TITLE:
Lift Force on a Circular Arc Wing
AUTHORS:
Kern E. Kenyon
KEYWORDS:
4632 North Lane, Del Mar, USA
JOURNAL NAME:
Natural Science,
Vol.9 No.10,
September
29,
2017
ABSTRACT: The
lift force is calculated for a gliding wing with a circular arc top and a flat
bottom in a uniform fluid. It is: constρU2/R0, whereis the constant
fluid density, U is the uniform flow speed far from the wing
andis the radius of curvature of the wing’s top surface. To obtain
this result two non-linear differential equations in pressure and velocity are
combined into one linear governing equation for velocity, which contains a
non-constant coefficient, R(z), the radius of curvature of
the streamlines above the wing as a function of the vertical coordinate z.
Bernoulli’s principle along a streamlineand the force balance across a streamline
(pressure gradient equals centrifugal force) are the starting equations. A
solution to the governing equation is derived by providing an algebraic
function for R(z)that is consistent with observations,
and the order of magnitude one constantin the lift force is worked out.
It is believed that the present approach to understanding the lift force on a
wing has not been tried before. More theoretical and observational work are
needed to better specify R(z).