Apparent Plane Speeds

The intent of this app is to show why planes flying at higher altitudes appear to be flying slower than those flying at lower altitudes.

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The green area represents the blocked portion of the field of vision for a viewer. The two red dots are planes and move at the same velocity. The lower plane, Plane 1, moves across the visible portion of the sky, the blue, a lot faster even though it is travelling at the same rate. This is because the two planes have different angular speeds despite having the same tangential velocity due to their different heights. These can be related by the differential equation ds/dt=r*dx/dt where ds/dt is velocity, r is the radius of the flight arc, and dx/dt is the angular speed.

App generated by Geometry Expressions