THE U N IV E R 0S T O M ICHI T G A N COLLEGE OF ENGINEERING Department of Aeronautical and Astronautical Engineering Final Report FALLING-SPHERE ISTRS'I NTATION DEVELOPMENT Prepared for the Project by: Jr Wo Peterson Do Ao Robinson Ho F Schulte Approved byo Lo Mo Jones UR I Project 2649 inder contract with; UNITED STATES AIR FORCE AIR RESEARCH AND DEVELOPMENT COMMNAND AIR FORCE CAMBRIDGE- RESEARCH CENTER GEOPHYSICS RESFAR. CH. DIRECTORATE CONTRACT NO. A 19(6044)-2415 BEDFORD MASSAiCHU-SETJTS administered by: THE UNIVERSITY OF MICHIGAN RESEARfCh INSTIT_:'.TE ANN ARBOR February 1960

TABLE OF CONTENTS Page LIST OF FIGURES v ABSTRACT vii THE UNIVERSITY OF MICHIGAN PROJECT PERSONNEL ix 1. INTRODUCTION 1 2. ACCELEROMETER INVESTIGATIONS 3 5. ELIMINATION OF CONTACT WIRE 15 3.1. Vibrating Cavity 15 5.2. Impact Transducer 19 5.3. Piezoelectric Materials 22 3.4. Caging 22 3.5. Multiple Circuit Cavity 23 4. SPHERE DATA-PROCESSING BY COMPUTER 27 4.1. Analysis of Accelerometer Raw Data 27 4.2. Derive Peak Time Routine 30 4.3. Trajectory Routine 33 4.4. Air-Density Routine 35 4.5. Adjust Peak Altitude Routine 39 4.6. Data-Processing 40 5. SPHERE ANTENNA BREAKDOWN 43 6. RECOMMENDATIONS 43 7. ACKNOWLEDGMENTS 43 8. REFERENCES 45 APPENDIX A. Formation of a Radiofrequency Plasma at an Antenna During Falling-Sphere Measurements APPENDIX B. Nike-Cajun Flights AM 6.02, 6.03, 6.05 iii

LIST OF FIGURES Figure Page 1 Magnetic tong release and microphone used in measuring moment of inertia of calibrating pulley. 4 2 Double-ended bullet and photocell drop indicator used in calibrating accelerometer. 4 3 Magnetic drop tester for accelerometers, disassembled. 6 4 Magnetic drop tester with photoelectric drop indicator. 6 5 Bobbin drop test for initial velocity. 8 6 Pyramidal caging finger to prevent bobbin rotation. 14 7 Vibrating cavity accelerometer schematic. 15 8 Yoke mount for cavity and crystal. 17 9 Various yoke mounts for cavities and crystals. 17 10 Three ping-pong-ball to crystal mounts. 18 11 Metal spherical cavity mount. 18 12 Mounts used with metal spheres. 20 13 Mounts used with metal spheres. 20 14 Impact pendulum. 21 15 Photo showing moving iron solenoids. 23 16 Schematic showing moving iron solenoid. 23 17 Multiple cavity accelerometer schematic. 24 18 Model of multiple cavity accelerometer. 25 19 Flow diagram for over-all data processing. 28 20 Flow diagram for fill-data and print-data routines. 29 v

LIST OF FIGURES (Concluded) F igure Page 21 Flow diagram for analyze-accelerometer-data routine. 31 22 Flow diagram for peak-time routine. 32 23 Flow diagram for trajectory routine. 34 24 Flow diagram for density routine and adjust-peak-altitude routine. 36 25 CD as a function of Mach number and Reynolds number. 37 26 Empirical drag coefficient functions. 38 27 Flow diagram for erase-bad-data routine. 41 vi

ABSTRACT Work on the continuing development of the falling-sphere technique for measuring upper-air density and temperature is described. The factors limiting the performance of the transit-time accelerometer were investigated, and a design concept was reached which, it is anticipated, will improve the performance. The data-reduction process for the sphere experiment was completely computerized and is reported. An investigation of the phenomenon of antenna breakdown in flight is described. Requests for additional copies by Agencies of the Department of Defense, their contractors, and other government agencies should be directed to the: Armed Services Technical Information Agency Arlington Hall Station Arlington 12, Virginia Department of Defense contractors must be established for ASTIA services or have their "need to know" certified by the cognizant military agency of their project or contract. All other persons and organizations should apply to the: U. S. Department of Commerce Office of Technical Services Washington 25, D. C. or to: The University of Michigan Research Institute Ann Arbor, Michigan vii

THE UNIVERSITY OF MICHIGAN PROJECT PERSONNEL (BOTH FULL-TIME AND PART-TIME) Finkbeiner, Richard Go, Electronic Technician Gleason, Kermit L., Instrument Maker Harrison, Lillian, Secretary Jones, Leslie M., B.So, Project Supervisor Malkani, Sundru Jo, MoSco. Assistant in Research Mosakewicz, Mary Co, Secretary Pattinson, Theodore Ro, Electronic Technician Peterson, John W., MoS., Associate Research Engineer Robinson, Douglas Ao, Technician Schulte, Hal. F., Jr., M.S.Eo(EE)9 Associate Research Engineer Thornton, Charles Ho, Consultant Wenk, Norman J., B.SoEo(ME), Research Engineer ix

1. INTRODUCTION This is the final report of a project carried on in the Department of Aeronautical and Astronautical Engineering of The University of Michigan, the purpose of which was to continue with certain developments of the falling-sphere method for measuring upper-air density and temperature. The work is a continuation of a program started in 1954 and continuing through 1958 in which the small-fallingsphere technique was developed and used. Support for that period was received under Air Force Contracts No. AF 19(604)-999 and No. AF 19(604)-1871. The former contract encompassed the International Geophysical Year as well as the so-called "pre-IGY" period, July, 1956, to July, 1957. Within this 2-1/2-year interval, seven successful (of a total of 10) flights of the small-sphere experiment were carried out. The results of these flights, together with a single small-sphere flight in 1955 and some still earlier work with large inflatable spheres, include a comparison of winter upper-air densities at 32~N vs. 580N, the detection of a latitude density gradient, and the detection of "explosive warming" at rocket altitudes in the winter Arctic atmosphere. Background information is contained in Refs. 1 through 8. The tasks of the contract of this report included the delivery to AFCRC of two Michigan-type accelerometers and one complete 7-in. falling sphere of the type used during the IGY. These items were delivered. In addition, the following research and development tasks were undertaken: "Conduct experiments and studies directed toward the determination of the lower limit of acceleration which can be measured with the existing Michigantype transit-time accelerometer and directed toward the refinements in design of that accelerometer for extending the range to lower values." "Initiate the development of a refined falling-sphere accelerometer system consisting of the following: a. A refined time of fall accelerometer of the type indicated in the statement above. b. A light rigid drag envelope communicating directly with the accelerometer bobbin in a manner consistent with a practical minimum mass-to-area-ratio for the envelope-bobbin structure and suspended or supported relative to the internal mass in a manner such that during rocket flight only, the system will withstand the associated accelerations. c. A radio transmitter system complete with power supply, slot antenna and necessary external controls and monitor mechanisms designed to make its performance equal to or better than the transmitter developed for the spheres flown in November 1956." 1

"Initiate the development of a device for holding the falling-sphere accelerometer system during rocket flight and for ejecting the falling-sphere accelerometer system from the rocket upon signal from a timer sometime after the end of powered flight." By Modification 3 of the contract, the following task was added: "Research and develop computer methods for reducing data from the small sphere experiment with the ultimate aim of developing an automatic data reduction system." Some of the development goals of the contract of this report have been achieved and some have not. To complete the work and bring the improved techniques to field test, a new contract, AF 19(604)-6185, to be carried out in the calendar year 1960, has been entered upon. 2

2. ACCELEROMETER INVESTIGATIONS In previous work with the transit-time accelerometer at low accelerations, an Attwood's machine technique described in Ref. 3 was used. With this apparatus, checks of the accelerometer at somewhat less than 0.01 g were successfully carried out. As a first step in exploring the practical lower limit of accelerations which could be measured with the existing accelerometer, a technique for accurately applying lower accelerations of 10-3 or perhaps 10-4 g was sought. Measurement of the moment of inertia of the pulley was improved by construction of a magnetic tong release which eliminated the slack in the thread and the lost motion in the trigger of the previous setup. A crystal microphone was used to provide a stop pulse to the counter at the time of contact of the small calibrating weight. These devices are shown in Fig. 1. Some improvements were also made in the heavy-bullet technique for calibrating the accelerometer. A light-beam and photo-cell apparatus was installed for starting the counter at the beginning of the fall of the accelerometer and "bullet" to eliminate the varied starting effects of the previously used micro-switch. A further improvement was the employment of a double "bullet" consisting of similar massive pieces mounted symmetrically on either end of the accelerometer. This arrangement placed the bobbin at the center of a very slight rotary motion which was observed to occur upon dropping the mass. The cause of the rotation was not investigated further but its effect was eliminated. With the new setup, an acceleration of 0.0067 g was measured. The apparatus is shown in Fig, 2. The Attwood's machine technique appears capable of being extended to 10-3 g and perhaps further merely by increasing the mass of the drop bullet. A practical difficulty peculiar to the technique is that of raising the mass through the larger and larger drop distances required for the increasing transit times of the decreasing accelerations. The larger drop-distance problem and the problem of air drag are, of course, common to any drop tester. To avoid the heavy mass of the Attwood's machine, a new technique described in the next paragraph was attempted. The results so far have been unsatisfactory. It may be that the best method will prove to be the Attwood's machine with some provisionforconveniently handling the massive bullet. A variation of the Attwood's machine was considered in which, instead of accelerating a pulley, a small mass attached by cord to the falling big mass is accelerated upward. In this case the cord must reverse direction over either one or two pulleys or smooth rods. To eliminate unwanted inertia of the pulleys, they are kept small or replaced with smooth rods. In either case the friction in these "reversers" has caused unacceptably large errors, and this variation of the drop technique has not been made to work well. 5

Fig. 1. Magnetic tong release and microphone used in measuring moment of inertia of calibrating pulley. ~?.. Fig. 2. Double-ended bullet and photocell drop indicator used in calib rating accelerometer. 4:::

As mentioned.above, an apparatus was conceived and built which induced test accelerations magnetically. Small permanent magnets were fastened to the accelerometer unit and to a weighted windshield which was released simultaneously with the accelerometero The geometric arrangement of the magnets was designed so that the magnetic forces are substantially constant in the small range of motion which results from the test force and the air drag force on the windshield, The accelerometer coils were energized by batteries external to the falling bodies. The initial work with this device was not successful. The difficulties are obscure, but may be due to inability to release the two bodies and break the current to the accelerometer coils at precisely the same instant. Perhaps satisfactory techniques could have been developed. In any case, other tests of accelerometer characteristics seemed more attractive at the time and were therefore given priority. However, the principle of reducing air drag by enclosing the accelerometer with a windshield should be of value whenever the low range of acceleration is tested. The magnetic drop tester is illustrated in Figs. 3 and 4. In Ref. 2, three sources of error in the accelerometer are discussed: (a) error in transit distance, (b) error in measuring transit time, and (c) error due to initial velocity of the bobbin upon release. The first two can be made acceptably small and are not proportional to the acceleration being measured. The magnitude of the error in acceleration due to initial velocity in per cent is bay = 200 vo/at (l) where Vo = initial velocity a = acceleration t = time Various sources of initial velocity can be supposed. If the center of the bobbin is displaced from the center of rotation of the sphere by an amount r, then vo = cr, where c is the spin angular velocity. This source of initial velocity is avoided in flight by achieving a low rocket spin and precise bobbin location ("balance"). Under no-spin conditions, initial velocity can result from mechanical imperfections in the uncaging process, perturbations due to collapse of the magnetic field of the caging coils, and perhaps otherso In view of the difficulties encountered with the drop testers, an alternate approach, namely, attempting to assess the initial velocity errors, was undertaken. From the equation above it may be seen that for a 1% error in acceleration due to initial velocity vo, the magnitude of vo is o = (1/200) /2 sa(2) where s = transit distance = ol87 in. 5

Fig. 3. Magnetic drop tester for accelerometers, disassembled.::.. A; 0;000S. 0000 ff TiLEE~~~... Fig. 4. Magnetic drop tester with photoelectric drop indicator. 6

Thus vO = 1.9 x 10-3 in./sec at 10-3 g for 1% erroro = 0.6 x 10-3 in./sec at 10-4 g for 1% error. The collapse of the magnetic field of the caging coils was disposed of as a source of significant initial velocity in the following mannero The bobbin was supported on a thread three feet in length in its normal cage position within the cavities. Considerable time and effort were required to reach a condition of no motion even with the aid of an air-motion shieldo With the bobbin in place, the caging coils were energized and de-energized and the bobbin observed for motion. To increase the sensitivity of the system, a shadow image of the bobbin was cast on a screen with an optical multiplication of 10 to 1. It can be shown that, with this experimental setup, initial velocities of.006 in./sec,.0019 in./sec, and.0006 in./sec (which would yield 1% errors at 10-2, 10-3 and 10-4 g, respectively) would result in lateral displacements of the bobbin image of about.02 in., 0.006 in., and 0.002 in., respectively. Since no motion of the image whatever was observed, it was concluded that perturbations of the bobbin due to magnetic field are negligible. Next, an experiment was performed to assess the magnitude of initial velocity resulting from release of the caging mechanism. An accelerometer from which the contact wire and cavities had been removed was set up over a free drop distance of 46.5 in. The bobbin was dropped on a piece of carbon paper resting on a piece of paper to mark the point of impact (see Fig. 5). The target to be hit in the absence of initial velocity was determined with the aid of a plumb bob. The initial velocity was then calculated from the displacement R between the impact point of the bobbin and the target point: vo = Rg/2h (5) h = 46o5 in. g = 386 in./sec2 The test was applied to three bobbins: (A) an aluminum bobbin of standard design with the caging surfaces in good condition; (B) an aluminum bobbin with a square caging hole, the caging surfaces in good condition (this bobbin was designed for a test on the contact wire described later); and (C) a magnesium bobbin of standard design. The average displacements R and calculated initial velocities vo with the standard deviations of 10 drops each are given in Table I. If we take the results for A and B to be typical of bobbins whose caging surfaces are in good condition and assume that the same impulse is available to move C as A and B, the initial velocity of C may be expected to be inversely proportional to its mass, say perhaps.06 in./seco The fact that the measured vo is more than twice as large may reasonably be attributed to a major defect in the caging action. The fact that the random error in the case of C is about the same as the other two supports this view. Even in the cases of A and B, the initial velocities are marginal at 10-2 g and too large for 10-3 go 7

Fig. 5. Bobbin drop test for initial velocity. TABLE I Bobbin Weight R v Bobbin..... grams lb in. in./sec I.i~iiii::::....-...i'i'i'i'i'i'i'i'~:'::....... A 52.2.071.017 ~.015.04 ~.05 B 55.32.075.014 ~.011.053.02 C ____ 14.9.033.068 ~.018.14 ~.04 8 A 32.2.071.017 ~.015 o4 ~.03~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~:::::::~. i::::j::~~ij: B 33.2.073 -o14 ~ oil -03 ~.02~~~~~~~~~~~~~~~~~~~~~~~~~:::::::::::..:.._.._ C 14.9.033 -o68 ~ o18.14 ~ o4~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~:~i:i~i~ii:: il:i:~:::iii:

