Deflection of a scaled down aircraft wing

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Discussion Overview

The discussion revolves around calculating the theoretical maximum deflection of a scaled-down version of a glider wing, comparing it to the original design. Participants explore the implications of scaling down parameters such as the uniformly distributed load (UDL) and the second moment of inertia, while also considering experimental validation of their calculations.

Discussion Character

  • Homework-related
  • Mathematical reasoning
  • Technical explanation

Main Points Raised

  • One participant presents a formula for maximum deflection and attempts to apply it to their scaled-down wing, using specific values for material properties and dimensions.
  • Another participant questions the accuracy of the second moment of area provided, suggesting it may be incorrectly calculated and pointing out the implications of such an error.
  • A different participant introduces the concept of Reynolds number and its relevance to the scaled-down model, suggesting the use of a program to calculate aerodynamic polars.
  • One participant calculates the scaled-down UDL based on the scale factor and presents a resulting maximum deflection value, which they express skepticism about due to its magnitude.
  • The same participant also calculates the mass needed for their experimental setup based on the scaled-down area and UDL, questioning whether this value seems appropriate.

Areas of Agreement / Disagreement

Participants express uncertainty regarding the scaling of the UDL and the accuracy of the second moment of inertia. There is no consensus on the correct approach to these calculations, and multiple viewpoints regarding the implications of scaling remain present.

Contextual Notes

Participants have not resolved the assumptions related to the scaling process, particularly how to accurately adjust the UDL and the implications of the second moment of inertia on deflection calculations.

SJ1234
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Homework Statement


As a project, I have had to design and build a scaled down version of a glider wing. The actual glider wing would be made of aluminium and have a length of 7.5m and have a uniformly distributed load of 30kg/m^2, the scaled down version is 0.9m and made of balsa wood. I want to work out the theoretical maximum deflection of my scaled down wing and then test it to compare results.
For balsa wood E=16GPa, for aluminium E= 69GPa.
second moment of inertia for the scaled wing is 5.72×10-10m^4

Homework Equations


dmax=(UDLxL^4)/(8EI)

The Attempt at a Solution


dmax=(UDLx0.9^4)/(8x16x5.72×10-10)

dmax=(30x7.5^4)/(8x69xI)

How do I scale down the UDL?
 
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SJ1234 said:

Homework Statement


As a project, I have had to design and build a scaled down version of a glider wing. The actual glider wing would be made of aluminium and have a length of 7.5m and have a uniformly distributed load of 30kg/m^2, the scaled down version is 0.9m and made of balsa wood. I want to work out the theoretical maximum deflection of my scaled down wing and then test it to compare results.
For balsa wood E=16GPa, for aluminium E= 69GPa.
second moment of inertia for the scaled wing is 0.572m^4

Homework Equations


dmax=(UDLxL^4)/(8EI)

The Attempt at a Solution


dmax=(UDLx0.9^4)/(8x16x0.572)

dmax=(30x7.5^4)/(8x69xI)

How do I scale down the UDL?
You might want to double check the second moment of area for the scaled-down wing. 0.572 m4 is pretty large. That's the second moment of area of a solid square cross section which measures 1.62 m on a side. Make sure that you haven't omitted a ×10-something
 
Changed, thanks
 
It would help if you can the "polars" of both wings noting the difference in Reynolds number in both cases. XFOIL is a program that can calculate polars if you can't find existing data. The scaled down version will have a smaller wing chord and travel at slower speed, so the Reynolds number will be less. The speed will be related to the wing loading more than the scale factor. If the scale ratio is 1/r, then to get the speed to scale down by 1/r, the mass of the smaller model would need to be (1/r)4 of the full size glider. More on this at this web site;

http://www.charlesriverrc.org/articles/design/ibtherkelsen_scalespeed.htm
 
The scaled down wing has a length 8.3 time smaller than the original, so the UDL of 30kg/m^2 would become 30/8.3^4 6.3x10^-3kg/m^2
giving: dmax=(6.3x10^-3x0.9^4)/(8x16x5.72x10^-10) = 56455.283m. (Obviously too big)
The area of the scaled down wing is 0.08m^2, therefore the mass I need to apply in experiment is: (0.08)(6.3x10^-3)=5.04x10^-4kg
(This seems a lot too small)