Nomographic Solution of the Momentum Equation for VTOL-STOL Aircraft

VTOL-STOL aircraft are characterized in general by the fact that in some portion of their flight envelope the wake is sharply inclined to the free stream. Under such conditions, the usual small-angle assumptions used in determining the induced velocities, and consequently, the power required, are no longer valid. Indeed, the use of small-angle assumptions leads to such anomalous results as infinite induced velocities and required power in the extreme case of hovering. The aforementioned difficulties may be avoided by a more complete examination of the horizontal and vertical momentum imparted to the air by the aircraft at low speeds. The resulting equation is a quartic in the induced velocity, and, as such, is difficult to apply. On the other hand, this quartic can be solved in its most general terms and the resulting solution then can be derived and presented in the form of a chart, or nomograph, from which the required induced velocities my be read directly. This paper presents such a chart.