# Trajectory Angle at Impact Calc.

Discussion in 'Rifles, Bullets, Barrels & Ballistics' started by sscoyote, Apr 5, 2011.

1. ### sscoyoteWell-Known Member

Messages:
1,255
Joined:
Feb 26, 2003
Anybody know a simple method of how to do this? I'm assuming it's a trigonometry calc. of some sort, but would be kinda' nice to know.

Messages:
633
Joined:
Mar 8, 2007
The angle of your trajectory will be very close to parallel with the line of sight, even for long range.

Consider a typical 1000 yard trajectory where you have ~30 MOA of elevation on the scope. 30 MOA is 1/2 of one degree, and that's about the angle the trajectory is making to the LOS at the muzzle.

At the 1000 yard mark, the bullet is falling at a little steeper angle, probably 3/4 of one degree or maybe even 1 degree.

Considering the chaos that happens when the bullet hits an animal, this small angle can be considered parallel to the LOS with no practical error.

-Bryan

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Joined:
Feb 26, 2003

4. ### WildcatBWell-Known Member

Messages:
461
Joined:
Jan 27, 2008
If you want the trig version: It's the inverse tangent of (the change in height divided by the change in distance)

You can get both the change in height and change in distance list for small increments at a give distance from a ballistics calculator.

I used jbmballistics.com using a 5 yard increment to get the initial "change in height" and "change in distance" then copy/pasted it into excel and entered the formula

=DEGREES((ATAN((B2-B1)/((A2-A1)*36)))))

in the top cell to the right of the distance column then "filled down". The trajectory below is for a 208gr amax going 2400 fps and 5000 ft elevation.

B2-B1 gives the change in height
A2-A1 gives the change in distance - the *36 converts the yards to inches

Looking at the long list below... at 1000 yards it's 1.5 degrees, at 2000 it's 5.96 degrees, and 3000 it's 13.6 degrees

If you really want to know, you should do this for your bullets' trajectory.