Having eliminated the collapse of the magnetic field as a source of significant initial velocity, we may attribute the above values of initial velocity to the caging mechanism with one reservation. It is necessary to show that the aerodynamic forces on the falling bobbin in the test contribute only a negligible portion of the measured deflections. The first step is to determine the aerodynamic flow regime within which the bobbin falls. Since the bobbin is a relatively massive object, we can make the vacuum calculation for the velocity after a fall of 4 ft. The velocity is 16 ft/sec. The Reynolds number is defined by Re = PV (4) where p and pI are the air density and viscosity and d is the bobbin diameter. The Reynolds number is therefore zero at the beginning of the fall and increases to 2000 at the end. The drag coefficient of a spherical bobbin in this range of Reynolds numbers is 0.4, approximatelyo To estimate an upper limit of the lateral displacement of the falling bobbin due to aerodynamic effects, let us assume a lateral force 10% of the drag. The lateral motion is therefore defined by m x = D A- pV2, (5) dt2 10 2 where V = gt A = bobbin cross-sectional area. Integrating, the result is C x 240 m P gt (6) 1 But y = - gt2; thus 2 CDA 2 x = py (7) In the case of bobbin "A" above which weighed.071 lb and with a drop distance of 3.88 ft, x =.007 in. In the case of bobbin "C", which weighed.033 lb, and with the same drop distance: x =.016 in. These values compare with measured deflections of.017 in. and.068 in., respectively. Thus we conclude that, although a small part of the measured deflections may be due 9

to aerodynamic forces, some of it is probably due to initial velocities of the magnitudes shown in Table Io The technique shows promise of working well for detecting initial velocity and is capable of improvement in making the spurious aerodynamic effects negligibleo Having examined the effect of drag in the case of the bobbin drop test for initial velocity, we will find it instructive to investigate whether or not, at the very low accelerations it is hoped to measure, drag on the bobbin in traversing its normal transit distance may introduce an error. If appreciable error from this cause were indicated, it would be necessary to evacuate the accelerometero We know from laboratory and flight tests that, if drag on the bobbin causes any error, it is at most a few percent, so that, for purposes of establishing the Reynolds number regime, we may use the dragfree velocitieso In Table II velocities and Reynolds numbers at impact of the bobbin are showno It is assumed that the accelerometer cavities are filled with air at sea-level pressure at room temperature and that the outside drag acceleration aD is constant at the values showno TABLE II Drag on Sphere (aD) Transit Disto Impact Drag-Free g ft/sec2 ino ft vel, ft/sec Re Time, sec 10-3 3522 x 10-2.187 o0156 3517 x 10-2 17.1.o98 10 3 3o22 x 10-2 0050 o0042 1064 x 10-2 8o9 o51 10-4 3o22 x 10-3 o187 o0156 1o003 x 10-2 5~4 35ll 10-4 322 x 10-3 o050 o0042 o518 x 10-2 2~8 1.64 At impact the Reynolds numbers are of the order of 10 and are less before impacto Thus throughout the transit the bobbin is in the Stokes regimeo The drag of a sphere not under the influence of cavity walls is D = 3 tdV, (8) where D = drag force I = viscosity d = diameter V = velocity The presence of the cavity walls tends to increase the drag but probably not enough to invalidate this order of magnitude analysiso The equation of motion is therefore 10

d2y _ 3D dy m = mass (9) dt2 aD m dt Integrating: t= -m In aD m d-) + C (10) la md dty/ when dy m t = 0, d 0, C1 = rtd In aD. Substituting for C1 and solving for: dy maD -3__dt dt = 3t 1d m) dy Substituting this value of - in the equation of motion, we have: d Y- a e -35dt (12) dt2 m Taking = 3.7 x 10-7 lb f sec/ft2 d = 1/12 ft m = 1.025 x 10-3 lb f sec2/ft we have d2 = aDe-2.83 xl t (15) dt2 Since the exponent of e is small, we may expand and write d2y d2 aD(l - 2.83 x 10-4t) (14) dt2 Thus for any transit time up to 35 seconds, the error due to drag on the bobbin will be less than 1% and we may ignore it completely in the "old" as well as the contemplated accelerometers. The final investigations of the characteristics of the "old" accelerometer concerned the contact wireo The contact wire is a pair of drawn gold wires 0.002 in. in diameter mounted in such a way as to resemble two cantilever beams (springs) each 1 ino long with mutually opposing forces. For a single spring: 3 yEI (15) 11

where P = force in lb E = Young's modulus = 11.4 x 106 lb/in. I = moment of inertia = 0.8 x 10-12 in.4 I = length = 1 in. y = deflection in. P = 2.69 x 10-5y lb for a single spring. For two springs the over-all spring constant is k = 5.38 x 10-5 lb/in. For that orientation of the sphere where the longitudinal axis of the accelerometer is perpendicular to the drag vector the spring, acting as a cantilever, will oppose the drag force and the equation of motion is: d2y = a ky (16) dt2 m where y = displacement of bobbin t = time aD = drag acceleration of sphere k = spring constant of contact wire m = mass of bobbin Integrating, and noting that both constants of integration are zero, we have: y = ma maD cos / t (17) k k m and t = m cos-1 (l - (18) maDj In the last expression, if y is taken as the complete transit distance, t will be the transit time in the presence of drag force and spring force. Without the spring, the transit time is: t1 = I (19) W aD Since the percentage error in acceleration caused by an error in transit time is bat = 200 t - t (20) tJ we have an expression for the percentage error in acceleration caused by the contact wire: 12

im cos-1 ( _ ) _k - @OS (21) 5a = 200 k I maD a (21) 2y V aD Expanding the cos-1 term and using the first two terms, we may write: 100 ky ta, = - (22) 6maD In Table III values of this error are tabulated for various values of acceleration and two transit distanceso It is apparent that for a transit distance of 0o1875 ino the contact wire causes an unacceptable error at 10-3 g, and with a transit distance of.050 ino the error is too large at 10-4 go The bobbin in this instance is taken to be a magnesium one of weight 14.9 grams or 353 x 10-2 lb, ioeo, bobbin "C" aboveo Other orientations of the accelerometer axis with respect to the drag vector will no doubt result in similar errors, but it is sufficient to demonstrate the difficulty in a single caseo TABLE III Percentage error in Acceleration Due to Wire 100 Aa/a Acceleration (g) For transit distance For transit distance (1 g = 386 ino/sec2) = 0o188 ino = ~050 in. 10-2 005 0014 5 x 10-3 loO 0028 10-3 5o0 104o 10-4 1400 Electrical contact between the contact wire and the bobbin and between the bobbin and cavity was investigatedo To check the bobbin to cavity contact at 1 g, a lead was soldered to the bobbino The accelerometer was operated 100 times at various orientations in a circuit which would trigger the indicating counter at a resistance of 3000 ohmso There were no misseso To investigate contact reliability at smaller impact velocities, the bobbin was suspended on a fine wire as a pendulum and swung against a replica of the cavity wall. At that impact velocity which would be experienced at 10-2 g, there were 50% "no-contacts" in 100 tries, but this was reduced to 5% after polishing the surfaces. The contact wire was checked at 1 g onlyo In flight the force of the wire against the bobbin does not fall below that of the wire acting as a spring. A lead, in addition to the contact wire, was soldered to the bobbino The accelerometer was then operated with two counters, one stopped through the contact-wire 13

circuit, the other through the soldered lead circuit. In 100 tries the contact wire circuit missed 5 times, the other did not miss at all. With interchanged counters the results were repeated. In anticipation of using a soldered lead instead of the contact wire to improve circuit reliability, a bobbin was fitted on one end with a square hole and a square pyramidal caging finger was placed in the corresponding end of the accelerometer. This arrangement prevented rotation of the bobbin (except for a small angle) to prevent breaking of the lead. In the drop test for initial velocity, the special bobbin and finger performed as well as the standard design, as noted previously. The new caging finger and bobbin are shown in Fig. 6. -,i Fig. 6. Pyramidal caging finger to prevent bobbin rotation. In summary, the results of the investigations of the accelerometer were that neither the magnetic field nor drag on the bobbin are sources of error but that initial velocity imparted by the caging mechanism and an error in transit time introduced by the contact wire begin to become appreciable sources of error in the measurement of accelerations below 10-2 g. In view of this, it was decided to design and construct a new accelerometer with three major changes in characteristics: (a) A free bobbin with no contact wire; (b) Precision construction to perhaps ~.0001in.; and (c) Mounting arrangement to permit precision balancing. In addition, an attempt would be made to decrease the power consumption. 14

3. ELIMINATION OF CONTACT WIRE Various schemes were conceived to eliminate the contact wire. Included were: (a) A double conductor, perhaps a double spiral printed circuit on the cavity. Contact by the bobbin would connect the conductors. (b) A mechanically vibrating cavity. Contact by the bobbin would damp the vibration causing amplitude and phase changes. (c) A displacement or velocity detector, i.e., a transducer attached to the cavity. Contact by the bobbin would generate an electrical signal in the transducer. (d) A multiple cavity with the segments separated electrically. Contact by the bobbin would connect the segments electrically. This is similar in principle to but considerably more practical than (a). Scheme (a) was rejected after tests with a small model in planar form showed that contact was obtained in only a small percentage of tries. Considerable effort was expended on (b), (c), and (d). 3.1. VIBRATING CAVITY An accelerometer based on the conception of a vibrating cavity is shown in Fig. 7. The cavity consists of a hollow, light-weight plastic sphere such as a ping-pong ball. The cavity is supported in a mounting which permits it to vibrate CAGING FINGER SPHERICAL BOBBIN ~/ / ~VIBRATING CAVITY RESILIENT CRYSTAL CAGING MOUNTING DETECTOR MAGNET Fig. 7. Vibrating cavity accelerometer schematic. 15

and is attached to the combined driver-sensor which could be a piezoelectric crystal4 The caging fingers pass through holes in the cavity. The bobbin is a metallic sphere with no contacts or attachments when in free fall. Ideally, the cavity and crystal would vibrate as a whole with no nodal patterns at a frequency just off resonance. Contact by the bobbin mass would cause damping as well as a phase shift accompanying the change in resonant frequency. Since it is desired to detect transit times of 0O010 sec with an error of ~ 1% or better, a natu4r tl ft -qu: >y of te. order of 1-0`T I indicated to avoid eltaborate phasesensitive circuitso In the first attempt a ping-pong ball was mounted on a steel reed driven electromagneticallyo The resonant frequency of the combination was only about 450 cps and the device was abandonedo Next, a ping-pong ball was attached to a crystal by means of a thin Micarta wafer in the form of a yoke, as shown in Figo 8. This combination resonated at 5900 cps but was too flimsy for practical application. In an attempt to increase the strength of the device, a second crystal-and-yoke combination was attached to the ball in one case 90~ displaced from the first yoke and in another 180~ displaced as in Fig. 9. Although matched crystals were used and an attempt was made to make the yokes identical, the two crystals could not be made to resonate at a common frequency. The result was a complex wave pattern orn the surface of the ball with many nodal points. Therefore the attempt to use two crystals was abandoned. Returning to the single crystal and yoke, the ball was next surrounded by sponge rubber which, although it would tend to damp the resonant peak, would still permit vibration while increasing the ruggedness of the combination. This arrangement resonated at 5900 cps but had a complicated mode of vibration as indicated by many nodal points. It began to appear that it would be difficult to vibrate the ping-pong ball as a whole without setting up vibratory patterns in the surface. Two more attempts were made, however. In one, a single mounting was once more resorted to in which the ball was cemented directly to the crystal which was in turn mounted in a thin metal disc with center hole. The arrangement was more rugged than the previous single point mounting but again exhibited the troublesome nulls. Finally, the ping-pong ball was mounted in a thin annular stiffening ring which was then supported in firm rubber locator pads and which rested against the crystal. The resonant frequency was 6600 cps. The vibration of the ball surface was not eliminated with this system and no further attempts to vibrate the ping-pong ball as a whole at frequencies approaching 104 cps were made. The various arrangemlents described are illustrated in Figo 10.'re next step was to try metal spheres in place of the ping-pong ball. Several were fabricated. The most practical in terms of weight and size was of Dral:, -1/2 in. in diaxiest-er with a wall thickness of 0.021 in. The sphere consis-ted of two hemispheres bonded with Armstrong cement. Various mounts were again tried. The most successful is shown in Figo 11. The rubber was sponge rubber slightly compressed. The sphere rests against a 1/2-in.2 laminated crystal. The apparatus was driven at frequencies varying over a wide range. Resonances in various modesw ere deteced as low as 2800 cps and as high as 83,000 cpse At 8700 cps the sphere: resonated with virtually no nodal points. 16

Fig. 8. Yoke mount for cavity and crystal. PING-PONG BALLS MOUNTS BAKELITE WAFERS CORNER MOUNTED CRYSTAL CRYSTALS Fig. 9. Various yoke mounts for cavities and crystals. 17

SPONGE RUBBER LOCATORS THIN METAL i~~1 BON D:.:A THy<'.\<- DISCS M i SCOTCH CAST CRYSTAL CRYSTAL METAL WASHER STIFFENER PLASTIC SPHERE ----- FIRM RUBBER LOCATOR PADS CRYSTAL Fig. 10. Three ping-pong-ball to crystal mounts. CRYSTAL METAL SPHERE Fig. 11. Metal spherical cavity mount. 18

Contact at virtually any point of the sphere would produce a phase shift. At very high frequencies where resonances occurred, for instance 59,000 cps, the vibration patterns in the surface of the sphere became very pronounced, the crests being very sensitive and the nodes having no sensitivity. The conclusions drawn from the foregoing investigations are: (a) That a workable accelerometer meeting the design requirements can probably be designed along the lines of the final model, that is with a metal spherical cavity, vibrating at nearly 104 cps with contact of a spherical bobbin being detected by a phase change in the crystal signal. (b) That certain problems which were not investigated would have to be met. These include: unwanted noise in the crystal, inaccuracies in the cavity location due to the resilient mounting, dead areas in the cavity occupied by orifices for entry of the caging fingers, the necessity for an oscillator and power supply and perhaps others. 3.2. IMPACT TRANSDUCER Instead of detecting the phase and amplitude changes in the driving signal caused by impact loading of the cavity attached to the driver, it should be possible to detect the impact of the bobbin by the energy of impact transmitted to a transducer attached to the cavity. A variety of mounts illustrated in Figs. 12 and 13 were tried. Although in each case signals were obtained, all the devices were rejected for one or more of the following reasons: fragility, lack of sensitivity for certain directions of impact, sensitivity to spurious noise, time delay between impact and signal, variable sensitivity in different orientations, and different accelerations. In summary it may be said that while an accelerometer with a transducer impact detector might conceivably be constructed, the approach had all the weaknesses of the vibrating cavity as well as some additional ones. No further investigations of this approach were made. In the work with the various impact detection schemes described above, bobbin impact was simulated in preliminary tests by finger pressure or with a ball probe touching the outside of the cavity. For the more successful arrangements (for example, the vibrating metal spherical cavity) the setup of Fig. 14 was used to simulate bobbin impact. A 19-gram ball was suspended on a wire in the form of a pendulum. Impacts corresponding to various accelerations were obtained by releasing the pendulum from the proper displaced position. In the case of metal cavities the circuit shown permitted measuring the time delay between impact of the pendulum and appearance of the signal at the terminals of the crystal. For a given configuration, the measured time delays were quite constant and varied from 0.2 to 0.6 millisecond among various models. Time delays of these magnitudes represent significant errors in accelerations as big as 1 g but, being constant, could be corrected for. 19

