
Showing the Lift Equation in its
Y = mX + b Form
Answers


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the problems.
NAME__________________________________ CLASS__________
1a. Identify each letter in the lift equation and list the units
for each.
Cl
= Lift Coefficient (no
units)
L
= Lift
(newtons)
r
= Density of Air
(kg/m^{3})
V
= Velocity
(m/s)
A
= Area of Wing
(m^{2})
1b. Identify each letter in the lift equation and list the units
for each.
Cl
= Lift Coefficient (no
units)
a
= Angle of Attack (radiians no
units)
Clo
= Lift Coefficient at
a
= zero (no units)
2. Write out the two equations for the value of Cl.
Cl = L / (r *
V^{2} / 2 * A).
Cl = 2 *
p
* a
+ Clo
3. Rearrange the two equations and solve for L as a function of
a.
L = (2 * p
* a
+ Clo) * (r * V^{2} / 2 * A)
OR
L = (2 * p
* r * V^{2} / 2 * A) * a
+ (Clo * r * V^{2} / 2 * A)
Notice this is in the form
Y
=
mX
+
b.
L
=
(2 * p
* r * V^{2} / 2 * A)
*
a
+
(Clo * r * V^{2} / 2 *
A)
Y = dependent
variable,
X = independent
variable,
m =
slope,
b = Y
intercept.
4. Record the values shown:
L = 3,030
newtons
A = 2 square
meters
V = 160 km/hr = 44.4
m/sec
r =
1.23 kg/m cubed
a =
zero
Clo
= 2 * L / r * v squared * A =
1.24
5 & 6
Calculated numbers may vary slightly from those
shown below due to roundoff errors.
angle in degrees

angles in radians

calculated values of lift

value of lift from Foilsim

20

.3491

2291

3024

15

.2618

959

1523

10

.1745

372

1.8

5

.08726

1704

1520

0

0

3036

3030

5

.08726

4367

4517

10

.1745

5699

5970

15

.2618

7031

7278

20

.3491

8363

8729

The
plots are different.
This is due to the fact that the thin airfoil equation contains an
approximation that is only good at small values of
a . Foilsim does not use this
approximation.
7. The value of lift scales linearly as a
function of the area of the wing as can be seen by the linear change
in the value of lift.