distance|drop|angle
0 -2.4 0.19
5 -1.8 0.16
10 -1.3 0.16
15 -0.8 0.16
20 -0.3 0.13
25 0.1 0.16
30 0.6 0.13
35 1 0.13
40 1.4 0.13
45 1.8 0.13
50 2.2 0.13
55 2.6 0.13
60 3 0.10
65 3.3 0.10
70 3.6 0.13
75 4 0.10
80 4.3 0.06
85 4.5 0.10
90 4.8 0.06
95 5 0.10
100 5.3 0.06
105 5.5 0.06
110 5.7 0.06
115 5.9 0.03
120 6 0.06
125 6.2 0.03
130 6.3 0.03
135 6.4 0.03
140 6.5 0.03
145 6.6 0.00
150 6.6 0.03
155 6.7 0.00
160 6.7 0.00
165 6.7 0.00
170 6.7 0.00
175 6.7 -0.03
180 6.6 0.00
185 6.6 -0.03
190 6.5 -0.03
195 6.4 -0.03
200 6.3 -0.03
205 6.2 -0.06
210 6 -0.06
215 5.8 -0.06
220 5.6 -0.06
225 5.4 -0.06
230 5.2 -0.06
235 5 -0.10
240 4.7 -0.10
245 4.4 -0.10
250 4.1 -0.10
255 3.8 -0.13
260 3.4 -0.10
265 3.1 -0.13
270 2.7 -0.13
275 2.3 -0.13
280 1.9 -0.16
285 1.4 -0.13
290 1 -0.16
295 0.5 -0.16
300 0 -0.16
305 -0.5 -0.19
310 -1.1 -0.16
315 -1.6 -0.19
320 -2.2 -0.19
325 -2.8 -0.19
330 -3.4 -0.22
335 -4.1 -0.19
340 -4.7 -0.22
345 -5.4 -0.22
350 -6.1 -0.25
355 -6.9 -0.22
360 -7.6 -0.25
365 -8.4 -0.25
370 -9.2 -0.25
375 -10 -0.25
380 -10.8 -0.29
385 -11.7 -0.25
390 -12.5 -0.29
395 -13.4 -0.32
400 -14.4 -0.29
405 -15.3 -0.32
410 -16.3 -0.32
415 -17.3 -0.32
420 -18.3 -0.32
425 -19.3 -0.35
430 -20.4 -0.35
435 -21.5 -0.35
440 -22.6 -0.35
445 -23.7 -0.38
450 -24.9 -0.35
455 -26 -0.38
460 -27.2 -0.41
465 -28.5 -0.38
470 -29.7 -0.41
475 -31 -0.41
480 -32.3 -0.41
485 -33.6 -0.41
490 -34.9 -0.45
495 -36.3 -0.45
500 -37.7 -0.45
505 -39.1 -0.48
510 -40.6 -0.45
515 -42 -0.48
520 -43.5 -0.48
525 -45 -0.51
530 -46.6 -0.48
535 -48.1 -0.51
540 -49.7 -0.54
545 -51.4 -0.51
550 -53 -0.54
555 -54.7 -0.54
560 -56.4 -0.54
565 -58.1 -0.57
570 -59.9 -0.54
575 -61.6 -0.60
580 -63.5 -0.57
585 -65.3 -0.60
590 -67.2 -0.57
595 -69 -0.64
600 -71 -0.60
605 -72.9 -0.64
610 -74.9 -0.64
615 -76.9 -0.64
620 -78.9 -0.67
625 -81 -0.64
630 -83 -0.67
635 -85.1 -0.70
640 -87.3 -0.70
645 -89.5 -0.70
650 -91.7 -0.70
655 -93.9 -0.70
660 -96.1 -0.73
665 -98.4 -0.73
670 -100.7 -0.76
675 -103.1 -0.76
680 -105.5 -0.76
685 -107.9 -0.76
690 -110.3 -0.80
695 -112.8 -0.80
700 -115.3 -0.80
705 -117.8 -0.83
710 -120.4 -0.83
715 -123 -0.83
720 -125.6 -0.83
725 -128.2 -0.86
730 -130.9 -0.86
735 -133.6 -0.89
740 -136.4 -0.89
745 -139.2 -0.89
750 -142 -0.89
755 -144.8 -0.92
760 -147.7 -0.92
765 -150.6 -0.95
770 -153.6 -0.92
775 -156.5 -0.95
780 -159.5 -0.99
785 -162.6 -0.99
790 -165.7 -0.99
795 -168.8 -0.99
800 -171.9 -1.02
805 -175.1 -1.02
810 -178.3 -1.05
815 -181.6 -1.05
820 -184.9 -1.05
825 -188.2 -1.05
830 -191.5 -1.08
835 -194.9 -1.11
840 -198.4 -1.08
845 -201.8 -1.11
850 -205.3 -1.15
855 -208.9 -1.11
860 -212.4 -1.15
865 -216 -1.18
870 -219.7 -1.18
875 -223.4 -1.18
