1. Chapter 5
Worked-Out Examples

2. 5.2 NACA 1412 airfoil 3 foot chord 5 degree alpha
100 ft/sec freestream speed at sea level
Compute lift, drag forces, and moment about quarter-chord per unit span

3. Approach: Appendix D

4. Approach First compute Reynolds number
Look up Cl, Cd, Cm at closest Reynolds number. In real world applications, a computer program will interpolate between Reynolds numbers.
Find L’, D’, and M at quarter chord using relationships that define these in terms of Cl, Cd, and Cm.

5. Problem 5.3 NACA 23012 airfoil Chord 0.3 m
Freestream velocity 42 m/sec at 1 atm, 303 degree K.
Find density r from equation of state.
8 degree angle of attack.
We are asked to compute L’, D’, and M’
Same approach as 5.2, different airfoil, SI units.

6. Problem 5.4
Same airfoil as 5.3, same freestream velocity, pressure, density, and temperature.
We are given L’, asked to find alpha
Approach: Find Cl first
Look up the chart in appendix D for this airfoil to see at which angle of attack will this Cl result.

7. Problem 5.5 Wing made of NACA 0009 airfoil
Given freestream velocity, freestream conditions, alpha.
Given total lift L for the entire wing.
Asked to find wing area S.
Approach:
Compute Reynolds number
Look up Cl at this Reynolds number and alpha from appendix D
This wing has the same Cl everywhere. Thus, CL of the wing is same as Cl of the airfoil.
Find S from L = ½ * r * V ∞ * V∞ * CL * S

8. Problem 5.6
We are asked to find max L/D for an airfoil (NACA 2412) at a Reynolds number of 9.
Approach: L/D = Cl / Cd since density, chord, etc. all cancel.
Select several angles of attack.
Look up Cl and Cd at these alphas for this airfoil at this Reynolds number.
Compute Cl/Cd for each of these angles of attack.
See when maximum value occurs.

9. Problem 5.7 Given freestream velocity
Standard sea level conditions (we know density and pressure p∞).
We are given p at a point on the surface.
Asked to find pressure coefficient Cp
Use

10. Problem 5.8 Given freestream velocity V∞ of an airplane
Given local velocity V at some point on the body.
Asked to find pressure coefficient Cp
Use Bernoulli’s equation.
Manipulate it to arrive at Cp= 1 – [V/V∞]2
Find Cp from supplied info.

11. Problem 5.9
Same approach as 5.8, since speed of the flow (160 feet/sec) is low compared to sound speed (~1100 ft/sec).