TWO distinct types of climb arise in aviation. In the first, it is necessary to climb to a given height without attaching any importance to horizontal distance covered. An example is a climb to take up patrol at a given height. Obviously the quickest way to do this is to climb at the maximum rate of climb possible at each instant. The second type of climb is more important. In this it is necessary to climb to cruising height while, at the same time, travelling as far as possible in a certain horizontal direction. Examples are the initial climb of transport 'planes and bombers, and the “chasing climb” of a fighter which has taken off to pursue an enemy. It seems possible that the first type of climb is not the best in this case; a flatter climb, such as that shown dotted in Fig. 1, may have a horizontal speed sufficiently great to more than compensate for the extra time required to reach cruising height—vertical distances are exaggerated to show more clearly.
Corner, J. (1940), "Optimum Climb to Height: The Quickest Method of Attaining Height at a Point Distant Horizontally from the Base", Aircraft Engineering and Aerospace Technology, Vol. 12 No. 5, pp. 147-148. https://doi.org/10.1108/eb030643
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