 2. VOLTAGE'-' PRESSURE VOLTAGE PRESSURE VOLTAGE PRESSURE VOLTAGE PRESSURE VOLTAGE PRESSURE.0... " gO'-:1 "8.-300E-03 2.200 2.00OE-02 3.500 3,420E-02 4.750 4.780E-02, RANGE: 3 ".. ~ VOL:TAGE':.,: -PRESSURE VOLTAGE'PRESSURE VOLTAGE PRESSURE VOLTAGE PRESSURE VOLTAGE PRESSURE.8.90'."550E-02 2.190" 9.1 00E-02 3.490 1.460E-01 4.740 1.980E-01 _ i~:.::..'.~.,RANGE ~: - V.t:GE PRESSURE VOLTAGE PRESSURE VOLTAGE PRESSURE VOLTAGE PRESSURE~ VOLTAGE PRESSURE..:00 1soE-o] 2.190 3.7 50E-C 3.500 6.OOOE-Or 4.750 8.180E-01l A':?ANGE!?'1 5.:'!..~ V-oi. VLtTGE PRESSURE VOLTAGE PRESSURE VOLTAGE PRESSURE VOLTAGE PRESSURE VOLTAGE PRESSURE " 0.'*890 6'200E-01 2].gO19 1.520E 00 3.490 2.420E 00 4.740 3.300E 00:R.AN GE?:.:''.6 VOLTAGE'PRESSURE VOLTAGE PRESSURE VOLTAGE PRESSURE VOLTAGE PRESSURE VOLTAGE PRESSURE 0.900 -2.480E 00 2.200 6.110'E 00 3.500 9.850E 00 4.750 1.360E 01 RANGE: 7 VOLTAGE PRESSURE VOLTAGE PRESSURE VOLTAGE PRESSURE VOLTAGE PRESSURE VOLTAGE PRESSURE 13.890 7;2'00'E 00 2.190',750E O1 3.490 2.800E 01 4.740 3.8],E 01 RANGE:. 8 VOLTAGE PRESSURE -' VOLTAGE PRESSURE VOLTAGE PRESSURE VOLTAGE PRESSURE VOLTAGE PRESSURE 0.900 2.870E 01 2.000 6.390E 01 3.100 9.940E 01 4.750 1.530E 02 RANGE: 9 VOLTAGE PRESSURE VOLTAGE PRESSURE VOLTAGE PRESSURE VOLTAGE PRESSURE VOLTAGE PRESSURE 0.890 1.170E 02 1.790 2.410E 02' 2.690 3.710E 02 3.590 5.100E 02 TIME CCRRECTICNS 0.0 0.0 500.000 C.O Fig.zre 19. PITOT output format. 5o

TIME ALTITUDE VELOCITY PRESSURE RHOIOt O2 ALPHA CORR, RHO2*CORR K RHO 36.101 30.000 1547.9 2.946E 02 1.758E-02 3.435E-02 36.265 30.250 1545.4 2.827E 02 1.693E-02 3.302E-02 36.431 3C.500 1543.1 2.683E 02 1.611E-02 3.139E-02 36.5 6 30.750 1540.7 2.556E C2 1.539E-02 2.994E-02. 36.762 31.000 1538.4 2.461E C2 1.487E-02 2.887E-02 36 927 31.250 1536.C 2.364E 02 1.433E-02 2.778E-02 37.093 31.500 1533.7 2.267E 02 1.378E-02 2.668E-02 37.258 31.750 1531.4 2.167E 02 1.321E-02 i2.554E-02 37.425 3 2.0003 1529.2 2.069E 02 1.265E-02 2.442E-02 37.592 32.250 1526.9 1.974E 02 1.210E-02 2.333E-02 37.759 32.500 1>52.4.7 1.895E C2 1.165E-02 2.244E-02 37.926 32.750 1522.5 1.825E 02 1.125E-02 2.164E-02 38.093 33.000 1520.3 1.773E 02 1.CS7E-02 2.106E-02 38.260 33.250 1518.1 1.697E 0'2 1.052E-02 2.018E-02 38.429 33.50.0 1515.9 1.626E C2 1.O11E-02 1.937E-02 38.597 33.750 1513.7 1.551E C2 9.671E-03 1.849E-02 38.765 34.000 1511.6 1.463E C2 9.147E-03 1.747E-02 38.934 34.250 1509.4 1.397E C2 8.758E-03 1.670E-02' 39.441 35.000 1503.1 1.258E C2 7.952E-03 1.511E-02 39.611 35.250 1501.C 1.220E C2 7.732F-03' 1.467E-02 39.781 35.500 1499.0 1.177E 02 7.476E-03. 1.417E-02 39.950 35.750 1496.9 1.129E C2 7.194E-03 1.361E-02 40.120 36.000 1494.9 1.C91E C2 6.972E-03 1.318E-02 4C.2S1 36.250 1492.9 1.OC8E 02 6.457E-03 1.219E-02 40.462 36.500 1491.0 1.002E C2 6.435E-03 1.213E-02 40.633 36.750 1489.1 S.548E Cl 6.145E-03 1.157E-02 4C.805 37.000 1487.2 9.119E C1 5.884E-03 1.107E-02 \J1 40.976 37.250 1485.3 E.792E C1 5.68,7E8-03 1.068E-02 F-H 41 147 37.500 1483.4 8.482E C1 5.500E-03 1.032E-02 41.319 37.750 1481.6 8.198E C1 5.329E-03 9.988E-03 41.492 38.000 1479.7 7.874E Cl 5.130E-03 9.605E-03 41.664 38.250 1477.8 7.524E 01 4.915E-03 9.189E-03 41.836 38.500 1476.0 7.227E 01 4.732E-03 8.837E-03 42.009 38.750 1474.1 6.877E 01 4.514E-03 8.421E-03 42.181 39.000 1472.2 6.613E 01 4. 351E-03 8. 108E-03 42.355 3S.250 147(.4 6 357E C1 4.193E-03 7.804E-03 42.52c 39.500 1468.6 6.078E 01 4.018E-03 7.470E-03 42.7C3 39.750 1466.8 5.840E C1 3.870E-03 7.186E-03 42.876 40.000 1465.0 5.611E C1 3.727E-03 6.913E-03 43.050 40.250 1463.2 5.411E 01 3.603E-03 6.675E-03 43.224 4C.500 1461.4 5.187E Cl 3.462E-03 6.406E-03 43.399 40.750 1459.6 5.010E 01 3.352E-03 6.196E-03 43.575 41.000 1457.7 4.738E 01 3.177E-03 5.866E-03 43.750 41h250 1455.9 4.510E C1 3.032E-03 5,591E-03 43.925 41.500 1454.1 4.344'E CI 2.927E-03 5 392E-03 44.100 41.750 1452.3 4.206E 01 2.842E-03 5.228E-03 44.276 42.000 1450.5 4.0C48E 01 2.741E-03 5.038E-03 44.452 42.250 1448,7 3.898E 01 2.646E-03 4.857E-03 44.o2S 42.500 1446.9 3.752E Cl 2.553E,03 4.681E-03 44,805 42.750 1445.1 3.626,E 01 2.473E-03 4.529E-03 44.982 43.000 1443,3 3.482E 01 2.380E-03 4.354E-03 Figure 19. (Continued)

TIME ALTITUDE VELOCITY PRESSURE RHOI. RHO2 ALPHA CORR RH02*CORR KRH 45.158 43.250. 1441.5 3.357E Cl 2.300E-03 4.203E-03 45.3335 43.500 14393.7 I3.242E 01 20227E-03 4.065E-03 45.6GC 44.000 1436.2 3.035E Cl 2.095E-03 3.814E-03 45.F86-7 44,250 1434.4 2.1930,E Cl 2.027E-03- 3.686E-03 46.045:44.500 1-43 2.7 2.82RE Cl L1.961E-03 3.563E-03 4 6.2 22 -4,4.7 50 1430.5 2.752E Cl 1.913E-03 3.472E-03 46.40)1 4'5.000 1429.2 2.613E Cl 1.820E-03 3.300E-03 46.530 45.25C 1427.5 2.a5974E Cl 17E-3 3.254E-03 4,6.759, -45.500 1425.7.2..4968 CI 1.747E-03 3.160E-03 46.9-38 45.750 1424.C 2.408E Cl 1.690E-03' 3.05?E-03 47.117 46.000 1422.2 2-.319E Cl 1.631E-03- 2.944E-03 47.296- 46.250 1420.5 2.2-288 01 1.5718F-03 2.8318-03 47.477 46.5,00 1418.7 2.161E Cl 1.5.27E-03 2.749E-03 47.657. 46.75-0 1417.0 2.0978 01. 1.4868F-03 2.6728-03.4. 837 47.000 14i1 5. 2 2.C33E Cl 1.4438-03 2.5938E-03 48.017 47.250 141-3.4 1.9558 01 1.3918-03 2.4968-03 48.15;7 47.500 1411.7 1.68888 Cl 1.347E-03 2.4148-03 48.379 47.750. 140'9.5 1.8168 Cl 1..2598E-03 2.325E-03.48.560 48.000C 1408.1 1.7628 Cl 1.2638-03 2.259E-103 489.742 48.250 ~1406.3 1.705E Cl 1.2258-03 2.1888-03 48.923 4-8.500 1404.6 1.6348 Cl 1.177E-03 2.1008-03 49.104 48.750 1402.8 1.5638 01 1.129E-03 2.0118-03 49.286 49.000 1401.C 1I.5088 Cl 1.0928-03 1.9438-03 49.4,69 49.250 1399.2 1.4558 Cl 1.01968-03 1.8778-03 49.65`2 45.500 13'97.5 1.3508E C,l 1.0178-03 1.8058-03.49.835 4.9.750 1395.7 1.3438 Cl 9.7938-04 1.7368-03 50.01-8 50'.000 1393.5 1.3038 CI 9..5288-04 1.6878-03 5C.201 50.250 1392.1 1.2708 Cl 9.3088-04 1.646F-03' ~ 50.385 50.500 1390.3 1.2338E Cl 9.0658-04 1.,6018-03 50.365 -50.750 1388.6 1.19-TE 01 8.8158-04 1.555E-03.50./53 51.0CC 1386.8 1.154E Cl 8.5.258E-0-4 1.5028-03.50.937 51.250- 1385.0 1.1148 01 8.2488-04.1.4528-03 51.121 51.500 1303.2 1.0,798 Cl 8'.0098-04 1.4088-03'51.306 51.7510 1381.4.1.045E Cl 7.7808-04 1.3668-03 51.491 52.000 1379.7 1.0138 01 7.556E-04 1.3258-03 51.677 52.250 1377.9. 5.7678 CC 7.3068-04 1.2798-03 51.8~2 52.5C0 1376.1 S-.A7CE CC 7.1018-04 1.2428-03 52.048.52.750 1374.4 9.1178 00 6.8548-04 1.197E-03 52.23 3 531.000 1372.6.8.7828 C 0 6.,6198-04 1.1558-03 52.420 53.250 13 70.. 8 P.4878 -CC 6.412E-04 1.1178-03 52.607 53.5C0 1369.1 8.1688 00 6.1888-.04 1.0778-03 52.981.54.0r00 1365.5 7.5768 00 5.7698-04 1.0018-03 53.168 54.250 1363.7 7.3578 CC 5.6168-04 9.7378-04 53.356.54.500 1361.9 7.1018 00.5.436E8-04 9.4118-04 53.544 54.750 136.0.1 6.8748 CC 5.2768-04 9.1228-04 53.7-32 55.000 1358.2 6.5858 CO.5.0688-04 8.'7518-04 53.920. 55.250 1356.4 6.3128 CC 4.8718. —04 8.4008E-04 54.108- 55.500 - 1354.5 6.0888 CC 4.'7118E-04 8.1138-04 54.25~7 55.750 1352.7 5.8598E.00 4. 57'78-04 7.8728-04 54.487 56.000 1350.5; 5.6988 CC 4.4338-04 7.180 54.676 56.250 1349.1 5.5188 CO 4.3048-04'7.382E-04 Figure 19. (Continued)

