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1 AD-A ARMY REsEARcH LA4oRATORY Variation in Gravity Droop Due to Gun Elevation: A Small but Predictable Source DT IC of Aiming Inaccuracy Q E- I9C4 Mark L. Bundy MAR s994 ARL-TN-26 February II!!) I l ii)1111 DTIC QU3--i" Z CTY "AMMROVDi IFuMnC RmzUM DLmVJu n IS UNmnf. A A

2 NOTICES Destroy this report when it is no longer needed. DO NOT return it to the originator. Additional copies of this report may be obtained from the National Technical Information Service, U.S. Department of Commerce, 5285 Port Royal Road, Springfield, VA The findings of this report are not to be construed as an official Department of the Army position, unless so designated by other authorized documents. The use of trade names or manufacturers' names in this report does not constitute indorsement of any commercial product.

3 1Form Approved REPORT DOCUMENTATION PAGE I WeB NO Pifli re"ri~ng burden for this collection of informatdin is estimated to average I hour per response, including the time for reviewing instructions. searching existing data sources. ateigand maintaining the data needed, and completing and reviewing the collection of information %*no commn~ts reigarding this burden estimate or any other aspect Of this colcinof information, including suggestions for reducing this ourden to V*ashiington i4eadouarters Services. Directorate tor Infrmation Operations and Reports Jefferson Davis Hlighway, Suitel Arf.ngto. VA , and to the Oftfice of managemenit and Budget. Paperworki Reduction Project ( U). Washington, DC AGENCY USE ONLY (eave blank) I2. REPORT DATE T3. -REPO3RT TYPE AND DATES COVERED I FebrlwUv 1994 I inlm h 1993-Auu TITLE AND SUBTITLE 5. FUNDING NUMBERS Variation in Gravrity Droop Due to Gun Elevatdion Source of Aiming Inaccuray * 6G. AUTHORMS Matk L Bandy A Small but Predictab PR: IL162618AH8 7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES) 8. PERFORMING ORGANIZATION REPORT NUMBER U.S. Arny Research Labwatory AM.l4 AMSRL-Wr-PS Aberdem Proving Ground. MD SPONSORING/ MONITORING AGENCY NAME(S) AND ADDRESS(ES) 10. SPONSORING /MONITORING AGENCY REPORT NUMBER U.S. Amy Research Ldabortoy AT7N: AMSRL-OP-CI-B Criech LAb) Aberd=e Poving Ground, MD SUPPLEMENTARY NOTES ARL-1h-26 12a. DISTRIBUTION/I AVAILABILITY STATEMENT 12b. DISTRIBUTION CODE Approved for public release disiuttion is unlimited. 13. ABSTRACT (Maximum 200 words) When a gun is elevated or deprssed from horizontal, fth component of gavity perpendicuiar to the gun axis is diminished resulting in a decreaed graity-inducedl drop of the munle angke. Mw fine control algorithm for the MIAl took does not take this change In "graity drwp Into a=cun when it computes the gun elievration required to engage a disaunt target. We show that this source. of aiming iwcurmy is smnall, but easily predictable, ang hence correctable. 14. SUBJECT TERMS 15. NMEOFPAGES gravity, droop, fire control, elevation, somcy. modeling gun, brrel, bend PRICE CODE 17. SECURITY CLASSIFICATION 18. SECURITY CLASSIFICATION 1 9. SECURITY CLASSIFICATION 20. LIMITATION OF ABSTRACT OF REPORT OF THIS PAGE I OF ABSTRACT NCIASSIF'IE! IUNCLASSIME) UNCLASSIFED UL NSN 7S Standard Form 298 (Rev. 2489) Presribd by ANSI Std Z39-1S

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5 ACKNOWLEDGMENTS The author would like to thank Major Bruce Held, assigned to the U.S. Army Research Laboratory, for discussions related to the tactical battlefield. He would also like to thank Arthur Cummings, U.S. Army Combat Systems Test Activity, for information pertaining to the M 1A 1 elevation characteristics. NTIS CRA&I DTIC TAB Unannounced 0] Justification... By Distribution I AvaiJability Codes Avail and/ or Dist Special Iii

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7 TABLE OF CONTENTS LIST OF FIGURES... LIST OF TABLES... vii vii 1. INTRODUCTION... I 2. ANALYSIS CONCLUSIONS AND RECOMMENDATIONS REFERENCES... 7 DISTRIBUTION LIST... 9 V