SOLDERED RIGID TEE DI\ / LECTRTIC \ / / CANTILEVER SPACER STEER DISCS E#:x+:= E SCOTCH SANDWICH.004" STEEL CAST BOND DISCS CRYSTAL CRYST MAGNESIUM (~s j 3 SPHERE MOUNT: / STEM MACHINED AS PARTS OF SPHERE \Vfi -t /9 -CRYSTAL ANCHOR FOUR CRYSTALS CRYSTAL NYLON SCREW Fig. 12. Mounts used with metal spheres, Fig, l5. M o unts u sed mt i th metal sph er es, 20

IOK START FINE 0 —-------- ~WIRE v" L FOIL L SEMI-FIRM RUBBER CUSHION-\ TRANSIT (if G \ DISTANCE 19Gr HEWLETT PACKARD CRYSTAL STOPI COUNTER MODEL 522 B Fig. 14. Impact pendulum. Observation of the form and magnitude of the crystal signal outputs was by means of a Tektronics type 545 oscilloscope. At 1 g a typical magnitude of voltage peak at the instant of impact was 1.2 volts, and at 0.01 g, 0.2 volt. At impacts corresponding to 0.001 g the signal peaks were often indistinguishable from noise, one source of which appeared to motions of the cavities in the resilient mountings. Under flight conditions, similar sources of noise could be expected and this situation probably constitutes a limitation on the low-acceleration end of the range of operation of an accelerometer using this method of detecting impact. In summary, the same general remarks may be made about the use of a transducer to detect impact as were made about the vibrating cavity-namely, that an accelerometer could probably be constructed using the idea but that certain difficult problems would have to be solved. 21

3,3. PIEZOELECTRIC MATERIALS Piezoelectric materials come in a large variety of physical makeups. For the applications employing the resonated or impacted cavity sphere, only those which combined a fairly high degree of physical strength and electrical sensitivity were considered. An early consideration was to make the cavity sphere entirely of a formed ceramic crystal. Consultation with engineers at Clevite Corporation, Cleveland, discouraged this approach. It seems that ceramic crystals of this nature are applicable only where the applied forces impinge large areas of the crystal-such as underwater transducers, etc. Point contacts as made between the cavity sphere and the reference sphere would be too insensitive. Several types of crystals were tested. Without entering a discussion of crystal design or the processes of elimination, the one selected had the following outline: it was a 1/2-in.2 laminated sandwich.025 in. thick. The segments of this sandwich were comprised of two oppositely oriented crystals. Applying a voltage across the two plates produced an elongation in one plate and contraction in the other. The resulting flexure, if reproduced mechanically, made the crystal an excellent voltage generator. Sensitivity to both bending and twisting action, good physical strength, and, when used as a driver, numerous resonanat points of an acceptably high frequency made it the best all-around device. Happily, with some modifications, it proved to be the most efficient of the tested crystals for both applications. Mountings were made of two Micarta hoops which were screwed together to hold the crystal around its perimeter. The leads of gold-plated brass shim stock,.001 in. thick, could be soldered to the surfaces of the crystal, but were found to be more efficient just pressed against the opposite faces by the Micarta hoops. The only further modification to the crystals was on the one mounting the impacted cavity sphere. Here a small hole was bored through the center of the crystal through which a nylon screw passed and screwed into the stem of the cavity sphere. 3 4. CAGING One of the disadvantages of the old accelerometer was the high power requirement of the caging mechanism. An air-core moving coil was chosen because its low mass and inductance would permit large acceleration during uncaging. The magnetic circuit was relatively inefficient, however, and the coils were operated at 54 watts to obtain the necessary caging force. A moving iron magnetic system was constructed during the course of the work with the crystals and used with the crystal accelerometer models as well as with the multiple cavity accelerometer described in the next section. The new caging solenoid is shown inFigs. 15 and 16 together with the small caging finger scheme used with various trial accelerometers. One factor contributing to the feasibility of the solenoid is the anticipated reduction of the transit distance from 0.187 to 0.050 or even 0.020 in. The coils were wound with 890 turns of NOe 28 wire and are operated at about 20 watts. The individual solenoids are 1-1/4 ine in diameter and 1-1/4 in. long; the corresponding dimensions in the previous design were 2-1/16 and 1-3/4 in. Because 22

Fiig. 15. Photo showing moving. iron solenoids Fig.6. Schematic showing moving iron solenoid the fo:rce increases with deoreasing gap (as contrasted with the eonstant force eo the old design), a relatively stiff spring can and must be used to provide sufficient initial acceleration at the instant of unca ging. The time lag of the motion of the solenoid ias redluced to the order of I millisecond by thie incorporation of() a 0.009-in. nonma.:gnetic shim between the slug and the core. In a flight accelerometer the residual time lag would be elimina. ted as a soure of error by tatking tue start pulse from the breaki of contact between fingers and bobbin. 5:5. MU4L:TIPTL.E CIRCUIT CA..VITY At this point a promisinvg new idlea for cavity and bobbin was conceived. it is il.lustrated in Fig'. I. TIhe bobbin consists of a cube on the face-centers of whi.ch are moun t ed six spheres. Four of the spheres are surrounded by hemispieri eal cai,it i.es separnatlea cby an appropriate transit di stancne. The distance which the bo.bbin t, ra vel. s fP rom the caged posito it.on to he ca viti es is as before, it'Ie sahme in any direct.ion,. in t this caseo, however, the bobbti n approaches at l.east t-wo l a ond. soa(etcimesndins o the dig o te drection) cavity segments. This permli. ts the tbob'ibi to bie empl.oyJ'ed as the circuit-compl.eting elemen t: bet.ween two cac.vity segtmen'ts wlh ch are elc'tricall...y insulated, thus eliminati.ng trile con1tGact wire One ii.Import0lan0 -t dif1ference between this scheme and the one mel t1i oledi )rIeniosltly (in wi i.ca t.e cavi ty would ha ve had printed onl itl a double spi ral ci rcuit t) is that, in t. he case of an accel erome. Ceter made wiith no di.mlensional. error, the bobbin of the new type w.ill contact "two surfaces simultaneously., wherea.ns iln t, ce spira... circuit. scheme tihis wilJ.l happen only a fract:i..on of the time. 25

Lf( ( { t \^^..... - -BOBBIN SPHERE |l 1 \\ \ ) s- 7rw —Ij_ p BOBBI N CUIBE \ 3 "^ t^ / ~ - CAVITY BLOCKS Fig: l*" Miul tip.ple caUv:iP t'by ac. eleromet er schematic* An experinmental mod l, of tie new configura.ion was construt.ed and re}liminary tes"-ts -were maxde It, iL; shonm in F:.ig. 16. 3.The he. ispil"er lcal. c cavi. ties ere rlachilned 3i2 four brass cubes>, tle..final. s,;.hape bei ng obtained by pressing Fig, 3..i Model of mu."':l:i..e., cav:i..oty aoccem.lero me'iIter.,;..'?i

a steel ball into the machined cavity. They were mounted on a base with clamping screws which permitted positional adjustment. The bobbin was formed of a square, soft iron cube 0.4 in. on a side, through each face of which a 00228-in.diameter hole was bored on center. Into each hole a 0.25-in.-diameter chrome steel ball was placed and soldered. Before installing the sixth ball the center chamber of the cube was filled with solder, Various jigs and fixtures were constructed to aid in the assemblyo The transit distance was 0.020 in. Because the bobbin was not a figure of revolution, it was necessary to orient it, each time it was caged, about the longitudinal axis of the device, This was accomplished by means of four small caging fingers, two on each end, engaging corresponding "dimples" in the opposite faces of the bobbin cube. The cavities were connected in series with series resistanceso On bobbin contact, a change in voltage across one of the series resistances resulted from the connection of two or three cavity segments by the bobbin. In the first tests (with steel bobbin and brass cavities), contact was made in 30% of the tries. Gold-plating the bobbin and cavities improved this figure to 75o% It had been anticipated that shop tolerances would prevent simultaneous contact in all cases. The first tests indicated that, while there were some misses, the percentage of contacts was encouragingly higho With the old accelerometer, contact was obtained in somewhat better than 95% of the trieso To improve the percentage of contacts, new bobbins were constructed with the spheres resiliently mounted to the cubeso In one case an adhesive, resilient when dry, was usedo In another, opposite spheres were connected with fine wireso In both instances contact was obtained in better than 90% of the trieso Work with the preliminary model of the multiple cavity accelerometer was very encouraging, The design of a prototype flight model was consequently undertaken. 25

4. SPHERE DATA-PROCESSING BY COMPUTER A major portion of the effort of the project was expended on the task specified in Modification 3 of the contract: "Research and develop computer methods for reducing data from the small sphere experiment with the ultimate aim of developing an automatic data reduction system." The work was accomplished with the aid of the LGP-30 digital computer of the High Altitude Engineering Laboratory. By Modification 5 of the contract, funds were made available by the Air Force Cambridge Research Center to purchase a high-speed Tape Punch and Reader Unit manufactured by Ferranti Electric, Inc., for the Royal Precision LGP-30 System (,computer). The new equipment when working with the LGP-30 is capable of reading tapes at 150 characters per second and punching tapes at 20 per secnd. These speeds comare with about 10 per second for both reading and punching for the Flexowriter which is furnished as standard equipment with the LFP-30 computer. The increased input-output speeds greatly facilitated the data work described in the following sections. The analysis of falling-sphere data using the LGP-30 digital computer was previously reported. Some of the parts of the analysis were carried out by hand calculation at that time. The present program performs all the data analysis automatically. Some refinements of the trajectory equations were also included in the new program. Three new functions are accomplished by the present program: (1) Accelerometer raw data are processed to obtain corrected time and acceleration data. (2) Trajectory peak time is derived from the acceleration data. (3) Trajectory peak altitude is adjusted by comparing sphere-derived densities with balloon-sonde densities. Trajectory iterations and density-pressure-temperature calculations are performed in essentially the same way as before. Data from three sphere flights were processed by the new program with satisfactory results. These were Nike-Cajuns AM 6.02, AM 6.03, and AM 6.05 fired at Fort Churchill in the winter of 1958. A condensed flow diagram for the over-all data-processing is shown in Fig. 19 and the flow diagram for the filldata and print-data routine is shown in Fig. 20. 4.1. ANALYSIS OF ACCELEROMETER RAW DATA This routine contains four subroutines: 27

FILL DATA ANALYZE ACCELEROMETER PRINT DATA DATA. PRINT DERIVE ERASE BAD PEAK TIME ACCELEROMETER PRINT DATA INITIALIZE INCREMENT INCREMENT VA C U UM VACUUM TRAJECTORY TRN TRAJECTORY PRINT I t <tD COMPARE INCREMENT SPHERE WITH DRAG BALLOON TRAJECTORY Z<50 COMPUTE ADJUST PRESSURE PEAK \ Y \C/D/C < I1 | DENSITY ^< 60,O< Fig. 19. Flow diagram for over-all data processing. 28

Fill (TL, TU)upleg, (TL, TU)downleg; Tmin 2S aT aT, aU, aD, AtU, AtD aTD a au D g, ro, cos 0, sin, cos G, sin 9 Uyi, m/A, k alno metric units Dn TK^ 0 ransfer Set up print out n tn - n+nill Z e P, T English units Pn > ~ Compute and fill pl / Stop M-| Input accelerometer data — |Stop JC —— al Store ZB Print (TL, TU)uplegn (TL, TU)downleg, Tmin, 2S aTU, aTD, aU, aD, AtU, AtD go, ro, cos 0, sin 0, cos g, sin G m/A JBalloon-.sond Upleg Dowleg n = -1 n -1 n - n ->+ n+l1 n + n+l | | n -+ n+1 | T sf Ier A I TYSAnalyze y-bransfer Y transfer YY ransfer Analyze s-a Y c-^ Y l c accelerometer --- - ----., —-------, -- data Print Z'P'T',p' Print upleg Print downleg accelerometer accelerometer data. 8 words data. 8 words Fig. 20. Flow diagram for fill-data and print-data routines. 29

(1) Find release pulses; (2) Compute transit time; (3) Reject noisy data; (4) Compute corrected time and accelerationo See Fig. 21 for the flow diagram. The accelerometer raw data consist of the times at which the accelerometer release pulses and contact pulses are recorded, i:.s:...ibers,.-..gr'e. -.1 spel'ene, are therefore monotonically increasing. Two tracks are reserved for upleg data and six tracks for downleg data; 64 numbers can be stored in each track. The release pulses are spaced equally in time because the accelerometer recycles periodically. The upper and lower limits which define the recycle period are denoted by TL and TU. If a pair of pulse times are separated by more than TL but less than TU, they are identified as release timeso This is accomplished by storing the negative of the release time in place of the release timeO At high accelerations the release time and contact time are closely spaced and both may satisfy these conditions. In this case, the first pulse of the pair is selected as the release pulse and no further pulses are considered until the elapsed time is TL. The presence of noise may also cause pulses to be closely spaced. Exit from this subroutine occurs when a pulse time is found which is smaller than the preceding release pulse time. The transit-time subroutine replaces each positive time by the difference between it and the preceding release time. The normal sequence is alternating release and contact pulses. In the presence of noise there may be two or more pulses between each pair of release pulses. In this case the subroutine which rejects noisy data chooses the transit time most nearly equal to the transit time of the preceding cycle and fills it in place of the last one in sequence and fills zeroes into the remainder of the sequenceo The corrected time is equal to the sum of the release time and half the transit time. The drag acceleration is 2s aD = 2 _ If the transit time is smaller than eight milliseconds, a zero is filled in place of the accelerationo If the transfer control button is depressed, corrected time and drag acceleration will be printed by the typewriter. 4.2. DERIVE PE-AK TA IME CO'UT INE See Figo 22 for the flow diagram. Peak time is computed by assuming that the drag function is symmletrical with respect to peak time. The upper portions of the trajectory where the drag accelerations are small give the best results. At lower a.ltbitudes the drag destroys the symmerty. On the other hand at very small drag accelerations the data become too scattered for the purpose of de30