TIM10E AL TI TUD E'VELCCITY PrFS SUPE RHOI R H 02 ALPHA CORR RH02*CORR K H 5. 61 -56.53 134 7.2 ~ "" 1%0 7.1351-'04 5~- 75C 1P45.4 ".154F "" 4 "41E 04 6.914F-04 57 1~~~~ f~~ 4.-3F CC j 933F ~~~~~04 66E-04 55. 3 57.2',0 134__t A4 74 7 __- 3.782E 04 6.453E1-04____ 55To 7 ~~57.5C6 oI 4A~[C 6(47E 04 6.248F1-04 5 5 -1P 5 7.7)50 1 3t 1l 4 5I F 0', 1 "6711 04 6.07011-04 57T6: 5S. 10) jl3'* 4560,F C, 3 63IF-014 6.170F>04 5 6.2 JI0 5 8. 12 0 1 334. 7 4 i/'1l C C. 31363F-1 14 5.709E1-04 _____ 5U303 %.5) 17I. 1 o 3~'F0 5.54011-04.. -.-. —--- 56.5 E5 5E.75C 1 34 1.C' 9-i.q2F CC 1. 1 iF 04- 5.345E1-04 5.0/C~1 59.2?% P27.3.635% "C 2.q28F 04 4,043F 04 57.1<' 59. 500 1325.5 3.5 3%,- FC 0?. 8'' " 4 4.9 R-(7F104 57. ~17 59.lo 7 I) 1-3236 3.942F CC 2. 7 8(`'F - 4 4.6'34F- 04 57-5 I 6 --- TF 73M0 C.".?7E c, 2.7 30 4 4,543E 04 5 7.144 6 C". 2 P P 3 C, 2.R1F C C 2. (1SfE-4 4. 39 1 304 5T~~s3~~ 6C.0 Su 1 3 1.f 1 —-- -- "41- 4 4 4F- 04 - 5 8.1I1'2 60C. 5) 1 3h. 1 2 0 24 4ECC 2. 7F-'4 4 414SF 34 5 8. 2 7 6 1.")0) 1 31 2.' 3 01 C C. 4o U'8 4 4.0?5F- 04 58.313 6FTSJ l~~~~~(8'.c c 6""E CL 2?~~~~~E e -4 3.91-04 59 1 9 6~~~1 20'1' 3 N( 2 i. 7119 CO 2. 2?(H0 3. 836F-4_ 59..~~ 6?.~~SC 13J~~ C ~1..4&3E CC? C;)' 3. 662E-04 59.2 6d 50. 1 6 " C 21.12 7F — 3.1370-04_______ 59.o'o 62 J U,0 29% CC 1 2*' 3.41C) 7-04 59."2 6325.1C -12+.4 2 2 2 761- (C (1 1'1 f: J4 3 1 IF - 04 60. ~ ~~~63.2"u C 7 I. 11 C C 1 7 C9 01 24?.7.1JE-04 6 C. ) 63 5_C)0 125% 7 2 06 CF C 1 74 1'4 2.8690r-04 6O~~4'~ 513 /5( C; 9 I -FC o E-4 2.781F1-04 60. H 3 6 4. 00 0 1? "2. 3__'11I, " I_.6 3`'".6811 -04 _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ 60. 1l5 64. 25 12')0. I2 1'6 C "I 51.70E14 61.~~~~)1 64 5"'" 129~~8. 3 1. /9S ( 1. 351 4?541 -4f 63. 9~~~~'4 7"-D 12.1FC3141 4 2. 407E-04 61.4P2 45.0C"" 12 ci4.6 u I 58E1' 1.426E0'4 2.3291-,04 -6 1.-" ~ 5 ]2.27 I 6C4'.8i-0.?.64F-04 6 1. ~2 6 5.5 0 146.8' 1 "5" F (,C 1..34S5F -04 2.191E0-04 6 2.') 2'".7 5C IP''7 8 C 15 0111 F C0 1. 30211 "4 12.11811-04 6,2.""', 66.O0u 1-'/7.1 1.45111 CC 1.263E 04.05111-04 _ _ 6 2 L 5 6,6.5 0 12 7 3. 1-'5711 C C 1.1391E 04 1.9-2 41-04____ 62.887 66.750 1271.3 1.31311 CO 1.19311 ~~~ ~~ ~~~~~04 161-04 63.061 6 7.000' 1 269C".4.1.2?6911 C C' 1.1111 u -4 1.804F1-04 -63.290) 67.250 1267.5 1.22411 CC 1.08111 04 1.74?F-04 63.4`93 67.500 1265.6 1.17711 00 1.0430 04 1.67811-04 63.696 6~~7.15C 1263.4 1.1-34E CC 1.00SF 04 1.62011-04 6 3.89 __ 9 8. 0 00C 12I1. 7 1.00)11 CC 9. 714E-0 5 1.9598F1-04 64.102 68.25 1259.1 1.3-611 C —C" 9.2640 -05 1.4 8 4 1- 04 64. 3 6- 68R.930 1257. &.1 F -C 1 8. ('73F053 1.41911-04 6 451 1 6E. 7 50C 1 2 5 5 3. 462E-ClI P. 517E1 05 1.36011-04 64.7 16 6_C, 6.C,000 1254.0 9.08911-Cl d. 2CS E_09 1.308E-04 64Q? 9.5 125 21. I.713C 79Tf-U 5 1.26511-04 Figure 19. (Continuied

T I ME ALTITUDE VELOCITY FRESSLRE R HOI RH02 AL PHA COJRR' RH02*CORR KRO 65.125 ~69.500 1250.1.8.517E-Cl 7.739E-05.1.230E-04,65.331 619.750 1248.2 P.207E-01 7.479E-05 1.187F-04 65.537 7C.000 1246.3 7.946E-01 7.2658-05'1.151E-04 65.743 7C.250 1244.4 7.686E-Cl 7.049E-09 1.115E-04 65. 95C 7C.5(]0 1242.5 7.333F-01 6.746E-05 1.065E-04 C66.363 71.0CC 1238.6 6.972E-C1 6.454E-05 1.0168-04 66.5,71 71.250 12 7 6'.6C2E-Cl 6.131E-05 9.636E.-05 66.7793 71.500" 1234-.8 6.346E-Cl 5.912F-05 9.277E-05__ ___ 66-.G87 71.750 1232.q (6.1268-Cl 5.724E-05 8.968E-05 67.195 72.000) 1231.0 5.918E-01 5.548E-05 8.678E-05 ___________ 67.404 72.2150 1229.1 5.65989-Cl -~5.32IF-05 8.311E-05 67.614 72.500 1227.1'5 4018-01 5.095F-05 7.944E-05 67.823 72.750 1225.2. 5.317E-Cl 5.031E-05 7.8338-05 68.033 73.000 122"3.3 51.1448-Cl 4.PP4F-C5 7.590E —05 _ 68.24/3 73.250 1221.3 4.95148-Cl 4.718E-05 7.321E-05 68.4574 73.500 1219.4 ti.7798-Cl 4.566E-05 7.073E-05 68-.66(-5 73.750 1217.4 4.5948-Cl 4..4038-05 6.811E-05 68.87.6 74.000 1215.4 4.424E-Cl 4.255E-05 6.570Ei-05 69.088.74.250 1213.5 4.078E-Cl 3.G348-05 6.0658-05 6 9.300 74.5CC 1211.5 3.861E-Cl 3.718E-09 5.7538-CS5 69.512 74.750 1209.5 3.6648E-Cl 3.5588-05 5.468E-05 69.725, 75.0CC 1207.6 3.411E-Cl 3.324E-OS 5.098E-05 69.9 38 7 5.250 1 20 5. C.159E-CI. 3.08>~E-05 4.730E-05 70.1511 75.5C0 1203.6 2.978E-C1 2.9218-05 4.4668-05 3.255 0.951 4.2498-05 0.0291E0 76.3645 75.750 1201.6 2.8428-Cl 2.7978 —05 4.2688-05 3.190.0.951 4.0618-05 0.02.980 7C.580 76.000 11,99.6 2.728F-01 2.6948-05 4.1048-05 3.126 0.952 3.9068-05 0.0264-0 70.79;5 76.250 119-7.7 2.6068-Cl 2.581-05. 3.9278-05 3.062 0.952 3.7378-05 0.02.8-0 71.0019 76.500~ 1105.7 2.4668-01 2.,451F-05 3.722E-05 2.997 0.952 3.5448-05 0.0 45-0 4 71.224' 76.750 1193.7 -2.334E-01 2.32S8-05 3.529E-05 2.933 0.952 3.360E-05 0.02.8-0 71.441 77.0'00, 1191.7.2.241E-01 2.2_438-0-5 3.3958-OS 2.868 0.952 3.2338-05 0.0224-0 71.657 77.250" 1189.7 2.1608-01 2.1698-05 3.2778-OS 2.803 0.952 3.1218-05 0.0216-0 71.873 77.500 118'7.7 2.08C8-Cl 2.096E-05 3.162E-OS 2.738 0.953- 3.0128-05 0.02.6-0 72.090 7-7.750 1185.7 2-.0018-Cl 2.01238-05 3.046F-OS 2.678 0.953 2.902E-05 0.0203-0 72.307 78.000.1183.,6 1.9208-01 1-.948E-05 2.9288-OS 2.623 0.953 2.791E-05 0.0194-0 72.5?5 78.250 1181.6 1.8298-01 1.8628-05 2.7948-05 2.S69 0.953 2.6638-05 0.0182-0 72.743 78.-500 1179.6- 1.7428-01. 1.7798-05 2.6658-05 2.514 0.953 2.541E-05 0.01.9-0 73. lO 79.000 1175.5 1.6188-01 1.6658-OS 2.4848-05 2.405 0.954 2.3698-05 0.001 1.6-0 7-3.4(0.79.250. 1173.51 1.5638-01 1.6138-05 -2.404F-05 2.350 0.954 2.2928-05 0.001 161-5 72.(20 79~.500.l171.4,- 1.5128-01Z- 1.5678-05 2.3308-05 2.295 0.954 2.2238-05 0.002 158-0 73.8410 79.750 1169.4 1.459E-C1 1.517F-05 2.2528-05 2.240 0.954 2.1488-05 0.003 159E5 74.06O 80.000 11167.3 1..3778-Cl' 1.437E-05 2.129E-05 2.197.0.954 2.032E-05 0.005 140-5 7/4.281 80C.2 50. 1 16 5.3 1.3098-01.14371F-05 2.028E-05 2.186 0.954 1.9358-05 0.006 137-0 74 5') 80.500 16. 1.291E-01 1.3.57E-05 2.0038-05 2.175 0.955 1.9128-05 0.006 136-0 74.724 80.750 1161.2 1.2508-Cl 1.3"188-,15 1.9438-05 2.164 0.954 1.8558-05 0.007 132-0 7,94.60 81.000 1191 1.2C8E-01 1.278E-OS 1.8818-05 2.153 0.954 1.79SF-OS 0.009 128-0 75_168 81.250 i1570C. 1.163E-Cl 1.235E-05 1.8148-05 2.142' 0.954 1.731E-05 0.011 124E0 75.3(2 81.500 1155.C 1.1198-Cl 1.1938-05 1.749E-05 2.130 094 1.669E-05 001119-5 75.615 81.750 1152.9 1,0688-01 1.1428-05 1.6718-05 2.119 0.954 1.5948-05 0.016 114-0 75.809, 82.000 1150.8- 1.6108E-Cl 1.0848-05 1.584E-05 2.108 0.954 1.5108-05 0.018 109-5 76.0ut? 82.250 1148.7 9.669F-02 1.042E-OS 1.5198-OS 2.109 0.954 1.4498-05 0.021 105-5?6.2t18 82.500 1146.6 9;.2C7E-C2 9.9538-06 1.449E-05- 2.143 0.953 1.3828-05 0.023 104-5 Figure 19. (Continued.)

