Maximum Speed of a Helicopter

Growing up as a kid my neighbor was a helicopter pilot for the local medical center, he would airlift patients who needed urgent care to the hospital as fast as possible to increase their chances of surviving whatever accident they had experienced.  I had always wondered just how fast he could get someone to the hospital, so I did a little research on the maximum speed of helicopters.

The topic ended up being much more complex than I had initially anticipated, and it has to do with the basic design of a helicopter's rotor blade.

If we consider a helicopter going 100m/s in the forward direction, and the blades are rotating at about 400m/s.  If we consider the one direction motion of the blades, then we can see that the blades will not be traveling at the same speed in when they are considered in the same direction as the  helicopter.  This causes our imagined helicopter above to have two blade speeds:

Traveling in the same direction of the copter (advancing blade) - 400m/s(blade speed) + 100m/s(copter speed)=500m/s
Traveling in the opposite direction of the copter (retreating blade) - 400m/s(blade speed) + 100m/s(copter speed)=300m/s

This disparity of speed causes the force of lift that the blades are experiencing to be unequal, providing different lift for each side of the copter.  To balance these forces, the blades are put on an angle so that the retreating blade can cause for force and the advancing blade can cause less force, putting them equal to one another.  But as we approach higher and higher speeds, the angle of the blades can only make up for so much of a difference in blade speed.  So, through much more advanced math than this class has covered, the aspects of unequal speed of the blade limit the helicopter to about 250mph, which covers a mile in a little more than 14 seconds!