Start n -[ n+l n=tR = 0 =tn- tR ~ I -:l Find release pulses rela rerlace i tn witn -tn. ___ ___,T -y m+l tm - tl N = n | n = L-o | [replace p t:R, 0t - n tR Y n N! n = -1N. n - n+ t - t Compute transit time Etn t t replace T = tn+ Fig. t n+ with T A I >n+1 >-. — I T| tm with 0 Y E ~ \n+l 0 -- c ITO-TI - IT - tn+11 y/" ~+1 i= YI - T = tn Reject noisy data n p r1 i_ nt ^ transfy tc and aD n + n+l Y Compute cor----- replace rected time and tn with 0 acceleration m=n T<Tl tc=tR+-T mRR =-tn2 m = ^~n / \aD = 2S/T2 replace T>.ooy tm with -t n^\ ^^ \ / tn with aD Eit T = tn Fig. 21. Flow diagram for analyze-accelerometer-data routine. 51

n = 0 Y _ n Y A T I UaD+ZaD+tm t _ -tM-t n + n+l NU + NU+i m.y, m + m+ tiu -t aD= tm M — - t m m+l n = 0 Y downleg a!D+tm D 0 = t = = l aD aDtm n n~l | ND + ND+i y,.,-I/ - —,L AD, ~ T. lg aD DaD = tm tiD =-tn t = 1 T m=n Yn - m+l Y N= t' =tn-ti t^= iu~ =, t' l = t'2 = Et log aD = rt log a /' t Y -Increment ett', t2,t' ~ log a 7, t' log aD pintD = _ t' = tn-ti i aTn n 0 ( o = Et' = Z log aD = Et' log aD n-n D D D Increment Et', 2t - log a Dn, -t' log aD|-J | D D D "^^aT aD= t 1 ( ) 1 /Et' + 1Et'+ print tp =2 (tiU+tiD) + 2 N iU 2 tDi t iUq tiD3 NU., N t2 2 log D. )o -- NU1 NDNUNDN N D __+_t_ 1 ( log___ ~ aD- -/u ~ a ] I+2 E/ t' I log aD t f log a t' log aD - --— + log aD - --- ) Exit _____N /u \__________N D Fig. 22. Flow diagram for peak-time routine. 32

riving peak time. A compromise value is therefore chosen. Several data points are used in a least-squares analysis. Three parameters must be specified: threshold acceleration, mean acceleration, and elapsed time. Data points for which the drag acceleration exceeds the threshold are taken in sequence until the elapsed time measured from the first point is exceeded. Then the mean drag acceleration is computed and compared with the specified value. If it is too high on the upleg or too low on the downleg, the first point is rejected and the process is repeated. A plot of drag acceleration logarithm vs. time is a good approximation to a straight line if the elapsed time is not too great. A least-squares' formula for the peak time was derived on this basis. t = (tU + tD) + 2 (nU +n t U U DD + - Z. t' log a + Z t' log a + - Zt' Z log a - -1 t' log a U D nU U U n D D Upleg values are denoted by U, downleg values by D. The time of the first upleg point is tU, downleg, tD. tU = t - tt - t - t tU, tD rnft, nD are printed. 4.3. TRAJECTORY ROUTINE See Fig. 23 for the flow diagram. The equations used for computing the trajectory are: -A = - g -a + u ( + + r os sin 0 Atr Au /U 2 - _-s - uz ( S + cos 0sin ~J - 0R sin 0 cos 0 cos ~ At z - 2 /z r = r + -- uz At 2 z g = gorO/F2 aD =- (aD+ aD) 33

Enter from Enter from peak time routine Er AZp routine n-*n-2k Initialize 1, densityroutine Initialize tiu, n+l Zp=5500ootp- 40,000 Print tp0 aD ~ * — r - t0 - t — m -m = t n aDz = tn At = tp - tDi r =rp 4 uz -0 t = tDi - (At+l) + r + u g = aD = 0 aD= + uz - g + Uy (uy/r + 20 cos 0 sin 9) + r Q2 cos2 r = r+ 1/2 u, + 4 v ^ u y + U - uz (u /F + - cos ( sin - r 2 sin 0 cos 0 cos ^_1 | n I |_~|T ^+ l |L' = t~l 1 aD | (1/2) (tD + aD / \ - At t t:tnr0 J t - tn A/ / \ F = r + (1/2) (uzAt) n 2 n+lo -- Y g = goro /r Enter | + (TUz U. y2 (gZ at f rom + v v 2v/ A ID aD routine z | ( y) = + (Ur) ( V) (~2V Exit to v Y )Z2 densit ^ routine I T uz = uz + -g - a ( + y + 2Q cos 1 sin ) + cos 0 st Uy = Uy + ) - ( + cos 0 sin ) - 2 sin 0 cos 0 cos At r -* r + uzAt Z = r - ro Fig. 23. Flow diagram for trajectory routine. 34

()=u T Z2 _fg\ V V \v V'2VJ /U 1U u gAt (9)= - + ( V V) (j-z) ( V v v V 2 The horizontal and vertical velocity components, Uy and uz, are referred to the earth's surface, a rotating coordinate system. The equations therefore contain Coriolis terms involving the earth's rotational velocity Q. The radius to the earth's center is r; g is the acceleration of gravity. The increments of the numerical integration, At, are approximately one second. Mean values, denoted by ( ), are required for some of the parameters. The latitude angle and azimuth angle of rocket launch are 0 and G. The absolute gravity at zero altitude is go. The present formulation of the equations is more satisfactory than the one employed previously~ where an inertial reference was used. Certain inaccuracies in resolving velocities led to small errors in the horizontal velocity component in the old system. The errors were not large enough to influence the density calculations, however. The initial peak altitude is computed from the peak time and is a function of the rocket and launch parameters.10 The following formula is applicable to Nike-Cajun rockets launched at 85~. Zp = 5500 tp - 540,000 The peak altitude must be adjusted by comparing with balloon-sonde data at the lower end of the trajectory. The initial vertical velocity at peak altitude is of course zero. The initial horizontal velocity depends principally upon the rocket launch angle. Nike-Cajun rockets launched at 85~ have about 500 ft/sec velocity at the peak altitude. It has been found that this is not a very critical parameter since an assumed vertical trajectory results in essentially unchanged density data. 4.4. AIR-DENSITY ROUTINE See Fig. 24 for the flow diagram. The air-density calculations are essentially the same as reported previously.6 The air density is related to the drag acceleration by the equation 2m aD p CDA V2 The sphere cross-sectional area, A, and the mass of the sphere, m, are constants. The drag coefficient CD is a function of Mach number M and Reynolds number Re; it is plotted in Fig. 25. It was found that all the useful information in Fig. 25 is contained in the two single-parameter functions of Fig. 26, which are the ones actually used in the data-processing. The Mach number is defined by 35

Enter from tra- [ gn - = M-gioR 4. jectory routine _CD = CD(X) M V/a| n -t n-1 a = a(Z) - e I p ^ = k(Z) Re, = ^^^ = CD Re ACiV v Y n1 I ----------- \ —--------, ____ \~L, n O S 0\ - - Re Initialize Y = /( — CDPrint t, a^i < — P T routine Uzi Uy) Z, CP p = 607710 p k> >< -tk-l 2ma + ACpV2 P P Z = Z4 T=P/pR P -t P-gP AZ i,n pP D> AP A ZP I Z p=p AZ =Z Z Print t, ai, uzi Initialize Y Up zY CD), p, P, ) As routine /First Z = ZB, / Entry P = p+ Y AZ/iAp50\ AS = (B-Z )2 _Y - 2H Inp = - (Inp+- np+) |n = -^ I Stop |Z = Z+ p = ^ || AS + In p AZ A<- aZ = Z - Z+ n - ni Z - Zf+ p P+p Exit. Increment Z drag trajectory __ _ _n - ZS y AB-tAB+inpAZ' n - n+I —--- = II,Initialize ^_________, ~Z14 = Z, n Ag routine Inp = (1/2) (inp+inp+) y P = Pn Az = Z'+ -Z' T~i -- Z' = Zs Z'4I^ PI = P3 Exit. Initialize ad- jZ, justed trajectory B 2Modify entry@ A^ =z A__p__95H AB-AS nz,.95HZB-ZS AS B! npdZ AB Z I np'dZ' ZS ZS Balloon-sonde data storage: Z1, Pi, T', P', 24, P', T6, p4 *** Fig. 24. Flow diagram for density routine and adjust-peak-altitude routine. 56

IO d Cd'Ni rd Cd o -_. 0 ^ o? 0 N m =^:==g-j| r_ i=f c^ ^ g I I ~ i t i,: ~f -- — )SDI I N T/ x (0 N 0 - 0D' ^-,4^ \ > \ \<\'- - c6 /- 0s - - - -!Q ^:^ - -- - ^ - - - - - -- - -- ^ -s -- ^ -^ - ^ -^ 57

Re< 100,000 CD = 2 X<.6 CD = 2.326-.5429 X.6< X < 2 CD = 1.643-.2015 X 2< X < 3.36 CD 1.122-.0465 X 3.36< X < 4.65 CD =.906 4.65< X Re >100,000 CD = -.468 + 1.363 M M<.98 CD.459 +.4176M.98< M < 1.32 CD = 1.010 1.32< M < 2.3 CD = 1.240-.OOOM 2.3< M< 2.8 2.0 CD = 1.057-.0348 M 2.8< M < 4.35 CD =.906 4.35<M 1.6 co lx) I-. 12 14.2 0 \ w 0 S~ / ~CD(M).4 o, I...I I I 0 I 2 3 4 5 6 M OR X (X=LOGo Re +1/4[M-4.6] ) Fig. 26. Empirical drag coefficient functions. 38

M = V/a The speed of sound a is a function of altitude.9 The Reynolds number is defined by Re = pVd/. or, eliminating the density, 2md aD Re = _ C -- A CDV where d is the sphere diameter. The viscosity ~. is also a function of the altitude 9 The atmospheric pressure is derived from the differential formula Ap = - g Az The logarithmic mean of the densities p and p+ is found from the formula C3_ in p+/p P = + f p -P Since the pressure equation is differential, one must begin the integration from an initial pressure at a high altitude. The initial pressure is found by assuming the temperature to be -105534~F from Ref. 9. At low altitudes the drag coefficient becomes smaller and its value less reliable. This point was previously discussed.6 The low altitude limit of the density data is defined by a drag coefficient of one if the altitude is less than 60,000 feet. 4.5. ADJUST PEAK ALTITUDE ROUTINE See Fig. 24 for flow diagram. The atmospheric density logarithm plotted as a function of altitude is approximately a straight line. The balloon-sondedensity plot must overlap the sphere-density plot if this routine is to function. Adjustments to the peak altitude are made so that the area between the two density lines is reduced to zero. The peak-altitude correction is found by the formula z =.95 H -A p The average difference in density between the sphere and balloon-sonde plots is Ap, H is the scale height, and.95 is an altitude correction factor. The last adjustment is considered satisfactory if it is less than 50 ft. 39

4.6. DATA-PROCESSING The first step of the data-processing is to load the program into the com-guter. -The CT^-g Ctll.^ 3^ t''Sc^-' ogff wtde SoTnater ACAXt seven mn-liu tes are required if the photoelectric tape reader is used. The data associated with each sphere flight must then be filled. This consists of various constants, balloon-sonde data, and the raw accelerometer data. Two tracks are reserved for the balyloon-sonde data, two for the upleg accelerometer data, and six for the downleg accelerometer data. About two minutes are required. When all the data have been filled, the computer begins to print all such data to verify that everything is correct. About twenty minutes are required. It is possible to omit the printing of balloon-sonde data and accelerometer data by depressing the transfer control button. The computer then processes the upleg accelerometer data and prints corrected time and drag acceleration if the transfer control button has been depressed. The computer stops at the end of the upleg data and the operator inspects these data to see if there are some which should be suppressed. If there are some bad data, the operator punches a tape with time he wants erased and fills it into the computer. See Fig. 27 for the flow diagram. The computer makes the necessary changes and then processes the downleg data in the same way. The peak time is then computed and the data points on which peak time depends are printed. The initial values for the first trial trajectory are printed. The first trial trajectory is then calculated and compared with the balloon-sonde results. The peak altitude is adjusted and the second trajectory computed. These adjustments are continued until the correction is less than 50 ft. Approximately three preliminary trajectories are required. Only initial values are printed for each trial. Each trajectory requires about three minutes. When the last trajectory is calculated, all trajectory data and density data are printed at each step where there is an accelerometer data point. This requires about twenty minutes. Approximately an hour is required for the entire data-processing, mostly for printing data. The typewriter output for this computer is relatively slow since only ten characters per second can be printed. The faster punch unit can be used when the operator does not need to observe the results as they come out of the computer. The reading of the magnetic tapes which contain the raw accelerometer data can be.accomplliheiin approximately two hours if done routinely. These data must then be punched onto paper tape for filling into the computer. Approximately one hour is required. With this system it should be possible to obtain processed data on the day of the sphere flight. The results of the use of the new computer program on NikeCajun flights AM 6.02, 6.05, and 6.05 are given in Appendix B. 40

Enter from Initialize for accelerometer Stop upleg or downleg data routine n = -1 Input time of bad data Fig. 27. Flow diagramforer n s + n+l E Exit to / k > 0 accelerometer k=-n tn < -t data routine Erase ak Fig. 27. Flow diagram for erase-bad-data routine. 41

5. SPHERE ANTENNA BREAKDOWN The received signal strength from spheres in flight has been observed to exhibit a significant attenuation in the region of from 20 to 60 miles. A group at Boeing Airplane Company, Seattle, became interested in the problem in the course of work with antennas on hypersonic high-altitude vehicles and performed some simulation tests in the Boeing laboratory on a Michigan sphere. Mr. Howard Steele of Boeing and Mr. Hal Schulte of The University of Michigan cooperated in the investigation and prepared a paperll (with coauthors) on the subject. The paper was presented at a symposium entitled "Aerodynamics of the Upper Atmosphere," sponsored by the RAND Corporation, and held at Santa Monica in June, 1959. The paper is reproduced as Appendix A, following the list of references. 6. RECOMMENDATIONS In view of the demonstration of the source of errors in the transit-time accelerometer and the real possibility of reducing the errors with a multiple-cavity design, continuation of work on the accelerometer to extend its useful range is recommended. Since computer techniques have been successfully applied to the complete data-reduction process of the sphere technique, the next logical step in the development is to accomplish automatic data read-out of the telemeter magnetic tapes. Completion of such a development is recommended. The sphere experiment continues to show potential for development. It is a nearly synoptic technique at present and could become more so (with an extended altitude range as well) if the recommended developments were carried out. 7o ACKNOWLEDGMENTS We are indebted to the Geophysics Research Directorate, Air Force Cambridge Research Center, for cooperation and financial support throughout the entire program. 45

8. REFERENCES 1. Bartman, F. L., Chaney, L. W., Jones, L. M., and Liu, V. C., "Upper-Air Density and Temperature by the Falling Sphere Method," Jo Appl. Phys., 27, 706-712 (1956). 2. Jones, L. M., "Transit-Time Accelerometer," Rev. Sci. Instr., 27, 374-377 (1956). 35 Jones, L. M., and Bartman, F. L., A Simplified Falling-Sphere Method for Upper-Air Density, Univ. of. Micho Eng. Res. Insto Rept. 2215-10-T, Ann Arbor, 1956. 4. Peterson, J. W., Analytical Study of the Falling-Sphere Experiment for UpperAir Density Measurement," Univo of Micho Eng. Res. Inst. Rept. 2533-2-T, Ann Arbor, 1956. 5. Jones, L. M., Fischbach, F. F., and Peterson, J. W., "Seasonal and Latitude Variations in Upper Air Density," Natl. Acad. Sci., IGY Rocket Rept. Series, 1, 47-57 (1958). 6. Peterson, J. W., Schulte, H. F., and Schaefer, Eo J., A Simplified FallingSphere Method for Upper-Air Density, Part II. Density and Temperature Results from Eight Flights, Univ. of Mich. Res. Inst. Rept. 2215-19-F, Ann Arbor, 1959. 7. Jones, L. M., Peterson, J. W., Schulte, Ho Fo, and Schaefer, E. J., "UpperAir Densities and Temperatures from Eight IGY Rocket Flights by the FallingSphere Method," Natl. Acad. Sci., IGY Rocket Repto Series, 5 (1959). 8. Jones, L. M., Peterson, J. W., Schulte, H. F., and Schaefer, E. J., "UpperAir Density and Temperature: Some Variations and an Abrupt Warming in the Mesosphere," J. Geoph. Res., 64, 2331-2340 (1959). 9. Minzner, Ro A., Champion, K.S.W., and Pond, H. L., The ARDC Model Atmosphere 1959, Air Force Cambridge Research Center Report TR-59-267, 1959. 10. Hansen, W. H., and Fischbach, F. F., The Nike Cajun Sounding Rocket, Univ. of Mich. Eng. Res. Inst. Report 2453-1-F, Ann Arbor, 1957. 11. Burns, G. A., Linder, W. J., Schorsch, J. F., Steele, H. Lo, and Schulte, H. F o, Formation of a Radiofreque ny Plasma at an Antenna During FallingSphere Measurements, RAND Corp. Rept. R-3559, pp. 18-1 to 18-25, 1959. 45

