# Question: The lift of a swept wing

### Help Support HomeBuiltAirplanes.com:

#### Aerowerx

##### Well-Known Member
I understand that the lift of a wing does down as it is swept backwards, buy the factor of the cosine of the sweep angle.

For example, for 20 degrees of sweep the loss in lift would be about 6%.

Ok, so what do you do with this information?

One thing I have thought of is to increase the wing area. If you calculate the wing area, given the stall speed, MTOW, and maximum cl, you could apply the factor to the maximum cl.

So now you have a wing area to get the desired stall speed, corrected for sweep. What now? Do you apply the factor again when calculating the design lift coefficient at the desired cruise speed? Or has it already been taken care of by virtue of the increased area?

And if you do apply the factor again, do you multiply or divide to get the design lift coefficient?

#### Aerowerx

##### Well-Known Member
Hello??

Anybody out there?

##### Well-Known Member
If I do know the desirable stall speed I just would size the wing area mixing the two upper equations, getting the other two. The first one if you know the stall speed to achieve and the cl of the airfoil, and the second equation if you know the area and want to know the stall speed.

regards

#### RPM314

##### Well-Known Member
Depends. If you sweep the wing based on angle, so that the span decreases, then sure. If you sweep the wing based on distance the tip is moved aft, there should be no change if you twist it correctly. The inboard region increases the AoA of the outboard region when it generates lift, so the stall of the tips is a limiting factor unless they are washed out.

#### Aerowerx

##### Well-Known Member
Depends. If you sweep the wing based on angle, so that the span decreases, then sure.
This would then reduce the area of the wing. So how would you apply the cosine(sweep) factor to get that loss of lift back?

If you sweep the wing based on distance the tip is moved aft, there should be no change if you twist it correctly. The inboard region increases the AoA of the outboard region when it generates lift, so the stall of the tips is a limiting factor unless they are washed out.
Now this would keep the same area. The twist would have to be such that the over all lift stays the same. So what would be the better way to compensate for the cosine(sweep) factor? Increase the area? Increase the AoA? Or what?

And what about my other question? When calculating the required coefficient of lift at cruise, do you have to apply the factor again? And, if so, how do you apply it?

By the way, I am getting good agreement with XFLR5 by increasing the area, then calculating the span, root, and tip (with preselected sweep, taper, and aspect).

##### Well-Known Member
You always have to take into consideration the correction factor regardless the flight speed.

Do not think to much in this, always that you see CL you have to correct it. So even for the spanwise lift distribution you can utilize the lifting line theory.

#### Aerowerx

##### Well-Known Member
I'm still not sure what to do here.

Maybe an example is needed.

Let us say that you have a wing with a sweep of 20 degrees. Stall speed is 50 ft/s, cruise speed 100 ft/s, weight is 1000 pounds.

I calculate the needed wing area as 265 square feet.

Using the wing area, weight, and cruise speed, I calculate a design lift coefficient at cruise of 0.318, without the correction for sweep.

Now, to correct for sweep would you divide or multiply by the correction? If I divide I get 0.375, and 0.269 when I multiply. Which value would you then use when calculating the wing twist?

Or would you need the correction factor again, at all, since you have already increased the wing area because of the sweep? As I stated in a previous post, when I plug the numbers into XFLR5 using the uncorrected cruise lift coefficient (0.318 in this example) I get the desired results (in this example, the model would "trim out" at 100 ft/s).

#### RPM314

##### Well-Known Member
This would then reduce the area of the wing. So how would you apply the cosine(sweep) factor to get that loss of lift back?

Now this would keep the same area. The twist would have to be such that the over all lift stays the same. So what would be the better way to compensate for the cosine(sweep) factor? Increase the area? Increase the AoA? Or what?

And what about my other question? When calculating the required coefficient of lift at cruise, do you have to apply the factor again? And, if so, how do you apply it?

By the way, I am getting good agreement with XFLR5 by increasing the area, then calculating the span, root, and tip (with preselected sweep, taper, and aspect).
No, think like F-14 swing wing. Area is preserved. Aspect ratio goes down.
I might be wading a bit out of my depth in this thread, but as I understand it one of the theorems of LLT says that a given lift distribution, swept by translating the tip back (preserving area and span) has the same properties as the original unswept one. I think that the cosine correction thing is used because homebuilders tend not to twist to correct the induced AoA.

