You need to make the animation with way more key frames.
That is the trick. Actually, simple like that.
It is because of how the engine calculates the 'betweens' of the frames, it interpolates from a vertex's position in one frame to the vertex's position in the next frame in an exact straight line. That's why it deflated when you turn it.
In MED search for the Options button, there you find a slider to adjust the measure of a turn.