APPENDIX A FORMATION OF A RADIOFREQUENCY PLASMA AT AN ANTENNA DURING FALLING-SPHERE MEASUREMENTS

R-559 18-1 FORMATION OF A RADIOFREQUENCY PLASMA AT AN ANTENNA DURING FALLING-SPHERE MEASUREMENTS G. A. Burns, W. J. Linder, J. F. Schorsch, and H. L. Steele Boeing Airplane Company, Seattle, Washington, and H. F. Schulte, The University of Michigan, Ann Arbor, Michigan Abstract A 7-in.-diameter sphere has been used extensively by University of Michigan personnel to measure air density up to 65 miles. The sphere is ejected from the nose of a Nike-Cajun rocket as it climbs past 35 miles and it continues up to over 100 miles. It telemeters to the ground its deceleration caused by the upper atmosphere as the sphere exits and then re-enters that atmosphere. The telemeter pulses are abnormally attenuated on the upward and downward passage in a region of from 20 to 60 miles. Boeing experiments show that a radiofrequency plasma occurs at the 400-Mc slot antenna at pressures simulating these altitudes. However, the attenuation of pulses does not cause a loss of data in the present case. The effect would be important in specific vehicles. Electrons near the antenna acquire sufficient energy from the radiofrequency power being radiated to ionize the low-density gas. Breakdown occurs and a plasma forms when the production of new electrons by ionization is equal to loss by various mechanisms. The breakdown field necessary is lowest at the altitude (35 miles) where the frequency at which the excited electrons collide with ambient gas atoms is equal to the radiofrequencyo A survey of experimental data indicates that within engineering accuracy diffusion and/or attachment predomi

R-339 18-2 nates as the loss mechanism, and therefore scaling laws can be used. The breakdown field for the antenna in the sphere is nonuniform. The breakdown voltages are roughly half the breakdown voltages measured in uniform field cavities scaled to the appropriate gap length, pressure, and frequency. This experience demonstrates that the breakdown characteristics of short gap or slot antenna at other frequencies can be predicted. Introduction Hypersonic vehicles traveling in or through the upper atmosphere expose their antennas to low pressures. The high-frequency energy from the antenna can sufficiently increase the electron energy to produce ionization in the neighborhood of the antenna. A loss in the power radiated by the antenna results. Since future communication, radar, and guidance systems demand high reliability, it is essential to study the case where the production of new electrons by ionization is greater than the loss by diffusion or other mechanisms. Of course the problem is solved for the antenna designer if the vehicle operates at a high enough altitude so that there are an insufficient number of ionizable atoms present. Few data were available on a specific antenna which had been tested in the laboratory and then carefully checked on an actual flight. Where both laboratory and flight data were available, the breakdown was influenced by the rocket exhaust of the vehicle so that correlation was uncertain. It was the objective of the experiments reported herein to test a given antenna under both flight and simulated conditions. The physics of this process will be discussed here so that the basic principles can be applied to other cases. The antenna selected for study

R-339 18-3 was that designed and developed by The University of Michigan for telemetering upper-atmosphere density measurements from a 7-in.-diameter sphere. The antenna is a 400-Mc slot 1 in. by 11 in. long, flush-mounted in the surface of the sphere. Flight Technique in The University of Michigan Experiments A technique for obtaining upper-air density and temperature by measuring the drag of a falling sphere was developed by The University of Michigan Aeronautical Engineering Department. The deceleration of the sphere as it re-enters 1-3 the atmosphere was telemetered to the ground so that the ambient density could be calculated directly from the drag equation. By careful design it was possible to pack within this sphere the accelerometer, the batteries, the telemetering transmitter and the antenna. Figure 1 shows the sphere components and assembly. A typical sphere trajectory is given in Fig. 2. Other flights went as high as 594,000 ft. In this figure the NACA radar data and estimated upleg trajectory for the rocket nose cone are shown for comparison with the calculated sphere trajectory. Note that the sphere is ejected from the rocket at 180,000 ft. The transmitter used in the high-altitude experiments was a master-oscillator power amplifier, operating at 400 Mc. The output was a square 104-sec pulse occurring at a repetition rate of two pulses per second. These pulses are referred to as the start pulse and the stop pulse. The start pulse was generated when a small metal bobbin was released in the hollow cavity of the accelerometer.1,2 It occurs at a rate of one pulse per second. The stop pulse was generated when the bobbin contacts the wall of the cavity. It varies from 5 msec for maximum acceleration to 750 msec for minimum acceleration. These pulses, when telemetered to

R-339 18-4 the ground, constituted the primary data of the high-altitude experiments. The antenna is a boxed-in slot extending half the circumference of the sphere. This type of antenna uses the surface of the sphere itself as a radiating element. Patterns were obtained using the sphere as the transmitting antenna and the groundstation helical antennas as the receiving elements. The helix windings of these antennas was such that the patterns obtained from the sphere were essentially omnidirectional. For structural reasons, the slot was partially filled with polystyrene, and, because of the heat generated during re-entry, the surface of the slot was covered with Teflon. Because the length of the slot was less than a half wavelength, the antenna presented an inductive impedance to the coupling point. It was therefore necessary to load the slot with a capacitive reactance to resonate with this inductance at 400 Mc. The capacitor loading point was chosen at one-third of the way down from the edge of the slot. At the request of the Boeing Company, the magnetic tape recordings of the pulsed telemetered signals were analyzed by the staff of The University of Michigan. The amplitudes of both the start and stop pulses were found to be attenuated identical amounts. The top part of Fig. 3 shows the amplitude of both start and stop pulses plotted against altitude. These data were for a particular flight in which the sphere antenna reached an altitude of 594,000 ft. Above a relative amplitude of 25, the magnetic tape became saturated so that the inverse square effect does not appear. Thus there is no reduction in the power level as the distance between the sphere and the receiving station varies. This method of ground-station detection clearly shows the region of break

R-339 18-5 down. The flight data show a marked attenuation of the signal level through an altitude range of 110,000 to 300,000 ft. The bottom part of Fig. 3 shows the velocity and Mach number for this flight. Note that the maximum in the velocity and Mach number curves does not coincide with the breakdown region shown at the upper part of the figure. This tends to indicate that these parameters have a secondary influence upon breakdown. Thus the attenuation in the signal level from the sphere antenna is probably caused by electrical breakdown. Experimental Procedure at Boeing The breakdown measurements were made in terms of power. However, a knowledge of the breakdown voltage is necessary if the measurements are to be compared to theory. Thus it was necessary to measure the antenna impedance. The details of these measurements are available in Boeing Report D2-3281. Several measurements were taken at various power levels and the average value of the slot impedance was found to be 200 ohms. The breakdown voltage was then determined from the breakdown power by using this value of impedance. The sphere was then placed in the bell jar vacuum chamber. A standard fore pump was capable of reducing the pressure to 5 x 10-2 mm Hg. A diffusion pump was added to the system and permitted pressures as low as 10-3 mm Hg to be obtained. This pressure was measured with an Alphatron ionization gauge which had been calibrated against a mercury McLeod gauge. The bell jar used in the experiments was 12 in. in diameter and about 18 in. in height.

R-339 18-6 The antenna voltage was varied by placing lengths of transmission line (attenuators) between an external transmitter and the antenna of the sphere. A block diagram of the experimental setup appears in Fig. 4. The power was measured by means of a 10-db attenuator, bolometer mount, and power meter. This circuit sufficed for pulse repetition rates of 50 pulses per second or greater. However, for a pulse rate of 1 pps, the pulse rate used during the flights, the power had to be determined by comparing the pulse height at 1 pps to that of 200 pps. The external receiver is also shown in the lower right-hand corner of Fig. 4. Positive 20-volt peak square waves from the pulse generator were used to trigger the oscilloscope circuit. Breakdown was determined on this oscilloscope. The methods of determining breakdown mentioned in published literature vary with the experimenter. In our case, breakdown power is that at which the pulse shape changes from that picked up at lower power. Change in the pulse shape is shown in Fig. 5. Curve (a) is the shape of the pulses normally radiated by the sphere antenna when breakdown is not present. Curve (b) is the pulse shape at a lower pressure when breakdown is present. It was found that this method of determining breakdown power is consistent with other methods. At a still lower pressure the breakdown caused the pulse shape to look like Curve (c). Note that there is a plateau present in each case, meaning that a given power is radiated even when breakdown is present. Breakdown was measured for various power levels by decreasing the pressure until breakdown was observed on the oscilloscope. At a given power level the breakdown would persist as the pressure was lowered until a critical pressure

R-339 18-7 was reached. The breakdown power for this low-pressure point was determined by pumping down the system to a pressure below that at which breakdown occurs. At this point the transmitter was turned on and the pressure was slowly increased until breakdown occurred. This procedure assured that fresh air was used for each determination of breakdown power. This is essential since the discharge can produce oxides of nitrogen which influence the breakdown for succeeding pulses. This procedure was repeated for various power levels to the antenna. Experimental Results Figure 6 shows the variation of breakdown voltage with altitude at 50 and 200 pulses per second. The altitudes corresponding to experimentally observed pressures were taken from the data of The ARDC Model Atmosphere. A second scale is shown giving the altitude calculated considering the effect of high-altitude temperature on pressure. Note that the minimum voltage needed for breakdown to occur decreased as the repetition rate was increased. This is to be expected since the electrons produced during a given pulse increased the initial electron density for the succeeding pulse. Breakdown at 1 pulse per second was not observed at all unless a microcurie alpha source enclosed in a glass needle was placed in the high-field region of the antenna, that is, within 1/4 in. of the Teflon. The effect of the alpha source on breakdown at 50 pulses per second is shown in Fig. 7- The effect was such as to increase the pressure range over which breakdown occurs and to decrease the breakdown power. The results with 1 pulse per second using the source are

R-339 18-8 given in Fig. 8. This figure is given in terms of power using the above-mentioned impedance of 200 ohms. Comparison with Flight Data The University of Michigan flight data mentioned above is given at the top of Fig. 8. The transmitter in the sphere was operated at 30 watts output at 2 pps during the flight. The horizontal line drawn at 30 watts in Fig. 8 intersects the laboratory data at 107,000 and 217,000 ft. Breakdown should then occur at altitudes between these extremes. The recordings of signal strength for four different flights are summarized in the table on the following page.. Figure 3 is typical of these flights. Comparison of the flight data given above and the laboratory data in Fig. 8 indicates a discrepancy above 215,000 ft. The laboratory results do not show breakdown above this altitude for a 30-watt power if the ambient ionization is equal to or less than that produced by the radioactive source. Figure 7 indicates that at 50 pps ambient ionization has the effect of lowering breakdown power at the higher altitudes. The discrepancy could also be caused by the fact that at altitudes above 215,000 ft the mean free path for electrons is 1 mm and greater. Under these conditions, a significant number of electrons may diffuse to the wall of the bell jar. This process causes the necessary voltage for breakdown to increase. Under these conditions, agreement between flight and bell jar tests would not be expected. Since a radioactive source was necessary to produce laboratory breakdown at 1 pps even at the most favorable altitude, it is interesting to speculate about

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R-339 18-10 the source or sources of additional energy that apparently must be present in the upper atmosphere. Ultra-violet photons, cosmic rays, soft X-rays, sphere-accumulated charge caused by friction, or other sources of additional electrons, perhaps in combination with the sphere velocity, are possibilities. It is hoped that night and also higher-altitude firings will provide additional data which will lead to a more conclusive interpretation. Comparison with Breakdown Data at Other Frequencies: Similarity Principles and Scaling It has been shown4 that the breakdown of hydrogen and helium gas is controlled by diffusion in and near the pressures where breakdown is most probable. There is evidencei that attachment also effects the breakdown in air under highpressure conditions. However, we now want to demonstrate that as long as diffusion or attachment are the dominant loss processes (either or both), breakdown voltages can be predicted to the accuracy needed for engineering purposes, using scaling laws. The scaling laws of plasma physics applied to breakdown can be stated as follows. The breakdown voltage will be the same for gaps with geometrically similar electrodes if the gap spacing (d), pressures (p), and wavelength (X), are related so that: Pil = P2%2 and Pidl = P2d2 As a demonstration of the degree to which these scaling laws hold in air, and thus the degree to which scalable processes (diffusion and/or attachment

R-339 18-11 predominates), the breakdown data of various investigations6,7 was assembled in the three-dimensional diagram shown in Fig. 10. The horizontal axes are p% and pd. The vertical axis is voltage. (The concept of diffusion length is being avoided to simplify the presentation.) Note that if gap spacing and frequency are kept constant in a given experiment and pressure is varied, one moves along the horizontal plane at a 45~ angle to either the pX or the pd axis. Each of the vertical slabs represents a breakdown curve taken in this manner. The curves to the rear are for gaps up to 0.05 of a wavelength in size while those in the right forward part are for gaps as small as 0.001X. The curves representing nonuniform field data7 are lower than the general trend at lower pressures, but all the data indicate a valley near d =.0035. A smooth surface could be made to fit the top of these curves and to this accuracy scaling laws can be used to compare even uniform and nonuniform field cases. A more practical form of the three-dimensional diagram is given by plotting contours representing voltage (the vertical dimension) on the horizontal plane. This has been done in Fig. 11 for uniform field data. Figures 10 and 11 should not be used for pulsed data unless the pressure times pulse length is great enough so that the breakdown voltage is the same as the C.W. value. The data should not be extrapolated beyond the various limits bounding the contours. However, the lowest breakdown voltage will appear within these limits. A comparison of the breakdown curve for the sphere and uniform field data for a gap of 1 cm is given in Fig. 12. The pressure times pulse length at minimum voltage breakdown is low (4 mm-ksec) but the pressure times gap spacing is low enough (0.4 mm-cm) that according to Fig. 6 of Ref. 8 the breakdown voltage for the sphere should be about 10* higher than if it had been a much longer pulse.

