User talk:Ctz

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

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Current method:

with:

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

First:

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

Then:

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

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:

$requiredelevation=ta{n}^{-1}(t)$