*How the slope of the lifting force characteristic C*_{L}= C_{L}(*α) changes with increasing thickness and camber of the airfoil according to the potential flow theory and according to the thin airfoil theory?*

**Potential flow theory:**
According to the potential flow
theory, the slope of the lift force characteristic for the Joukovsky’s
non-symmetrical airfoil with zero thickness (

*ε = 0*) is expressed by the approximate formula:
where

*f*is the camber ratio (ratio between the maximal deflection of the mean camber line and the chord of the airfoil).
The small correction is
proportional to the square of the camber. The thicker the profile of the
airfoil, the more the slope of

*C*_{L}= C_{L}(*α)*is increased.
The formula for the lift force
coefficient can be written as follows:

where β is negative and corresponds to zero lift
condition.

The deflection of the airfoil
(AoA) leads to the vertical shift in the characteristic

*C*_{L}= C_{L}(*α)*curve, as the equation is*α*dependent.

__Thin airfoil theory__:
The slope of the lift force
characteristic

*C*_{L}= C_{L}(*α)*is equal:
From which it can be clearly seen
that the slope does not depend on the airfoil camber. It does not include also
the correction as it was in the potential flow theory.

The formula for the lift force
coefficient can be written as follows:

where

is the negative angle
of attack at which the camber airfoil is not producing any lift.

Summarizing it:

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