Chapter 5 Worked-Out Examples

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

Approach: Appendix D

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.

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.

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.

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

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.

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

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.

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).