A S tu dy on th e E s t im at ion of A ir t o Grou n d W e ap on Im p act P oint 200 1 2
A S tu dy on th e E s t im at ion of A ir t o Grou n d W e ap on Im p act P oint 200 1 2
200 1 2 ( ) ( ) ( )
..., (sight ) (sight depression), (bombing table).,,, [8].,, 8Ft 2Mil, 227Ft 14Mil. - i -
A B S T RA CT When a pilot fires a cannon or a rocket, or releases a bomb in air craft, he must set a sight depres sion to accord w ith a w eapon impact point. T o solve this problem, w e need a m athematical m odeling oft the flight tr ajectory of a w eapon released fr om an air craft and a quantitativ e data about an estimation of impact point through a simulation. In this report, w e induced a dynamic equation of w eapon firing fr om an air craft and so w e pr oduced a trajectory of w eapon through a simulation. Also, w e established a geom etrical structur e of aircr aft w eapon firing sy stem mathem atically and calculated a sight depression mat ching a w eapon r eleasing condition based on a dat a to the simulation of w eapon tr ajectory, compar ed to the bomb table in the USAF T.O. manual in the same condition s. - ii -
ABST RACT i ii iii v vi vii 1. 1 2. 4 2.1 4 2.2 9 3. 13 3.1 13 3.2 13 3.3 15 3.4 15 3.5 20 4. 21 4.1 21 4.2 23 - iii -
5. 26 5.1 26 5.2 27 5.3 44 6. 52 7. 53 55 - iv -
[ 1] 22 [ 2] 22 [ 3] 23 [ 4] MK- 82 LDGP 24 [ 5] MK- 82 LDGP ( ) 25 [ 6] 26 [ 7] 27 [ 8] 28 [ 9] 29 [ 10] ( ) 40 [ 11] ( ) 41 [ 12] 42 [ 13] ( ) 43 [ 14] 44 [ 15] ( ) 45 [ 16] ( ) 50 - v -
[ 1] 4 [ 2] 5 [ 3] (AOD) 6 [ 4] (SDFFP ) 7 [ 5] 8 [ 6] 8 [ 7] 10 [ 8] 10 [ 9] 16 [ 10] 20 [ 11] 21 [ 12] 0 ( ) 30 [ 13] 0 ( ) 31 [ 14] 20 ( ) 32 [ 15] 20 ( ) 32 [ 16] 30 ( ) 33 [ 17] 30 ( ) 34 [ 18] 45 ( ) 35 [ 19] 45 ( ) 35 [ 20] 60 ( ) 36 [ 21] 60 ( ) 37 [ 22] 0 ( ) 37 [ 23] 20 ( ) 38 [ 24] 30 ( ) 38 [ 25] 45 ( ) 39 [ 26] 60 ( ) 39 [ 27] 60 ( ) 40 - v i -
[ 28] 20 ( ) 46 [ 29] 20 ( ) 46 [ 30] 30 ( ) 47 [ 31] 30 ( ) 47 [ 32] 45 ( ) 48 [ 33] 45 ( ) 48 [ 34] 20 ( ) 49 [ 35] 30 ( ) 49 [ 36] 45 ( ) 50 - v ii -
AOD : a : C L 0 : D : g : I sp : I tota l : m : SDFFP : T : U a : x V : V a : W : W a : z W bom b : z W e : X E : x X br : Y E : y X p : Z E : z Z p : Z rel : - v iii -
x : x y : y z : z : bom b : : bom b : : : - ix -
1.,,,..,....., (sight ) (sight depression ), (bombing table)...,.,. - 1 -
