There are many theories of how lift is generated.
Unfortunately, many of the theories found in encyclopedias, on web
sites, and even in some textbooks are incorrect, causing unnecessary
confusion for students.
The theory described on this slide is one of the most widely
circulated, incorrect explanations. The theory can be labeled the
"Longer Path" theory, or the "Equal Transit Time" theory.
The theory states that airfoils are shaped with the upper
surface longer than the bottom. The air molecules
(the little colored balls on the figure) have
farther to travel over the top of the airfoil than along the bottom.
In order to meet up at the trailing edge,
the molecules going over the top of the wing must travel
faster than the molecules moving under the wing.
Because the upper flow is faster, then, from Bernoulli's
equation, the pressure is lower. The difference
in pressure across the airfoil produces the lift.
Before considering what is wrong with this theory, let's investigate
the actual flow around an airfoil by doing a couple of experiments
using a Java simulator which is solving the correct
flow equations. Below the simulator
is a text box with instructions. Be sure that the slider on the right
of the text box is pulled to the top to begin the experiments
Let's use the information we've just learned to evaluate the
various parts of the "Equal Transit" Theory.
{Lifting airfoils are designed to have the upper surface longer than
the bottom.} This is not always correct. The symmetric airfoil in our
experiment generates plenty of lift and its upper surface is the
same length as the lower surface.
Think of a paper airplane. Its airfoil is a
flat plate --> top and bottom exactly the same length and
shape and yet they fly just fine.
This part of the theory probably got started because early
airfoils were curved and shaped with a longer distance along the
top. Such airfoils do produce a lot of lift and flow turning, but it is the
turning that's important, not the
distance.
There are modern, low-drag airfoils which produce lift on which the
bottom surface is actually longer than the top.
This theory also does not explain how airplanes can fly
upside-down
which happens often at air shows and in air-to-air
combat. The longer surface is then on the bottom!
{Air molecules travel faster over the top to meet molecules
moving underneath at the trailing edge.} Experiment #1 shows us that
the flow over the top of a lifting airfoil does travel faster
than the flow beneath the airfoil.
But the flow is much faster than the speed
required to have the molecules meet up at the trailing edge. Two
molecules near each other at the leading edge will not end up next
to each other at the trailing edge as shown in Experiment #2.
This part of the theory attempts to provide us with a value for the
velocity over the top of the airfoil based on the
non-physical assumption that the molecules meet at the aft end. We
can calculate a velocity based on this assumption, and use
Bernoulli's equation to compute the pressure, and perform the
pressure-area calculation and the answer we get does not agree
with the lift that we measure for a given airfoil. The lift
predicted by the "Equal Transit" theory is much less than the
observed lift, because the velocity is too low. The actual
velocity over the top of an airfoil is much faster than that
predicted by the "Longer Path" theory and particles moving over the top
arrive at the trailing edge before particles moving under the airfoil.
{The upper flow is faster and from Bernoulli's equation
the pressure is lower. The difference in pressure
across the airfoil produces the lift.}
As we have seen in Experiment #1, this part of the theory is
correct. In fact, this theory is very appealing because
many parts of the theory are correct. In our discussions
on pressure-area integration to
determine the force on a body immersed in a fluid, we mentioned
that if we know the velocity, we can obtain the pressure and
determine the force. The problem with the "Equal Transit" theory
is that it attempts to provide us with the velocity based on a
non-physical assumption as discussed above.
You can download your own copy of the program to run off-line by clicking on this button:
You can further investigate all the
factors affecting lift by using the
FoilSim II Java Applet.
You can also
download
your own copy of FoilSim to play with
for free.
