What is the optimum wing angle and corresponding travelled?

[sama3505]

The forces acting on the glider are the gravitational force, the lift force and the drag (air friction).

The drag () and lift force () are a function of the angle that the wings have with the gliding direction. =122 with: =0.1+3∙10−32

=122 with: =0.2+0.1− 3∙10−32

In the above equations, is in decimal degrees. Calculate and plot the traveled ground distance as a function of the gliding angle .
The gliding angle is the angle of the gliding direction with respect to the ground (see figure 1).

Note that the angle is determined by the wing angle .

What is the optimum wing angle and corresponding traveled maximum distance?

 

[David Lewis]

It's the maximum lift/drag angle of attack. Note the wing may have to produce more force than the weight of the glider because it has to counteract down force from the horizontal stabilizer. You have to plug the lift and drag of the whole glider (not just the wing) into the equations.

The free-body diagram will reduce down to two equal and opposite colinear forces:
total aerodynamic force = sq rt (L² + D²), and weight.

The F_w force vector in the diagram is not drawn to scale (it's too long)

 

[sama3505]

it is not clear ,how do we know the weight ?

 

[David Lewis]

weight = -sq rt (L² + D²).

 

[David Lewis]

At what angle of attack is L/D maximum? (I believe you can substitute C_L/C_D. You don't have to bother with actual forces, just their coefficients.) So when the derivative of C_L/C_D (with respect to angle of attack) equals zero, I think that will be the solution.

Glide ratio = L/D = C_L/C_D.

 

[David Lewis]

Note that in this problem the same reference area (A) is used for both the lift and the drag coefficients. Please respond if you need better or simpler explanation. There's also an algebraic solution.

 

[DrClaude]

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