[Illustration: CIRCULAR FLIGHT]
We are looking downward on an aeroplane _ab_ which has been moving
along the straight path _cd_. At _d_ it begins to describe the circle
_de_, the radius of which is _od_, around the center _o_. The outer
portion of the plane, at the edge _b_, must then move faster than the
inner edge _a_. We have seen that the direct air pressure on the plane
is proportional to the square of the velocity. The direct pressure
_P_ (see sketch on page 22) will then be greater at the outer than at
the inner limb; the lifting force _L_ will also be greater and the
outer limb will tend to rise, so that the plane (viewed from the rear)
will take the inclined position shown in the lower view: and this
inclination will increase as long as the outer limb travels faster than
the inner limb; that is, as long as the orbit continues to be curved.
Very soon, then, the plane will be completely tipped over.
Necessarily, the two velocities have the ratio _om_:_om´_; the
respective lifting forces must then be proportional to the squares of
these distances. The difference of lifting forces, and the tendency to
overturn, will be more important as the distances most greatly differ:
which is the case when the distance _om_ is small as compared with
_mm´_. The shorter the radius of curvature, the more dangerous, for a
given machine, is a circling flight: and in rounding a curve of given
radius the most danger is attached to the machine of greatest spread of
wing.