Aeroelasticity - Aileron Reversal 3D

8/13/2019 Aeroelasticity - Aileron Reversal 3D

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SMF4143 Aircraft Structures II Aeroelasticity Aileron Reversal p1 Ainullotfi bin Abdul Latif

SMF4143 AIRCRAFT STRUCTURES IIAeroelasticity

Aileron Reversal of a Finite Wing

Strip Theory

Consider the half-wing shown in the diagram below, of half-span s, and flying at a speed ofV. On the deflection of the aileron by an angle of , the aircraft rolls at an angular speed of prad/s.

The wing is rolling at a rotational speed of p rad/s. As such, at the location y from thesymmetrical plane of the aircraft, the wing experiences a relative air speed downwards of py.

py

yV

py

V

p rad/s (roll)


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This effectively reduces the angle of attack by: The increment in lift L over the strip y comes from both the angle of attack and the

deflection of the aileron: = + ()where:

()= 0 : 0 < 1 : Similarly, the increment in pitching moment M

ois given by:

= ()Consider equilibrium of moments on the strip y.

+ + + = 0

From earlier notes, torsion T is given by:

= Thus: = Substituting this and the values for L and M

ointo the equilbrium equation:

+ () + + () = 0Rearranging to group the terms with together and those with together, and dividing by GJand y, we have:

+ = () ()


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where:

= Putting:

=

we have the following second order differential equation:

+ = where: = 1 + 1 ()The above second order differential equation can be solved using the known boundaryconditions:

= 0 = 0

= 0 = A possible solution to the differential equation is:

= 1 + 1 ()1 ( ) ( ) with ( )= 0 for y < s1.The change in the total lift coefficient locally is given by the strip theory as:

= + + ()where is given by the equation above, and is the steady state angle of attack.

Aileron effectiveness in this finite (3D) wing case can be defined as the ratio of the helixangle (of flight) at the wing tip with respect to aileron deflection angle:

=


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In the steady state situation, the moments due to the aileron deflection , wing twist and

aerodynamic damping are in equilbrium.

Thus we have, for two sides of the wing:

2 = 02 + () = 0 = () Substituting for : 1 + 1 ()1 ( ) ( ) = () Rearranging, we have:

= () +1 + 1 ()1( )

( ) Working out the integration in the right hand terms:

=

1 1 + 1 2 1

1 Reversal occurs when the aileron effective is zero i.e. when the aileron is no longer effective.This happens when the numerator becomes zero, giving: + 1 ( ) 2 1 = 0Looking back at the infinite (2D) wing case:

=


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=

= = Normally, for small values of e, < .Normally in real cases,

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Thus reversal happens first before divergence if the flexural axis is ahead of 0.4c location,which is the common situation.

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Aeroelasticity - Aileron Reversal 3D