2900-250-T Report of Project MICHIGAN DYNAMIC BALANCING OF SCANNER DRUM AND GYROSCOPIC EFFECT DURING MANEUVERS OF AIRCRAFT.,.. W. L.,BROWN l C. T.ANG February 1961 Infrared Laboratory Ettte i Scince aW 7eSo THE UNIVERSITY OF MICHIGAN Ann Arbor, Michigan

11) - - -,, I I 14 , k ( " i NOTICES Sponsorship. The work reported herein was conducted by the Institute of Science and Technology for the U. S. Army Signal Corps under Project MICHIGAN, Contract DA-36-039 SC-78801. Contracts and grants to The University of Michigan for the support of sponsored research by the Insttute of Science and Technology are administered through the Office of the Vice-President for Research. Distribution. Initial distribution is indicated at the end of this document. Distribution control of Project MICHIGAN documents has been delegated by the U. S. Army Signal Corps to the office named below. Please address correspondence concerning distribution of reports to: U. S. Army Liaison Group Project MICHIGAN The University of Michigan P. 0. Box 618 Ann Arbor, Michigan ASTIA Availability. Qualified requesters may obtain copies of this document from: Armed Services Technical Information Agency Arlington Hall Station Arlington 12, Virginia Final Disposition. After this document has served its purpose, it may be destroyed. Please do not return it to the Institute of Science and Technology. ii

Institute of Science and Technology The University of Michigan PREFACE Project MICHIGAN is a continuing research and development program for advancing the Army's long-range combat-surveillance and target-acquisition capabbilities. The program is carried out by a full-time Institute of Science and Technology staff of specialists in the fields of physics, engineering, mathematics, and psychology, by members of the teaching faculty, by graduate students, and by other research groups and laboratories of The University of Michigan. The emphasis of the Project is upon basic and applied research in radar, infrared, information processing and display, navigation and guidance for aerial platforms, and systems concepts. Particular attention is given to all-weather, longrange, high-resolution sensory and location techniques, and to evaluations of systems and equipments both through simulation and by means of laboratory and field tests. Project MICHIGAN was established at The University of Michigan in 1953. It is sponsored by the U. S. Army Combat Surveillance Agency of the U. S. Army Signal Corps. The Project constitutes a major portion of the diversified program of research conducted by the Institute of Science and Technology in order to make available to government and industry the resources of The University of Michigan and to broaden the educational opportunities for students in the scientific and engineering disciplines. Progress and results described in reports are continually reassessed by Project MICHIGAN. Comments and suggestions from readers are invited. Robert L. Hess Technical Director Project MICHIGAN iii

Institute of Science and Technology The University of Michigan CONTENTS Notices................................ ii Preface................................. iii List of Figures............................. vi Abstract....................... 1 1. Introduction.1......................... 1 2. Equations for the Dynamic Balancing of a Scanner Drum.......... 1 2.1. General Theory 1 2. 2. Application of Theory to Scanner Drum Assembly 4 3. Gyroscopic Effects on Scanner Drum during Maneuvers of the Aircraft 9 Distribution List........................ 13 V

Institute of Science and Technology The University of Michigan FIGURES 1. Forces Acting Upon a Scanner Drum................. 2 2. Body with Hollow Portion..................... 3 3. Scanner Drum Assembly..................... 4 4. Construction of Scanner Drum................... 5 5. Cylinder.......................... 5 6. 45~ Ring................6... 6 7. Ring (2)............................ 6 8. Aperture Opening........................ 7 9. Gyroscopic Effect during Turn of Aircraft.............. 9 vi

DYNAMIC BALANCING OF SCANNER DRUM AND GYROSCOPIC EFFECT DURING MANEUVERS OF AIRCRAFT ABSTRACT This report presents the equations for determining the dynamic balancing and gyroscopic effect of a rotating scanner drum assembly of the type used in the Project MICHIGAN wide-angle scanner. The parameters used in the numerical example are those of the wide-angle scanner, and the theoretical calculations of the dynamic balancing agree excellently with the actual mechanical dynamic balancing of the drum assembly. The calculations also indicate that gyroscopic forces in the drum are negligible even during maximum rate of turn and maximum rate of climb of the aircraft carrying the scanner. 1 INTRODUCTION This report presents the equations for calculating, from a purely analytical viewpoint, the physical changes needed to balance a rotating mechanism. The Project MICHIGAN wide-angle scanner drum assembly was used in the numerical examples. The results obtained from a mathematical analysis were compared with the results of conventional mechanical measurements and a close agreement was found, indicating that such an analysis could be useful in reducing the amount of trial-and-error work required for dynamic balancing. This report also discusses the gyroscopic effects on the balanced scanner during maneuvers of the transporting aircraft. It is shown that the gyroscopic forces which would be encountered in a rotating scanner during the most extreme maneuvers of conventional reconnaissance aircraft are negligible compared to the weight and centrifugal forces in the scanner. 2 EQUATIONS for the DYNAMIC BALANCING of a SCANNER DRUM 2.1. GENERAL THEORY Equilibrium,whether static or dynamic, depends on the forces acting upon the system in question. A system is in equilibrium when and EM= 0 1

