FoilSim 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 = 3,036 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 = 1.25

 

5 + 6

angle in degrees	angles in radians	calculated values of lift	value of lift from Foilsim
-20	-.3491	-2291	-3039
-15	-.2618	-959	-1526
-10	-.1745	372	0
-5	-.08726	1704	1523
0	0	3036	3036
5	.08726	4367	4527
10	.1745	5699	5982
15	.2618	7031	7392
20	.3491	8363	8746

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.