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9 LIST OF FIGURES Figure 1. illustrating the effect of gravity on muzzle angle, Correction factor, vs. cl... 4 LIST OF TABLES Table 1. Correction Factor. vs. a... 4 vii

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11 1. INTRODUCTION In 1984, the U.S. Army began a program to identify and reduce, if possible, sources of tank gun inaccuracies (error). Not surprisingly, as this program progressed, the magnitude of reported error sources decreased. For example, a retrospection of the program review for the year 1987 (Schmidt 1987) shows that topics of discussion then included the following: tube-to-tube variability and the effects of fleet zero; temperature-dependent jump; and thermal jacket design. The variation in fall-of-shot associated with these subjects ranges from several tenths of a mil (6,400 mils = one revolution) to 1 or more mils. On the other hand, a sampling of recent studies shows that the discussion of error sources has diminished by almost an order of magnitude (e.g.. see Held, Webb, and Schmidt [to be published)). This report documents yet another small error source - variation in gravity droop with gun elevation - an effect that is typically less than 0. 1 mil in magnitude for the M IAl tank gun. Unlike many sources of error, however, this inaccuracy is easily predictable and, therefore, could be eliminated by a simple correction to the fire control algorithm. 2. ANALYSIS If the gun is mechanically elevated from horizontal to an angle a, the current fire control algorithm assumes the muzzle pointing angle, 0, see Figure 1, has changed by precisely a. However, the gravity-induced curvature also changes as the gun elevates. This will impart an additional muzzle angle change, P(a), so that the new muzzle pointing angle is actually: e(a) = 0(a-O) + a + P(a). (1) The correction, 0, is small, 0(a) - O(i0-): nevertheless, it is very a predictable. 1

12 Gravity..-._. Horizontal S...Droop Relative Muzzle Angle... :::... Gun Elevation, a Figure 1. Iustrating the effect of gavity on muzzle angle. 0. To describe the problem, we will first need to specify/define several terms. We will consider the gun barrel to be supported at two points. The barrel will be at zero elevation, a = 0, if a line drawn between the two supports is horizontal relative to the (vertical) earth's gravitational field. If there were no gravity, or inherent tube curvature, the muzzle pointing angle would be zero when the gun elevation was zero. However, following the treatment given in Bundy (1993), we can show that the muzzle pointing angle when the gun elevation is zero and the acceleration due to gravity is g will be given by: 0(a--0) = c, (2) where C is a constant which depends on the gun barrel geometry, material properties, and location of the support points. The minus sign indicates that the muzzle angle due to gravity droop is below horizontal at zero elevation. Rather than derive the expression for C here, we will simply use the result given in Bundy (1993) for the muzzle pointing angle when the barrel is at the ambient temperature of 2 10 C, viz.: 2

13 0(a=0) = mil. (3) (Note, it was shown in Bundy [ 1993) that the change in gravity droop with a change in temperature of the barrel, from firing, is very small, less than 2% from ambient, for any reasonable barrel temperature change, i.e., firing scenario.) From Equations 2 and 3. we find, for W = 9.8 m/s 2. C = mil's2 (4) When the gun is elevated by an angle a, the muzzle pointing angle will be: O(a) = a - C g cos(a) (5) Thus, from Equations 1, 2, 3, and 5, the gravity droop correction to the muzzle pointing angle will be: 0 = O(a) -0(a=0) - a = C I I - cos(a)) = cos(a)) mil. (6) From Equation 6, P3(a) = 0.82 I- cos(a)) (7) a a where it is assumed that a will be expressed in mils. For a = 172 mils (a 100). for example, P(a) = 7.2 x 10-5 (7) When the MiAI tank is on flat level ground, mechanical constraints between the gun and the hull limit the range of a from mil (-100) to +344 mil (+200) (Hoffman 1987). However, if the hull were pitched up or down, in a mountainous terrain for example, the range of a may exceed these limits. We have plotted 3 vs. a in Figure 2 and tabulated the comparison in Table 1. As shown, the correction 3 is less 3

14 than mil when a is less than 86 mils (50), but it exceeds mil when a is greater than 258 mils (150). a (degrees) L a (mils) Figure 2. Correction factor.. vs. a. Table 1. Correction Factor, I3, vs. a (mnils) (degrees) (mils)

