For years, understanding one aspect of bullet trajectory has eluded my comprehension, so I thought:
Ask the SDMB gurus to explain physics to a dummy (me).
My question revolves around the old hunter’s adage about shooting uphill or downhill… “Always shoot
UNDER your intended target”.
My experience has proven this to be true, but I’ll be dammed if I can explain it.
To expand: (For the gun nuts out there, I know the numbers used here are unrealistic. I use them for the sake
of simplicity, so please don’t get into a snit.) A good rifle, scope, ammunition, and shooter are employed here,
so precision and/or accuracy are not the issue. It is sighted in at 100 yards horizontal to 1 MOA.
Why then, when shooting at the same target 100 yards away on a 45 degree incline or decline, must I “hold off”
(shoot under) the intended point of impact by 5 MOA to achieve the same hit?
It’s because the 100 yard distance is on the hypotenuse but the bullet drop is based on the distance travelled horizontally, so the bullet will drop only as far as it would in approximately 71 yards. Actually half the square root of two times the actual distance.
Reductio ad absurdum, suppose you were on top of a building and firing 1000 yards straight down, what would your bullet drop be? Nothing of course, zero distance horizontally, zero bullet drop. The same if you fired straight up except for loss of velocity due to gravity.
Also consider that the barrel points at a slight upward angle when the sight line is perfectly horizontal.
This means that for a straight up or down shot, with the barrel dead plumb, the sight line will be well “under” the point of impact. Additionally, when the sight line is vertical, The barrel is PAST vertical, so gravity will actually cause the bullet to “climb” with respect to a vertical sight line. I used the scare quotes because at these angles, it isn’t really up and down, just with respect to the gun’s frame of reference in the usual horizontal firing position.
I understand the Trig related to the distance traveled on a horizontal plane compared to the ACTUAL distance it traveled in your reply, but I’m confused… Is not the bullet drop defined by the flight TIME in relationship to the force of gravity? In either case, (horizontal, versus 45 degrees up OR down) the flight time would be the same to travel any given distance.
I can not see a correlation between the force of gravity acting differently upon a projectile traveling at something other than horizontal. Sorry.
Gravity does act based on the time. But the direction of that action is perpendicular for horizontal shots, and along the flight path for vertical shots. So for horizontal shots, it moves the point of impact, and for vertical shots it just adds or subtracts a little speed.
After years of gun “expert” forum discussions and suffering various physics “expert” quadratic equation explanations… For some reason your explanation just now clicked.
It’s assumed that a rifle has been zero’d in horizontally. The Line Of Sight is a straight line between the shooter and the target. A rifle’s sights can be .5" (iron sights) to 2" (telescopic sights) above the rifle’s Axis Of Bore (ballistic charts/programs usually assume a 1.5" difference). The gravitational force has been compensated for over the horizontal distance to target.
If the bullet’s Muzzle Velocity and Ballistic Coeffient is known, the bullet’s drop and impact at distance can be closely estimated.
Because bullet drop begins as soon as the bullet clears the muzzle, the Axis Of Bore (barrel angle) must be raised to allow the projectile to intersect the LOS at the sighted in distance. (The bullet crosses the LOS twice. Once on the way up and once on the way down.)
In order to judge how much lower a shooter must hold when shooting uphill/downhill, the shooter needs to know the distance to target mutiplied by the cosine of the angle. Assume the rifle is sighted-in to a horizontal point of aim at 300 yards, and your firing a similar bullet at the same muzzle velocity, and intend to hit a target 30 degree uphill, and 300 yards away. The cosine of 30 degrees is .866.
300 yds x .866 = 260 yds (40 yards less than a horizontal shot).
Or, knowing that a bullet would drop 24" at 300 horizontal yards.
24" x .866 = 20.78" (3.2" less drop than a horizontal shot).
