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National Advisory Committee for Aeronautics, Technical Notes - Airplanes in Horizontal Curvilinear Flight

War airplanes require not only high speed and the ability
to climb rapidly, but also the ability to traverse sharp curves
Quickly. An attempt is made, in the following note, to give a
simple method of calculating horizontal curvilinear flight.

A method for determining the area of the aileron and rudder sur-
faces will also be indicated. The following discussion applies
primarily to single and two-seater airplanes, although it can
be extended to larger airplanes.

Horizontal Curvilinear Flight.- Two conditions must be dis-
tinguished in connection with flight on_a horizontal turn,
circular and spiral flight. While circular flight can be main—
tained continuously, spiral flight forms a transition between
two circular flights. Between rectilinear flight, which may bevm
considered as flight in a circle of infinite radius, and the
smallest circle in which the airplane can fly, circular flights
of any desired radius can be flown. The most important equilib—
rium condition to be observed, in connection with flight in a
circle, is that the air resistance must be overcome by the pro—
peller thrust.

The resultant R (of the weight W and the horizontal centrifu~
gal force F at right angles to W) acts outward against the
lift L (Fig. 1). This resultant, as well as the lift, must be
at right angles to the supporting surfaces. This is only possi—
ble when the airplane is banked in the turn. The angle of bank
is determined by the magnitude of the centrifugal force, whithin
turn, depends on the speed of the airplane and the radius of
the flight curve.

The rudder and ailerons are used to maintain equilibrium
in the turn. The action of the forces and the primary condi-
tions of equilibrium will be explained later., It is only neces-
sary to observe here that the total resistance or drag of the
airplane is increased by the deflection of the control surfaces.
In the case of combat airplanes, where turning is of special
importance, this increase, however, is very slight. The increase
in airplane resistance may, therefore, be disregarded and atten-
tion concentrated on the calculation of the forces, the incli-
nation of the airplane and the radius of the turn.