..[1],..,,,.... [2]. [2],. [2]. - 2 -
.... 2, 3. 4, 5. 6. - 3 -
2. 2.1 2.1.1, (Zero Sight Line), (Flight Path ) (Sight Line) [ 1]. [ 1 ],.. (Sight Depression From Flight Path, SDFFP)., - 4 -
..,.. Mil(Milliradian ). 1Mil 1000 ft 1ft. 1 17.45 Mil. 2.1.2,. [ 2]. [ 2 ],,, - 5 -
.. 2.1.3 (A im Off Dis t ance, A OD ) 90.. (Aim Off Point, AOP ), (Aim Off Distance, AOD). [ 3]. [ 3] (AOD) - 6 -
2.1.4 (S ig ht D epres s ion From Flig ht P ath, S DF FP ). (SDFFP ) (Bomb Depression From Flight Path).,. SDFFP... (T AS ).,... (Mil). (SDFFP ). (SDFFP ). [ 4 ] (SDFFP) - 7 -
. (SDFFP ) (SDFFP ). ([ 5]),.([ 6]) [ 5 ] [ 6] - 8 -
.., (AOD) (IPP ). 2.2 2.2.1. (SDFFP ) (SDFFP ). [ 7],,.. Mil. = 17.45 ( 90 - - t an - 1 X br Z re l ) (1), Z rel, X br. - 9 -
[ 7 ] 2.2.2 (1) [ 8 ] - 10 -
... [ 8]., X py lon, Y py lon.. = 17.45 ( 90 - - t an - 1 X p Z p ) (2) X p Z p. X p = X br - X ' (3) Z p = Z rel - Z ' (4) X py lon, Y py lon X ', Z '. X ' = X py lon cos + Y py lon sin (5) Z ' = X py lon s in - Y py lon cos (6) - 11 -
(2 ).. = 1 a ( 2 W V 2 S - C L o) (7) a, C L o. - 12 -
3. 3.1...,,..[1]... 3.2. x z - 13 -
, x z y. (flight path angle)... X E Y E. Z E. X E. Z E... Z E y. xz.. x y z = cos 0 - sin 0 1 0 sin 0 cos cos sin 0 - sin cos 0 0 0 1 X E Y E Z E (8) - 14 -
3.3 (1). (2). (3). (4). (5). (6). 3.4. V = g [ T - D W - sin ] (9) = 0 (10) = - g V cos (11) T (thrust ), D (drag ).. ( ), ( ) 0.,. - 15 -
. X E = V cos cos (12) Y E = V cos sin (13) Z E = - V sin (14) 3.4.1.. [ 9]. [ 9 ] - 16 -
a V a,. U a = V a cos a W a = V a s in a (15) W e,. W bom b = W a + W e (16). bom b = t an - 1 W bom b U a W bom b U a (17). bom b = - bom b (18). V bom b = U 2 a + W 2 bom b (19) - 17 -
3.4.2. 40 60% (9). W 0 m, W. W= W 0 - g m t bu rn (20) (19) ( m ). (Specific impulse). (Specific thrust ) ( m ). (sec),. 200-480.. I sp = T m g (21) T, m, g. (T ). - 18 -
I t = t 0 T dt = t 0 I s m g dt (22),. I t = T t = I s m g (23). ( m ). ( I s ) ( I t ).. I s = I t m g (24). m = T I s g (25) - 19 -
3.5 3.5.1 [1] KDEM ( K D E stim ation M ethod ), [ 10]. [ 10 ] KDEM Eglin.. 3.5.2 [3] [ 11]. - 20 -
[ 11] 4. 4.1 1970.[1][19].[1] 4.1.1,,.. - 2 1 -
(ft ) (kts) ( ) ( ) 50 10 0.1 0.2 [ 1 ] 4.1.2.,,.. (lbs) (inch ) (%) ( slug - f t) 2 20 0.5 4 5 [ 2 ] 4.1.3,,,. 5%. - 22 -