TIME ALTITUDE VELCCITY PRESSURE RHOI RHO2 ALPHA CORR.RH02*CORR KRO 76.t13 82.750 1,144. 5 8.86S7E-02 96E-6.3E05 2.177 0.953 1.333E-0 0.025 9.1E0 76.739 8.000 1142.4 8.594E-02 9.357E —06 1.358E-05 2.1 095 124E0 006 945E6 76.965 8 3.-2-50 1140.3 8.286E-02 9.055E-06 1.312E-05 2.245 0.953 1.250E-05 0.028 9.5E0 77.191 83.500. 1138.2 8.003E-C2 8.777E-06 1.269E-05.2.279 0.952. 1.209E-05 0.030 886E0 77.418 83.750 1136.1 7.738E-02 8.518E-06 1.229E-05 2.313 0.952 1.17IE-05 0.032 8.2E0 77.646 84.000 1134.0 7.492E-02 8.277E-06 1.193E-05 2.347 0.952 1.135E-05 0.034 838E0 77.874 84.2 50 1131.9 7.-252E-C2 84E-6 1.156E-05 2.381 0.952 1.101E-05 0.036 817-0 78.102 84.500 1:12'9.8 69E-2 7.759E-06 1.114E-05 241 092 1.060E-05 0.038 786E0 78.331 84.750 1127'.6 6.674E-C2 7.455E-06 1.068E-05 2.499 0.951. 1.016E-05 0.041 756E6 78.560 85.000 1125.5 6.'347E-02 7.116E-06 1.0-18E-05 2.568 0.951 9.680E-06 0.044 29E0 78.790 8-5-.2 50 1123.3 -5.1955E-C2 6.701E-06 9.569E-06 2.637 0.951 9.098E-06 0.048 6.1E6 79.020 85.500 1121.2`5.!~67E-02 6.288E-06 8.962E-06 2.706 0.951 8.518E-06 0.053 640-6 T9. 250 85.750 1119.1, 5.179E-C2 5.872E-06 8.354E-06 2. 775- 0.950 7.938E-06 0.058 599EO 79.482 86.000- 1.1 16.9 4.852E-C2 5.522E-06 7.841E-06 2.845 0.950 740-06 0.063 564E6 79.714 86.250 111-4. 8. 4.6CIE-C2 5.256E-06 7.449E-06 2.914 0.950 7.075E-06 0.067 537-0 79.946 86.500 1112.6 4.438E-02 5.0.89E-06 7.199E'-06 2.984 0.950 6.83-6E-06 0.070 521E6 80.178 86.750 1 11 0. 4 4.311E-02 4.962E-06, 7.008E-,06 3.170 0.949 6.651E-06 0.072 504-O 80.645 87.250 1106.1 3.948E-02 41579E-06 6.442E-06 3.619 0.948 6.11OE-06 0.080 470E6 80.879 87.500 1139 3.757E-C2 4.375E-06 6.144E-06, 3.844 0.948 5.824E-06 0.084 449E6 81.113 8.iSO 1101.7,3.607E-~02 4.216E-.06 5.909E-0 408 0.948 5.600E-06 0.088 433-6 81.348 88.000.1099. 5 3.4.80E-C2 4.084E-06 5.713E-06 4.294 0.947 5.412E-06 0.091 424E0 81.584 838.250 1,097. 3 -3.332E-C2 3.926,E-06 5.481E-06 4.521 0.947 5.191E-06 0.094 404E6 81.820 88.500 1095. 1 3.181E-C2 3.762E-06.5.243E-06 4.747 0.947 4.964E-06 0'.098 380E6 82.056 88.750 1092.'9 3.066E-02 3.641E-06 5.063E-06 4.974 0.947 4.793E-06 0.101 375E6.8.93 89.000 1090.7 3':.0IIE-C2 3.590E —06 4.984E-06 5.201 0.946 4.,716E-06 0.103 3.0E6 82.5311. 89.0250 1088.5 2.877E!-C2 3.444E-06 4. 77j1 E-06 5.430 0.946 4.514E-06 0.107 357E6 \l 82.769 89.500 IC186.2 2.754E-C2 3.309E-06 4.576E-06 5.6,59 0.946 4.328E-06 0.111 3.2E0 83.0,08 89.750 10,84.0 2.6-48E-02 3.195E-06 4.410E-06 5.887 0.946 4.170E-06 0.115 338E6 83.246 90.000 1081.8 2.538E-C2 3.074E-06 4.23.4E-06 6.116 0.,946 4.004E-06 0.119 315E6.83.487 90.250 1079.6 2.450E-C2 2.980E-06 4.096E-06 6.347 0.945 3.872E-06 0.123 309E0 83.727 9050 1077.3 2.346E-C2 2.865E-06 3.930E-06 6.578 0.945 3.715E-06 0.127 2.3E6 83.967 90.750 1075.1 2.257E-02 2'.768E-06 3.789F-06 6.809 0.945 3.582E-06 0.131 285E0 84.208 91.000 1072.9 2-.159E-C2 2.'658E-06 3.633E-06 7.039 0.945 3.433E-06 0.136 2.4E0 84.450 91.250 1070.6 2.060E-02 2~.547E~ —06 3.473E-06 7.2'72 0.945 3.282E-06 0.142 265E6 84.693 91.500 1068.4 1.978E-02 24455E-06 3 342E-06 7.505 0.945 3.158E-06 0.147 258E0 84.9.36 91.750 1066.1 1.883E-C2 2.34.6E-06 3:188E-06 7.738 0.945 3.OI1E-06 0.154 248E0 85.179 92.000 1063.8 1.8C8E-02 2.262E-06 3.067E-06 7832 0.944 2.8'97E-06 -0.160 233-0 85.423 92.250 10O6 1. 7 1.723,E-C2 2.164E-06 20929E-06 7.876.0.944 2.767E-06 0.167 225E0 85.668 92.500 1059.5 1.667E-C2 2.102E-06 2.840E-06 7.920 0.944 2.682E-06 0.172 222-6 85.913 92.750 1057.31 1.599E-02 2.025E-06 2. 73 1E-0 7.964- 0.944 2.578E-06 0.178 213E6 86.157 93.000 1055.1 1.541E-02 I.S58E-06 2.636E-06 8.008.0.944 2*488E~-06 0.185 205E6 86.4C4 93.250.1052.9 1.492E-02 1.904E-06 2,.558E-06 ~8.053 0.944 2.414E-06 0.0191 201E6 86.651 93.500 LJ50.6 1.427E-02 1.828E-06 2.452E-06'8. 097 0.944 2.314E-06 0.199 192-0 86.898 93.750. 1046.4 1.364E-C2 1.755E-06 2.349E-06 8.142' 0.944 2.216E-06 0.208 85E6 87.145 94.000 10 4 6.]. 1.294E-02 1.671E-06 2.232E-06 8.186 0.943.~2.105E-06 0.219 176E0 Figure 19. (Continued)

ICCMMU TATOR VALUES TIME CHIL 1 CHL 4 CHL 5 35.275 4.153 2.5C3 4.448 39.365 4.142 2.503 4.077:45.675 4.113 2.5C3 3.462 s52'896 4.092- 2.503 3.102 58.846 4.076 2.s503.493 66.387 4.047 2.503 2.14e.73.'127 4.027 2.503 1.528.'5e7 - 4.002 2.503 1.157 ERROR RETURN Figure 19. (Continued) k7