Institute of Science and Technology T he University of M i ch i a If the x-axis is the axis of rotation (Figure 1), the system is in equilibrium when EF = F + F =0 2 F - JJV pc ydV - ffvpgdV + F + F = 0 FZ = JffV pc zdV + F + F =0 CxSVz zfV f fPz EM = fffpC 2zydV - f f yz dV + fffJpgzdV +F c+F f-F b-F e=0 y y z z 2 EM = fJfVpo zxdV - Fz a + F d = 0 and EMz = ffJJpw yxdV - fJJvpgxdV - F b - F e -Fa + F d xv x y y where 2 p pound-seconds p = density inch 4 -inch o = angular velocity (radians/second) 2 g = acceleration of gravity (inches/second ) F', F" = bearing forces (pounds) F ' F" y 2pwy dV y (a, b, c) (d, e, f) z I / ' F! p/ 2zdV F \ po zdV z FIGURE 1. FORCES ACTING UPON A SCANNER DRUM 2

Institute of Science and Technology The University of Michigan If the origin is located at the centroid, the system is in "static balance" and ffJVpgxdV = IJf pgydV = ffJfVJgzdV = 0 There are no x- or y-components of the bearing forces in the balanced drum, since "balance" implies that there is no bearing force other than that required to support the weight of the drum. Hence, for the dynamically balanced drum (neglecting gravity), where the axes are located at the centroid of the system and the x-axis is the axis of rotation, t t I 1? i F =F = F =F = F = F =0 x x y y z z and The integrals and fJffpzxdV = 0 fffpyxdV = 0 f f pzxdV- Izx f ffpyxdV Iyx are known as the "products of inertia" of the system. The drum assembly of the wide-angle scanner is an extremely complicated mechanism geometrically, and as a result it would be very difficult to evaluate the products of inertia for the entire drum at one time. However, if a body B1 of density p1 has a hollow region B2 in its interior (Figure 2), then the products of inertia are I.. - ffJJ plijdV- fffB plij dV R B. B FIGURE 2. BODY WITH HOLLOW PORTION r~~~~~~~~~~~~~~~~~j...... 'I;=~==~' ~..... 3

Institute of Science and Technology The University of Michigan Hence, as far as the products of inertia are concerned, a body of irregular shape may be thought of as a combination of regularly shaped bodies. One further consideration may be made. If a body has a cross section which is independent of x, the products of inertia become Iy = pVyx yx and I = pVzx zx where x, y, and z are the coordinates of the centroid of the body. In many cases it is simpler to calculate the product of inertia in this fashion. 2.2. APPLICATION OF THEORY TO SCANNER DRUM ASSEMBLY A scanner drum assembly is shown in Figure 3. Essentially, the drum is constructed by taking an aluminum cylinder and drilling two holes (of equal radii) through it, one axially and one normal to its longitudinal axis. The resulting member is cut along a 450 plane (Figure 4). The two halves are then separated sufficiently to allow an elliptical mirror and a mounting ring to be inserted in the 450 cut. Screws are placed longitudinally into the drum to hold the parts together (Figure 3). Finally, balancing is accomplished by mounting two 900 rings (whose thickness will be determined by the analysis) onto the drum shown in Figure 3. (Balancing Ring) (Aperture) o 0 \ -_, I - l- -\ Drum \ (Balancing Ring) (Mirror-Mounting Ring) (Mounting Screws) (Balancing Ring) (Mirror-Mounting Ring) FIGURE 3. SCANNER DRUM ASSEMBLY The yx products of inertia of several bodies follow. (The zx products all cancel or go to zero due to the symmetry of the drum assembly.) 4

Institute of Science and Technology The University of Michigan Inttt fSineadTcnloyTeUiest fMcia FIGURE 4. CONSTRUCTION OF SCANNER DRUM (A) Cylinder. The longitudinal axis of the cylinder is parallel to the x-axis, and the centers of the two ends have the coordinates (x0, y0, z0) and (x0 + L, y,0 z0). The length of cylinder is L and its radius is r (Figure 5). I= pVyx = pTr L (x0 + L/2) (y0) y (X )' Yo' Zo) \ \ I I * 2r ' / (x0 + L, yO, Z0) 0 i — L - z FIGURE 5. CYLINDER 5