4.1.4.,... (kts) ( ) ( ) ( / sec) 5 5 50 2 [ 3 ] 4.2 [ 4] 450, 860 Knot s 45 MK- 82 LDGP. [ 5] 4. [ 4] 450 Knots 57%. 31%, 10%, 2%. 450 Knot s 10%, 860 Knots - 23 -
30%. 0. ( ) ( ) Inertia ( ) ( ) (ft) (Kts) (lbs) (Inch) (%) / sec (%) Ft/ sec ( ) (ft) (TAS) 50 10 0.1 0.2 20 0.5 4 5 5 5 5 50 2 450 76 125 41 45 7 20 14 12 11 36 9 61 44 0 5000 860 117 130 127 80 67 170 14 90 90 83 19 68 68 450 33 25 5 29 2 3 4 3 2 18 1 25 24 45 8000 860 27 75 3 35 3 5 2 2 4 26 1 19 17 [ 4 ] MK - 82 LDGP - 24 -
(ft) ( ) (ft) (TAS) 0 5000 45 8000 450 501 287(57%) 53(10%) 11(2%) 150(31% ) 860 1123 454(40%) 341(30%) 90(8%) 238(22% ) 450 174 92(53% ) 12(7%) 2(1%) 68(39%) 860 219 140(64%) 12(5%) 4(2%) 63(39%) [ 5 ] MK - 82 LDGP ( ).. 57%. 287ft 25ft..,..,.,... - 25 -
150ft 10ft.... 53ft 5ft.. 5. 5.1, (lbs) (Inch) (Inch) ( ) 531 10.8 87-1 :22.93 : 7.2 2.75 55.125-1 [ 6 ]. - 26 -
5.2.,,,,,,. 5.2.1 (1).. (F t ) ( ) (Kt s ) 1000 0 500 1 500-2000 0 400-600 2000 20 500 2 1000-6000 20 400-600 4000 30 500 3 3000-8000 30 400-600 8000 45 500 4 8000-12000 45, 60 400-600 [ 7 ] - 27 -
(2 ),,,... (ft ) (Kts) ( ) (lbs) (Inch) (%) (%) (ft/ sec) 50 10 0.1 20 0.5 5 5 2 [ 8 ] 5.2.2 (1) [ 9]. - 28 -
(ft ) (Mil) (sec) (Kt s (ft) ( ) ) 1000 500 0 6366 6366 0 157 157 0 7.76 7.74 0.02 2000 500 20 4147.0 4144 3 104 102 2 5.35 5.34 0.01 4000 500 30 5297 5300 3 126 124 2 7.49 7.46 0.03 8000 500 45 6100 6108 8 135 134 1 10.76 10.69 0.07 [ 9 ] 8ft, 10ft 50ft 250ft., [ 12] - [ 21 ]. [ 12] 0 500ft - 2000ft, 400kts- 600kts, [ 13]., 600kt s, 2000ft 140ft. 400-500kt s, - 29 -
500kts- 600kts. 400kt s 500-2000ft. 450-500kts 500-1500ft,. [ 12 ] 0 ( ) - 30 -
[ 13 ] 0 ( ) [ 14] 20 1500ft - 6000ft, 400kts- 600kts, [ 15]., 600kts, 6000ft 87ft. 400-500kts, 500kts- 600kts. 400kt s 1500-6000ft. 450-500kts 1500-4000ft,. - 3 1 -
[ 14 ] 20 ( ) [ 15 ] 20 ( ) - 32 -
[ 16] 30 3000ft - 8000ft, 400kts- 600kts, [ 17]., 600kt s, 8000ft 80ft. 400-500kts, 500kts- 600kts. 400kt s 3000-8000ft. 450-500kts 3000-6000ft,. [ 16 ] 30 ( ) - 33 -
[ 17 ] 30 ( ) [ 18] 45 6000ft - 10000ft, 400kts- 600kts, [ 19]., 600kts, 10000ft 62ft. 400-500kts, 500kts- 600kts. 400-450kts 6000-9000ft. 500kts 6000-8000ft,. - 34 -
[ 18 ] 45 ( ) [ 19 ] 45 ( ) - 35 -
[ 20] 60 8000ft - 12000ft, 400kts- 600kts, [ 21]., 600kts, 12000ft 38ft. 400-500kts, 500kts- 600kts. 400-450kts 8000-12000ft. 500kts 8000-10000ft,. [ 20 ] 60 ( ) - 36 -
