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National Advisory Committee for Aeronautics, Technical Notes - A Comparison of Several Tapered Wings Designed to Avoid Tip Stalling

Optimum proportions of tapered wings were investigat-
ed by a method that involved a comparison of wings de—
signed to be aerodynamically equal. The conditions of
aerodynamic equality were equality in stalling speed, in
induced drag at a low speed, and in the total drag at
cruising speed. After the wings were adjusted to aerody—
namic equivalence, the weights of the wings were calcu-
lated as a convenient method of indicating the optimum
wing. The aerodynamic characteristics were calculated
from wing theory and test data for the airfoil sections.
Various combinations of washout, camber increase in the
airfoil sections from the center to the tips, and sharp
leading edges at the center were used to bring about the
desired equivalence of maximum lift and center—stalling
characteristics.

In the calculation of the weights of the wings, a
simple type of spar structure was assumed that permitted
an integration across the span_to determine the web and
the flange weights.. The covering and the remaining weight
were taken in proportion to the wing area. The total
weights showed the wings with camber and washout to have the
lowest weights and indicated the minimum for wings with a
taper ratio between 1/2 and 1/3.

Many investigations have been made of the aerodynamic
and the structural aspects of tapered wings with a view to
finding the best taper ratio. Investigations of taper
ratio are reported in references 1 and 2. A general dis—
cussion of tapered wings is given in reference 3. Although

drag and weight were considered'in references 1 and 2, the
effect of taper ratio on the maximum lift and the manner
of stalling of wings was not considered. The effect of
taper ratio on the maximum lift is censiderable. The tip
stall that usually results from the use of tapered wings.
moreover, evidences itself as instability‘in roll at an-
gles of attack less than that corresponding to the maximum
lift coefficient. This condition is generally recognized
as undesirable from the point of view of handling charac—
teristics in low—speed flight.

It is accordingly considered herein that wings should
be designed to avoid tip stalling. With this point of view,
.-wings-of different taper ratio were designed to be aerody—
namically-equal; that is. equal in stalling speed, in in-
duced drag at a low speed, and in'total drag at cruising
speed. The weights were then calculated to indicate the
"optimum" wing (the wing of lowest weight).