Institute of Science and Technology The University of Michigan Institute of Science and Technology The University of Michigan (B) Ring (1). The ring is centered at the origin but makes a 450 angle with the yz-plane (Figure 6). Its inside radius is ri, its outside radius is r0, and its width is 2a. r a-r cos 0 I = p(x)(rcos ) rdxdrd0 = — (r - ri p 0 r. -a-r cos 0 1 (C) Ring (2). The ring is symmetric about the xy-plane and parallel to the yz-plane (Figure 7). Its inside radius is ri, its outside radius is ro, its width is 2b, and x = Q. The ring subtends an arc of 2a. r a o C+b / I f f f p(x) (r cos 0)r dx dr dO =b (r - r (sin a) - i -b y y z -J2bL FIGURE 6. 45~ RING FIGURE 7. RING (2) (D) Aperture Opening. The aperture opening is the intersection of three cylinders (Figures 3, 4, and 8). The aperture radius is r., and the outside radius of the tube is r0, and x =a. 2 2 2 2 r. + r -z + r. -z ' c1 O 1 Iyx= P p -. 2 2 22 + -r. Z -z r. -z 1 u 1 (x +)(y) a = 2 - r12) ( 2 Pi (x + a)(y) dx dy dz = - 7Tr 2 6

Institute of Science and Technology The University of Michigan Institute of Scienceand Technology The Uiversity of Michiga r I / I / 0 FIGURE 8. APERTURE OPENING Each part of the scanner drum assembly in Figure 3 may be classed as one of the above bodies. All that remains is to put the proper numbers into the product of inertia expressions, add them up, and set the total equal to zero. The only unknown will be either e, b, a, r, or r. for the balancing ring. For example, the balancing of the Project MICHIGAN wide-angle scanner drum assembly may be calculated as follows. (a) Apertures (quantity = 2)-aluminum: a = 9/16V2 inch, ro = 3 15/16 inches, r. = 3 1/16 inches. Total Iyx -2 (r2 - ri2) (ri2r yx [2 \ o i P i = -71.79(2.62 X 10-4) = -0.0188 inch-pound-second2 (b) Drum: Total I = 0 yx (c) 450 cut in drum-aluminum: a = 9/16v inch, r = 3 15/16 inches, r. = 3 1/16 inches. Iy = 72a r4 - r )p = 95. 24(2. 62 X 104) = 0. 0250 inch-pound-second2 yx 2 0 7

Institute of Science and Technology T he University of M i ch i a (d) Mirror-mounting ring-Invar: a = 9/16VJinch, r = 3 15/16 inches, r. = 3 3/16 inches. = (r 4 - r4)p = -85. 70 (7. 63 X 10) = -0. 0654 inch-pound-second2 (e) Mirror-quartz: a = 9/1612 inch, r = 3 3/16 inches, r. = 0. -I = -7 r - ri ) = -64.51 (2. 07 X 10) = -0. 0134 inch-pound-second2 yx 2 o i (f) Slot for balancing rings (quantity = 2)-aluminum: b = 1/2 inch, a = 7/4, f = 4 inches, r = 3 15/16 inches, r. = 3 3/16 inches. 0 1 Total I = -2 b r 3 - r) sin a p = -21. 24 (2. 62 10 ) = -0. 0041 inch-pound2 second (g) Mounting screw holes- aluminum and Invar: Total I = 26. 29(2. 62 X 10) + 4. 80(7. 63 X 10) = 0.0106 inch-pound-second2 yx (h) Mounting screws-steel: Total I = - 10. 40(7. 50 x 104) = - 0. 0078 inch-pound-second2 yx (i) Balancing rings- GE Hevimet: b = 1/2 inch, a = r7/4, 2 = 4 inches, r = r, r. = 3 13/16 inches. 1 Total I = 2 J V r - r.3) sin a p = (3.77r 3 -209. 36)(16. 00 X10) L 3 \O 11 = 0.0060r 3 0.3350 inch-pound-second2 o Since the total product of inertia of the balanced drum should be zero, EI =o yx Adding up all the parts of the drum assembly, the result is 3 0. 0060r 3- 0.4089 = 0 0 8

