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

Answers

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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/m3)

V = Velocity (m/s)

A = Area of Wing (m2)

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 * V2 / 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 * V2 / 2 * A)

OR

L = (2 * p * r * V2 / 2 * A) * a + (Clo * r * V2 / 2 * A)

Notice this is in the form Y = mX + b.

L = (2 * p * r * V2 / 2 * A) * a + (Clo * r * V2 / 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 round-off 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.

 

Please send any comments to:
Curator: Tom.Benson@grc.nasa.gov
Responsible Official: Kathy.Zona@grc.nasa.gov