This is a fun problem that I am doing in my time off.
First, let me give you an intro. Helicopter medical evacuation (MEDEVAC) flies out of a hospital (H1), lands at the point of injury (P), and returns to H. This must be completed within X flying distance. Thus, the coverage of the MEDEVAC is said to be pi*(X/2)^2 around point H. Sometimes coverage areas overlap and we have to subtract the overlapping region. That is the easy part.
Now comes to the fun stuff. Let's say that a hospital (H2) is placed outside of the normal coverage area (somewhere between 0 and X from H1), but no MEDEVAC is placed there. This makes is a hospital that patients can be dropped off at, but helicopters coverage cannot be based out of. Thus, the helicopter must fly out of H1 and land at H2 within X distance. Now, we have to figure out the area of additional coverage due to the addition of H2 (but no additional helos).
I'm trying to do this in Matlab. I also would like to figure out a way to display all of this coverage some sort of a 2D graph.
The hardest part is explaining the problem.
I've been able to figure out the coverage area with just hospitals that have MEDEVAC capabilities. Once I throw the hospitals without the MEDEVAC capabilities, I don't even know where to begin to define the shape created by the additional coverage.
Since the MEDEVAC circles have equal radii, the following equations work for calculating the overlap between circles.
X = 100; %max distance MED aircraft can fly
r = X/2; %radius of the MED circle
d = 80; %distance from centers of two circles
q = 2*acos(d/(2*r)); %angle in radians
overlap = r^2*(q-sin(q)); %area of overlap
Area = 2*pi*r^2-overlap
I just need help moving on to calculating the area created by hospitals without MEDEVAC facilities.