An Odd Ballistics, Trajectory question…

[spamanon]

brickeyee,

That is why I specified subsonic only in my solution. I think that even if the bullet leaves the muzzle supersonically, as long as it 'quickly' slows to subsonic speeds (going straight up against gravity and air), the v^2 solution should give a reasonable approximation.
I think the general solution for the case where the trajectory is not vertical must be solved numerically because we would have two coupled differential equations. Vertical travel makes things a lot simpler!

 

[DaveBeal]

spamanon & brickeyee -

Thanks for this stuff - it's fascinating. I knew that subsonic drag is roughly proportional to the square of airspeed, but I'm amazed that drag decreases max height by 80% in a real world situation.

And I wasn't aware that in the supersonic realm, drag decreases with velocity. That's really counterintuitive.

 

[brickeyee]

...'quickly' slows to subsonic speeds...

Not quick enough.
The supersonic drag force is the largest force acting on the bullet, even in vertical flight.
You can get an idea of the magnitude by comparing the energy at the muzzle to the energy at 100 yards.
That energy was lost to drag.
If you assume a linear loss over the 100 yards you can find the drag force easily enough.

 

[spamanon]

Not quick enough.

You really don't know that for the case I was talking about! If the speed of sound is 1087 ft/s and the bullet leaves vertically at 1090 ft/s, I believe that the solution I gave would provide an accurate enough account because the bullet would drop below the speed of sound fairly quickly. Now for a bullet traveling at, say, 1300 ft/s I would have to agree with you. It all depends on your need for accuracy. I don't think we are going to find a solution that can get us the maximum height within 10 feet without taking into account the exact measured drag, the variation in air density with height, and many other smaller effects, (which means a numerical solution anyway) do you?

 

[Jim Watson]

I think you are close enough for practical purposes, lacking access to a major serious ballistics facility.

Your B.C. was way too high, though; .4 is a pretty good rifle bullet. Sierra shows the B.C. of a 180 gr .40 JHP as .170 from 850 to 1000 fps and .120 below 850; the kluge required to use G1 tables for bullets not the standard shape.

 

[TheBluesMan]

Another site that has statistics on this experiment: http://www.frfrogspad.com/miscella.htm#straight

 

[spamanon]

Hey thanks Jim Watson, I hadn't seen that site when I was looking for data. That would seem to bump the maximum height to around 4/5 mile. Interesting...