What is the optimum wing angle and corresponding travelled?

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Discussion Overview

The discussion revolves around determining the optimum wing angle and the corresponding traveled distance for a glider. It includes theoretical considerations of forces acting on the glider, particularly focusing on lift and drag as functions of the wing angle. The conversation touches on calculations, equations, and the implications of various angles of attack.

Discussion Character

  • Technical explanation
  • Mathematical reasoning
  • Homework-related

Main Points Raised

  • One participant outlines the forces acting on the glider, including gravitational force, lift, and drag, and presents equations relating these forces to the wing angle.
  • Another participant suggests that the optimum angle corresponds to the maximum lift-to-drag ratio and notes that the wing may need to produce more force than the glider's weight due to the horizontal stabilizer's downforce.
  • A question is raised about how to determine the weight of the glider, indicating uncertainty in the parameters needed for calculations.
  • One participant proposes that the angle of attack for maximum lift-to-drag can be found by setting the derivative of the lift-to-drag ratio with respect to the angle of attack to zero.
  • Another participant emphasizes that the same reference area should be used for both lift and drag coefficients in the calculations.
  • A participant expresses concern that the original post is a homework question that should be redirected to a specific homework forum, suggesting that the original poster should provide their own attempt at a solution.

Areas of Agreement / Disagreement

Participants express differing views on the appropriateness of the thread's placement in the forum, with some focusing on the technical aspects of the problem while others highlight the need for adherence to forum guidelines regarding homework questions. There is no consensus on the optimum wing angle or the method to calculate it, as various approaches and uncertainties are presented.

Contextual Notes

There are unresolved assumptions regarding the weight of the glider and the specific conditions under which the lift and drag coefficients are calculated. The discussion also reflects varying levels of understanding about the application of aerodynamic principles in this context.

sama3505
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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?
 

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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 Fw force vector in the diagram is not drawn to scale (it's too long)
 
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it is not clear ,how do we know the weight ?
 
weight = -sq rt (L2 + D2).
 
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At what angle of attack is L/D maximum? (I believe you can substitute CL/CD. You don't have to bother with actual forces, just their coefficients.) So when the derivative of CL/CD (with respect to angle of attack) equals zero, I think that will be the solution.

Glide ratio = L/D = CL/CD.
 
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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.
 
This is a homework question that should have been posted in a homework forum, and the OP has to make an attempt at a solution. Please do not reply to such a thread and report it instead.

OP: Please post again in a homework forum, filling out the homework template, including your own attempt at a solution.

Thread closed.
 

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