880 -227.1 -1.18
885 -230.8 -1.21
890 -234.6 -1.24
895 -238.5 -1.21
900 -242.3 -1.27
905 -246.3 -1.24
910 -250.2 -1.27
915 -254.2 -1.27
920 -258.2 -1.30
925 -262.3 -1.30
930 -266.4 -1.30
935 -270.5 -1.34
940 -274.7 -1.34
945 -278.9 -1.37
950 -283.2 -1.37
955 -287.5 -1.37
960 -291.8 -1.40
965 -296.2 -1.43
970 -300.7 -1.40
975 -305.1 -1.43
980 -309.6 -1.46
985 -314.2 -1.46
990 -318.8 -1.46
995 -323.4 -1.50
1000 -328.1 -1.50
1005 -332.8 -1.53
1010 -337.6 -1.53
1015 -342.4 -1.56
1020 -347.3 -1.56
1025 -352.2 -1.56
1030 -357.1 -1.59
1035 -362.1 -1.59
1040 -367.1 -1.62
1045 -372.2 -1.62
1050 -377.3 -1.65
1055 -382.5 -1.65
1060 -387.7 -1.65
1065 -392.9 -1.69
1070 -398.2 -1.72
1075 -403.6 -1.72
1080 -409 -1.72
1085 -414.4 -1.75
1090 -419.9 -1.78
1095 -425.5 -1.75
1100 -431 -1.81
1105 -436.7 -1.78
1110 -442.3 -1.85
1115 -448.1 -1.85
1120 -453.9 -1.85
1125 -459.7 -1.85
1130 -465.5 -1.91
1135 -471.5 -1.88
1140 -477.4 -1.94
1145 -483.5 -1.91
1150 -489.5 -1.97
1155 -495.7 -1.94
1160 -501.8 -2.00
1165 -508.1 -1.97
1170 -514.3 -2.04
1175 -520.7 -2.00
1180 -527 -2.07
1185 -533.5 -2.07
1190 -540 -2.07
1195 -546.5 -2.10
1200 -553.1 -2.10
1205 -559.7 -2.13
1210 -566.4 -2.16
1215 -573.2 -2.16
1220 -580 -2.16
1225 -586.8 -2.23
1230 -593.8 -2.20
1235 -600.7 -2.23
1240 -607.7 -2.26
1245 -614.8 -2.29
1250 -622 -2.26
1255 -629.1 -2.32
1260 -636.4 -2.32
1265 -643.7 -2.35
1270 -651.1 -2.35
1275 -658.5 -2.35
1280 -665.9 -2.42
1285 -673.5 -2.42
1290 -681.1 -2.42
1295 -688.7 -2.45
1300 -696.4 -2.48
1305 -704.2 -2.48
1310 -712 -2.51
1315 -719.9 -2.51
1320 -727.8 -2.54
1325 -735.8 -2.58
1330 -743.9 -2.58
1335 -752 -2.61
1340 -760.2 -2.64
1345 -768.5 -2.64
1350 -776.8 -2.64
1355 -785.1 -2.70
1360 -793.6 -2.70
1365 -802.1 -2.70
1370 -810.6 -2.74
1375 -819.2 -2.77
1380 -827.9 -2.80
1385 -836.7 -2.80
1390 -845.5 -2.83
1395 -854.4 -2.83
1400 -863.3 -2.86
1405 -872.3 -2.89
1410 -881.4 -2.89
1415 -890.5 -2.93
1420 -899.7 -2.96
1425 -909 -2.96
1430 -918.3 -2.99
1435 -927.7 -3.02
1440 -937.2 -3.02
1445 -946.7 -3.05
1450 -956.3 -3.08
1455 -966 -3.08
1460 -975.7 -3.12
1465 -985.5 -3.15
1470 -995.4 -3.18
1475 -1005.4 -3.18
1480 -1015.4 -3.18
1485 -1025.4 -3.24
1490 -1035.6 -3.24
1495 -1045.8 -3.28
1500 -1056.1 -3.31
1505 -1066.5 -3.31
1510 -1076.9 -3.34
1515 -1087.4 -3.37
1520 -1098 -3.40
1525 -1108.7 -3.40
1530 -1119.4 -3.43
1535 -1130.2 -3.43
1540 -1141 -3.50
1545 -1152 -3.50
1550 -1163 -3.53
1555 -1174.1 -3.53
1560 -1185.2 -3.59
1565 -1196.5 -3.59
1570 -1207.8 -3.62
1575 -1219.2 -3.62
1580 -1230.6 -3.69
1585 -1242.2 -3.69
1590 -1253.8 -3.72
1595 -1265.5 -3.72
1600 -1277.2 -3.78
1605 -1289.1 -3.78
1610 -1301 -3.81
1615 -1313 -3.85
