User talk:Ctz

Good stuff with the Alan Turing photo; it's a nice addition. &mdash; Matt 00:29, 17 Jun 2004 (UTC)

Current method:

with:


 * 1) $$r$$ as the required range as the crow flies.
 * 2) $$v$$ as the muzzle velocity.
 * 3) $$g$$ as gravity.
 * 4) $$\Delta H$$ as the difference in height between gun and target.

First:

$$A := \frac{-g r^2}{2v^2}$$

Then:

$$k := r^2 - 4A(A - \Delta H)$$

If $$k$$ here is negative, then the required range can never be met.

Now:

$$t := \frac{-r \pm k}{2A}$$

(The negative solution here is the parabolic trajectory, the positive is the direct trajectory.)

Finally:

$$required\ elevation = tan^{-1}(t)$$