# 2-D Inviscid, Linearized, Thin Airfoil Theories

14.6.1.1 Incompressible Flow (Mo = 0)

Airfoil Design

Consider a thin airfoil of chord c with parabolic camberline. The design requirements are the following:

• the take-off lift coefficient is (Ci)t-o = 1.8

• the location of the center of pressure at take-off is {xC-)t_o = 0.4

The airfoil geometry will be completely determined by the airfoil Fourier coefficients.

First, write Cl in terms of the Fourier coefficients.

Second, express the center of pressure location in terms of the Fourier coefficients. Write as a system and solve for A0 and A1. Check your solution carefully.

Find the take-off incidence.

Find the profile relative camber.

Can you think of a profile that can fulfill these requirements?

Lift Curve

Give the value of the lift slope ^0..

Give the value of the Cl0 corresponding to a = 0. Sketch the lift curve on a graph Cl (a) = ^0.a + Cl0.

Equilibrium with Tail

If the center of gravity of the wing+tail configuration is located at Xa. = 0.5 at take-off, what sign do you expect the tail lift coefficient to be, Cl >=< 0?

Sketch this situation.

14.6.1.2 Supersonic Flow (M0 > 1, в = JM^ — 1)

A flat plate equips the fins of a missile cruising at Mach number M0 > 1ina uniform atmosphere. The chord of the airfoil is c.

Pressure Distribution and Global Coefficients

Plot —C + and —C – versus x for this airfoil at a > 0.

Write the formula for the lift coefficient C;(a), moment coefficient Cm, o(a) and drag coefficient Cd (a) according to inviscid, linearized supersonic flow theory.

Maximum Finess and Flow Features

Given a viscous drag coefficient Cd0 independent of incidence, form the expression of the inverse of the finess, 1/f = Cd / Ci where Cd now includes the viscous drag and find the value of a that maximizes f (minimizes 1/f).

Sketch the profile at incidence and indicate on your drawing the remarkable waves (shocks, expansions).

## Leave a reply