Institute of Science and Technology The University of Michigan or 1/3 r = (67.78)1 = 4. 0775 inches 0 Hence, the thickness of the ring is r = r. 4. 0775 - 3. 8125 = 0. 2650 inch o 1 The thickness of the balancing weights used on the actual scanner assembly was determined experimentally to be slightly over 0. 250 inch. Hence, the theoretical results agree very closely with the experimental results. 3 GYROSCOPIC EFFECTS on SCANNER DRUM during MANEUVERS of AIRCRAFT The scanner is carried by an aircraft whose line of flight is parallel to the axis of rotation of the scanner drum. During maneuvers of the aircraft, the rotating drum assembly experiences a "precession ' or rotation about an axis normal to the axis of rotation. A gyroscopic couple is produced in the scanner drum as shown in Figure 9. This couple produces forces in the bearings which support the drum. y Couple (M) ) ~\/>/Sp/Spin (S) [/T 7i~ \I~ / \ \ -I \Line of Flight I I/ Precession (P) z FIGURE 9. GYROSCOPIC EFFECT DURING TURN OF AIRCRAFT 9

Institute of Science and Technology The University of Michigan The equation for the gyroscopic couple is -- _ rI PSk (turn)~ M = I (P x S) = i-P (dive)j xx PSj1 (dive)X where M = couple (inch-pounds) I = moment of inertia about x-axis (inch-pound-seconds ) xx P = precession vector (radians/second) S = spin vector (radians/second) j, k = unit vectors in y, z directions,respectively Again, the wide-angle scanner drum is used as an example. The moments of inertia of the components (see Section 2. 2 for descriptions) may be evaluated as follows: (A) Cylinder I = - r. p (rL 4 4 xx 2 o i (B) Ring (1) I = 7a r - r.) p xx o 1 (C) Ring (2) I = ab 4 - r.)p xx i /P (D) Aperture Opening Volume = V = 3 r2R K(k) +E(k) R [K(k) - E(k) - 2r3} where k = ri/r and E(k) and K(k) are elliptic functions. O \2 r + r. I -pV 0 IL xx ' 2 The calculations based on the dimensions of the wide-angle scanner follow. (a) Apertures (quantity = 2)-aluminum: 2 Total I = -2pV (0 ) = -2 (2. 62 x 104) (25. 78 ) = -0. 1654 inch-poundsecond (b) Drum — aluminum: = - (r r4)p = (2482)(2. 62 x 104) = 0. 6504 inch-pound-second2 xx 2 0 1 10

Institute of Science and Technology T he University of M i ch i a Institue of Scence an Technlogy Th Univerity of ichiga (c) 45 cut in drum-aluminum: I -a (r4 - ri )p = -(190. 5)(2. 62 X 104) = -0. 0499 inch-pound-second2 (d) Mirror-mounting ring-Invar: /4 4\ -4 2 I = ra r 4 - r.)p = (171.4)(7.63 x 10 ) = 0. 1308 inch-pound-second2 xx 0 i (e) Mirror -quartz: IX = a r - r 4)p = (129. 0)(2. 07 X 10- ) = 0. 0268 inch-pound-second2 xx i o (f) Slots for balancing rings (quantity = 2) -aluminum: Total I = -2 ab 4 - r.)i = -(10. 80)(2. 62 X 10) = -0. 0028 inch-pound-second2 (g) Mounting screw holes-aluminum and Invar: Total I = -0. 0047 inch-pound-second2 xx (h) Mounting screws-steel: Total I = 0. 0089 inch-pound-second2 xx (i) Balancing rings-GE Hevimet: Total I = 2 Iab (r4 - r.4) = (35.10)(16. 00 x 10) = 0. 0561 inch-pound-second2 xx O o 1* ' / The total moment of inertia is the sum of the moments of inertia of the parts. Hence, Total I = E I = 0. 6502 inch-pound-second2 Since the drum rotates at 5000 rpm, the magnitude of the gyroscopic couple is Sie te dm r a 50002 pm, h m gnid o h gc cp [MI = I PS = (0. 6502)(P) 5000 = 342.6 Pinch-pounds xx 60 11

Institute of Science and Technology The University of Michigan If the scanner is carried by an aircraft cruising at 150 mph, the maximum rate of precession about any axis is 360~ per minute. Therefore, the maximum gyroscopic couple is |max| = 342.6 P maximum = (342.6) ( = 35. 88 inch-pounds maximum maximum 60 Since the distance between the bearings is 1 foot, the maximum bearing force is about 3 pounds. 12

