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Old November 28, 2007, 08:44 PM   #1
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Leupold Rangefinders and "True Ballistic Range"

Hey all,

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.
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Old November 29, 2007, 01:32 PM   #2
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Old November 29, 2007, 04:09 PM   #3
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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
The hypotenuse is always the longest angle........with the horizontal line being shorter......If I am understanding you are saying the hypotenuse is shorter than the horizontal line.....
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Old November 29, 2007, 05:40 PM   #4
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1. Gravity acts on a plane that intersects the central axis of the earth and so in effect, if you could plot the strength of gravity on a cross section of the earth, gravity would be illustrated as rings around the earth.

2. Gravity affects everything! Even light, so what we think of as a straight line of sight is actually curved, albeit ever so slighlty.

3. Gravity acts on the mass of an object and not its size. A cardboard box and a rock having the same mass would be acted on equally by gravity.

4. As you move farther away from the center of the earth, the force of gravity becomes less.

If bullets were like rockets and could sustain peak velocities, the could travel much further before hitting the ground, however, they are not and gravity, in conjunction with friction, acts upon the bullet causing it to lose velocity and eventually stop. Likewise, if a bullet were fired in a vacuum, it would retain near peak velocity and travel much farther before stopping.

I think one could assume that a bullet fired on a line of sight parallel to the earth's surface would have a higher amount (over time) of gravitational forces applied to it than a bullet fired on a path perpendicular (sp) to the earth's surface, and being such would travel a slightly shorter distance within a measured time frame (may be fractional). Assuming that this is true, a bullet fired on a horizontal path would have slightly less gravitational forces acting on it producing an altered flight path.

Bclark1 is any of this making sense to you? It works out in my head!
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Old November 30, 2007, 12:25 AM   #5
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When you fire a bullet on an incline, the force of gravity acting on the bullet is the sine of the angle.
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Old November 30, 2007, 12:58 AM   #6
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Full analysis

You can't just use a simple angle correction. The reason is that the bullet is decelerating along its true path, not some shorter path you compute.

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Old December 2, 2007, 12:44 AM   #7
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Splat!! - That was a typo, sorry! I meant the hypotenuse is longer horizontal distance by a factor dependent upon the angle, specifically the multiplicative inverse of the cosine.

Zak, I assume you were asserting that the explanation I disagree with is false? I am actually just using this as a 5-minute work break (00:38 on Sunday morning and this is what I'm doing, ugh), so I don't have time to read that thoroughly at the moment, but plan to as soon as things calm down a bit. However, the diagrams in the website you put up make a bit more sense than the explanation I was operating under - I suspected it had more to do with the relationship of the line of sight through the sights and the bore-line as a result of the incline, which this article appears to suggest. Hopefully I'm looking at it correctly, it's been a long week unfortunately.

Thanks for the discussion, happy for the clarification.
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