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I am trying to get the lift distribution of a swept wing with taper (in chord and thickness along the span), twist, and dihedral. I know that Kuchemann Index method is used for swept wings but I am not sure how to account for the other geometric variations. The image below is what I found for a swept wing w/o twist and a swept wing with lots of twist. Not sure how many degrees means "lots". How to account for the dihedral and taper?

Lift distribution of a swept wing

I am simply looking for the rough shape of the distribution so I can get an idea of where the maximum loading is and what the loading looks like around the root and tip regions. Also, is there an equation (or can an equation be derived) to get numerical values for how the lift varies along the span?

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The easiest way (I believe) will be to run a simple VLM aerodynamic analysis.

For this, I suggest you use OpenVSP and VSPAERO.

Dihedral won't change the lift distribution in a significant way (in straight-ahead flight).

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I am trying to get the lift distribution of a swept wing with taper (in chord and thickness along the span), twist, and dihedral.

The change in spanwise lift distribution due to taper ratio, twist, sweep angle, ... is well known and easy to find. A typical example is the following picture which shows the trend according to different taper ratios (slide number 6 from this presentation):

enter image description here

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The lift coefficient Cl is linear with angle of attack. Twist is extra angle of attack. For every section of the wing dx, you're reducing lift relative to wing twist.

Schrenk's method has provisions for twist

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