Institute of Science and Technology The University of Michigan PROJECT MICHIGAN DISTRIBUTION LIST 7 1 February 1961-Effective Date Copy No. Addressee 1 Army Research Office, ORCD, DA Washington 25, D. C. ATTN: Research Support Division 2-3 Commanding General U. S. Army Combat Surveillance Agency 1124 N. Highland Street Arlington 1, Virginia 4-40 Commanding Officer U. S. Army Signal Research & Development Laboratory Fort Monmouth, New Jersey ATTN: SIGRA/SL-ADT 41-42 Commanding General U. S. Army Electronic Proving Ground Fort Huachuca, Arizona ATTN: Technical Library 43 Chief, Human Factors Research Division Office of the Chief of Research & Development Department of the Army, Washington 25, D. C. 44-45 Commander, Army Rocket & Guided Missile Agency Redstone Arsenal, Alabama ATTN: Technical Library, ORDXR-OTL 46-47 Commanding Officer U. S. Army Transportation Research Command Fort Eustis, Virginia ATTN: Research Reference Center 48 Commanding General Army Medical Research & Development Command Main Navy Building, Washington 25, D. C. ATTN: Neuropsychiatry & Psychophysiology Research Branch 49 Commanding Officer, Ordnance Weapons Command Rock Island, Illinois ATTN: ORDOW-GN 50-53 Director, U. S. Army Engineer Research & Development Laboratories Fort Belvoir, Virginia (50) ATTN: Chief, Topographic Engineer Department (51-52) ATTN: Chief, Electrical Engineering Department (53) ATTN: Technical Documents Center 54 Commandant, U. S. Army War College Carlisle Barracks, Pennsylvania ATTN: Library 55 Commandant, U. S. Army Command & General Staff College Fort Leavenworth, Kansas ATTN: Archives Copy No. Addressee 56 Commandant, U. S. Army Infantry School Fort Benning, Georgia ATTN: Combat Developments Office 57-58 Assistant Commandant U. S. Army Artillery & Missile School Fort Sill, Oklahoma 59 Assistant Commandant, U. S. Army Air Defense School Fort Bliss, Texas 60 Commandant, U. S. Army Engineer School Fort Belvoir, Virginia ATTN: ESSY-L 61 Commandant, U. S. Army Signal School Fort Monmouth, New Jersey ATTN: SIGFM/SC-DO 62 Commandant, U. S. Army Aviation School Fort Rucker, Alabama ATTN: CDO 63-64 President, U. S. Army Intelligence Board Fort Holabird, Baltimore 19, Maryland 65 Commanding Officer, U. S. Army Signal Electronic Research Unit, P. 0. Box 205 Mountain View, California 66-69 Office of Naval Research, Department of the Navy 17th & Constitution Avenue, N. W. Washington 25, D. C. (66-67) ATTN: Code 463 (68-69) ATTN: Code 461 70 The Hydrographer, U. S. Navy Hydrographic Office Washington 25, D. C. ATTN: Code 4100 71 Chief, Bureau of Ships Department of the Navy, Washington 25, D. C. ATTN: Code 690 72-73 Director, U. S. Naval Research Laboratory Washington 25, D. C. ATTN: Code 2027 74 Commanding Officer, U. S. Navy Ordnance Laboratory Corona, California ATTN: Library 75 Commanding Officer & Director U. S. Navy Electronics Laboratory San Diego 52, California ATTN: Library 76-77 Department of the Air Force, Headquarters, USAF Washington 25, D. C. ATTN: AFOIN-1B1 78 Commander in Chief, Headquarters Strategic Air Command, Offutt Air Force Base, Nebraska ATTN: DINC 13

