The Circular Arc Aerofoil

Following the same procedure as before for finding the distribution of k, it can be shown that for a circular arc aerofoil at an angle of attack a to the flow k can be expressed as:

From Equations (6.12) and (6.14) is seen that the effect of camber is to increase k distribution by (2U x 2в sin в) over that of the flat plate. Thus:

k — ka + kbі

arises from the incidence of the aerofoil alone and:

which is due to the effect of the camber alone. Note that this distribution satisfies the Kutta-Joukowski hypothesis by allowing k to vanish at the trailing edge of the aerofoil where в = n.

Example 6.2

If the maximum circulation caused by the camber effect of a circular arc aerofoil is 2 m2/s, when the freestream velocity is 500 km/h, determine the percentage camber.

Solution

Given, kb = 2 m2/s, U = 500/3.6 = 138.9 m/s.

By Equation (6.22), the circulation due to camber is:

kb = 4ив sin в.

This circulation will be maximum when sin в = 1, thus:

kbmax = 4UP.

Therefore:

kbmax

4U

_ 2 = 4 x 138.9 = 0.0036.

The % camber becomes:

%Camber = — x 100

0.0036

2