[ 21 ] 60 ( ), [ 22] - [ 26 ]. [ 22 ] 0 ( ) - 37 -
[ 23 ] 20 ( ) [ 24 ] 30 ( ) - 38 -
[ 25 ] 45 ( ) [ 26 ] 60 ( ) - 39 -
[ 27 ] 60 ( )., [ 10]. (Mil) 0 20 30 45 60 500-2000 ft 1500-6000 ft 3000-8000 ft 6000-10000 ft 8000-12000 ft 400 0.1 1.4 1.1 0.5 0.2 450 0.4 1.6 1.7 1.2 0.6 500 0.5 2.7 1.9 1.5 1.0 550 0.9 2.2 2.3 2.1 1.2 600 1.3 3.2 3.3 3.1 2.2 [ 10 ] ( ) - 40 -
(2 ). (ft) (Kts) ( ) (lbs) (Inch) (%) (%) (Kts) 50 10 0.1 20 0.5 5 5 2 400 132 128 (40%) (38.8%) 1 0 1000 500 164 123 (40.3%) (30.3%) 600 194 119 (40.5%) (24.9%) 400 72 42 (48.3%) (28.2%) 2 20 2000 500 83 31 (52.5%) (19.6%) 600 92 20 (60.9%) (13.2%) 400 46 53 (33.3%) (38.4%) 3 30 4000 500 54 38 (40.3%) (28.3%) 600 59 24 (44.0%) (17.9%) 400 26 62 (18.3%) (43.7%) 4 45 8000 500 30 44 (24.5%) (36.1%) 600 33 26 (28.9%) (22.8%) 23 (6.9%) 35 (8.6%) 49 (10.2%) 11 (7.4%) 14 (8.9%) 15 (9.9%) 13 (9.4%) 16 (11.9%) 18 (13.4%) 15 (10.6%) 17 (13.9%) 19 (16.7%) 3 (0.9%) 2 (4.9%) 11 (2.3%) 2 (1.3%) 3 (1.9%) 5 (3.3%) 2 (1.4%) 5 (3.7%) 0 (0%) 2 (1.4%) 3 (2.4%) 7 (6.1%) 3 1 (0.9%) (0.3%) 16 9 (3.9%) (2.2%) 19 15 (4.0%) (3.1%) 0 3 (0%) (2.0%) 0 4 (0%) (2.5%) 3 2 (2.0%) (1.3%) 5 0 (3.6%) (0%) 0 0 (0%) (0%) 5 3 (3.7%) (2.2%) 4 4 (2.8%) (2.8%) 6 1 (4.9%) (0.8%) 8 1 (7.0%) (0.9%) 1 39 (0.3%) (11.8%) 9 48 (2.2%) (11.8%) 15 56 (3.1%) (11.7%) 3 16 (2.0%) (10.7%) 4 19 (2.5%) (12.2%) 2 12 (1.3%) (7.9%) 0 19 (0%) (13.8%) 0 21 (0%) (15.7%) 3 22 (2.2%) (16.4%) 4 25 (2.8%) (17.6%) 1 20 (0.8%) (16.3%) 1 19 (0.9%) (16.7%) (ft) 330 406 478 149 158 151 138 134 134 142 122 114 [ 11 ] ( ) - 4 1 -
(3 ),, 400-500kts 500kts- 600kts. 500-600kts.... [1], 2000-5300ft, 450-600kts, 0-25.. ( ) 134.3 ft 75.7 ft 17.3 ft 28.2 ft 5.3 Mil 2.98 Mil 1.5 Mil 0.93 Mil [ 12 ] [1] - 42 -
. [1],,,,. 10 ft... ( ) (kts) (ft ) 0 400-500 500-1500 20 400-600 1500-3000 30 400-600 3000-4000 45 400-550 6000-7000 60 400-550 8000 [ 13 ] ( ),,.. - 43 -
. 5.3 5.3.1.. (Ft ) ( ) (Kt s) 1 2 3 2000 500 20 1000-3000 400-550 2000-5000 500 30 1500-4000 400-550 8000 500 45 3000-6000 400-550 [ 14 ] 5.3.2 (1) [ 15]. - 44 -