15 3. CONCLUSIONS AND RECOMMENDATIONS When elevation or depression of the M la1 tank gun barrel is less than 86 mils (50) in magnitude, the correction in the muzzle pointing angle due to a change in gravity droop with elevation is negligible, less than mil. However, if the change in elevation or depression exceeds 258 mils (150) in magnitude. the change in muzzle pointing angle due to the change in gravity droop is about ten times larger. exceeding mil. The muzzle pointing angle can be compensated/corrected for the change in gravity droop with elevation by adding fi = 0.82 (1 - cos(a)) mil to the elevation angle, a. Situations where the tank gun may be elevated or depressed by several hundred mils would include tank-to-tank engagements in mountainous terrain, precision firing in a high-rise urban setting, or the use of the tank gun as an antihelicopter weapon. Admittedly, the gravity droop correction for elevation of the gun is small, even in the special situations listed previously; however, accumulation of small errors ultimately leads to a large error. Since it would be relatively simple to eliminate this small error by changing the M 1A1 fire control algorithm, doing so may warrant consideration in the next algorithm revision. 5

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17 4. REFERENCES Bundy, M. L. "Gun Barrel Cooling and Thermal Droop Modeling." ARL- TR-189, U.S. Army Research Laboratory, Aberdeen Proving Ground, MD, August Held, B. J., D. W. Webb, and E. M. Schmidt. "Identification and Quantification of Sources of Occasion-to-Occasion Elevation Variability in Tank Gun Accuracy." Proceedings of the Seventh Gun Dynamics Symposium, to be published. Hoffman, T. C. "M1Al Tank Characteristics and Description Book." NP , General Dynamics Land Systems Division, Contract DAAE07-86-C-R032, September Schmidt, E. M. "BRL Enhanced Accuracy Gunfire Program Review." internal report for Dr. J. Frasier, U.S. Army Ballistic Research Laboratory, Aberdeen Proving Ground, MD, October

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19 No. of No. of 2 Administrator I Commander Defense Technical Into Center U.S. Amy Missile Command ATIN: DTIC-DDA ATTN: AMSMI-RD-CS-R (DOC) CQuan Station Redstone Arsenal, AL Alexandria, VA Commander Commander U.S. Army Tank-Automotive Command US. Army Materiel Command ATTN: AMSTA-JSK (Armor Eng. Br.) AMN: AMCAM Warns, MI Eisenhower Ave. Alexandria, VA Director U.S. Army TRADOC Analysis Command Director ATIN: ATRC-WSR US. Army Research Laboramory White Sands Missile Range, NM 880J ATTN: AMSRL-OP-CI-AD, Tech Publishing O indi) I Commuandat 280 Powder Mill Rd. US. Army Inftury School Adelphi MD ATIN: ATSH-CD (Security Mgr.) Fort Benning, GA Director US. Army Research Laboratory (,,m. e*)1 Commandant ATIN: AMSRL-OP-CI-AD, US. Army Infantry School Records Management ATIN: ATSH-WCB-O 2800 Powder Mill Rd. Fort Beaning, GA Adepi MD WL/MNOI 2 Commander Eglin AFB, FL US. Army Armament Research, Development, and Engineering Center Aberdeen EMin Ground ATIN. SMCAR-TDC Pikatinny Arsenal, NJ Dir, USAMSAA ATTN: AMXSY-D Directr AMXSY-MP, IL Cohen Bernt Weapons Laboratory US. Army Armamenat Research1 C, USATECOM Development, uid Engineering Cener ATTN: AMSTE-TC ATN-: SMCAR-CCB-TL Watervliet, NY Dir, USAERDEC ATTN: SCBRD-RT IDirector US. Army Advanced Systems Research 1 C, USACBDCOM and Analysis Offie (ATCOM) ATTN- AMSCB-CII ATTNI: AMSAT-R-NR, M/S Ames Research Center 1 Dir, USARL Moffett Field, CA ATIN: AMSRL-SL-I 5 Dir, USARL ATIN: AMSRL-OP-CI-B (Tech Lib) 9

