# Coefficient of Lift on a Swept Wing

Discussion in 'Aircraft Design / Aerodynamics / New Technology' started by Aerowerx, Jul 11, 2015.

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1. Jul 11, 2015

### Aerowerx

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I have read here on HBA, and elsewhere, that the coefficient of lift on a swept wing changes with the sweep.

There is an equation given, something like cl[SUB]1[/SUB]=cl[SUB]2[/SUB]/cos[SUP]2[/SUP](theta), where theta is the sweep angle.

Ok, if you have an airfoil with a certain section lift coefficient, does this mean that you have to use a higher lift coefficient to get the desired lift? Or is it the other way around?

2. Jul 11, 2015

### djschwartz

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The overall lift coefficient of a wing is always less than the section coefficient of the airfoil used for that wing. Many factors affect that difference including aspect ratio, sweep, wash-out, and disturbances such as nacelles or open gear wells. What generally increases to get the desired total lift at the desired minimum flight speed is wing area. The above equation is very much an over-simplification, useful for getting you in the general ballpark; but, not sufficient for design work.

3. Jul 11, 2015

### Vigilant1

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Not to nit-pick, but I've always figured that increasing span (rather than area) was the way to make a 3d wing behave closer to the 2d stated cl. It reduces the relative impact of the activity at the tip.

4. Jul 11, 2015

### djschwartz

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As I said, aspect ratio is one of the factors affecting how much less the lift coefficient of the actual wing will be than that of the section. But unless the AR is infinite, it will be less. So yes, if you can increase the AR while still meeting all of your other design requirements you can improve the situation. But any real wing will still need more area than what you would calculate if you just used the section lift coefficient directly without taking into account the characteristics of the finite wing.

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5. Jul 11, 2015

### Aerowerx

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OK, then. Just how does sweep affect the needed lift coefficient? What is a better equation?

I was hesitant to post too many details on what I am working on because everyone will latch on to what they think I am asking, and I will get all kinds of comments but no answer.

Anyway, to clarify....Suppose you have a desired lift distribution on a certain wing. To choose the airfoil and twist you need to know the lift coefficient across the span of the wing. How do you account for sweep?

6. Jul 12, 2015

### Aerowerx

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I found a paper on it, but you have to pay to see the whole thing.

I believe the equation given on the first page can be rearranged to give the same equation as I cited in my OP, but the description continues on the second page, which you have to pay for.

It was first published in 1942, so there has got to be a free copy somewhere, I would think.

7. Jul 12, 2015

### Norman

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I think you have the exponent in the wrong place see pages 12 and 22 of this PDF. You want the one for incompressible flow. The paper you sited is an early work on what's now called "simple sweep theory". This would be to correct the 2D data for sweep effect then you would do the span correction which will lop off at least another 10% then you would do the span efficiency correction which will remove another 30% of the span from the lifting surface. It seems like a lot but a typical low wing general aviation airplane has a pretty low span efficiency too. The difference between that low wing GA plane and a flying wing though is that the GA box is taking that 30% out of the root and the 'wing losses it from the tip which is never very efficient anyway and much smaller due to taper.

Well no the CL per AoA is lower so you would have to go to a higher angle of attack to achive a given CL. Sweep splits the free-stream the pressure into two components that point parallel and perpendicular to the leading edge. The vector that is perpendicular (normal) to the leading edge is the one that counts in the lift equations and the one parallel (tangential) to the leading edge is lost. The curve of cl/alpha becomes shallower with increasing sweep so for a given AoA the wing produces less lift at greater sweep or yaw angles. This is why swept flying wings have 30 to 40% more area than un-swept GA planes of the same weight and speed. It still comes out to less wetted area than a fuselage and empenage.

Last edited: Jul 12, 2015
8. Jul 13, 2015

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