I am aware that one can calculate instantaneous velocity (velocity at any point of travel) by using calculus (the differential for a point tangent to a curve) but I am not aware of the formula that makes up the curve in order to fine a tangent point.

What is the formula for a line of flight for a bullet?

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Mccoy?

I have to admit I have never heard of it.

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quote:

Originally posted by 22WRF:
What is the formula for a line of flight for a bullet?

Unless you just want the Formula for a specific reason, any of the External Ballistic Software Programs I am familiar with will calculate it for you. All you have to do is enter a few things, tell it the distance you are interested in and it will be pretty close.

I'm real surprised alf hasn't "dumbed the Formula down" for everyone.

Actually, what I am interested in is the method that powder companies and cartridge companies use to state velocities at various ranges.

For example, one will state that the velocity is 2700 FPS out of the barrel, and 2300 FPS at 100 yards and 1900 FPS at 200 yards and so on and so forth. And of course, as that bullet travels downrange it is making an arc in its travel. Because rate of change is not linear I assume that the way to calculate the change at various yardages was to take the derivative at those points in flight. But you can't take a derivative of something at some point if you don't have the formula for the line of flight.
Just as (f)x= 2x + 1 is a formula for a certain curve, there must also be some formula for the line of flight of a bullet.

Or am I mistaken?

The simplified formula for path of flight is a parabola. However, this version only considers the influence of gravity, and calculus gives you the linear distance traversed. The projectile never slows until it runs out of elevation. When you add in air resistance, you're dealing with fluid dynamics, and things get complicated in a hurry, especially when considering both laminar flow and turbulent drag in supersonic flight. My guess is that the mfr's BC's are determined empirically, and probably for a good reason. It's rocket science until the rocket clears the atmosphere; then things get simpler for the rocket.