SPACE PHYSICS RESEARCH LABCRATCRY THE UNI VERSI T Y IF M ICHIGAN ANN AR9CR, MICHtGAN 17:46-. 1 DECEMVBER 18,196 NASA'14.386 GAGE 1 F LAUNCH TIME: 20: 4:59.-813 5 INPUT FILE.- 1 CHANNEL INDEX 1 TAPE IU: SPRL NASA 14.386 12/12/69 8020 F1 0o 0' CALIBRATE LEVELS; 5.003 O.C04 2.503 V TCAL: 3.7CO RANGE 1 INDICATE:. 0.500 STEP eETGNEEN RANGES: 0.5 C( RANGE: 2 VOLTAGE PRESSURE VOLTAGE PRESSURE VOLTAGE. PRESSURE VOLTAGE PRESSURE VOLTAGE PRESSURE c.900 8.30COE-03 2.2CC 2.0COE —02 3.500 3.420E-02 4.750 4.780E-02 RANGE: 3 VOLTAGE PRESSURE VCLTAGE'PRESSURE VOLTAGE PRESSURE VOLTAGE PRESSURE VOLTAGE PRESSURE 0.890 3.550E-C2 2.1SC S.1CCE-02 3.490 1.460E-01 4.740 1.980E-01 RANGE: 4 VOLTAGE PRESSURE VOLTA.GE PRESSURE VOLTAGE PRESSURE VOLTAGE PRESSURE VOLTAGE PRESSURE -.900 1.510E-O1 2.190 3.75GE-C1 3.500, 6.OOOE-01 4.750 8.180E-01 RANGE: 5 -VOLTA.GE PRESSURE VOLTAGE PRESSURE VOLTAGE PRESSURE VOLTAGE PRESSURE VOLTAGE PRESSURE 0.890 6.200E-01 2.190 1.520E 00 3.490 2.420E 00 4.740 3.300E 00 RANGE: 6 VOLTAGE PRESSURE VOLTAGE PRESSURE VOLTAGE PRESSURE VOLTAGE PRESSURE VOLTAGE PRESSURE C.900 2.480E 00 2.200 6.110E 00 3.500 9.850E 00 4.750 1.360E 01 RANGE: 7 VOLTAGE PRESSURE VOLTAGE PRESSURE VOLTAGE PRESSURE VOLTAGE PRESSURE VOLTAGE PRESSUtRE C.890 7.2?00E 00 2.190 1.75CE 01 3.490 2.800E 01 4.740 3.810E 01 RANGE: 8 VOLTAGE PRESSURE VOLTAGE PRESSURE VOLTAGE PRESSURE VOLTAGE PRESSURE VOLTAGE PRESSURE 0.900 2.87GE Cl 2.000 6.390E 01 3.100 9.940E 01 4.750 1.530E 02RANGE: 9 VOLTAGE PRESSURE VCLIAGE PRESS'URE VOLTAGE PRESSURE VOLTAGE PRESSURE VOLTAGE PRESSURE 0.890 1.170E 02 1.'79C 2.410E 02 2.690 3.710E 02 3.590 5.100E 02 TIME CCRRECTICNS 0.0 0.0 500.CCG C. Figure 19. (Continuea) 57

TI KE ALTITUDE VELOCITY PRESSURE RHOI RHO? ALPHA CORR RH02*co"- KRH 81.:'-3 48 88.000 1099.5 3.462E-02 4.062E-06 5.683E-06 4.294' 0.947 5.384E-06' 0.09,1 4.8E6 81.584 88.250 1097.3 3.34,9E-C2 3,.945E-06 5.509E-06 4.521 0.947 5.21'78-06 0.094 406E6 81.820 88.500 1095.1 3.233E-02 3..824E-06 5.329E-06 4.747 0.947 5.046E-06 0.096 394E0 82.056 88.750 1092.91 3.122E-02 3.7C8E-06, 5.156E-06 4.974' 0.947 4.881E-06 0.100 3.2-6 82.293 8S.000 1090.7 3.020E-02 3.601E-06 4.99PE-06 5.201 0.946 4.730E-06.0.102 3.186 82.531 -89.250 1-088. 5 2.8838-C2 3.451E-06 4.781E-06 5.430 0.946 4.523F-06 0.106 3.6-0 82.769 ~~~89.500 1086.2 2.759E-C2 3.3158-06 4.584E-06 5.659 0.946 4.3368-06 0.111 34280 83.008 89.750 1084.0 2.654E-C2 3.2C3Er-06 4.419E-06 5.;887 0.946 4.1808-06 0.115 3.1-6 83.24f6 90.000 1081.8 2.5618-02 3.102E-06 4.2'728-06 6.116 0.946 4.040E-06 0.118 321-0 83.487 90.250 1 0'7.6.2.4648-02 2.9988-06 4.120E-06 6.347 0.945 3.8968-06 0.122 3.0E6 Ff3.7 27 90.500 1077.3 2.363E-02 2.885F-06 3.958E-06 6.578 0.945 31.7428-06 0.126 2.380 83.967 90.750 1075.1 2.2628-02 2.7738-06 3.797E-06 6.809 0.945 3.589E-06 0.131 280-6 84.208 91.000 1072.9 2.1 728E-0C2 2.6748-06 3.654E-06 7.039 0.945 3.453E-06 0.136 27986 84.4-50 91.250 1070.6 2.081E-02 2.5738-06 3.509E-06 7.272 0.945 3.3168-06 0.140 267-0 8 4. 693. 91.500 1068.4 1.9S6E-02'2.4778-06 3.372E-06 7.505 0.945 3.185E-06 0.146 258-6 84.936. 91.-750 1066.1 1.8968-C? 2.362E-06 3.209E-06 7.7 38 0.945 3.032E-06 0.152 246-0 85.179 92.000 1063.8 1.809E-02 2.263E-06 3.0698-06 7.832 0.944 2.8998-06 0.159 236-0 85.423'92.250 10 61.7 1.7328-C2 2.176E-06 2.945E-06, 7.876 0.944 2.7828-06 0.166 227-0 85.668 ~~~92.500 1095 1.629E-02 2.054E-06 2.7758-06 7.920 0.944 2.620E-06 0.176 215-0 85=. 9 13 92.750 1057.3 1.5,33E-02 1.9418-06 2.6178-06 7.964 0.944 2.4718-06 0.187 20486 86.157 93.000 1055.1 1. 505E-02 1. 9128E-06 2.5748-06 8.008 0.944 2.4308-06 0.190 201-6 86.404 93.250 1052.9 1.447E-C2 1.8478-06 2.4818-06 8.053 0.944- 2.3418-06 0.197 1940 86.651. 93.500 1050.6- 1.3898-02 1.7808-06 2.3868-06 8.097 0.944 2.2528-06 0.205 187-0 86. 89 8 93.750 1048.4 1.33C8-C? 1.711E-06 2.2898-06 8.142 0.944 2.1608-06 0.214 180-6 87.145 94.,000 10461.1 1.279E-02 1.6528-06 2.207F-06 8.186 093 2.082E-06 0.222.480 87.394 94.250 104.3. 8 1.24i28E-02 1.6118-06 2.1478-06 8.231 0.,943 2.0258-06 0.227 17086 87.644 9 4.5 00 1041.5- 1.1478-C2 1.4958-06.1.9898-06 8.276 0.943 1.8758-06 0.250 l50E6 U 87.R93 94.750 1039.2 1.0908-C2 1.425E-06 1.8928-06 8.321 0.943 1.785E-06 0.264 150-6 co 88.l' t 2 9 5.00, 0 1036.9 I.C36E-C2 1.362E-06 1.8048-06 8.366 0.943 1.701E-06 0.279 146-0 88.394 95.250 1034.6 S.868E-03 1.3028-06 1.7228-06 8.411 0.943, 1.6238-06 0.294 139E0 88.6-45 95.500 1032.2 9. 3 148E-03 1.234E-06 1.6298-06 8.456 0.943 I..535E-06 0.311 132-0 8 8.89 7 95.750 102'9.93 93.0748E-0C3 1.2CBE-06 1.5908-06 8.502 0.942 1.499E-06 0.318 130-6 8 9.1,49 96.000 1027.6 8.6408-03 1.1558-06 1.5188-06 8.547 0.942 1.430E-06 0.337 124-0 89.403 96.250 1025.3 8.25.-2E-C3. 1.1088-06 1.4538-06 8.593 0.942 1.369E-06 0.354 12086 89.657 96.500 1022.9 7. 8778E-0C3 1.0628-06 1.3908-06 8.638 0.942 1.309E-06 0.371 115-0 89.911. 96.750 1020.6 7.553E-C3 1.0-238-06 1.3368-06.8.684 0.942 1.2588-06 0.386 1.4-0 90-. 166 97.000 1018.3 7. 2708-03 9.8858-07 1.2898-06 8.760 0.942 1.214E-06 0.401 107-6 90.422 937.250 101 5.9 6.9~818-03 9.5358-07 1.2408-06 8.852 0.942 1.168E-06 0.419 10486 90.679 S7.500 101-3.6 6.6938-03 918-7 1.1928-04 8.944 0.942 1.1238-06 0.436 107-6 90.935 97.750 IG1011.2 6.4278-C3 8.8568-07 1.1478-06 9.037 0.942 1.0818-06 0.455 974-7 91.192 9l8.000 1008.9C~ 6.1638-03 8.5288-07 1.1038-06 9.129 0.942 1.0398-06 0.474 941-0 91.451 98.250 1006.6 5.S08E-C-3 8.2138-07 1.059E-06 9.222 0.942 9.9828-07 0.493 908-7 91.710 l98.500 100-4.2 5.6648-03 7.9088-07 1.0188-06 9.316 0.942 9.5938-07 0.515 875-0 91.9369 98.750 1001.8 5.4418-03 7.6318-07 9.85038-"07 9.409 0.942 9.2388-07 0.536 849-0 92.229 99c.000 1999. 5 5.2188-03 7.351E-07 9.4248-07 9.502 0.942 8.8818-07 0.557 823E0'92.491 99.250- 997.0 5.0118-03 7.0928-07 9.0,71E-07 9~.597 0.943 8.5508-07 0.579 793-0 92.752 99.500 1994..6 4.8098-03 6.8378-07 8.727E-07 9.691 0.943 8.2278-07 0.607 768-0 93.014 99.750 )9 92,. 2 4.6178-03 6.5.968-07 8.4008-07 975 093 718-7 0.633 743-0 93.277.1 00.000'989. 7 4.4258-03 6.3498-07 8.0698-07 9.880 0.943 7.6088-07 0.660 7.8-0 93.541.100.250'987. 3 4.2338-03 6.1038-07 7.7388-07'9.975 0.943 7.2978-07 0.6'91 692-0 93.806 100.500 984.9 4.0398-03 5.8508-07 7.4028-07 10.070 0.943 6.9818-07 0.732 667-7 Figu~re 19. (Continued.)

