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Trajectory Angle at Impact Calc.

 
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  #1  
Old 04-05-2011, 02:53 AM
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Trajectory Angle at Impact Calc.

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.
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  #2  
Old 04-05-2011, 08:14 AM
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Re: Trajectory Angle at Impact Calc.

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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  #3  
Old 04-06-2011, 05:28 PM
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Re: Trajectory Angle at Impact Calc.

Thanks Bryan--'preciate the simplified answer sir...just like your 1st book!
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  #4  
Old 04-06-2011, 10:32 PM
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Re: Trajectory Angle at Impact Calc.

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
DEGREES converts the answer from radians to degrees


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





Quote:
Originally Posted by sscoyote View Post
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.
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  #5  
Old 04-07-2011, 10:14 AM
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Join Date: Jan 2004
Location: Blackfoot, Idaho
Posts: 8,090
Re: Trajectory Angle at Impact Calc.

Paul,

You're my kind of guy!!

So how to I calc Inches/Foot
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  #6  
Old 04-07-2011, 11:50 AM
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Join Date: Apr 2010
Location: Allen, TX
Posts: 2,608
Re: Trajectory Angle at Impact Calc.

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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Old 04-07-2011, 12:51 PM
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Re: Trajectory Angle at Impact Calc.

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
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Bryan Litz
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And: Accuracy and Precision for Long Range Shooting

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