R-339 18-12 Summary The object of the study reported herein was to investigate the degree of correlation existing between antenna electrical breakdown data obtained in still air in a vacuum chamber with that obtained from rocket firings which take an identical antenna transmitting 10-p4sec radiofrequency pulses to an altitude of over 590,000 ft. At the lower altitudes where the flight data showed decreased signal strengths, reasonable correlation between flight and laboratory data was possible provided that a radioactive alpha source was placed near the antenna in the vacuum chamber. Since such a source is not adjacent to the antenna during flight, several sources of energy known to be present in the upper atmosphere and which might enhance antenna radiofrequency breakdown are mentioned. At the upper altitudes, poor correlation between flight and laboratory data was observed. Electron diffusion to the bell jar walls is postulated to explain the discrepancy. The correlation between experimental and uniform field data obtained by use of the scaling laws of plasma physics was found satisfactory. Thus scaling laws can be used for engineering predictions of the altitude at which breakdown is most probable and for prediction of the breakdown voltage at and near that altitude. These results are not directly comparable with the recent analysis by MacDonald because he considered antennas with a gap-to-wavelength ratio much greater than used here.

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R-339 18-14 Trajectory Using Telemetered Acceleration EstimatedJ _ Vacuum Trajectory —-- --- Trajectory Using -- Trajectory Standard Densities 350- T a c o /I —— _ _ —' \ - Nose Cone / Nose Cone Nose Cone / Traectry %/ \-. —- Trajectory: 300 Trajectory: raDr T 350 - EM O^ —- ---- RADAR POINTS ESTIMATED --- lo/\ 250 |o 200- ------— ig.1- --— _ phere altitudeversus ----- 4 I -SPHERE EJECTED 0 i 200 I 100- ---— / —-4 — - -SPHERE EJECTED o! RADAR 00 50 100 150 200 250 300 350 400 Time From Take-off (Seconds) Fig. 2-Typical sphere altitude versus time

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R-339 18-17 r Q o w: o z I m w va: o c- ( 1 1 C C 0 \z w ~ m C~~-0 N- (0 11) II) N-u CM ~^- D 0 ^ ro c\I(SIINn A:IV~ lI8aV) IH913H 3S'lnd CALC _______________REVISED DATE C|HECK -— | ~ I - T TYPICAL PULSE ENVELOPES FIG. 5 APR APR _ ------- _ ------— 11 BOEING AIRPLANE COMPANY PAGE SEATTLE 24, WASHINGTON

R-339 -8-18 9080 _705 \ 0 > 0 3( 60-< 60- I; cn ul) 50 50 PPS 200 PPS 40 PRESSURE (mm OF Hg) 7.0 5.0 3.0 2.0 1.0 0.7 0.5 0.3 0.2 0.1 0.07 0.05 I30 I I I I 1oo0 120 140 160 80 20O 210 2D0 ALTITUDE IN THOUSANDS FEET 112 120 127 136 160 165 176 190 200 220 225 237 ALTITUDE (THOUSANDS OF FEET-TEMP. CORRECTED) __CAC _ _ REVIED DTE BREAKDOWN VOLTAGE VS ALTITUDE - FIG. 6 CHECK KAR —.__.___. ___ _..... AACTIVE SOURCE APR I J.-_ —-__ - -_ —__ t EBOEING AIRPLANE COMPANY PAG E _ _ 3 _ _ r SEATTLE 24, WASHINGTON _ _ P

R-339 18-19 90 80c) O 5 w O o 60-:E 40O PRESSURE (mm OF Hg) 7.0 5.0 3.0 2.0 1.0 0.7 0.5 0.3 0.2 0.1 0.07 005 30 —I I I I I I60 1210 140 16o 160 2o 0 220 240 ALTITUDE IN THOUSANDS FEET / I I I I i I i I I 112 120 127 136 160 165 176 190 200 220 225 237 ALTITUDE (THOUSANDS OF FEET-TEMP. CORRECTED) _CALC _CHECREVISED DATE BREAKDOWN VOLTAGE VS ALTITUDE - FIG. 7 CHECK 50 PPS WITH AND WITHOUT A APR ______RADIOACTIVE SOURCE APR _ __ _ A — -- --- W BOEING AIRPLANE COMPANY PAGE JJ___ ________ ____ ______________ ___ SEATTLE 24, WASHINGTON

R-339 (_ -3O/SNO081333) AISN30 N0813313 18 -20 a o O io O O 0 LO ro 0 I L 0 0 (9O ~ ~ ~ ~ ~ ~ ~ o W d- bUJ I I UJ:2 1 L__(0 o o: o o I z 20 )Oo I - AOM l.2 E T L 4 W S G O J I 3: -i U. w o (S.LLVIA) 83MOd N/MOGIV3i8 CALC REVISED DATE BREADOWN POWER AND AMBIENT FIG CHECK ELECTRON DENSITY VS ALTITUDE APR APR j BOEING AIRPLANE COMPANY PAGE SEATTLE 24, WASHINGTON

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o8 R-339 -iii, \ I. 1 1 1 1 C- 1 I18-23 o Ij,-,v; -!)\!tNJv<::^^^ -,! I I 0~~~~~~~ 0,0L m/v\. co Lb ~I0>' 0- ~ ~ (I-H IU -C) d ay3i an ans0,E r- -

i -339 1.8-24 160 - 140 ( \ UNIFORM FIELD DATA 140 \ 0 w > \ 0 8 z \ I PPS W I TH SOURCE 40 0 PRESSURE (m m OF Hg) 12 10020 127 136 160 165 176 190 200 220 225 237 ALTITUDE (THOUSANDS OF FEET-TEMP. CORRECTED) 80-:OL F 60IPPS WITH SOURCE 40PRESSURE (mrm OF Hg) 7.0 5.0 3.0 2.0 1.0 0.7 0.5 0.3 0.2 0.1 0.07 0.05 3 0 t-1 ---,,, - 1 - i -—,,, - Ii I I I 100 120 140 160 180 200 220 240 ALTITUDE IN THOUSANDS FEET 112 120 127 136 160 165 176 190 200 220 225 237 ALTITUDE (THOUSANDS OF FEET-TEMP. CORRECTED) CALO ______ __ REVISED DATE COMPARISON OF BREAKDOWN FIG.12 CHECK ______ 11 VOLTAGES FOR IPPS WITH SOURCE APR --- _ _ _ AND THAT FROM UNIFORM FIELD.,PR --------- — BOEING AIRPLANE COMPANY PAGE SEATTLE 24, WASHINGTON

R-339 18-25 References 1. Jones, L. M., and Bartman, F. L., "Satellite Drag and Air-Density Measurements," in: Van Allen, J. (ed.), Scientific Uses of Earth Satellites (Ann Arbor: University of Michigan Press, 1956), pp. 95-98. 2. Meteorological Rocket Soundings in the Arctic, IGY Bulletin Noo 14, pp, 4-5, August, 1958. 3. IGY Rocket Report No. 1, p. 47, July 30, 1958. 4. MacDonald, A. D., and Brown, S. C., "Limits for the Diffusion Theory of High Frequency Gas Discharge Breakdown," Phys. Rev., 76, 1629 (1949). 5. Brown, S. C., "Microwave Gas Discharge Breakdown," Appl. Scio Res. B, 5, 97 (1955). 6. Rose, D. J., and Brown, S. C., "Microwave Gas Discharge Breakdown, in Air, Nitrogen and Oxygen," J. Appl. Phys., 28, 561 (1957). 7o Worth, F., A Study of Voltage Breakdown in the Cavity Fed Slot Antenna, Lockheed Internal Report, MSD 2030. 8. Gould, L., and Roberts, L. W., "Breakdown of Air at Microwave Frequencies," J. Appl. Phys., 22, 1162 (1956). 9. MacDonald, A. D., "High Frequency Breakdown in Air at High Altitudes," Proc. IRE, 47, 436 (1959).

APPENDIX B NIKE-CAJUN FLIGHTS AM 6.02, 6.03, 6.05

AM 6.02 Fort Churchill 1-25-58 1312 CST Accelerometer Recycle Period, Seconds Upleg Downleg Minimmi Transit Upper Lower Upper Lower Transit Distance x 2 Limit Limit Limit Limit Time Feet.92000 1.01000.92000 1.01000.00800.0313 Threshold Acceleration Mean Acceleration, Ft/Sec2 Elapsed Time Upleg Downleg Upleg Downleg Upleg Downleg.40.40 1.60 1.30 13. 10. g 2 r cos sinos sin in Ft/Sec2 Fe8t 32.2270 20903520..51877000.85491000 -.60182000.79864000 M/A 2 Slugs/Ft 1.3400 Balloonsonde Data Altitude Pressre Temperature Density3 Feet Lb/Ft Deg Fahr Slug/Ft 2105. -4.0.00269146 1214. 2007. 5.7.00251239 3281. 1846. 15.4.00226381 6693. 1612. 8.6.00200586 7283. 1574. 6.4.00196817 7874. 1537. 11.5.00190064 9514. 1441. 7.1.00179834 10417. 1388. 7.0.00173385 13369. 1232. -5.8.00158161 14107. 1194. -6.9.00153701 16371. 1088. -14.8.00142489 18077. 1010. -23.3.00134935 18766. 981. -2303.00131032 22464. 855. -39.5.00115815 28149. 645. -62.5.00094350 29494. 605. -66.1.00089648 30511. 576. -64.3.00084932 34186. 484. -67.0.00071883 34973. 467. -61.1.00068370 35761. 449. -62.5.00065861 37040. 421. -59.5.00061406 41043. 350. -59.8.00051116 42847. 321. -61.1.00047004 43930. 307. -59.8.00044726 49540. 236. -58.4.00034258 574142.162. -64.9.00024035 60892. 137. -65.4.00020365 67224. 102. -67.4.00015196 78260. 60. -77.8.00009239 98295. 20. -100.3.00003385 101846. 18. -92.8.00002984

AM 6.02 Raw accelerometer data, upleg and downleg, time in seconds 45.77000 45.86286 46.77000 47.77000 47.87782 48.77000 48.88802 49.75000 50.74000 50.87881 51.72000 51.87011 52.69000 53.69000 53.86733 54.67000 54.86651 55.65000 55.85394 56.63000 56.85718 57.61000 58.59000 58.84649 59.57000 59.86091 60.55000 61.53000 61.87933 62.53000 62.92681 63.49000 63.92415 64.47000 64.92212 65.44000 65.95826 66.41000 66.91972 67.41000 67.98283 68.39000 69.00702 69.37000 70.11741 70.35000 71.09827 71.33000 72.06819 72.31000 73.06142 73.29000 74.04219 74.27000 75.02202 75.25000 76.00350 76.23000 76.98492 77.21000 77.96539 78.20000 78.95541.00000 299.8330 300.6163 300.8270 301.6111 301.8240 302.6041 302.8120 303.5893 303.8000 304.5808 304.7900 305.5731 305.7860 306.5706 306.7840 307.5664 307.7740 308.5552 308.7630 309.5389 309.7550 310.5286 310.7360 311.4681 311.7270 312.4068 312.7220 313.4709 313.7070 314.2862 314.6900 315.2511 315.6630 316.2554 316.6370 317.1099 317.6180 318.0673 318.6000 319.0657 319.5880 319.9872 320.5730 320.9442 321.5610 321.9195 322.5400 322.8422 323.5300 323.8229 324.5200 324.7942 325.5000 325.7364 326.4800 326.7050 327.4600 327.6716 328.4400 328.6268 329.4100 330.3900 330.5559 331.3700 331.5182 332.3000 332.4418 333.3300 333.4592 334.3100 334.4283 335~3000 335.4107 336.2700 336.3707 337.2500 337.3430 338.2200 338.3063 339.2000 339.2790 340.1800 340.2509 341.1600 341.2239 342.1600 342.2181 343.1500 343.2027 344.1400 344.1890 345.1300 345.1734 346.1300 346.1691 347.1200 347.1549 348.0500 348.0812 349.0900 349.1178 350.0700 350.0948 351.0700 351.0924 352.0600 352.0800 353.0500 353.0681 354.0400 354.0562 355.0300 355.0595 356.0300 356.0436 357.0200 357.0326 358.0200 358.0317 359.0100 360.0000 360.0212 360.9800 361.0230 361.9700 361.9808 362.9400 362.9508 363.9200 363.9310 364.9000 364.9281 365.8800 365.8915 366.8500 366.8621 367.8200 367.8325 368.8100 368.8358 369.7800 369.7935 370.7600 370.7744 371.7400 371-7552 372.7300 372.7460 373.7200 373.7368 374.6900 374.7078 375.6800 375.7596 376.6700 376.6890 377.6600 377.6817 378.6400 378.6629 379.6300 379.6537 380.6200 380.6435 381.6100 381.6329 382.5900 382.6143 383.5800 383.6056 384.5600 384.5859 385.5300 385.5557 386.5100 386.5358 387.4900 387.5149 388.4700 388.4958 389.4500 389.4751 390.4300 390.4569 391.4000 391.4269 392.3800 392.4068 393.3600 393.3861 394.3400 394.3671 395.3200 395.3467 396.3100 396.3378 397.2900 397.3172 398.2800 398.3057 399.2600 399.2865 400.2400 400.2668.00000.00000.00000.00000

2 AM 6.02 Acceleration ft/sec vs time, upleg and downleg 45.81643 3.63295 300.2247.05106 351.0812 62.26898 47.82391 2.69471 301.2191.05095 352.0700 78.00676 48.82901 2.24903 302.2140.05149 353.0591 95.52225 50.80941 1.62581 303.2006.05185 354.0481 119.37855 51.79506 1.59026 304.1904.05139 355.0447 35.99690 53.77867.99619 305.1816.05108 356.0568 170.38515 54.76826.81122 306.1783.05089 357.0263 198.91299 55.75197.75320 307.1752.05117 358.0259 228.07389 56.74359.60698 308.1646.05133 360.0106 69.83772 58.71825.47618 309.1510.05203 361.0015 16.91888 59.71546.37017 310.1418.05254 361.9754 270.6056 61.70467.25671 311.1020.05845 362.9454 266.1053 62.72841.19895 312.0669.06779 363.9255 258.4615 63.70708.16620 313.0964.05586 364.9140 39.72966 64.69606.15325 313.9966.09338 365.8858 237.28984 65.69913.11663 314.9705.09951 366.8561 213.28203 66.66486.12057 315.9592.08926 367.8263 200.49439 67.69642.09547 316.8735.14008 368.8229 47.13599 68.69851.08228 317.8426.15521 369.7868 170.88963 69.74371.05608 318.8329.14443 370.7672 151.08179 70.72414.05595 319.7876.19658 371.7476 135.95225 71.69910.05749 320.7586.22733 372.7380 121.92052 72.68571.05548 321.7403.24369 373.7284 110.46529 73.66610.05537 322.6911.34291 374.6989 98.53980 74.64601.05539 323.6764.36520 375.7198 4.95162 75.62675.05517 324.6571.41668 376.6795 86.41996 76.60746.05497 325.6182.56041 377.6708 66.83723 77.58770.05490 326.5925.61880 378.6515 59.58425 78.57771.05490 327.5658.69946 379.6419 55.67851 328.5334.89785 380.6318 56.48401 330.4729 1.13876 381.6215 59.63384 331.4441 1.42652 382.6022 52.92415 332.3709 1.55841 383.5928 47.76287 333.3946 1.87782 384.5730 46.59326 334.3691 2.23996 385.5429 47.28285 335.3553 2.55682 386.5229 46.91700 336.3204 3.08740 387.5024 50.64775 337.2965 3.62202 388.4829 47.06288 338.2631 4.20720 389.4626 49.56610 339.2395 5.01816 390.4434 43.35838 340.2155 6.23020 391.4135 43.13161 341.1919 7.67681 3923.934 43.61795 342.1891 9.27082 393.3731 45.95208 343.1763 11.29253 394.3536 42.62633 344.1645 13.05285 395.3333 44.07469 345.1517 16.62428 396.3239 40.56570 346.1496 20.46005 397.3036 42.34284 347.1374 25.79432 398.2929 47.43031 348.0656 32.24318 399.2732 44.60935 349.1039 40.53516 400.2534 43.64900 350.0824 51.10130 3550' 5600' Time in seconds (xlO) 3610' of rejected data points 3649' 3688' 3757"

