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).

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