.TIME ALTITUDE'VELOCITY PRESSURE RH0l RHVJ2 ALPHA CORR RH02*CORR KRH 94.070 100.750 982.4 3.840E-03 5.589E-07 7'.056E-07 10..165 0.943 6.655E-07 0.777 641EO 94.336 101h000 980.0 3.643E-03 5.325E-07 6.709E-07 10.261 0.943 6.329E-07 0.831 615E0 94.603 101.250 977.6 3.435E-03 5.045E-07 6.342E-07 -10.357 0.944 5.983E-07 0.0891 581E0 94.870 101.500 975.1 -3~.39IE-0-3 5.C04E-07 6.277E-07 10.453.0.944 5.923E-07 0.902 5.3E0 95.137 101.750~ 97 2. 7 3.004E-03 4.454E-07 5.575E-07 10. 514 0.944 5.261E-07 1.000 526E7 951.406 102.000 970.2 2.Bl1E-C3 4.186E-07 5.229E-07 10.541 0.944 4.934E-07 1.000 494E0 95-.676 10 2.2Z50 — 967.8 2.633E-03 3.941E-07 4.911E-07 10.568 0.944 4.634E-07 1.000 464~0 95.946 102.500 965.3 2.479E-C3 3.728E8-07 4.636E-07 10.595 0.944 4.375E-07 1.~000 435E0 96.348 102.750 961,.6 2.203E-03 33707 4.'135E-07 10.635 0.944 3.903E-0 1.000 3.3-0 96.489 103.000 960.3 2.139E-03 3.248E-07- 4.020E-07 10.649 0.944'3.794E-07 1.000 3.9-0 96.762 103.250 957..8 2.002E-03 3.0548-07 3.772E-07 10.676 0.944 3,560E-07 1.000 356E0 97.034 lC3.500 955.3 1.856E-C3 2.846E-07 3.507~-07 -10.703 0.944 3.310E-07 1.000 331E0 97.30.8 103.750 952.7 1.711E-031 2.637E-07- 3.242E-07 10.731 0.944 3.060E-07 1.000 306-0 97.584 104.000 950.2. 1.587E-C3 2.458E-07 3.016E-07 10.758 0.944 2.846E-07 1.000 284-7 1971.860 104.250 947.7 1.480E-03 2.303E-07 2-.819E-07 10. 786. 0.944 2.660E-07 1.000 2.6E7 98.135 104.500 945.1 1. 3938-:0-3 2.179E-07 2. 6618E-0-O7 10.814 0.944 2.5118-07 1.000 251-0 98.413 104.750 942.6 1.3120E-03 2.074E-07 2.5278-07 10.841 0.944 2.385E-07 1.000 23580'98.691 105.000 940.0, 1.257E-C3 1.985E-07 2.414E-d7 10.869 0.944 2.2788-07 1.000 227-0 938.97G 105.250 9-37. 5 1.215E-C3 1.929E-07 2.339E-07 10.897 0.944 2.208E-07 1.000 22080 99.249 105.500 934.9; 1.1 598E-0 3 1.850E-07 2.238E-07 10.925 0.944 2.114E-07 1.000 2.1E0 993.530 1 05..7 50 932.3 1.158EIC3 1.858E-07 2.2428-07 10.953 0.944 2.1188-07 1.000 218-0 99.811 106.000 9 29. 7 1'.0 7 9E- C3 1.739E-07 2.094E-07 10.981 0.945 1.9788-07 1.000 1.780 1C0.C93 106.250 927.1 1.042E-03 1.688E-07 2.0288-03 -10.983 0.945 1.916E-07 1.000 196-0 100.376 106.500 924.5- 1.010E-C3 1.645E8-07 1.9728-07 10.932 0.944 1.862E-07 1.000 186-0 100.660 106.750 92 1.0 cj.762E-0-4 1.599E-07 l.911E-07 10.881 0.944 1.805E-07 1.000 18580 100.945 107.000 919.3 9.488E-04 1.562E-07 1.863E-07 10.830 0.944 1.759E-07 1.000 175-0 101.229 107.2590 91; 6.17 9.190E-0C4 1.521E-07 1.0810E-07 10.779 0.944 1'.7 019E- 07 1.000 170-7 \.1 101.517' 107.500 914,.C 8.79517E-C4 1..457E-07 1.729E-07 10.727 0.944 1.6338-07 1.000 163-0 1~ 01.F04 1 07.7 50 911.14 8.487F-C4 1.420E-07 1*.(81E-07 10.675 0.944 1. 587E-07 1.000 157-0 102.092.108.000 908.7 8.200E-C4 1.3798-07 1.6298-07 10.623 0.944 1.5378-07 1.000 153-0 10-2,381 108.250 9016.1I 7.892E-04 1.334E-07 1.5728-07 10.571 0.944 1.484E-07 1.000 1.8-7 102.,672 1C8.500 903.4 7.592E-04 1.290E-07 1.517E-07 10.519 0.944 1.432E-07 1.000 143-0 102.90631 108.750 900.8a 7.340E-04 1.255F-07 1.4718-07 10.467 0.944 1.388E-07 1.000 138-0 103.254' 1CS.000 89P.2 7.565E-04 1.3008 —0'7 1.520E-07 10.414 0.944 1.434E-07 1.000 143-0 103.548 109.2510 895.5 6.863E-04 1.1868E-07 1.3838-07 10.361 0.943 1.305E-07 1.000 130-0 103.842. 109.500 892.93 6.6C6 E-C4 1.1478 —07 1.3368-07.10.308 0.943.1.2608-07 1.000 1.680 104.136 109.750 890.2 6.348F-04 1.109E-07 1.287E-07 10.256 0.943 1.214E-07 -1.000 1.180 104.432 110.000 887. 5 6. 107E-CA 1.C728-07 1.2428-07 10.202 0.943 1.171E-07 1.000 117-0 104.729 110.250 884.9 5.8698-04 1.037E-07 1.197E-07 10.149 0.943 1. 129E-07 1.000 112-0 1051.026 110.500 882.2 5.6268-C4 9.9908-08 1. 1518,-07 10.093 0.943 1.085E-07 1.000 108-7 105.3125 110.750 879. 5 5.2948-04 9.455E-08 1.086E-07 10.009 0.943' 1.0248-07 1.000 10480 105.626 1111.000 876.8 5.0398-04 9.0438-08 1.037E-07 9.925 J.943 9.777E-08 1.000 97788 105.926 111.250' 874.2 4.717E-04i 8.5148-08 9.739E-08' 9. 841 0.942 9.1768E-08 1.000 9.780 106. 2 27 111.500 871.5 4.374E-C4 7.9358-08 9.0608-08 9.-756 0.942 8.537E-08 1.000 8.3-0 106.531 111.750 868.7 4.061E-C4 7.4118-08 8.4378-08 9.671 0.942 7.948E-08 1.000 794E0 106.835, 112.000 866.0 3.7328-04 6.8468-08 7.7'798-08 9.586 0.942 7.3278-08 1.000 7.280 107.1.39, 112.250 8363.2 3.4358-04 6.3398-08 7.1838-08 9.501 0. 942 6.7648E-08 1.000 67480 107.446 112. 500 860.4 3.1618-04 5-.865E-08 6.6328-08 9.415 0.:942 6.2458-08.1.000 6.480 107.753 112.750 857.6 2.9198-04. 5.4498-08 6.1448-08 9.6329 0.941 5.7848-08 1.000 5.8-0 108.061. 113.000 854.8 2.700E-04 5.0658-08 5.700E-08 9.243 0.941 5.3658-08 1.000 53580 108.370 113.250.852.0C 2.5118-04 4.741E-08 5.'3208-08 9.156 0.941 5.0068-08 1.00 50680 Figure 19. (Continued)

