Calculating firing solution with angle

J

jonnefudge

New member
I am rather new to shooting and just bought this app ballistic arc. I have a really hard time understanding the results when it is calculating firing solution when firing in a angle uphill or downhill. I can not understand how it can more hold over on flat ground than shooting upward and also how small the hold over difference is between uphill or downhill.

Three solutions is provided below with 0, 30 and -30 degrees respectively.

Any input is greatly appreciated!

Jonne
Sweden



Rifle Scenar n140
Position 65.8° 21.7°
Shot Bearing 229°
Shot Angle 0.2°
Wind 2.1 m/s @ 360°
Pressure 29.9 in Hg
Temperature 1 °C
Relative Humidity 84%
Density Altitude -4041 m
Range (m) Elevation (mils) Wind (mils) Velocity (m/s) Energy (J) Time (sec)
0.0 * * 792 3150 0.00
100.0 0.0 R 0.1 727 2657 0.13
200.0 U 0.6 R 0.2 666 2226 0.28
300.0 U 1.6 R 0.3 607 1852 0.43
400.0 U 2.8 R 0.4 552 1529 0.61
500.0 U 4.1 R 0.5 499 1250 0.80
600.0 U 5.6 R 0.6 448 1008 1.01
700.0 U 7.5 R 0.7 400 803 1.24
800.0 U 9.6 R 0.8 355 632 1.51
900.0 U 12.1 R 1.0 319 511 1.81
1000.0 U 15.1 R 1.1 302 459 2.13


Rifle Scenar n140
Position 65.8° 21.7°
Shot Bearing 229°
Shot Angle 29.9°
Wind 2.1 m/s @ 360°
Pressure 29.9 in Hg
Temperature 1 °C
Relative Humidity 84%
Density Altitude -4041 m
Range (m) Elevation (mils) Wind (mils) Velocity (m/s) Energy (J) Time (sec)
0.0 * * 792 3150 0.00
100.0 D 0.1 R 0.1 727 2653 0.13
200.0 U 0.5 R 0.2 665 2221 0.28
300.0 U 1.4 R 0.3 606 1847 0.43
400.0 U 2.4 R 0.4 551 1525 0.61
500.0 U 3.6 R 0.5 498 1247 0.80
600.0 U 5.0 R 0.6 448 1007 1.01
700.0 U 6.7 R 0.7 400 803 1.24
800.0 U 8.6 R 0.8 355 633 1.51
900.0 U 10.9 R 1.0 319 511 1.81
1000.0 U 13.6 R 1.1 302 457 2.13




Rifle Scenar n140
Position 65.8° 21.7°
Shot Bearing 232°
Shot Angle -29.8°
Wind 2.1 m/s @ 360°
Pressure 29.9 in Hg
Temperature 1 °C
Relative Humidity 84%
Density Altitude -4041 m
Range (m) Elevation (mils) Wind (mils) Velocity (m/s) Energy (J) Time (sec)
0.0 * * 792 3150 0.00
100.0 D 0.1 R 0.1 728 2660 0.13
200.0 U 0.3 R 0.2 666 2230 0.28
300.0 U 1.1 R 0.3 608 1856 0.43
400.0 U 2.1 R 0.4 552 1532 0.61
500.0 U 3.2 R 0.5 499 1251 0.80
600.0 U 4.4 R 0.6 448 1008 1.01
700.0 U 5.9 R 0.8 399 801 1.24
800.0 U 7.7 R 0.9 354 629 1.51
900.0 U 9.8 R 1.1 318 509 1.81
1000.0 U 12.3 R 1.3 303 460 2.13
 
The bullet thinks that the distance to the target is the cosine of the angle up or down from the gun.

For 30 degrees, the cosine is 0.866. On a 300-yard shot, the apparent distance is 259.6 yards. Call it 260.

For a 200-yard zero on the usual Bambi rifle, the drop at 300 yards is typically around six inches. The drop at 260, I'm guessing, is maybe four to five inches. That's not enough difference to worry about. "Point it and pull; Hell ain't half-full."

Steeper angles and longer distances are needed for there to be serious amounts of correction.

For instance, my '06 has two feet of drop at 400 yards and four feet of drop at 500. 30 degrees and 500 yards = 433 yards as the holdover need. Easy to be off by eight to ten inches. Even worse at 45 degrees, since the cosine is 0.7071. The laser says 500, but the bullet thinks 350. Oops.
 
Stated differently, a rifle typically is zeroed over mostly flat terrain by elevating the bore axis above line of sight to the target. That angular difference, when applied to a target that is not level with the firing location, means you're kinda shooting at a more distant target than you intend. Thus, your progo's trajectory goes over your intended target.
 
