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Lift Equation in its
Y = mX + b Form
Activity
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If so instructed by your teacher, print out a worksheet
page for these problems.
The Lift
Equation
Lift = lift
coefficient x air density x velocity squared / two x wing
area
The lift
coefficient, Cl,
contains all the complex dependencies and is usually determined
experimentally.
For thin airfoils
with camber and at angle of attack:
Cl
= 2 p
a
+ Clo
(
p
= 3.1416) and ( a
is
in radians)
NOTICE: This equation holds
true only at small angles of a.
( [a] < 10 degrees)
1a. Identify each letter in the lift equation and list the units
for each.
Cl = _________________
L = _________________
r = _________________
V = ________________
A = ________________
1b. Identify each letter in the thin airfoil equation and
list the units for each.
Cl = _________________
a = _________________
Clo = _________________
2. Write out two equations for Cl (one from the lift equation and
the other from the thin airfoil equation).
3. Combine the two equations into one equation that shows L as a
function of a. Notice that this
is in the form of y = mx + b, where y is now L , x is
a , and m and b are combinations
of the other variables.
4. Now use
FoilSim
to determine Clo. On FoilSim set
units to Metric Units. Set the camber to 10%
the angle to 0.0, and the area to 2 sq m. Record the values shown for lift
(L) , density (r) , and the other input values. Then use the equation
from #3 to solve for Clo.
5. The value of Clo (constant) you solved for in #4 can now be
used to solve for the lift as a function of the angle of attack by
graphing methods. Make a graph using your equation from #3 and using
angles ( a ) of -20, -15, -10,
-5, 0, 5, 10, 15, 20 (changed to radians). Notice that when
a = zero, the lift is NOT zero.
It is the y intercept (b).
6. Verify you answers using Foilsim. Use the same angles and
record the lift values. Graph these results in a different color on
your graph. Are the lines the same? If they are different, what do
you think causes them to be different?
7. Use FoilSim and replace the area of the wing with a
different value. Report what happens to the lift.
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