Lift due to Bernouilli effect only. (was BPA Ops manual technical
errors)
I finally dug out some numbers (from someoen else, admittedly).
A QUANTITATIVE APPLICATION OF THE COMMON (INCORRECT) EXPLANATION
If the pressure, in Newtons per square meter (Nm-2 = kgm-1s-2), on the
top of a wing is notated ptop , the pressure on the bottom pbottom , the
velocity (ms-1) on the top of the wing vtop, and the velocity on the
bottom vbottom ,and where ? is the density of air (approximately 1.2
kgm-3), then the pressure difference across the wing is given by the
first term of Bernoulli's equation: ptop- pbottom= 1/2 ? (vtop2 -
vbottom2).
A rectangular planform (top view) wing of one meter span was measured as
having a length chordwise along the bottom of 0.1624 m while the length
across the top was 0.1636 m. The ratio of the lengths is 1.0074. This
ratio is typical for many model and full-size aircraft wings. According
to the common explanation which has two adjacent molecules separated at
the leading edge mysteriously meeting at the trailing edge, the average
air velocities on the top and bottom are also in the ratio of 1.0074. A
typical speed for a model plane of 1m span and 0.16m chord with a mass
of 0.7 kg (a weight of 6.9 N) is 10 ms-1, which makes vtop=10.074 ms-1.
Given these numbers, we find a pressure difference from the equation of
about 0.9 kgm-1. The area of the wing is 0.16 m2 giving a total force of
0.14 N. This is not nearly enough--it misses lifting the weight of 6.9 N
by a factor of about 50. We would need an air velocity difference of
about 3 ms-1 to lift the plane.
The calculation is, of course, an approximation since Bernoulli's
equation assumes nonviscous, incompressible flow and air is both viscous
and compressible. But the viscosity is small and at the speeds we are
speaking of air does not compress significantly. Accounting for these
details changes the outcome at most a percent or so. This treatment also
ignores the second term (not shown) of the Bernoulli equation--the
static pressure difference between the top and bottom of the wing due to
their trivially different altitudes. Its contribution to lift is even
smaller than the effects already ignored. The use of an average velocity
assumes a circular arc for the top of the wing. This is not optimal but
it will fly. None of these details affect the conclusion that the common
explanation of how a wing generates lift--with its naïve application of
the Bernoulli equation--fails quantitatively.
date: Fri, 09 Nov 2007 15:02:01 +0000
author: moschops
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