AM 6.02 45.82 325.62 10. 10. - -- Points used in peak time calculation Time aD ft/sec2 Vert.Vel. Horiz.Vel. Alt. C Density Pressure Temp 191.649lugs/cu ft lbs/sq ft OF x 10.649. 500 494902. x 103 191.649.000. 500. 516103. 191.649.000 500. 515108. 191.649.000. 500. 515101. 311.102.058 -3684. 515. 295870. 1.424.00000795 312.067.068 -3714. 515. 292301. 1.380.00000937 5.8 -99.8 313.097.056 -3746. 516. 288462. 1.431.00000732 6.8 80.4 313.997.093 -3774. 516. 285078. 1.282.00001345 7.8 -119.6 314.971.099 -3804. 516. 281388. 1.261.00001435 9.4 -75.6 315.959.089 -3835. 516. 277612. 1.289.00001240 11.0 59.2 316.874.140 -3864. 516. 274093. 1.213.00002037 12.8 -93.3 317.843.155 -3894. 517. 270334. 1.202.00002243 15.3 -61.4 318.833.144 -3925. 517. 266463. 1.208.00002045 17.9 51.5 319.788.197 -3955. 517. 262702. 1.178.00002813 20.8 -29.2 320.759.227 -3985. 517. 258848. 1.163.00003245 24.4 -20.8 321.740.244 -4015. 517. 254922. 1.155.00003450 28.5 23.0 322.691.343 -4045. 518. 251090. 1.122.00004927 33.5 -62.7 323.676.365 -4076. 518. 247090. 1.117.00005193 39.9 -11.6 324.657.417 -4106. 518. 243079. 1.108.00005888 46.9 4.6 325.618.560 -4136. 518. 239119. 1.083.00007987 55.5 -54.8 326.593.619 -4166. 518. 235075. 1.076.00008745 66.1 -18.9 327.566.699 -4196. 519. 231006. 1.068.00009823 78.0 3.2 328.533.898 -4225. 519. 226933. 1.047.00012681 92.4 -35.1 330.473 1.139 -4284. 519. 218681. 1.031.00015899 129.4 14.7 331.444 1.426 -4314. 519. 214506. 1.012.00020008 153.0 -14.2 332.371 1.558 -4342. 519. 210496. 1.007.00021700 179.4 21.9 333.395 1.878 -4372. 519. 206036..992.00026168 213.0 14.5 334.369 2.240 -4401. 519. 201762..979.00031250 251.7 9.5 335.355 2.557 -4430. 519. 197408..969.00035563 297.6 27.9 336.320 3.087 -4457. 519. 193120..963.00042670 350.5 18.9 337.297 3.622 -4485. 519. 188756..961.00049589 414.0 26.8 338.263 4.207 -4512. 519. 184409. o.958.00057074 487.3 37.8 339.240 5.018 -4538. 519. 179991..955.00067508 574.2 35.9 340.216 6.230 -4563. 518. 175550..951.00083228 679.9 16.3 341.192 7.677 -4588. 518. 171083..947.00101966 810.5 3.5 342.189 9.271 -4611. 517. 166497..943.00122447 973.2 3.4 343.176 11.292 -4632. 516. 161935..939.00148475 1168.6 -1.1 344.165 13.053 -4651. 515. 157349..936.00170788 1400.6 18.1 345.152 16.624 -4668. 514. 152750..930.00217265 1682.5 8.5 346.150 20.460 -4681. 512. 148086..925.00267373 2040.2 -15.2 347.137 25.794 -4690. 510. 143458..920.00337908 2483.3 -31.6 348.066 32.243 -4692. 507. 139104..914.00424397 3008.5 -46.7 349.104 40.535 -4688. 504. 134235..909.00537863 3750,1 -53.5 350.082 51.101 -4674. 499. 129655..906.00684169 4636.2 -64.9 351.081 62.269 -4650. 493. 124999..906.00842643 5763.6 -61.2 352.070 78.007 -4612. 486. 120420..906.01073020 7153.4 -71.3 353.059 95.522 -4558. 478. 115886 e. 906.01345402 8892.9 -74.6 354.048 119.379 -4484. 467. 111415..906.01737796 11077.9 -88.4 356.037 170.385 -4261. 438. 102720..909.02739075 17178.7 -94.4 357.026 198.913 -4110. 419. 98579..913.03420754 21232.3 -98.1 358.026 228.074 -59530. 398. 94561..918 o.04266738 26143.1 -102.8 361.975 270.605 -3076. 301. 80728..946.08028461 52434.5 -79.2 362.945 266.105 -2848. 276. 77855..954.09132650 60306.6 -75.0 365.926 258,461 -2623. 251. 75174..968.10308824 68631.9 -71.9 365.886 237.290 -2202. 206. 70446. 1.010.12875716 86099~2 -70.1 366.856 213,282 -2016. 186. 68400. 1.010.13819482 94836.7 -59.9 367.826 200.494 -1847. 167. 66527. 1.010.15479974 103613.1 -69.8 369.787 170.890 -1547. 135. 63201. 1.010.18819224 121818.7 -82.6 570.767 151.082 -1421. 122. 61747. 1.010.19723407 130795.2 -73.4 371.748 135.952 -1312. 110. 60408. 1.010.20822276 139491.4 -69.4

AM 6.03 Fort Churchill 1-29-58 1306 CST Accelerometer Recycle Period, Seconds Upleg Downleg Minimum Transit Upper Lower Upper Lower Transit Distance x 2 Limit Limit Limit Limit Time Feet 1.09000 1.21000 1.09000 1.21000.00800.0313 Threshold Acceleration Mean Acceleration, Ft/Sec2 Elapsed Time Upleg Downleg Upleg Downleg Upleg Downleg.10.20.60.60 14. 10. go ro cos b sin p cosG sin Ft/Sec2 Feet 32.2270 20903520..51877000.85491000 -.60182000.79864000 M/A Slugs/Ft2 1.3360 Balloonsonde Data Altitude Pressure Temperature Density Feet Lb/Ft Deg Fahr Slug/Ft3 2121. 1.9.00267792 1066. 2034. -4.3.00260171 1936. 1963. 6.4.00245369 4298. 1783. 5.7.00223265 5905 1668. 1.6.00210761 6266. 1649. 5.0.00206853 8005. 1537. 5.0.00192714 10417. 1390. -4.0.00177829 11729. 1319. -7.9.00170162 14961. 1148. -21.1.00152580 21325. 866. -48.4.00122734 22195. 835. -48.1.00118246 23589. 785. -49.0.00111394 25623. 710. -55.9.00102435 30381. 572. -58.9.00083180 36089. 438. -53.2.00062848 40682. 355. -52.9.00050832 43143. 317. -54.8.00045672 45275. 288. -54.4.00041429 53182. 196. -61.6.00028730 55413. 179. -59.7.00026155 68405. 96. -69.7.00014351 89239. 35. -97.6.00005712 98780. 20. -85.9.00003255

AM 6.03 Raw accelerometer data, upleg and downleg, time in seconds 51.05000 52.22000 53.39000 53.54193 54.56000 55.73000 56.89000 57.09534 58.06000 59.23000 59.50903 60.40000 61.57000 62.73000 63.11052 63.90000 65.07000 65.54575 66.24000 66.73547 67.40000 68.56000 69.07136 69.73000 70.41241 70.90000 71.64093 72.06000 72.69300 73.22000 73.91000 74.39000 75.28078 75.56000 76.39237 76.72000 77.61167 77.88000 78.77689 79.05000 79.94047 80.21000 81.10746 81.37000 82.26349 82.54000 83.43527 83.700CO 8452065 84.86000ooo 85.75528 86.01000 86.74982 87.18000 87.79655 88.3300c 89.04384 89.49000 90.08779 90.65000 91.54829 91.81000 92.70724 92.97000 93.86311.00000.00000.00000.00000.00000.00000.00000 301.7700 302.6584 302.8800 303.7633 304.0000 304.8796 305.1100 305.5881 306.2300 306.5817 307.3400 308.2236 308.4600 309.3451 309.5800 310.4688 310.6900 311.5780 311.8100 312.6948 312.9200 313.8039 314.0400 314.9245 315.1600 316.0221 316.2700 317.1544 317.3800 317.9239 318.5000 319.3852 319.6200 320.5069 320.7300 321.6160 321.8500 322.7330 322.9600 323.8467 324.0700 324.8015 325.1900 325.7800 326.3000 327.1823 327.4200 328.0747 328.5400 329.3436 329.6500 330.3185 330.7700 331.3553 331.8800 332.3579 332.9900 333.4646 334.1100 334.5654 335.2200 335.9149 336.3300 336.7191 337.4500 337.8062 338.5600 338.8473 339.6800 339.9463 340.7800 341.0321 341.9000 342.1375 343.0100 343.2246 344.1300 344.3214 345.2400 345.4067 346.3500 346.4977 347.4700 348.5800 349.6900 349.7972 350.8000 350.8987 351.9100 352.0006 353.0200 353.1019 354.1400 354.2130 355.2500 355.3150 356.3600 356.4189 357.4700 357.5235 358.5800 358.6288 359.7000 359.7453 360.8100 360.8511 361.9200 361.9576 363.0300 363.0642 364.1300 364.1610 365.2500 365.2780 366.3600 366.3858 367.4600 367.4834 368.5700 368.5907 369.6900 369.7166 370.7900 370.8060 371.9000 371.9143 373.0100 373.0227 374.1300 374.1420 375.2400 375.2510 376.3500 376.3603 377.4600 378.5800 378.5903 379.6900 379.7102 380.8000 380.8108 381.9200 381.9311 383.0300 383.0417 384.1400 384.1676 385.2600 385.2731 386.3700 386.3837 387.4700 387.4846 388.5800 388.5957 389.7000 389.7165 390.8100 390.8275 391.9200 391.9385 393.0300 393.0495 394.1400 394.1616 395.2400 395.2630 396.3500 396.3738 397.4600 397.4845 398.5600 398.5847 399.6700 399.6952 400.7800 400.8059 401.8800 401.9056 402.9900 403.0163 404.0900 404.1167 405.2000 405.2261 406.3100 406.3364 407.4100 407.4365 408.5100 408.5711 409.6300

AM 6.03 Acceleration ft/sec vs time, upleg and downleg 53.46597 1.35713 302.2142.03970 356.3895 9.01756 56.99267.74295 303.3217.04015 357.4967 10.95703 59.36952.40236 304.4398.04049 358.6044 13.17626 62.92026.21635 305.3491.13704 359.7226 15.30645 65.30788.13841 306.4059.25321 360.8306 18.52726 66.48774.12761 307.7818.04013 361.9388 22.20597 68.81568.11980 308.9026.03999 363.0471 26.78330 70.07121.06727 310.0244.03966 364.1455 32.61942 71.27047.05706 311.1340.03973 365.2640 39.93013 72.37650.07818 312.2524.04001 366.3729 47.13599 73.56500.06580 313.3620.04010 367.4717 57.50877 74.83539.03948 314.4823.04005 368.5804 72.82991 7597619.04522 315.5911.04215 369.703 44.17571 77.16584.03940 316.7122.04005 370.7980 122.67845 78.32845.03894 317.6520.10589 371.9071 153.40977 79.49524.03951 318.9426.03998 373.0164 192.71299 80.65873.03889 320.0634.03983 374.1360 217.92141 81.81675.03924 321.1730,03990 375.2455 261.3062 82.98764.03909 322.2915.04018 376.3552 293.0149 84.11033.04652 323.4033.03985 378.5851 297.0565 85.30764.03909 324.4358.05854 379.7001 76.47081 86.37991.05724 325.4850.08998 380.8054 266.6204 87.48828.08241 326.7411.04025 381.9256 252.4346 88.68692.06148 327.7473.07309 383.0358 230.43056 89.78890.08766 328.9418.04851 384.1538 41.21374 91.09915.03882 329.9842.07010 385.2665 183.67431 92.25862.03892 331.0627.09144 386.3768 167.89611 93.41656.03928 332.1190.13716 387.4773 147.36944 333.2273.13909 388.5878 127.42437 334.3377.15108 389.7083 114.92491 335.5675.06487 390.8187 102.76076 336.5246.20691 391.9293 91.43284 337.6281.24691 393.0397 82.81397 338.7036.37957 394.1508 67.33466 339.8131.44191 395.2515 59.48039 340.9060.49302 396.3619 55.44648 342.0188.55532 397.4723 52.06345 343.1173.68028 398.5724 51.35025 344.2257.85495 399.6826 49.33000 345.3233 1.12770 400.7930 46.73739 346.4239 1.43598 401.8928 47.98776 349.7436 2.72394 403.0032 45.32419 350.8493 3.21834 404.1033 43.97713 351.9553 3.81470 405.2131 45.91851 353.o609 4.67377 406.3232 44.84783 354.1765 5.88013 407.4232 44.67680 355.2825 7.42595 408.5405 8.40516 3254' 3267' 3289' Time in seconds (xlO) 3352' of rejected data points 3696' 3796' 3841"'

