# 13.5 Climbing Flight

Any excess in power beyond that required to overcome drag will cause the vehicle increase kinetic or potential energy. We consider this case by resolving forces about the direction of flight, Figure 13.6, and equating these with accelerations.

where is the acceleration normal to the flight path and is the acceleration tangent to the flight path. So the change in height of the vehicle (the rate of climb, ) is

which is instructive to rewrite in the form

or

In words:

For steady climbing flight,

and the time-to-climb is

where , for example, and . The power available is a function of the propulsion system, the flight velocity, altitude, etc. Typically it takes a form such as that shown in Figure 13.7. The shortest time-to-climb occurs at the flight velocity where is a maximum. We conclude this section with a dramatic photograph of an F-16 in a vertical, accelerated climb, Figure 13.8.

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