Maximum Escape Angle
When firing, the Maximum Escape Angle (MEA) is the largest angle offset from zero (i.e., HeadOn Targeting) that could possibly hit an enemy bot, given the Game Physics of Robocode.
Calculation
Let's assume a triangle with sides a
, b
and c
and angles (vertices) A
, B
, and C
. A
is the angle opposite to a
, B
is opposite to b, and C
is opposite to c
. The Law of sines says that:
Now let's say that your bot is in the vertex A
and the enemy bot is in the vertex C
. We will fire a bullet with angle A
to hit the bot in vertex B
. We know the value of b
(it is the distance D
from your bot to the enemy).
We don't know c
, but we know that it will be the distance traveled by the bullet. Also, we know that a
will be the distance traveled by the enemy bot. If we put a
, b
, and c
as a function of time, we have:
b = D c = Vb * t (Vb is the bullet speed) a = Vr * t (Vr is the enemy bot velocity)
Now, using the Law of sines:
a/sin(A) = c/sin(C) > Vr*t / sin(A) = Vb*t / sin(C) > sin(A) = Vr/Vb * sin(C) > A = asin(Vr/Vb * sin(C))
We don't know the value of C
, but we can take the worst scenario where
C = PI/2
(sin(C) = 1
) to get a Maximum Escape Angle of
A = asin(Vr/Vb * 1) = asin (Vr/Vb)
.
With a maximum Robot velocity of 8.0, a theoretical Maximum Escape Angle would be asin(8.0/Vb)
. Note that the actual maximum depends on the enemy's current heading, speed, and Wall Distance.
See Also
 Maximum Escape Angle/Precise Positional  A more precise method of calculating Maximum Escape Angle, that doesn't require movement simulation.
 Maximum Escape Angle/Precise  A sophisticated calculation for Maximum Escape Angle, using Precise Prediction.
