In bicycle/car races, the vehicles have a maximum acceleration potential. For simplicity's sake, let's assume that the max acceleration in any direction is capped at a certain constant. When going around corners, these vehicles "go wide", so that they don't go beyond their maximum acceleration when turning the corner. On the other hand, their ability to "go wide" is limited by the width of the road/track. So, one way to produce an egg-shape is to consider a racing track of a certain width, whose overall shape is in the form of an isosceles triangle. If the triangle is equilateral, and the width is wide enough, then the curve is circular. However, when we start reducing the width, we get a curve which starts getting pinched in 3 places. If we then lengthen the altitude of the triangle so that it is no longer equilateral, then the curve starts looking egg-shaped. I assume that curves such as these have been studied. Does anyone know what their equations are? Can anyone point me to any references?