Institute of Science and Technology The University of Michigan Distribution List 7, 1 February 1961-Effective Date Copy No. Addressee 79 Aerospace Technical Intelligence Center U. S. Air Force Wright-Patterson AFB, Ohio ATTN: AFCIN-4Bla, Library 80-89 ASTIA (TIPCR) Arlington Hall Station, Arlington 12, Virginia 90-98 Commander, Wright Air Development Division Wright-Patterson AFB, Ohio (90-93) ATTN: WWDE (94) ATTN: WWAD-DIST (95) ATTN: WWRDLP-2 (96-98) ATTN: WWRNOO (Staff Physicist) 99-100 Commander, Rome Air Development Center Griffiss AFB, New York (99) ATTN: RCOIL-2 (100) ATTN: RCWIP-3 101-103 Commander, AF Command & Control Development Division Laurence G. Hanscom Field Bedford, Massachusetts ATTN: CCRHA-Stop 36 104 APGC(PGTRI) Eglin Air Force Base, Florida 105-108 Central Intelligence Agency 2430 E Street, N. W. Washington 25, D. C. ATTN: OCR Mail Room 109-114 National Aeronautics & Space Administration 1520 H Street, N. W. Washington 25, D. C. 115 Combat Surveillance Project Cornell Aeronautical Laboratory, Inc. Box 168, Arlington 10, Virginia ATTN: Technical Library 116 The RAND Corporation 1700 Main Street Santa Monica, California ATTN: Library 117-118 Cornell Aeronautical Laboratory, Inc. 4455 Genesee Street Buffalo 21, New York ATTN: Librarian VIA: Bureau of Naval Weapons Representative 4455 Genesee Street Buffalo 21, New York 119-120 Director, Human Resources Research Office The George Washington University P. O. Box 3596, Washington 7, D. C. ATTN: Library 121 Chief, U. S. Army Air Defense Human Research Unit Fort Bliss, Texas ATTN: Library Copy No. Addressee 122 Chief, U. S. ArmyArmor HumanResearch Unit Fort Knox, Kentucky ATTN: Security Officer 123 Chief, U. S. Army Infantry HumanResearch Unit P. O. Box 2086 Fort Benning, Georgia 124 Chief, USA Leadership Human Research Unit P. O. Box 2086, Presidio of Monterey, California 125 Chief Scientist, Department of the Army Office of the Chief Signal Officer Research & Development Division, SIGRD-2 Washington 25, D. C. 126 Columbia University Electronics Research Laboratories 632 W. 125th Street New York 27, New York ATTN: Technical Library VIA: Commander, Rome Air Development Center Griffiss AFB, New York ATTN: RCKCS 127 Coordinated Science Laboratory University of Illinois, Urbana Illinois ATTN: Librarian VIA: ONR Resident Representative 605 S. Goodwin Avenue Urbana, Illinois 128 Polytechnic Institute of Brooklyn 55 Johnson Street Brooklyn 1, New York ATTN: Microwave Research Institute Library VIA: Air Force Office of Scientific Research Washington 25, D. C. 129 Visibility Laboratory Scripps Institution of Oceanography University of California, San Diego 52, California VIA: ONR Resident Representative, University of California Scripps Institution of Oceanography, Bldg. 349 La Jolla, California 130 U. S. Army Aviation, Human Research Unit U. S. Continental Army Command P. 0. Box 428, Fort Rucker, Alabama 131 Commanding General Quartermaster Research & Engineering Command U. S. Army, Natick, Massachusetts 132 Cooley Electronics Laboratory University of Michigan Research Institute Ann Arbor, Michigan ATTN: Director 133 U. S. Continental Army Command Liaison Officer, Project MICHIGAN The University of Michigan P. 0. Box 618, Ann Arbor, Michigan 134 Commanding Officer, U. S. Army Liaison Group, Project MICHIGAN The University of Michigan P. 0. Box 618, Ann Arbor, Michigan 14