1620 -1325.1 -3.85
1625 -1337.2 -3.88
1630 -1349.4 -3.91
1635 -1361.7 -3.94
1640 -1374.1 -3.97
1645 -1386.6 -3.97
1650 -1399.1 -4.04
1655 -1411.8 -4.04
1660 -1424.5 -4.04
1665 -1437.2 -4.10
1670 -1450.1 -4.10
1675 -1463 -4.16
1680 -1476.1 -4.16
1685 -1489.2 -4.19
1690 -1502.4 -4.19
1695 -1515.6 -4.26
1700 -1529 -4.26
1705 -1542.4 -4.29
1710 -1555.9 -4.32
1715 -1569.5 -4.35
1720 -1583.2 -4.35
1725 -1596.9 -4.42
1730 -1610.8 -4.42
1735 -1624.7 -4.45
1740 -1638.7 -4.48
1745 -1652.8 -4.51
1750 -1667 -4.54
1755 -1681.3 -4.54
1760 -1695.6 -4.61
1765 -1710.1 -4.61
1770 -1724.6 -4.64
1775 -1739.2 -4.67
1780 -1753.9 -4.70
1785 -1768.7 -4.73
1790 -1783.6 -4.73
1795 -1798.5 -4.80
1800 -1813.6 -4.80
1805 -1828.7 -4.83
1810 -1843.9 -4.86
1815 -1859.2 -4.89
1820 -1874.6 -4.92
1825 -1890.1 -4.95
1830 -1905.7 -4.95
1835 -1921.3 -5.02
1840 -1937.1 -5.02
1845 -1952.9 -5.05
1850 -1968.8 -5.11
1855 -1984.9 -5.11
1860 -2001 -5.14
1865 -2017.2 -5.17
1870 -2033.5 -5.17
1875 -2049.8 -5.24
1880 -2066.3 -5.27
1885 -2082.9 -5.27
1890 -2099.5 -5.33
1895 -2116.3 -5.33
1900 -2133.1 -5.40
1905 -2150.1 -5.40
1910 -2167.1 -5.43
1915 -2184.2 -5.46
1920 -2201.4 -5.49
1925 -2218.7 -5.52
1930 -2236.1 -5.55
1935 -2253.6 -5.58
1940 -2271.2 -5.62
1945 -2288.9 -5.65
1950 -2306.7 -5.68
1955 -2324.6 -5.68
1960 -2342.5 -5.74
1965 -2360.6 -5.77
1970 -2378.8 -5.77
1975 -2397 -5.84
1980 -2415.4 -5.84
1985 -2433.8 -5.90
1990 -2452.4 -5.90
1995 -2471 -5.96
2000 -2489.8 -5.96
2005 -2508.6 -6.03
2010 -2527.6 -6.03
2015 -2546.6 -6.06
2020 -2565.7 -6.12
2025 -2585 -6.12
2030 -2604.3 -6.15
2035 -2623.7 -6.21
2040 -2643.3 -6.21
2045 -2662.9 -6.25
2050 -2682.6 -6.31
2055 -2702.5 -6.31
2060 -2722.4 -6.34
2065 -2742.4 -6.40
2070 -2762.6 -6.40
2075 -2782.8 -6.43
2080 -2803.1 -6.50
2085 -2823.6 -6.50
2090 -2844.1 -6.56
2095 -2864.8 -6.56
2100 -2885.5 -6.62
2105 -2906.4 -6.62
2110 -2927.3 -6.69
2115 -2948.4 -6.69
2120 -2969.5 -6.75
2125 -2990.8 -6.75
2130 -3012.1 -6.81
2135 -3033.6 -6.84
2140 -3055.2 -6.87
2145 -3076.9 -6.87
2150 -3098.6 -6.94
2155 -3120.5 -6.97
2160 -3142.5 -7.00
2165 -3164.6 -7.03
2170 -3186.8 -7.06
2175 -3209.1 -7.13
2180 -3231.6 -7.13
2185 -3254.1 -7.16
2190 -3276.7 -7.22
2195 -3299.5 -7.22
2200 -3322.3 -7.28
2205 -3345.3 -7.28
2210 -3368.3 -7.34
2215 -3391.5 -7.38
2220 -3414.8 -7.41
2225 -3438.2 -7.41
2230 -3461.6 -7.50
2235 -3485.3 -7.50
2240 -3509 -7.53
2245 -3532.8 -7.56
2250 -3556.7 -7.63
2255 -3580.8 -7.63
2260 -3604.9 -7.69
2265 -3629.2 -7.72
2270 -3653.6 -7.72
2275 -3678 -7.78
2280 -3702.6 -7.84
2285 -3727.4 -7.84
2290 -3752.2 -7.88
2295 -3777.1 -7.94
2300 -3802.2 -7.94
2305 -3827.3 -8.00
2310 -3852.6 -8.03
2315 -3878 -8.06