AM 6.03 53.47 356.52 6. 10. --- Points used in peak time cnlculation Time aD ft/sec2 Vert.Vel. Horiz.Vel. Alt. C Density Pressure Temp. 199.861.000. 500. 539251.slugs/cu ft bs/sq ft x 103 K 103 199.861.000 500. 557685. 199.861.000 500. 556961. 199.861.000. 500. 556974. 322.292.040 -3762. 516. 327546. 1.522.oooo00000489 323.403.040 -3796. 516. 323344. 1.521.00000477 3.5 -24.3 324.436.058 -3829. 516. 319409. 1.410.00000743 4.3 -122.7 327.747.073 -3932. 517. 306561. 1.356.00000929 7.6 19.4 329.984.070 -4001. 517. 297689. 1.341.00000858 10.1 227.8 331.063.091 -4035. 518. 293356. 1.262.00001170 11.5 112.3 332.119.137 -4068. 518. 289077. 1.208.00001804 13.4 -25.4 333.227.139 -4103. 518. 284550. 1.205.00001803 16.5 74.1 334.338.151 -4137. 519. 279976. 1.196.00001941 19.2 116.8 336.525.207 -4205. 519. 270855. 1.164.00002645 25.7 106.8 337.628.247 -4240. 519. 266196. 1.146.00005155 29.9 93.4 338.704.579 -4273. 520. 261618. 1.104.00004959 35.7 -40.3 339.813.442 -4307. 520. 256859. 1.088.00005764 43.7 -18.0 340.906.493 -4341. 520. 252134. 1.077.00006401 52.7 20.3 542.019.555 -4375. 520. 247285. 1.066.00007170 63.0 52.9 343.117.680 -4409. 520. 242460. 1.051.00008776 75.1 39.2 344.226.855 -4443. 521. 237554. 1.033.00011048 90.4 17.0 345.323 1.128 -4477. 521. 232660. 1.011.00014676 110.1 -22.7 346.424 1.436 -4510. 521. 227715..992.00018771 136.0 -37.5 349.744 2.724 -4608. 521. 212583..961.00035241 260.9 -28.4 350.849 3.218 -4639. 521. 207471..958.00041190 322.4 -3.6 351.955 3.815 -4670. 521. 202324..956.00048318 395.1 16.7 353.061 4.674 -4700. 521. 197144..952.00058655 482.4 19.5 354.177 5.880 -4730. 520. 191885..948.00073192 591.7 11.3 355.283 7.426 -4757. 520. 186639..944.00091761 728.0 2.5 356.390 9.017 -4783. 519. 181359..941.00110610 896.7 12.6 357.497 10.957 -4807. 518. 176050..938.00133530 1101.5 20.9 358.605 13.176 -4829. 517. 170714..934.00159807 1348.9 32.1 359.723 15.306 -4849. 516. 165303..931.00184813 1644.0 58.6 360.831 18.527 -4865. 514. 159923..927.00223196 1991.3 60.1 361.939 22.206 -4878. 512. 154525..923.00267301 2410.4 65.7 363.047 26.783 -4886. 510. 149115..918.00323024 2916.1 66.3 364.146 32.619 -4888. 507. 143748..913.00395186 3526.6 60.2 365.264 39.930 -4883. 505. 138284..908.00487443 4290.5 53.1 366.373 47.136 -4870. 498. 132876..906.00580070 5206.4 63.2 367.472 57.509 -4848. 493. 127537.906.00714343 6302.3 54.3 368.580 72.830 -4811. 486. 122183..906.00918617 7687.1 27.8 370.798 122.678 -4666. 465. 111675..906.01645602 11863.1 -39.7 371.907 153.410 -4549. 450. 106565..906.02165408 14949.4 -57.5 373.016 192.713 -4394. 431. 101606..906.02916847 18941.0 -81.4 374.136 217.921 -4200. 409. 96795..909.03595489 23923.2 -72.1 375.245 261.306 -3971. 384. 92263..916.04788107 29950.1 95.3 376.355 293.015 -3700. 355. 88007..925.06127617 37334.5 -104.8 378.585 297.056 -3117. 293. 80407..945.08578713 55033.4 -86.o 380.806 266.620 -2564. 235. 74101..974.11032657 74710.4 -65.2 381.926 252.434 -2311. 209. 71371. 1.000.12530007 84989.8 -64.6 383.036 230.430 -2079. 185. 68935. 1.010.13995839 95323.9.62.9 385.267 183.674 -1690. 145. 64751. 1.010.16888414 116049.2 -59.4 386.377 167.896 -1532. 128. 62945. 1.O10.18815238 126264.4 -68.8 387.477 147.369 -1394. 114. 61534. 1.010.19945666 136252.2 -61.8 388.588 127.424 -1277. 102. 59851. 1.010.20545136 145869.7 -46.1

AM 6.05 Fort Churchill 3-4-58 1330 CST Accelerometer Recycle Period, Seconds Upleg Downleg Minimum Transit Upper Lower Upper Lower Transit Distance x 2 Limit Limit Limit Limit time Feet 1.02000 1.11000 1.02000 1.11000.00800.0313 Threshold Acceleration Mean Acceleration, Ft/Sec2 Elapsed Time Upleg Downleg Upleg Downleg Upleg Downleg.20.20 2.70 1.20 14. 13. g Fro cos sin cos sin Ft/Sec2 Feet os n 32.2270 20903520..51877000.85491000 -.44932000.89337000 M/A2 Slugs/Ft 1.3290 Balloonsonde Data Altitude Pressure Temperature Density Feet Lb/Ft2 Deg Fahr Slug/Ft3 2128. -19.2.00281420 394. 2090. -21.9.00278153 853. 2055. -21.9.00273429 1280. 2015. -16.9.00265098 2231. 1938. -13.4.00252981 4068. 1791. -16.6.00235608 4495. 1762. -13.4.00230082 5971. 1654. -12.5.00215472 8186. 1507. -17.4.00198585 8989. 1457. -15.0.00190974 10236. 1382. -16.0.00181492 13878. 1182. -24.4.00158187 20407. 885. -50.1.00125946 21699. 835. -52.3.00119447 24869. 720. -60.4.00105112 28740. 601. -60.4.00087746 36975. 413. -52.3.00059126 51506. 208. -58.9.00030358 56693. 162. -62.2.00023872 58268. 152. -64.3.00022464 63386. 119. -62.5.00017461 78576. 58. -68.8.00008715 92815. 29. -65.8.00004324 96139. 25. -61.0.00003661

AM 6.05 Raw accelerometer data, upleg and downleg, time in seconds 45.88000 45.95086 46.98000 47.05931 48.07000 48.15885 49.16000 49.25786 50.24000 50.34962 51.32000 51.44318 52.40000 52.46592 53.48000 53.63752 54.57000 54.74340 55.66000 56.74000 56.95245 57.82000 58.91000 59.18196 59-99000 61.07000 61.37614 62o15000 63.24000 63.59721 64.32000 65.41000 65.86722 66.49000 66.87460 67.57000 68.19445 68.66000 69.08394 69.74000 70.57207 70.82000 71.36152 71.90000 72.69661 72.99000 73.69966 74.06000 74.59400 75.14000 75.75628 76.22000 76.83205 77.30000 77.80142 78.38000 79.02905 79.45000 79.91135 80.53000 81.31215.00000.00000.00000 328.8300 329.6635 329.8800 330.7131 330.9300 331.7189 331.9800 332.6463 333.0300 333.5504 334.0800 334.7308 335.1300 335.7609 336.1800 336.6152 337.2400 338.0689 338.2800 338.7077 339.3300 339.9770 340.3800 341.0503 341.4300 342.2417 342.4800 342.9808 343.5300 344.1544 344.5800 345.0437 345.6300 346.1840 346.6800 347.3800 347.7300 348.3293 348.7800 349.4655 349.8300 350.2619 350.8700 351.3390 351.9200 352.3084 352.9700 353.3716 354.0200 354.3767 355.0700 355.4422 356.1200 357.1600 357.4563 358.2200 359.2600 359.4924 360.3100 360.5300 361.3600 361.5744 362.4000 362.7639 363.4500 363.6139 364.5000 364.6444 365.5500 365.6810 366.6000 366.7160 367.6400 367.7442 368.6900 368.8537 369.7400 370.7900 370.8679 371.8400 371.9102 372.8900 372.9536 373.9400 373.9969 374.9800 375.0317 376.0300 376.0767 377.0800 377.1219 378.1200 378.1578 379.1700 379.2040 380.2200 380.2504 381.2700 381.2973 382 3200 382.3444 383.3600 383.3811 384.4100 384.4294 385.4600 385.4772 386.5000 386.5154 387.5500 387.5642 388.6000 388.6131 389.6500 389.6716 390.6900 390.7012 391.7400 391.7506 392.7900 392.8317 393.8400 393.8502 394.8900 394.9002 395.9500 395.9603 396.9900 397.0006 398.0400 399.0900 399.1014 400.1400 400.1521 401.1800 401.1925 402.2300 402.2433 403.2800 403.3025 404.3300 404.3442 405.3800 405.4292 406.4400 406.4568 407.4700 407.4880 408.5200 408.5386 409.5600 409.5805 410.6000 410.6219 411.6500 411.6728 412.6900 412.7132 413.7300 413.7533 414.7800 414.8049 415.8300 415.8546 416.8700 416.8941 417.9100 417.9360 418.9600 418.9865 420.0000 420.0265 421.0400 421.0663 422.0900 422.1166 423.1300 423.1554 424.1800 424.2060 425.2200 425.2463 426.2700 426.2972 427.3100 427.3359 428.3500 428.3771 429.3900 429.4173 430.4300 430.4574 -395.3333

2 AM 6.05 Acceleration ft/sec vs time, upleg and downleg 45.91543 6.23892 329.2468.04510 381,2836 42.18878 47.01966 4.98035 330.2965.0514 582.3322 5283707 48.11443 3.96819 331.3245.05033 383.3705 70.63062 49.20893 3.27117 332.3131.07056 384.4197 82.89541 50.29481 2.60697 333.2902.11570 385.4686 106.26017 51.38159 2.06459 334.4054.07397 386.5077 131.58465 52.43296 7.20899 3355.455.07870 387.5571 155.81302 53.55876 1.26252 336.3976.16537 388.6065 184.23872 54.65670 1.04187 337.6545.04559 389.6608 67.08522 56.84623.69406 338.4938.17128 390.6956 247.95690 59.04598.42355 339.6535.07484 391.7453 278.2972 61.22307.33424 340.7151.06973 92.8108 18.04120 63,41861.24550 341.8358.04755 393.8451 299.3873 65.63861.14986 342.7304.12490 394.8951 304.0752 66.68230.21178 343.8422.08036 395.9552 296.4501 67.88223.08034 344.8118.14571 396.9953 280.4104 68.87197.17431 345.9070.10207 399.0957 240.23184 70.15604.04525 347.0300.06394 00.1460 216.12991 71.09076.10683 348.0297.08721 401.1862 200.83140 72.29831.04937 349.1228.06666 402.2366 177.37610 73.34483.06221 350.0460.16792 403.2913 61,93656 74.32700.10986 351.1045.14245 404.3371 155.37377 75.44814.08248 352.1142.20767 405.4046 12.92575 76.52603.08362 353.1708.19425 406.4484 111.39695 77.55071.12459 354.1983.24627 407.4790 97.12171 78.70453.07436 355.2561.22618 408.5293 90.55366 79.68068.14718 357.3081.35692 409.5702 74.76314 80.92108.05121 359.3762.58002 410.6110 65.13920 360.4200.64748 411.6614 60.10310 361.4672.68149 412.7016 58.30182 524" 362.5820.23659 413.7417 57.70669 363.5319 1.16644 414.7924 50.69045 364.5722 1.50339 415.8423 51.76523 365.6155 1.82462 416.8821 53.84888 366.6580 2.32846 417.9230 46.16438 367.6921 2.88462 418.9733 44.57719 368.7718 1.16928 420.0132 44.77998 370.8290 5.15689 421.0532 45.18643 371.8751 6.36589 422.1033 44.37588 372.9218 7.75926 423.1427 48.59543 373.9685 9.67931 424.1930 46.37795 375.0059 11.72495 425.2332 45.22241 376.0533 14.39488 426.2836 42.34284 377.1009 17.88697 427.3230 46.69961 378.1389 21.89024 428.3636 42.56336 379.1870 27.17897 429.4036 42.03270 380.2352 33.91979 430.4437 41.66514 3625' 3687' Time in seconds (xlO) 3896' of rejected data points 3928' 4032' 4054t

AM 6.05 45.91 355.26 10. 10. - Points used in peak time calculation Time aD ft/sec2 Vert.Vel. Horiz.Vel. Alt. C Density Pressure Temp. D D slugs/cu ft lbs/su ft OF 208.756.00. 500. 587283. slugs/cu ft Ibs/sq ft F x 103 x 103 208.756.000. 500. 594264. 208.756.000. 500. 594290. 348.030.087 -4273. 520. 298153. 1.251.00001000 349.123.067 -4307. 520. 293465. 1.324.00000711 7.3 137.2 350.046.168 -4336. 520. 289476. 1.180.00001984 8.8 -200.3 351.104.142 -4369. 521. 284870. 1.194.00001638 11.4 -52.6 352.114.208 -4400. 521. 280443. 1.157.00002430 14.2 -118.4 353.171.194 -4433. 521. 275777. 1.162.00002230 17.6 1.4 354.198.246 -4465. 521. 271206. 1.139.00002846 21.2 -24.3 355.256.226 -4498. 522. 266467. 1.145.00002560 25.3 115.8 357.308.357 -4561. 522. 257173. 1.100.oooo00004093 34.8 36.2 359.376.580 -4625. 523. 247674. 1.053.00006761 50.7 -22.6 360.420.647 -4658. 523. 242830. 1.046.00007488 61.5 19.4 361.467.681 -4690. 523. 237936. 1.046.00007778 73.3 89.6 363.532 1.166 -4753. 524. 228189. 1.003.00013520 105.2 -6.2 364.572 1.503 -4784. 524. 223229..983.00017552 129.4 -30.2 365.616 1.825 -4815. 524. 218222..969.00021342 160.O -22.9 366.658 2.328 -4846. 524. 213186..962.00027079 198.3 -33.0 367.692 2.885 -4876. 524. 208160..959.00033263 246.0 -28.7 370.829 5.157 -4962. 524. 192731..949.00058001 463.1 5.5 371.875 6.366 -4989. 523. 187527..946.00071094 569.o 6.6 372.922 7.759 -5015. 523. 182292..943.00086071 698.9 13.4 373.969 9.679 -5039. 522. 177030..939.00106781 859.0 9.0 375.006 11.725 -5061. 521. 171792..935.00128772 1054.0 17.2 376.053 14.395 -5080. 520. 166481..931.00157637 1294.3 18.7 377.101 17.887 -5097. 519. 161151..926.00195614 1591.9 14.4 378.139 21.890 -5109. 517. 155855..922.00239367 1956.3 16.5 379.187 27.179 -5117. 515. 150497..917.00298044 2411.7 11.7 380.235 33.920 -5118. 512. 145134..911.00374014 2982.0 4.8 381.284 42.189 -5111. 509. 139772..906.00469144 3697.5 -.5 382.332 52.837 -5095. 504. 134421..906.00591419 4596.0 -7.0 383.371 70.631 -5064. 498. 129147..906.00800331 5755.2 -40.8 384.420 82.895 -5018. 490. 123859..906.00957031 7230.8 -19.5 385.469 106.260 -4952. 481. 118631..906.01259539 9065.1 -40.4 386.508 131.585 -4862. 470. 113532..906.1618156 11391.1 -49.6 387.557 155.813 -4745. 455. 108492..906.02011756 14296.8 -45.7 388.607 184.239 -4601. 439. 103588..906.02530533 17834.4 -49.1 390.696 247.957 -4218. 397. 94377..908.04043283 27327.1 -66.0 391.745 278.297 -3977. 371. 90076..916.05065621 33557.8 -73.8 393.845 299.387 -3440. 316. 82290..933.07150974 48610.3 -63.7 394.895 304.075 -3158. 287. 78827..943.08526302 57269.6 -68.4 395.955 296.450 -2875. 258. 75630..953.09924970 66686.9 -68.3 396.995 280.410 -2609. 232. 72778..969.11208361 76316.9 -63 399.096 240.232 -2132. 184. 67800. 1.010.13816167 96182.9 -54.1 400.146 216.130 -1926. 164. 65670. 1.010.15223278 106081.6 -53.8 401.186 200.831 -1744. 146. 63762. 1.010.17272870 115999.5 -68.5 402.237 177.376 -1579. 129. 62017. 1.010.18601999 126020.0 -65.0 404.337 155.374 -1298. 101. 58996. 1.010.24133294 146587.0 -105.9

UNIVERSITY OF MICHIGAN 3 9015 03483 3528