AD Div. 6/3 Institute of Science and Technology, U. of Michigan, Ann Arbor DYNAMIC BALANCING OF SCANNER DRUM AND GYROSCOPIC EFFECT DURING MANEUVERS OF AIRCRAFT by W. L. Brown and C. T. Yang. Rept. of Proj. MICHIGAN. Feb 61. 12 p. incl. illus. (Rept. no. 2900-250-T) (Contract DA-36-039 SC-78801) Unclassified report This report presents the equations for determining the dynamic balancing and gyroscopic effect of a rotating scanner drum assembly of the type used in the Project MICHIGAN wide-angle scanner. The parameters used in the numerical example are those of the wide-angle scanner, and the theoretical calculations of the dynamic balancing agree excellently with the actual mechanical dynamic baiancing of the drum assembly. The calculations also indicate that gyroscopic forces in the drum are negligible even during maximum rate of turn and maximum rate of climb of the aircraft carrying the scanner. (over) (over) UNCLASSIFIED I. Title: Project MICHIGAN II. Brown, W. L., Yang, C. T. III. U. S. Army Signal Corps IV. Contract DA-36-039 SC-78801 Armed Services Technical Information Agency UNCLASSIFIED UNCLASSIFIED I. Title: Project MICHIGAN II. Brown, W. L., Yang, C. T. III. U. S. Army Signal Corps IV. Contract DA-36-039 SC-78801 Armed Services Technical Information Agency UNCLASSIFIED AD Div. 6/3 Institute of Science and Technology, U. of Michigan, Ann Arbor DYNAMIC BALANCING OF SCANNER DRUM AND GYROSCOPIC EFFECT DURING MANEUVERS OF AIRCRAFT by W. L. Brown and C. T. Yang. Rept. of Proj. MICHIGAN. Feb 61. 12 p. incl. illus. (Rept. no. 2900-250-T) (Contract DA-36-039 SC-78801) Unclassified report This report presents the equations for determining the dynamic balancing and gyroscopic effect of a rotating scanner drum assembly of the type used in the Project MICHIGAN wide-angle scanner. The parameters used in the numerical example are those of the wide-angle scanner, and the theoretical calculations of the dynamic balancing agree excellently with the actual mechanical dynamic balancing of the drum assembly. The calculations also indicate that gyroscopic forces in the drum are negligible even during maximum rate of turn and maximum rate of climb of the aircraft carrying the scanner. (over) AD Div. 6/3 Institute of Science and Technology, U. of Michigan, Ann Arbor DYNAMIC BALANCING OF SCANNER DRUM AND GYROSCOPIC EFFECT DURING MANEUVERS OF AIRCRAFT by W. L. Brown and C. T. Yang. Rept. of Proj. MICHIGAN. Feb 61. 12 p. incl. illus. (Rept. no. 2900-250-T) (Contract DA-36-039 SC-78801) Unclassified report This report presents the equations for determining the dynamic balancing and gyroscopic effect of a rotating scanner drum assembly of the type used in the Project MICHIGAN wide-angle scanner. The parameters used in the numerical example are those of the wide-angle scanner, and the theoretical calculations of the dynamic balancing agree excellently with the actual mechanical dynamic balancing of the drum assembly. The calculations also indicate that gyroscopic forces in the drum are negligible even during maximum rate of turn and maximum rate of climb of the aircraft carrying the scanner. (over) (over) UNCLASSIFIED I. Title: Project MICHIGAN II. Brown, W. L., Yang, C. T. III. U. S. Army Signal Corps IV. Contract DA-36-039 SC-78801 Armed Services Technical Information Agency UNCLASSIFIED UNCLASSIFIED I. Title: Project MICHIGAN II. Brown, W. L., Yang, C. T. III. U. S. Army Signal Corps IV. Contract DA-36-039 SC-78801 Armed Services Technical Information Agency UNCLASSIFIED AD Div. 6/3 Institute of Science and Technology, U. of Michigan, Ann Arbor DYNAMIC BALANCING OF SCANNER DRUM AND GYROSCOPIC EFFECT DURING MANEUVERS OF AIRCRAFT by W. L. Brown and C. T. Yang. Rept. of Proj. MICHIGAN. Feb 61. 12 p. incl. illus. (Rept. no. 2900-250-T) (Contract DA-36-039 SC-78801) Unclassified report This report presents the equations for determining the dynamic balancing and gyroscopic effect of a rotating scanner drum assembly of the type used in the Project MICHIGAN wide-angle scanner. The parameters used in the numerical example are those of the wide-angle scanner, and the theoretical calculations of the dynamic balancing agree excellently with the actual mechanical dynamic balancing of the drum assembly. The calculations also indicate that gyroscopic forces in the drum are negligible even during maximum rate of turn and maximum rate of climb of the aircraft carrying the scanner. (over) (over)

AD UNCLASSIFIED DESCRIPTORS Infrared detection Infrared scanners Mathematical analysis Equations UNCLASSIFIED AD UNCLASSIFIED DESCRIPTORS Infrared detection Infrared scanners Mathematical analysis Equations UNCLASSIFIED UNCLASSIFIED DESCRIPTORS Infrared detection Infrared scanners Mathematical analysis Equations AD UNCLASSIFIED DESCRIPTORS Infrared detection Infrared scanners Mathematical analysis Equations AD UNCLASSIFIED UNCLASSIFIED