2320 -3903.5 -8.09
2325 -3929.1 -8.13
2330 -3954.8 -8.16
2335 -3980.6 -8.22
2340 -4006.6 -8.25
2345 -4032.7 -8.25
2350 -4058.8 -8.31
2355 -4085.1 -8.34
2360 -4111.5 -8.41
2365 -4138.1 -8.41
2370 -4164.7 -8.47
2375 -4191.5 -8.50
2380 -4218.4 -8.50
2385 -4245.3 -8.59
2390 -4272.5 -8.59
2395 -4299.7 -8.62
2400 -4327 -8.69
2405 -4354.5 -8.72
2410 -4382.1 -8.75
2415 -4409.8 -8.78
2420 -4437.6 -8.81
2425 -4465.5 -8.87
2430 -4493.6 -8.87
2435 -4521.7 -8.94
2440 -4550 -8.97
2445 -4578.4 -9.03
2450 -4607 -9.03
2455 -4635.6 -9.09
2460 -4664.4 -9.12
2465 -4693.3 -9.15
2470 -4722.3 -9.18
2475 -4751.4 -9.25
2480 -4780.7 -9.28
2485 -4810.1 -9.31
2490 -4839.6 -9.34
2495 -4869.2 -9.37
2500 -4898.9 -9.43
2505 -4928.8 -9.46
2510 -4958.8 -9.49
2515 -4988.9 -9.52
2520 -5019.1 -9.59
2525 -5049.5 -9.62
2530 -5080 -9.65
2535 -5110.6 -9.68
2540 -5141.3 -9.71
2545 -5172.1 -9.77
2550 -5203.1 -9.80
2555 -5234.2 -9.86
2560 -5265.5 -9.86
2565 -5296.8 -9.93
2570 -5328.3 -9.96
2575 -5359.9 -9.99
2580 -5391.6 -10.05
2585 -5423.5 -10.08
2590 -5455.5 -10.11
2595 -5487.6 -10.14
2600 -5519.8 -10.20
2605 -5552.2 -10.23
2610 -5584.7 -10.27
2615 -5617.3 -10.33
2620 -5650.1 -10.36
2625 -5683 -10.39
2630 -5716 -10.42
2635 -5749.1 -10.48
2640 -5782.4 -10.51
2645 -5815.8 -10.54
2650 -5849.3 -10.60
2655 -5883 -10.64
2660 -5916.8 -10.67
2665 -5950.7 -10.70
2670 -5984.7 -10.76
2675 -6018.9 -10.79
2680 -6053.2 -10.85
2685 -6087.7 -10.88
2690 -6122.3 -10.91
2695 -6157 -10.94
2700 -6191.8 -11.00
2705 -6226.8 -11.03
2710 -6261.9 -11.10
2715 -6297.2 -11.10
2720 -6332.5 -11.16
2725 -6368 -11.22
2730 -6403.7 -11.25
2735 -6439.5 -11.28
2740 -6475.4 -11.31
2745 -6511.4 -11.37
2750 -6547.6 -11.40
2755 -6583.9 -11.46
2760 -6620.4 -11.49
2765 -6657 -11.52
2770 -6693.7 -11.59
2775 -6730.6 -11.62
2780 -6767.6 -11.65
2785 -6804.7 -11.71
2790 -6842 -11.74
2795 -6879.4 -11.80
2800 -6917 -11.80
2805 -6954.6 -11.89
2810 -6992.5 -11.89
2815 -7030.4 -11.95
2820 -7068.5 -12.01
2825 -7106.8 -12.04
2830 -7145.2 -12.07
2835 -7183.7 -12.13
2840 -7222.4 -12.16
2845 -7261.2 -12.19
2850 -7300.1 -12.26
2855 -7339.2 -12.29
2860 -7378.4 -12.35
2865 -7417.8 -12.38
2870 -7457.3 -12.44
2875 -7497 -12.44
2880 -7536.7 -12.53
2885 -7576.7 -12.56
2890 -7616.8 -12.59
2895 -7657 -12.65
2900 -7697.4 -12.68
2905 -7737.9 -12.71
2910 -7778.5 -12.77
2915 -7819.3 -12.83
2920 -7860.3 -12.83
2925 -7901.3 -12.92
2930 -7942.6 -12.92
2935 -7983.9 -13.01
2940 -8025.5 -13.01
2945 -8067.1 -13.10
2950 -8109 -13.10
2955 -8150.9 -13.16
2960 -8193 -13.22
2965 -8235.3 -13.25
2970 -8277.7 -13.28
2975 -8320.2 -13.35
2980 -8362.9 -13.41
2985 -8405.8 -13.44
2990 -8448.8 -13.47
2995 -8491.9 -13.53