TIHE.'ALTITUDE VELGCITY PRESSURE RHO! RH02' ALPHA C'ORR'RHO2*CORR'- K RHO'I08.'681' 1i3o500 849.3 2.344E-G4, 4o448E-0.8 4.982E-08 9.069 0o941'" *o687E-08..'I.000. ~o687E"-08 108'992 113.750 846.6 2.201'E-04 4. 203E-08 4. 694E-08 8,,982 0.941 4.415E-08 loOO0 ~o415E-08 1.09.304 1i4.000 843.8 2.081E-C,4 3.993E-08 4.450E-08 8,,895 0.940 4,,, 186E-08 t.000 4,,. Ie6E-oe 109.619 114.250' 841.0 1.958E —C4 3.781E-08 4. 203E-,08 8~807 0.940' 3o952E-08 1o000 3o952E-08 109.934 114.5'00 838.2 1. 864E-04 3.619E-08 4. 014E-08 8.719 0.940 3o 773E-08 "1.000 3o773E-08 110.249'114.750.835.4 1.769E-04 3.457E-08 c 3. 823E-08 8.635 0,,9*0'3o 594E-08 1.000 3. 594E-08 110.567. 115,,000 ~ 832.6 1o688E-04 3.316E-08 3o660E-08., 8.552 0,,940. 3o440E-08 1.000 3o440E-08 110.;886 115.250 829.7 1.612E-04 3. 186E-08 3.506E-08 8.470 0.940 3o295E-08 1.000 3o295E-08 111.204 115.500 826.9 1. 547E-C4 3. 075E-08 3.378E-08, 8.387 0.940 3.174E-08 1.000 3.174E-08 111o526 115,750 82,4.0 ].484E-C4 2. 968E-08 3. 250E-08 8,303 0.94-0 3,054E-08 1o000 3o054E-08 111.849 116.000 821.2 1.429E-04 2.875E-08 3.141E-08 8.219 0.940 2.953E-08 1.000 2o953E-08 112,171 116.2-50 818.3 1.376E-C4 2.787E-08 3.036E-08 8,136 0,940 2.853E-08 1.000 2o853E-08 112.497 116.500 815.4 1,330E-04 2,709E-08 2o945E-08 8,051 0,940 2.769E-08 1,000 2o769E-08 113.040 116.750 810.5 1.269E-04 2. 612E-08 2. 825E-08 7,,910 0.940 2.656E-08 1.000 2. 656E-08 113.149 117.000 809.5 1.256E-04 2. 590E-08 2,801E-08 7,881 0.940 2.634E-08 1,000 2. 634E-'-08 113.479 117.250 806.6 1,213E-04 2. 517E-08 2,713E-08' 7,795 0~940 2,551E-08 1,000 2,551E-08 113 809 117.500 803.7 1. 176E-04 2. 454E-08 2. 640E-08 7.710 0.940 2.483E-08 1.000 2.483[ —-08 114.140 117.750 800.8 1.137E-04 2. 390E-08 2. 564E-08 7.624 0.940 2.411E-08 1.000 2.411E-08 114.473 118.000 797.8 1.103E-04 2.330E-08 2o496E-08 7.537 0.941 2. 347E-08 1o000 2. 347E-08 11.4.808 118.250 794.9 1.071E-C4 2.277E-08 2.431E-08 7.450 0.941 2.287E-08 1.000 2.287E-08 115.142 118,500 791.9 1.040E-04 2. 225E-08 2. 370E-08 7.376 0.941 2. 229E-08 1.000 2.229E-r08 115.480 118.750 788. q 1.010E-04 2. 176E-08 2.310E-08 7.320 0.941 2.173E —08 1.000 2.173E-05 115.819 119.000 785.9 9.817E-05 2. 128E-08 2.255E-08 7.264~ 0.941 2. 121EL08 1.000 2o121E-08 116. 157 119.250 782.9 c~, 538E-C~ 2. 083E,08 2. 199E-08 7.207 0,941 2,069E-08 1,000 2o069E-08 116.500 ~19.500:,779.~ 9.292E-~5 2.041E-08 2. 151E'08 7.150 0.941 2.024E-08 I~oQo 2.024E-08 O~ 116,842,119,750, 776.8 9.049E-05 2.002E-08 2.103E-08 7.093 0.941 1,979E-08 1.000 "' I, o979E-08 0 1,17 185 120.000 773.8 8.813E-05 1.962E-08 2.056E-08 7.036 0.941 1:935E-08 1.000 1.935[-08 i17.532 120.250' 770.7 8.559E-C5 1.919E-08 2.005E-08 6.978 0..941 1,887E-08 1,000 1o 887E-08 117.88'0 120.500 767.7 8. 340E-05 1.881E-08 1.961E-08 6.920 0.942 1,846E-08 1o000 1,846E-08 118.228 120.750 764.6 8,120E-C5 1. 845E-08 1.917E-08 6.911' 0.9.42 1. 805E-08 1o000 1. 805E-08 118.579 121.0'00 761.5 7.915E-0~ t.808F-08 1. 876E-08 6,929 0.942 1.768E-08 1.000 1.768E-08 118.931 121.250 758,3 7.707E-C5 1.774E-08 1.835E-08 6.947 0,942 1,729E-08 1.000 1.729E-08 119.284 121.500?'55.2 7.497E-C5 1,734E-08 1.792E-08 6.964 0.94.3 1o690E-08 1.000 1o690E-08 119.641 121.750 752.1 7 335E-C5 1.709E-08 1.761E-08 6,982 0.943 1,661E-08 1,000 1,661E-08 119.497 122.000 748.9 7.129E-C5 1.670E-08 1.718E-08 7,000 0.944 1.622E-08 1.000 1.622E-08 120.356 122.250 745.8 6.954E-C5 1.641E-08 1,683E-08 7.085 0.944 1,589E-08 1,000 1. 589E-08 120.717 122.500 742.6 6.777E-05 1.607E-08 1.647E-08 7.172 0.945 1. 556E-08 1.000 1.556E-08 121,079 122.750 73~. 5 6.622E-C 5 1. 583E-08 1,616E-08 7.259 0.945 1. 528E-08 1.000 1.528E-08 121.444 123,000 736.3 6.454E-C5 1. 551E-08 1,582E-08 7.346 0.946 1,496E-08 1.000 1.496E-08 121.810 123.250 733.1 6.299E-05 1.525E-08 1.551E-08 7.434 0.946 1.467E-08!.000 1 o467E-08~ 122.177 1'23.500 729. 8 6. 141E-C5 1.445E-08 1.519E-08 7.522 0.947 1.438E-08 1.000 Io438E-08 122.54! 123.750 726.6 5.995E-C5 1.470E-08 1.489E-08 7.61'1 0,947 1,411E-08 1,000 1,411E-08 122.919 124.000 723.4 5.849E-05 1.442E-08 1,459E-08 7,701 0,948 1.383E-08 1.000 1.383E-08 123.292 124.2.50 Z20.2 5.710E-C5 1.419E-08 1.431E-08 7.790 0.948 1.357E-08 1.000 1.357E-08 123.668 124.500 717.(] - 5,575E-05 1. 393E-08 1. 404E-08 7.880 0.94-9 1,332E-08 1,000 1,332E-08 124,045 124.750'713.7 5,430E-05 1.367E-08 1,373E-08 7,971 0,949 1,304E-08 Io000 I. 304E-08 124.425 125.000 710.4 5.317E-05 1.346E-08 1.~351E-08 8.062 0.950 1.284E,08 1.000 1.284['-08 Figure 19. (Continued)

,COMMUTATOR VALUES. T IME. CHL. 1. CHL 4. CHL 5 48.786 3.522'2.503 3.4C2 68.147. 3.459 2.503' 3.346, 78.777 3.462 2.503 2.947 81.458 3.459 2.503 2.412 96.318.3.454 2.503 1.993 103.349 3.455 5 2 503 1.45 E 113,020 3.456 2.503 1.C63 ERIOR. RETURN, Figure 19. (Continued) Col

SPACE PHYS-ICS RESEARCH LABORATORY tHE UNIVERSITY OF MICHIGAN ANN ARBOR, MICHIGAN 1-1:47.15, DECEMBER 18,1961969 14.3F6 HOUSEKEEPING LAUNCH TIME: 20: 4:5.8.15 z INPUT FILE 1 CHANNEL INCEX 3 TAPE ID: SPRL NASA 14.386 12/12/69 8C20 Fl. 08 Q CALIBRATE LEVELS: 5.003 0.004 NO TEPPERATURE CCRRECTICN WILL EE MACE COP'MUTATOR VALUES TIME'CHI I CHL 4 CHL-. 5 47.355 0.005 4.974 4.505 61.136 0.007 4.969 3.845 74.957 0.00.8 4.973 3.224 68.77,8 00027 4.976 2.873 102.609'.006 4.970 2.753 116.460 0.001 4.968.2.726 130.341 0.007. 4.972 2.779 144.242 0.005 4.967 2.e63' 158.152 0.005 4.968 2.572 172.113 0.C10 4.967 3.06E 186.104, -0.002 4.975 3.18C 200.115 -0.0,02 4.964 3.2722.14.166 0.01 0 4.-9 7 C 3.379 228.246 0.013 4.966 3.*467 242.357 -0.005 4.970 3.552 256.498 0.004 4.978 3. 64,6 270.649.0.009 4.974 3.715 284.839 0. 01.8 4.975 3. 78'4 299.050 0.010 -4.967 3.832 31-3.291 0. 00 8 4.970 3.90 8 -327 592 0.009.4.972 3.'63 341.932 -0.001 4.9,71 3.94 ERROR RETURN. Figure 19. (Concludea)

5o5, OBTAINING FINAL DATA An atmospheric density profile for the whole flight can be obtained from the density data given by the PITOT program, At high altitudes the profile consists of atmospheric density calculated by using free molecular flow theory, As we trace down the altitude profile, we enter the transition region, and we use the corresponding values of atmospheric density. At the end of the transition region and down to the bottom of the density profile, the value of atmospheric density used is that calculated from continuum flow theory, From the resulting atmospheric density profile, values of density and altitude are recorded at 0.5 km intervals, A value for atmospheric temperature at the highest altitude is estimated with. the aid of an atmospheric model or the U. S. Standard Atmosphere, 1962. The estimated temperature is used as the starting temperature for the density integrationo Atmospheric temperature and pressure profiles are calculated by means of a computer program written for thie IBM 360/67 of the MTS, called FLOP. Inputs to FLOP (Final Listed Output and Plot) are (1) altitude and density in km and kg/m3, respectively, and from high to low altitudes, and (2) starting temperature or reference temperature in Ko. After integrating the atmospheric density profile (Equation (28)), atmospheric temperature and pressure are calculated by means of Equations (30) and (31), respectively. Finally, the ratios of atmospheric density and pressure to the corresponding values given by the U. S. Standard Atmosphere, 1962 are calculated, and the difference between the calculated atmospheric temperature and the temperature given by the U. So Standard Atmosphere, 1962 is determined, An abbreviated flow chart of the program is given in Figure 20. The output from the program is shown in Figure 21,o

READ HEADING INFORMATION (FIRST FORTY COLUMNS OF FIRST SEVEN LINES) REFERENCE TEMPERATURE (T1) ORDERED ALTITUDE-DENSITY PAIRS (HIGHEST ALTITUDE FIRST), NUMBER OF PAIRS (NUM) CENTER SEVEN HEADINGS ON TTY PAGE OF 80 COLUMNS p1 = P1kT1 n>NUM n = n+ y PRINT RESULTS (LOWEST ALTITUDE FIRST)'ALTITUDE, DENSITY, TEMPERATURE, Api = gr02 j (h 1 [11 1 P(hi) RATIO, TEMPERATURE DIFFERENCE 1 (r + hi+l) (ro + hi)n I P(hi) - kT1 + Ap PLOT ALTITUDE'VS. PRESSURE RATIO Pn m 1 1kT1 m p PLOT ALTITUDE VS. DENSITY RATIO T = 1 PlkT1 + m APi n kPn1 PLOT ALTITUDE VS. TEMPERATURE DENSITY RATIO (n) = P /P STD DENTY RATIO (n) = P/P STD PLOT ALTITUDE VS, TEMPERATURE DIFFERENCE PRESSURE RATIO (n) = P /p STD DELTA T (n) = Tn-T STD Figure 20. FLOP abbreviated flow chart.