AD Div. 6/3 Institute of Science and Technology, U. of Michigan, Ann Arbor DYNAMIC BALANCING OF SCANNER DRUM AND GYROSCOPIC EFFECT DURING MANEUVERS OF AIRCRAFT by W. L. Brown and C. T. Yang. Rept. of Proj. MICHIGAN. Feb 61. 12 p. incl. illus. (Rept. no. 2900-250-T) (Contract DA-36-039 SC-78801) Unclassified report This report presents the equations for determining the dynamic balancing and gyroscopic effect of a rotating scanner drum assembly of the type used in the Project MICHIGAN wide-angle scanner. The parameters used in the numerical example are those of the wide-angle scanner, and the theoretical calculations of the dynamic balancing agree excellently with the actual mechanical dynamic balancing of the drum assembly. The calculations also indicate that gyroscopic forces in the drum are negligible even during maximum rate of turn and maximum rate of climb of the aircraft carrying the scanner. (over) UNCLASSIFIED I. Title: Project MICHIGAN II. Brown, W. L., Yang, C. T. III. U. S. Army Signal Corps IV. Contract DA-36-039 SC-78801 Armed Services Technical Information Agency UNCLASSIFIED UNCLASSIFIED I. Title: Project MICHIGAN II. Brown, W. L., Yang, C. T. III. U. S. Army Signal Corps IV. Contract DA-36-039 SC-78801 Armed Services Technical Information Agency UNCLASSIFIED AD Div. 6/3 Institute of Science and Technology, U. of Michigan, Ann Arbor DYNAMIC BALANCING OF SCANNER DRUM AND GYROSCOPIC EFFECT DURING MANEUVERS OF AIRCRAFT by W. L. Brown and C. T. Yang. Rept. of Proj. MICHIGAN. Feb 61. 12 p. incl. illus. (Rept. no. 2900-250-T) (Contract DA-36-039 SC-78801) Unclassified report This report presents the equations for determining the dynamic balancing and gyroscopic effect of a rotating scanner drum assembly of the type used in the Project MICHIGAN wide-angle scanner. The parameters used in the numerical example are those of the wide-angle scanner, and the theoretical calculations of the dynamic balancing agree excellently with the actual mechanical dynamic balancing of the drum assembly. The calculations also indicate that gyroscopic forces in the drum are negligible even during maximum rate of turn and maximum rate of climb of the aircraft carrying the scanner. (over) (over) UNCLASSIFIED I. Title: Project MICHIGAN II. Brown, W. L., Yang, C. T. III. U. S. Army Signal Corps IV. Contract DA-36-039 SC-78801 Armed Services Technical Information Agency UNCLASSIFIED UNCLASSIFIED I. Title: Project MICHIGAN II. Brown, W. L., Yang, C. T. III. U. S. Army Signal Corps IV. Contract DA-36-039 SC-78801 Armed Services Technical Information Agency UNCLASSIFIED AD Div. 6/3 AD Div. 6/3 Institute of Science and Technology, U. of Michigan, Ann Arbor DYNAMIC BALANCING OF SCANNER DRUM AND GYROSCOPIC EFFECT DURING MANEUVERS OF AIRCRAFT by W. L. Brown and C. T. Yang. Rept. of Proj. MICHIGAN. Feb 61. 12 p. incl. illus. (Rept. no. 2900-250-T) (Contract DA-36-039 SC-78801) Unclassified report This report presents the equations for determining the dynamic balancing and gyroscopic effect of a rotating scanner drum assembly of the type used in the Project MICHIGAN wide-angle scanner. The parameters used in the numerical example are those of the wide-angle scanner, and the theoretical calculations of the dynamic balancing agree excellently with the actual mechanical dynamic balancing of the drum assembly. The calculations also indicate that gyroscopic forces in the drum are negligible even during maximum rate of turn and maximum rate of climb of the aircraft carrying the scanner. (over) (over) Institute of Science and Technology, U. of Michigan, Ann Arbor DYNAMIC BALANCING OF SCANNER DRUM AND GYROSCOPIC EFFECT DURING MANEUVERS OF AIRCRAFT by W. L. Brown and C. T. Yang. Rept. of Proj. MICHIGAN. Feb 61. 12 p. incl. illus. (Rept. no. 2900-250-T) (Contract DA-36-039 SC-78801) Unclassified report This report presents the equations for determining the dynamic balancing and gyroscopic effect of a rotating scanner drum assembly of the type used in the Project MICHIGAN wide-angle scanner. The parameters used in the numerical example are those of the wide-angle scanner, and the theoretical calculations of the dynamic balancing agree excellently with the actual mechanical dynamic balancing of the drum assembly. The calculations also indicate that gyroscopic forces in the drum are negligible even during maximum rate of turn and maximum rate of climb of the aircraft carrying the scanner. (over) (over)

AD UNCLASSIFIED DESCRIPTORS Infrared detection Infrared scanners Mathematical analysis Equations UNCLASSIFIED UNCLASSIFIED DESCRIPTORS Infrared detection Infrared scanners Mathematical analysis Equations UNCLASSIFIED AD UNCLASSIFIED DESCRIPTORS Infrared detection Infrared scanners Mathematical analysis Equations UNCLASSIFIED CA - 0 c ~z _ --- o 4 N.) o 00 -n 0 ---- c (' I 00 C) 0) AD AD UNCLASSIFIED DESCRIPTORS Infrared detection Infrared scanners Mathematical analysis Equations UNCLASSIFIED