(ft ) (ft) (CAS) ( ) *1 *2 200 0 400 0 800 0 [ 15 ] ( ) (Mil) (sec) *1 *2 *1 *2 500 20 5152 5121 31 35 38 2 2.34 2.32 0.02 500 30 6558 6467 91 36 43 7 3.23 3.20 0.03 500 45 7622 7435 227 30 43 13 4.77 4.73 0.04 *1 : *2 :,, [ 27] - [ 32]. [ 28] 20 1000ft - 3000ft, 400kts- 550kts, [ 29]... 550kts, 3000ft 73ft. - 45 -
[ 28 ] 20 ( ) [ 29 ] 20 ( ) [ 30] 30 2000ft - 5000ft, 400kts- 550kts - 46 -
, [ 31].. 550kts, 5000ft 140ft. [ 30 ] 30 ( ) [ 31 ] 30 ( ) - 47 -
[ 33] 45 4000ft - 8000ft, 400kts- 550kts, [ 34].. 550kts, 8000ft 205ft. [ 32 ] 45 ( ) [ 33 ] 45 ( ) - 48 -
, [ 35] - [ 37]. [ 34 ] 20 ( ) [ 35 ] 30 ( ) - 49 -
[ 36 ] 45 ( ).,., [ 16]. (Mil) 20 30 45 1000-3000 ft 2000-5000 ft 4000-8000 ft 400 kts 3.9 1.0 8.7 450 kts 2.7 2.8 13.2 500 kts 2.7 7.2 7.2 550 kts 2.8 7.4 7.4 [ 16] ( ) - 50 -
(2 )..,........... - 5 1 -
6.,,,...,, 8Ft 2Mil, 227Ft 14Mil.,.... - 52 -
7. [1] R.j.Arnold and J.B.Knight, W eapon Delivery Analysis and Ballistic Flight T esting AGARD- AG- 300 Vol.10, July 1992 [2],,, 1984 [3],,,, 1996. 12 [4] 2,, 4 -, 1994.9.9 [5] Sighard F. Hoerner, Fluid Dynamic Drag, Published by the Auther, 1965 [6] Robert H.M Surface- based air defense sy stem analysis, Artech Hou se Bost on London, 1992 [7] USAF, T O. 1F - 4D- 34-1- 1 [8] USAF, T O. 1F - 4D- 34-1- 2 [9] USAF, T O. 1A - 37B- 34-1- 1 [10] USAF Fighter Weapon School, Fighter Weapon School Instruction T ext Non - Nuclear Weapons Course 1115070D F - 4, USAF Fighter W eapon School, Feb.1971 [12] Bryan L. Wilkins, F - 4 Formal Flying T raining Conventional Weapon Delivery Reference T ext RT - 17, 35 T actical Fighter Wing, June 1990 [13] Bryan L. Wilkins, F - 4 Formal Flying T raining Conventional Weapon Delivery Computation Work Book, 35 T actical Fighter Wing, December 1989 [14],,, 1999.3 [15],,, 1994.12-53 -
[16] John H. Blakelock, Automatic Control of Aircraft and Missiles, John Wiley & Son s, May 1990 [17],,, 2 2, 1999.12 [18] Robert F.T omaro, Frank C.Witzeman, William S.Strang, Simulation of Store Separation for the F/ A - 19C Using Cobalt, Journal of Aircraft Vol.37, No3, May - June 2000 [19] Gonzales,J.M and Danny,A.R., Lt, USAF, T heoretical Sensitivity Analy sis and Sy stem Delivery Accur acy Computation s for High and Low Drag Weapon s at Sever al Subsonic Deliv ery Condition s, AFAT L- T R- 70-110, Air F or ce Arm ament Laborat ory, Eglin AFB, Florida, October, 1970-54 -
2.. 2...,,,..,,,,,,,.,,,,,,,,,,,.,, 2.,.,,. 2000 12-55 -