SPACE PHYSICS RESEARCH LABORATORY THE UNIVERSITY OF MICHIGAN ANN ARBOR, MICHIGAN 12:00.55 DECEMBER 17,1969 NASA 14.386 19 NOVEMBER 1968 15:04:59,815 EST 20:04:59.815 GMT WALLOPS ISLAND, VIRGINIA LAT. 37 DEG 50 MIN N LONG. 75 DEG 29 MIN W PRESSURE RATIO - P/P STD. DENSITY RATIO - RHO/RHO STD. DELTA T - T-T STD. ALTITUDE DENSITY TEMP. PRESSURE DENSITY PRESSURE DELTA T KM KG/CU-M K TORR RATIO RATIO 30.0 1.76E-02 222.1 8.42E 00 0.96 0.94 -4.4 30.5 1.62 E-02 223.6 7.80E 00 0.95 0.94 -3~4 31.0 1.49E-02 225.5 7.24E 00 0.94 0.94 -2.0 31.5 1.38E-02 225.9 6.72E 00 0.95 0.94 -2. 1 32.0 1.26E-02 229.7 6.23E 00 0.93 0.93 1.2 32.5 1.16E-02 231.9 5.79E 0 0.93 0.94 2~3 33.0 1.10E-02 227.2 5.38E 00 0.95 0.93 -3,8 33.5 1.00E-02 232.2 5.00E 00 0.93 0.93 -0.1 34.0 9.20E-03 234.8 4.65E 00 0.93 0.93 1.1 34.5 8.47E-03 237.4 4.33E 00 0.93 0.94 2.3 35.0 7,95E-03 235.5 4.03E 00 0.94 0.94 -1.0 35.5 7.48 E-03 232.9 3.75E 00 0.95 0.94 -5.0 36.0 6.96E-03 232.8 3.49E 00 0.96 0.93 -6.5 36.5 6.45E-03 233.6 3.25E 00 0.96 0.93 -7.0 37.0 5.90E-03 237.8 3.02E 00 0.95 0.93 -4.2 37.5 5.50E-03 237.6 2.81E 00 0.95 0.93 -5.9 38.0 5.12 E-03 237.7 2.62E 00 0.95 0.93 -7.1 38.5 4.72 E-03 240.3 2.44E 00 0.95 0.93 -5.9 39.0 4.35E-03 243.1 2.28E 00 0.94 0.92 -4.5 39.5 4.01E-03 246.2 2.13E 00 0.93 0.92 -2,8 40.0 3.73 E-03 247.2 1.99E 00 0.93 0.92 -3.2 40.5 3.46E-03 248.9 1.86E 00 0.93 0.92 -2.8 41.0 3.19E-03 252*4 1.73E 00 0.92 0.92 -0.7 41.5 2.93E-03 257.3 1.62E 00 0.092 2.8 42.0 2.74E-03 257.7 1.52E 00 0.92 0.92 1.8 42.5 2.54E-03 260.4 1.42E 00 0.91 0.93 3.2 43.0 2.37E-03 261.7 1.34E 00 0.91 0.92 3.1 43.5 2.21E-03 263.2 1.25E 00 0.91 0.92 3.2 44.0 2.10E-03 259.7 1.17E 00 0.93 0.92 -1.7 44.5 1.97E-03 259.4 1.10E 00 0.94 0.93 -3.4 45.0 1.86E-03 257.4 1.03E 00 0.94 0.92 -6.8 45.5 1.75E-03 256.3 9.66E-01 0.95 0.92 -9.3 46.0 1.63E-03 257.7 9.05E-01 0.95 0.92 -9.2 Figure 21. FLOP output format. 65

NASA 14.386 2 ALTITUDE DENSITY TEMP. PRESSURE DENSITY PRESSURE DELTA T KM KG/CU-M K TORR RATIO RATIO 46.5 1. 53E-03 257.2 8.48E-01 0.96 0.92 -11.1 47.0 1.44E-03 255.9 7.94E-01 0.96 0.91 -13.8 47.5 1.35E-03 255.6 7.43E-01 0.96 0.91 -15.0 48.0 1.26E-03 256.4 6.96E-01 0.95 0.91 -14.2 48.5 1.17E-03 258,7 6.52E-O1 0.94 0.90 -11.9 49.0 1.09 E-03 260.2 6.11 E-O 1 0.94 0.90 -10.4 49.5 1.01 E-03 263.4 5.73E-01 0.93 0.90 -7.2 50.0 9.51E-04 262.4 5.37E-01 0.92 0.90 -8.2 50.5 9.03E-04 259.1 5.04E-01 0.94 0.90 -11.5 51.0 8.51 E-04 257.6 4.72E-01 0.94 0.89 -13.0 51.5 8.00E-04 256.7 4.42E-01 0.94 0.89 -13.9 52.0 7.52E-04 255.7 4.14E-01 0.94 0.89 -14.9 52.5 7.10E-04 253.6 3.88E-01 0.94 0.88 -1 7.0 53.0 6.64E-04 253.8 3.63E-01 0.94 0.88 -15.7 53.5 6.15E-04 256.6 3.40E-01 0.92 0.88 -11.9 54.0 5.76E-04 256.6 3.18E-01 0.91 0.87 -11.0 54.5 5.44E-04 254.4 2.98E-01 0.91 0.87 -12.2 55.0 5.09 E-04 254.5 2.79E-01 0.91 0,87 -11.1 55.5 4.73E-04 256.5 2.61E-01 0.90 0.87 -8.1 56.0 4.43E-04 256.5 2.45E-01 0.89 0.87 -7.1 56.5 4.17E-04 255.2 2.29E-01 0.89 0.87 -7.4 57.0 3.90E-04 255.5 2.15E-01 0.88 0.86 -6.2 57.5 3.68E-04 253.5 2.01E-01 0.89 0.86 -7.2 58.0 3.,45E-04 253.1 1.88E-01 0.88 0.86 -6.6 58.5 3.25E-04 251.4 1.76E-01 0.88 0.86 -7.3 59.0 3.04E-04 251,4 1.65E-01 0.88 0.86 -6.3 59.5 2.87E-04 249.1 1.54E-01 0.88 0.86 -7.7 60.0 2.70E-04 247.5 1.44E-01 0.88 0.86 -8.3 60.5 2.53E-04 246.8 1.35E-01 0.88 0.85 -8.0 61.0 2.40E-04 243.0 1.26E-01 0.89 0.85 -10.8 61.5 2.27E-04 239.7 1.17E-01 0.89 0.85 -13.1 62.0 2.13E-04 238.1 1.09E-01 0.89 0.85 -12.9 62.5 1.99E-04 237.6 1.02E-01 0.88 0.84 -11.5 63.0 1.86E-04 236.8 9.49E-02 0.87 0.84 -10.3 63.5 1.74E-04 235.9 8,84E-02 0.87 0.83 -9.3 64.0 1.63 E-04 234.5 8.23E-02 0.87 0.83 -8.7 64.5 1.53E-04 232.5 7.66E-02 0.86 0.83 -8.7 65.0 1.435 E-04 231.5 7.13E-02 0.86 0.83 -7.8 65.5 1,35E-04 228.0 6.63E-02 0.86 0.83 -9.3 66.0 1.27E-04 225.1 6.16E-02 0.86 0.83 -10.3 66*5 1.19E-04 222.9 5.71 E-02 0.86 0.82 -10.5 67.0 1.11E-04 221.7 5.30E-02 0.85 0.82 -9.7 67.5 1.05E-04 217.2 4.91E-02 0.86 0.82 -12.3 68.0 9.70E-05 217.7 4.55E-02 0.85 0.82 -9.8 68.5 8.87E-05 220.5 4.21E-02 0.83 0.81 -5.1 69.0 8.23 E-05 220.3 3.91 E-02 0.82 0.81 -3.3 69.5 7.70E-05 218.2 3.62E-02 0.82 0.81 -3.5 70.0 7.24E-05 214.9 3.35E-02 0.83 0.81 -4.8 70.5 6.74E-05 213.5 3.10E-02 0.82 0.81 -4.2 71.0 6.32E-05 210.4 2.86E-02 0.83 0.81 -5.4 71.5 5.92E-05 207.4 2.64E-02 0.83 0.80 -6.4 Figure 21. (Continued) 66

NASA 14.386 3 ALTITUDE DENSITY TEMP. PRESSURE DENSITY PRESSURE DELTA T KM KG/CU-M K TORR RATIO RATIO 72,0 5.54E-05 204.4 2.44E-02 0.83 0.80 -7.5 72.5 5.20 E-05 200.5 2.25E-02 0.84 0.80 -9.4 73.0 4.87E-05 196.8 2.06E-02 0.84 0.80 -11.2 73.5 4.56E-05 192.9 1.90E-02 0.85 0.79 -13.1 74.0 4.20E-05 192.1 1.74E-02 0.84 0.79 -12.0 74.5 3.73 E-05 198.6 1.60E-02 0.80 0.79 -3.5 75.0 3.30 E-05 206.7 1.47E-02 0.76 0.79 6.5 75.5 2.92E-05 215.9 1.36E-02 0.72 0.79 17.7 76.0 2.69E-05 217.0 1.26E-02 0.72 0.80 20.8 76.5 2.45E-05 220.7 1.16E-02 0.71 0.80 26.4 77.0 2.25E-05 222.9 1.08E-02 0.70 0.81 30.6 77.5 2.10 E-05 221.6 1.00E-02 0.71 0.82 31.2 78.0 1.94E-05 222.5 9.30E-03 0.71 0.83 34.1 78.5 1.78E-05 225.2 8,63E-03 0.70 0.85 38.7 79.0 1.67E-05 222.8 8.01E-03 0.71 0.86 38.3 79.5 1.57E-05 219.8 7.43E-03 0.72 0.87 37.2 80.0 1.47E-05 217.5 6.89E-03 0.74 0.89 36.9 80.5 1.37E-05 216.1 6.38E-03 0.75 0.90 35.5 81.0 1.28E-05 214.1 5.90E-03 0.77 0.91 33.5 81.5 1.19E-05 213.0 5.46E-03 0.79 0.93 32.4 82,0 1.09 E-05 215.2 5.05E-03 0.79 0.94 34.6 82.5 1.01 E-05 214.9 4.68E-03 0.80 0.95 34.3 83.0 9.44E-06 212.8 4.33E-03 0.82 0.97 32.2 83.5 8.85E-06 209.8 4.00E-03 0.84 0.98 29.2 84.0 8,40E-06 203.9 3.69E-03 0.88 0.99 23.3 84.5 7.90E-06- 199.7 3.40E-03 0.91 1.00 19.1 85.0 7.20 E-06 201.7 3.13E-03 0.90 1.01 21.1 85.5 6.42 E-06 208.5 2.88E-03 0.88 1.02 27.9 86.0 5.64E-06 219.6 2.67E-03 0.85 1.04 39.0 86.5 5.21 E-06 220.5 2.47E-03 0.86 1.05 39.9 87.0 4.83 E-06 220.5 2.29E-03 0.88 1.07 39.9 87.5 4.52E-06 218.5 2.13E-03 0.90 1.09 37,9 88.0 4.18E-06 219.0 1.97E-03 0.91 1.11 38.4 88.5 3.91 E-06 216.9 1.83E-03 0.94 1.13 36.3 89.0 3.67E-06 214,0 i.69E-03 0.96 1.14 33.4 89.5 3.43 E-06 211.7 1.56E-03 0.99 1.16 31.1 90.0 3. 18E-06 211.1 1.45E-03 1.00 1.18 30.5 90.5 2.97E-06 208.9 1.34E-03 1.03 1.19 26.8 91.0 2.77E-06 206.8 1.23E-03 1.07 1.21 23.2 91.5 2.57E-06 205.6 1.14E-03 1.09 1.22 20.5 92.0 2.36E-06 206.6 1.05E-03 1.10 1.22 20.0 92.5 2.19 E-06 205.4 9.69E-04 1.13 1.23 1 73 93.0 2.07E-06 200.3 8.93E-04 1.18 1.24 10.7 93.5 1.93 E-06 197.6 8.22E-04 1.21 1.24 6.5 94.0 1.77E-06 198.2 7.56E-04 1.21 1.25 5.6 94.5 1.59E-06 203.1 6.96E-04 1.20 1.25 9.1 95.0 1.46E-06 203.9 6.41 E-04 1.21 1.26 8.4 95.5 1.34E-06 204.8 5.91E-04 1.22 1.26 7.8 96.0 1.24E-06 204.1 5.45E-04 1.23 1.26 5.7 96.5 1.15E-06 202.9 5.03E-04 1.25 1.27 3.0 97.0 1.08E-06 198.9 4.63E-04 1.28 1.27 -2.5 Figure 21. (Continued) 67

