Leupold Rangefinders and "True Ballistic Range"
This has been bothering me since they came out a year or two ago. I am wondering if anyone can fill in the blank I'm drawing here?
I know the tests - Sierra and others have shown bullets hit high when aiming on an incline, whether uphill or downhill.
I understand trigonometry. The straight line distance when on an incline is the hypotenuse, the straight line distance being shorter than the horizontal by a factor dependent upon the incline's angle. Obviously this makes sense empirically, as bullets hit high on an incline, suggesting the "true distance" is less than the line-of-sight.
However, when we get to the physics, that is where it seems to come apart for me. The bullet is travelling the length of the hypotenuse. It does travel your line of sight in reaching the target. A component of the bullet's absolute velocity will be in a non-horizontal direction when fired at an angle. As an example, if you shoot a rifle bullet straight up in the air, it covers no horizontal distance, as the vertical component is the whole of the velocity - but gravity is still acting on the bullet (which will bring it back down on you barring external stimuli) without any horizontal component to its travel. Therefore, the flight time of the round should be the same whether fired 400m on the horizontal or 400m uphill - it is still travelling 400m, meaning that a velocity of 1000m/s will require 4/10 of a second to arrive whether it is fired at, above or below the horizontal. The bullet drop is dependent upon gravity and the total flight time (recall from high school d=.5at^2).
The theory I've heard advanced is that gravity acts perpendicular to the horizontal distance, and that is the distance over which it acts upon the bullet for. However, recalling the above, it seems to make more sense that gravity is dependent upon flight time, not the horizontal component or distance. Again, the flight time will not be the result of multiplying the line-of-sight distance and the cosine of the incline angle, because the bullet is travelling that full line-of-sight distance (actually slightly more to account for the bullet's arc) to the target, whether or not the flight distance is anywhere close to the horizontal distance. As with my "shoot a bullet straight up" example, the assertion that gravity only acts on a horizontal component is misapplied at best.
I am not saying the phenomenon of bullets being higher than aimed at distance on an angle is not true - I am just wondering if it has been mis-explained to me, on account of the fact that it seems violative of the most basic trig and physics.