The chart on page 24 (see also the diagram of page 23) shows that the
lifting power of an aeroplane increases as the angle of inclination
increases, up to a certain limit. The resistance to propulsion also
increases, however: and the ratio of lifting power to resistance is
greatest at a very small angle--about five or six degrees. Since the
motor power and weight are ruling factors in design, it is important to
fly at about this angle. The supporting force is then about two pounds,
and the resistance about three-tenths of a pound, per square foot of
sail area, if the velocity is that assumed in plotting the chart:
namely, about fifty-five miles per hour.
But the resistance _R_ indicated on pages 23 and 24 is not the
only resistance to propulsion. In addition, we have the frictional
resistance of the air sliding along the sail surface. The amount of
this resistance is independent of the angle of inclination: it depends
directly upon the area of the planes, and in an indirect way on their
dimensions in the direction of movement. It also varies nearly with
the square of the velocity. At any velocity, then, the addition of
this frictional resistance, which does not depend on the angle of
inclination, modifies our views as to the desirable angle: and the
total resistance reaches a minimum (in proportion to the weight
supported) when the angle is about three degrees and the velocity about
fifty miles per hour.
This is not quite the best condition, however. The skin friction does
not vary exactly with the square of the velocity: and when the true law
of variation is taken into account, it is found that the _horse-power_
is a minimum at an angle of about five degrees and a speed of about
forty miles per hour. The weight supported per horse-power may then be
theoretically nearly a hundred pounds: and the frictional resistance is
about one-third the direct pressure resistance. This must be regarded
as the approximate condition of best effectiveness: not the exact
condition, because in arriving at this result we have regarded the
sails as square flat planes whereas in reality they are arched and of
rectangular form.
At the most effective condition, the resistance to propulsion is only
about one-tenth the weight supported. Evidently the air is helping the
motor.