I can not understand how it can more hold over on flat ground than shooting upward and also how small the hold over difference is between uphill or downhill.
Click to expand...


Leaving out the confusing math details, the way to understand the principle is actually simple.

Imagine a right triangle (90 degree angle).

set the base on the ground, so one leg points straight up.

put yourself (the shooter) on either of the end points, shooting from the "ground" up (uphill) , or from the upper point, down (downhill), in this case at a 45 degree angle.

the distance the bullet actually travels is the hypotenuse (the longest leg) BUT the distance that gravity acts on the bullet is the shorter leg's length, the leg on the "ground".

Since gravity is acting over the shorter leg, drop is less. SO, your hold over is different.

l\
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Another way to explain the same thing and I'll use Art's numbers. Suppose you are in an elevated stand hunting deer. From the base of the stand to a deer you are trying to shoot is 260 yards. But from the elevated position you are in a rangefinder might show the distance as 300 yards. In reality the bullet is only traveling the 260 yards. You'd get the same thing if shooting uphill.

And just to reinforce what others have said it is only a problem at longer ranges, or steep angles. The amount of bullet drop between 260 yards and 300 yards isn't significant with modern rifles. Maybe 19th century cartridges. But the difference between 500 and 550 yards requires more accurate ranging info. This is a major concern for archery hunters because of an arrow's trajectory and since shots are much closer the angle tends to be more severe in elevated stands.

My range finder not only tells me the distance to the target, but the degree of angle and the amount of hold over needed for that range and angle. There are ways to compensate.
 
Wow, I haven't seen anything that complicated since I used to hang around with "cannon cockers".
Angles up/down shorten the horizontal distance which is what affects bullet drop.
 
Gravity has the greatest effect on the trajectory of a bullet when the bullet travels at a 90 degree angle to it.

Gravity has the least effect on the trajectory when it's in the same direction. Imagine shooting at a target directly overhead or directly below. How much holdover/under would you need? Almost none.

As for uphill/downhill difference, imagine the change in vertical distance the bullet now travels. Imagine just dropping the bullet that distance. How much momentum is that? That's as much momentum as the bullet loses or gains by being fired uphill or downhill. That's not much in either direction.
 
I agree with what has been explained. I think for all practical purposes,its enough. I get that relative to gravity,the horizontal distance is key.

But I'm puzzling a bit over minor variables.
The bullet still travels the length of the hypotenuse in terms of air friction/velocity loss.
And the bullet still travels the length of the hypotenuse for time of flight.

So...Drag and wind and time/lead are different forces ,different "dimension" Different equations...? I think.

But it makes my brain ache to try to think about it.
 
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Yes, a full analytical solution would have to consider air resistance over the hypotenuse and the slightly longer time of flight. But the cosine correction for the angle is adequate for any usual range.
 
Seems gravity will also affect bullet velocity; a beneficial effect when shooting downward and a negative effect when shooting upward.
 
Fortunately for me,proficiency in "Mann's Flight Of The Bullet" calculations have been pretty well incorporated into user friendly ballistic programs that can work remarkably well.
Brother is working up loads for a 300RSAUM Armalite AR-10 top end he pins on his 308 occasionally.
A shooting buddy of his has a private range with a Doppler chrono setup. He can easily get very accurate chrono reads to 300 yds at this range.
He then can derive more accurate BC data than the advertised number.
Its amazing what we have access to today.
 
The process of the bullet dropping less when shooting up or down a significant slope is easier to understand if you realize that gravity affects the bullet over the horizontal distance to the target.
When you shoot up or down slopes the measured distance to the target is more than the horizontal distance to the same position. The bullet still travels the measured distance but is only affected by gravity over the horizontal distance. Since gravity doesn't make the bullet drop as much your point of impact will be higher when shooting up or down slope.

Now a bit of a spoiler:
Shooting up slope a tiny bit of gravity will also decelerate the bullets forward velocity while shooting down slope the same tiny bit of gravity will accelerate its forward velocity. If the distance is far enough you will notice that the down slope shot will hit a tiny bit higher than the upslope shot. Under normal hunting distances this affect on the velocity of a bullet is so small it is hardly worth considering.
 
"...firing solution..." That's about torpedoes and arty. You won't have time to fiddle with ballistics calculators(that were made by some programmer who likely had never seen a real firearm) when hunting.
Aim low when shooting in either direction and you'll be fine.
"..."Weaponization of Math"..." It was always a weapon being used against me in both grade and high school. snicker.
 
KISS
shooting low , aim high
shooting High, aim low

Was squirrel hunting, 20 foot away from truck, squirel was about 18 foot high, aimed @ middle of head, hit the shoulder,
 
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