5. ### royinidahoWriters Guild

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Jan 20, 2004
Paul,

You're my kind of guy!!

So how to I calc Inches/Foot

6. ### rscott5028Well-Known Member

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2,608
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Apr 18, 2010
nose up, nose down, or level flight on final approach?

and, wouldn't these small numbers be quickly offset by your angle of attack? i.e. shooting uphill/downhill

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633
Joined:
Mar 8, 2007
The bullets axis will be parallel to the flight path (nose down).

The angle will be relative to the LOS. So if you're shooting 5 degrees uphill, the bullet may be falling at a 1.5 degree angle to the LOS, which is actually a 3.5 degree angle with 'true' level.

-Bryan

8. ### rscott5028Well-Known Member

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Apr 18, 2010
Bryan - Thanks!

9. ### edgeWell-Known Member

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Joined:
Nov 4, 2005
Hmmm, I always envisioned the path to be parabolic

With that said, the base is following the nose so the angle of the bullet to the muzzle, OR the angle to the animal should be irrelevant!

If you shot far enough the bullet should be coming down near a 45 degree angle, BUT nose first as if you were 30 feet up a tree and the animal were 30 feet away....IMO.

edge.

PS are you assuming that the twist will cause the bullet to impact with significant yaw??

Last edited: Apr 7, 2011
10. ### LouBoydWell-Known Member

Messages:
770
Joined:
Oct 15, 2007
Here's an example of calculating the terminal angle of a 300 Win Mag shooting 210 Bergers at 2850 FPS MV, Altitude 5800 ft (Where I live). The target is at 1500 yards.
The computer program I used to get the bascic trajetory table was "Quicktarget" the companion progrom to Quickload> Most ballistic programs will work.
I set the range increment to 10 yards. and the distance to 1510 yards To determine the angle at 1500 yrds:
It
distance drop
1490 yards 1065.8"
1510 yards 1108.7"

convert the differences to the same units:
20 yards x 36 in/yd is 720 inches
1108.7" - 1065.8" = 42.9 inches drop over the 20 yard distance centered at 1500 yards.

divide the drop by the distance
42.9 divided by 720 is 0.0596 (a dimensionless ratio)
Take the arc-tangent (aka inverse tangent) of the ratio of drop to distance at the target.
ATAN (0.0596) = 3.41 degrees above horizontal.

I don't know of an accurate shortcut.. The needed inputs are only bullet BC, muzzle velocity, Distance, and air density for a horizontal shot. Its more complcated for uphill or downhill shots.

For every trajectory which will hit the target there is a second high angle trajectory which will also impact the target for the same bullet fired with the same muzzle velocity. It will hit the target with a higher angle (up to 90 degees for close tragets). It will always carry lower energy and have a longer time of flight. It's not very
useful for hunting.

Last edited: Apr 7, 2011