NASA 14.386 4 ALTITUDE DENSITY TEMP. PRESSURE DENSITY PRESSURE DELTA T KM KG/CU-M K TORR RATIO RATIO 97.5 1.01 E-06 195.6 4.25E-04 1.31 1.26 -7.2 98.0 9.40E-07 193.0 3.91 E-04 1.34 1.26 -1 1.3 98.5 8.78E-07 189.5 3.58E-04 1.36 1.25 -16.2 99.0 8.20E-07 185.7 3.28E-04 1.39 1.24 -21.5 99.5 7.68E-07 181.2 3.00E-04 1.42 1.23 -27.4 100.0 7.15E-07 177.5 2.73E-04 1.44 1.21 -32.5 100.5 6.67E-07 173.1 2.49E-04 1.46 1.19 -39.3 101.0 6.15E-07 170.5 2.26E-04 1.48 1.17 -44.4 101.5 5.60E-07 169.9 2.05E-04 1.47 1.14 -47.3 102.0 5.OO0 E-07 172.8 1.86E-04 1.43 1.12 -46.8 102.5 4.40E-07 178.7 1.69E-04 1.37 1.10 -43.3 103.0 3.84E-07 187.0 1.55E-04 1.31 1.08 -37.4 103.5 3.31 E-07 1992 1.42 E-04 1.22 1.07 -27.6 104.0 2.86E-07 212.7 1.31E-04 1.15 1.07 -16.5 104.5 2.52 E-07 223.8 1.21E-04 1.10 1.06 -7.7 105.0 2.31 E-07 226.9 1 13E-04 1.09 1.05 -7.0 105.5 2.13E-07 228.8 1.05E-04 1.09 1.05 -7.4 106.0 1.99E-07 227.8 9.77E-05 1.11 1.04 -10.8 106.5 1.87E-07 225.4 9.08E-05 1.12 1.04 -15.5 107.0 1.75E-07 223.8 8.44E-05 1.14 1.03 -19*4 107.5 1.65E-07 220.3 7.83E-05 1.15 1.02 -25.2 108.0 1.54E-07 219.0 7.26E-05 1.17 1.02 -28.8 108.5 1.44E-07 217.1 6.73E-05 1.17 1.01 -33.0 109.0 1.34E-07 216.2 6.24E-05 1.18 1.00 -36.2 109.5 1.25E-07 214.7 5.78E-05 1.18 0.98 -40.0 110.0 1. 17E-07 212.3 5.35E-05 1.19 0.97 -44.7 110.5 1.08E-07 212.8 4.95E-05 1.19 0.95 -48.9 111.0 9.74E-08 218.6 4.59E-05 1.17 0.94 -47.8 111.5 8.52E-08 232.2 4.26E-05 1.10 0,93 -38.9 112.0 7.30E-08 253.2 3.98E-05 1.02 0.92 -22.6 112.5 6.25E-08 277.9 3.74E-05 0.94 0.92 -2.6 1 13.0 5.40E-08 303.9 3.53E-05 0.88 0.92 18.7 113.5 4.71E-08 330.7 3.36E-05 0.82 0.92 40.9 114.0 4.19E-08 354.3 3.20E-05 0.79 0.93 59.8 114.5 3.73E-08 380.5 3.06E-05 0.75 0.94 81.3 115,0 3.42 E-08 397.8 2.93E-05 0.74 0.95 94.0 115.5 3.17E-08 412.1 2.81E-05 0.73 0.96 103.7 116.0 2.94E-08 427.2 2.71E-05 0.73 0.97 114.2 116.5 2.78E-08 434.9 2.60E-05 0.73 0.98 117.3 117.0 2.61E-08 446.2 2.51E-05 0.74 1.00 124.0 117.5 2.47E-08 454.5 2.42E-05 0.74 1.01 127.7 118.0 2.33 E-08 464.9 2.33E-05 0.75 1.02 133.6 118.5 2.22E-08 471.1 2.25E-05 0.76 1.03 135.3 119.0 2.11E-08 47808 2.18E-05 0.77 1.05 138,4 119.5 2.01E-08 485.7 2.10E-05 0.77 1.06 140.7 120.0 1.93 E-08 489,1 2.03E-05 0.79 1.08 139,6 120.5 1.85E-08 493.4 1.97E-05 0.81 1.09 134.6 121.0 1.76E-08 501.8 1.90E-05 0.83 1.10 133.6 121.5 1.70E-08 502.8 1.84E-05 0.86 1.11 125.3 122.0 1.62 E-08 510.7 1.78E-05 0.88 1.12 123.9 122.5 1.56E-08 513.6 1.73E-05 0.90 1.13 117.5 123.0 1.50E-08 517.4 1.67E-05 0.93 1.14 112.0 123.5 1.45E-08 518.5 1.62E-05 0.95 1.14 103.9 124.0 1.39E-08 524.2 1.57E-05 0.97 1.15 100.3 124.5 1,33E-08 531.0 1.52E-05 0.98 1.16 97.8 125.0 1.28E-08 535.0 1.47E-05 1.00 1.17 92.6 Figure 21. (Continued) 68

GEOMETRIC ALTITUDE (KM) 30.00 q0.00 50.00 60.00 70.00 80.00 90.00 100.00 110.00 120.00 49-~~~~~~~ I UI -~I O r~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~LO " 0,..= rvl o~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~$L o ~~ e ~ ~ ~~~~~~~~~~~~~..cm, o,= o ~~~~~~~~~~~~~~~~LOL Pm ~ \10 I0 0 P1 Q~ ~, "O ~ ~s 6~~~~~~~~~~~~~~~~~~~~ rnl 6~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~ -ICR rN SF2 ~o ~ n~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~,i0 0 0 -~~ ~~~ ~. ~~' ~ 0' 0 0 O ~~Fgr e 21 (Cntnud

C0 s RLTITULDE V5. OENSITT RATIO _ S.l~,..~~ NASA 14.386 oC a 0a~~~~~~~~~~~~~a 0 0 as as v~~~~~~~~~~~~~~~~~~~~~~~-q t~~~ 0 a o 55: e Do as I.- (~~~~~~~~~~~~i an MM~~~~~~~~~~~~ CC. 0 ee 0 C~ ~~~~i~ ~ H F- ~1) Im.I 0~~~~~~~~~~~~~~~~~~ C — Lt~~~~~~~~~~~~~~~t (r U, C I I I I I I ~ tA0.60.80 1.0O0 1.20 1.1Wt 1.60 DENSITT lRFTIO?/.~ 70

3.0 0.00 50.oo GEOHETR I C Ft T I TLUDE (KM) 100 0.00 70.o0 120 9.0 0-0 100 -u cz & n-M LO~~~~~~~~~~~~~~~~~~~~~~~~~ % 0S -u.guro 21 (coat nued,)

GEOMETRIC ALTITUDE (KM) 30.00 4L0.00 50.00 60.00 70.00 80.00 90.00 100.00 11O.00 120.00 I I I I I I I I m~T n I~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~'~f" D |~ m.-| nc Il -— I. - mIv - m r'r]2i ~c r'rlon~ m 8n ~ rn1 II * -io S I"-I 0 II r~..,A -" -. ~ j.-' z*1F.1.,"' ( r a __ z S i-.ri *.S S -. n~~~~~~~~~~~~~~~ M~~~~~~~~~~~~~~~~~~ flu~~~~~~~~~~~~~~~~~~~~~~~~~~~...... 0S 0 S Figure 21. (Concludea) *IS 0 Figu~re 21. (Conclud~ed)

6,. REFERENCES Ainsworth, Jo E., D, F. Fox, and H. E. LaGow, "Upper Atmosphere Structure Measurement Made with the Pitot-Static Tube," Journal of Geophysical Research, 66 No. 10, ppo 3191-3212, 1961. Breckenridge, Sally, "Evaluation of the Main Geomagnetic Field by Means of Spherical Harmonic Analysis," University of Michigan Internal Note and Program, October 28, 1965o Cain, Joseph C., WO E, Daniels, Shirley J. Hendricks, and Duane C. Jensen, i"An Evaluation of the Main Geomagnetic Field, 1940-1962,' Jlournal of Geophysical Research, 70, No. 15, pp. 3647-3674, August 1, 1965. Caldwell, Jack, The Space Physics Research Laboratory Data Conditioning System, University of Michigan Engineering Report No. 1, 05776-1-E, January 1966. Handy, P. 0, Design of a Radioactive Ionization Gauge for Upper Atmosphere Measurements, University of Michigan Instrumentation Report 05776-1-I, February 1970. Horvath, J. JO, R. W. Simmons, and L. H. Brace, Theory and Implementation of the Pitot-Static Technique for Upper Atmospheric Measurements, University of Michigan Scientific Report NS-1, 03554, 04673-1-S, March 1962. Pearl, J. C. and U'Vogel, Application of the Green's Function to Analysis of Internal Flows of Rarefied Gases. University of Michiga:n Scientific Report, 02770, to be published in 1970, Range Co-mmanders Council, Telemetry Standards (Revised March 1966), White Sands Missile Range, New Mexico, Document 106-66 (AD 635857), April 1966o Simmons, R. TJ., An Introduction to the Theory and Data Reduction Method for the Pitot-Static Technique of Upper Atmosphere Measurement, University of Mlichigan Sci entific Report No, RS-1, 05776-1-S, March 1964, U. S, Standard Atmosphere, 1962, U. S. Government Printing Office, Washington, Do C., December 1962, Wainwright, Jo B, and K. WO Rogers, Impact Pressure Probe Response Characteristics in High Speed Flows, with Transition Knudsen Numbers, NASA Contractor Report CR-61119, NASA-George C. Marshall Space Flight Center, Huntsville, Alabama, February 18, 1966, 73

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