20 No. of No. of Qoig 9MMin" Cooi Oraizai 3 Commander 10 Commander US. Army Armor Center U.S. Army Tank-Automotive Command ATTN: ATSB-CDC ATTN: AMCPEO-HFM ATSB-WP-ORSA, AMCPSO-HFM-F A. Pomey AMCPSO-HFM-C FL Knox, KY AMCPM-ABMS AMCPM-BLOCKIII 4 Commander AMSTA-CF U.S. Army Armament Research, AMSTA-Z Development, and Engineering Center AMSTA-ZD ATTN: SMCAR-CCH-W, AMCPM-ABMS-SW, Mr. J. Dekrenzo Dr. Pattison Mr. K. Femal Alan Havrilla Mr. S. Musalli Warren, MI Mr. E. Fennell Picatinny Arsenal, NJ Commander Tank Main Armament Systems 2 Commander ATMT." AMCPM-TMA, U.S. Army Armament Research, R. Biilington Development, mad Engineering Center D. Guziewicz ATTN: SMCAR-CCH-V, K. Rubin J. Pdty COL F. Harline A. Gowarty C. Kimker PicMiny Arsenal, NM B. Potter V. Rosamilia 3 Commander L Kopscz U.S. Army Armament Research, Picatinny Arsenal. NJ Development, and Engineering Center ATTN: SMCAR-QAT-A, I Commander G. M4aio US. Army Watervlift Arsenal R. Roeser ATTN: SMCWV-QAR, T. McCloukey C. Pare Watervlet NY Picauiny Arenal, NJ Commander 2 Commander AMCCOM US. Army Armament Research, ATTN- AMSMC-QAT-A(D), Development and Engineering Center R. Schubert ATIN: SMCAR-ATE-AP, R. Kline Picatinny Arsenal, NJ SMCAR-ATE-A, Mr. Chiu Ng Picatunny Arsenal, W Commander AMCCOM 4 Commander ATTN: AMSMC-ASR-A, Mr. Cmwford US. Army Armanent Research, Rock Island, EL Devlopment and Engineering Center ATTN." SMCAR-FSF-GD, Mr. K. Pfleger SMCAR-FSF-BV, Mr. V. Gdguo Mr. C. Gonzales Mr. C. Lawng Picainny Arsenal, M

21 No. of No. of c~i orgaizatin Cgj Qruwnzaugn 13 Director 7 Alliant Techsysnems, Inc. Benet Weapons Laboratory ATTN: G. L. Cambell U.S. Army Armament Research, C. Candland Deveopment, and Engineering Center R. Buretta ATMN: SMCAR-CCB, R. Becker W. Kitchens R. Gartner T. Simkins G. Stilley A. Gabriel R. Kenyon T. Allen 7225 Northland Dr. R. Hassenbien Brooklyn Park, MN J. Haas C. A. Andrade 2 General Dynamics Land Systems Division G. Carofano ATTN: S. P. Czeniak R. Gast S. Lucas D. Porter P.O. Box 2074 V. Nuris Warren, MI SMCAR-CCB-RA, B. Pflegi 1 AAl Corporation P. O'Hara ATMN: J. Hebeut Watervliet, NY P.O. Box 126 Hunt Valley, MD Commander USAOTEA ATTN: CSTE-CCA, Dr. Russell Aberdeen Pfovinf Ground Alexandria, VA Dir, USAMSAA 6 Commander ATIN: AMXSY-G, US. Army Armament Research, Development P. Topper and Engineering Center W. Brooks ATrN: SFAE-ASM-AF, R. Conroy COL D. Napolieflo B. Siegel L Yung R. Norman T. Kuriata ATTN. AMXSY-GI, E Delcoco Mr. L Delantre J. Delabor H. Tran I Cdr, USATECOM Picatinny Arsenal, NJ ATTN: AMSTE-TA-R, Defense Research Technologies, Inc. Mr. E. Keele ATMN: LTC Walter J. Pidlka USA (Ret) 4 Dir, USACSTA 354 Hungerford Drive ATTN. STECS-AS-LA, Rockville, MD Mr. G. Nieweabous ATIN: STECS-CC-PC, Keewan Research Center Mr. P. Durkin ATN. Mr. Keith R. Johnson ATTN: STECS-AA-HT, 1400 Townsend Drive Mr. J. Ze7& Houghto MI Mr. C. Mwick 11

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BR1L DTIC AD-A Q i BALLISTIC RESEARCH LABORATORY ABERDEEN PROVING GROUND, MARYLAND TECHNICAL REPORT BRL-TR-3319 TIME ZERO TRIGGERING SYSTEM 3319 BR1L AD-A248 454 TECHNICAL REPORT BRL-TR-3319 TIME ZERO TRIGGERING SYSTEM WALLACE H. CLAY LAWRENCE W. BURKE, JR. WILLIAM G. THOMPSON JAMES B. HARMON DTIC FLECT, ~APR 14 19921 MARCH 1992 IR4 U APPROVED