[REDACTED]

Last edited:

#### Aerowerx

##### Well-Known Member
No, think like F-14 swing wing. Area is preserved. Aspect ratio goes down.
Not the same thing I believe. When you design a wing with sweep, the chord line remains parallel to the direction of flight. With a swing wing it does not, and the effective chord gets longer, does it not?

.... but as I understand it one of the theorems of LLT says that a given lift distribution, swept by translating the tip back (preserving area and span) has the same properties as the original unswept one.
I thought LLT did not apply to swept wings, unless it is modified somehow, because of the spanwise flow.

I think that the cosine correction thing is used because homebuilders tend not to twist to correct the induced AoA.
From what I have been reading, it is because when you sweep the wing there is a component of the air flow that is span-wise, thereby reducing the relative flow across the chord, thereby reducing lift.

#### RPM314

##### Well-Known Member
Well it seems like you know more than I do about this, so it doesn't make sense for me to give advice. *moves to bleachers*

#### Topaz

##### Super Moderator
Staff member
Log Member
Not the same thing I believe. When you design a wing with sweep, the chord line remains parallel to the direction of flight. With a swing wing it does not, and the effective chord gets longer, does it not?
To the air, there's absolutely no difference between the two. And it's the air you care about. Everything else is human semantics.

I thought LLT did not apply to swept wings, unless it is modified somehow, because of the spanwise flow.
Except at very small sweep angles, it really doesn't, or at least not very well. You need a more-comprehensive analysis that takes spanwise effects into account.

#### Norman

##### Well-Known Member
HBA Supporter
To the air, there's absolutely no difference between the two. And it's the air you care about. Everything else is human semantics.
It's not just semantics. At high aspect ratios the effective chord is perpendicular to the leading edge. The Reynolds number is along that line and the speed component to calculate it is reduced by the vector quantity that splits at the leading edge with one vector parallel to the LE and the other normal to the LE i. e. the spanwise velocity vector is lost. The effective airfoil cross section is also normal to the LE but fortunately this only amounts to a change in the apparent thickness of the airfoil so its characteristics, other than drag, are largely unchanged by sweep. The same vector diagram as the critical mach number applies at subsonic speeds because true airspeed is the flight Mach number times the the speed of sound. This is from simple sweep theory which unfortunately breaks down for less than infinite span and less than perfect smoothness of the leading edge but even in those cases the boundary layer flow is never parallel to the free-stream all over the wing. The net result is that the slope of the CL over alpha curve is shallower for swept wings than for straight wings of the same span.

Except at very small sweep angles, it [lifting line theory] really doesn't, or at least not very well. You need a more-comprehensive analysis that takes spanwise effects into account.
Panel codes such a AVL and XFLR5 seem to be able to handle sweep effect.

#### Attachments

• 29.1 KB Views: 164
Last edited:

#### Aerowerx

##### Well-Known Member
Ok, Norm. Good discussion.

It seems that every time I ask what I think is a good question, everyone skirts around it.

So, Norm, after increasing the area of a swept wing to retain the desired stall speed, is there anything else that needs to be done? My question is about calculating the design lift coefficient (at cruise) AFTER increasing the wing area. And a secondary question, is increasing the area the best way to compensate for the loss of lift with sweep?

#### Norman

##### Well-Known Member
HBA Supporter
It seems that every time I ask what I think is a good question, everyone skirts around it.
Sadly the expertise and willingness to help us amateurs understand difficult aeronautical concepts that Orion brought to this forum has not been replaced since his passing. It's not that people are skirting round your question, it's just that very few us us have the expertise to give you a detailed answer. Although Eduardo Fadul was very helpful with the equations and brief explanation of how they apply. Very few people in general aviation have any experience with swept wings and most of those who do deal with such small sweep angles, less than 10º, that sweep effects can be ignored with impunity (hopefully). remember the NACA graph I posted here? Washout moves the curve up and to the right ie more planes fall on the stable side of the curve. However it would take a huge amount of twist to eliminate the possibility of stall so the goal is to make it fairly docile.

after increasing the area of a swept wing to retain the desired stall speed, is there anything else that needs to be done? My question is about calculating the design lift coefficient (at cruise) AFTER increasing the wing area. And a secondary question, is increasing the area the best way to compensate for the loss of lift with sweep?
Power-on cruise should be at the AoA of minimum drag. Since sweep decreases lift coefficient for any given AoA minimum drag is at a lower CL than for un-swept wings. I think this is why flying wings are almost always faster than conventional planes with the same wing loading. I helped a guy design camber flaps for a flying wing model a few years ago and wrote an article for RC Souring Digest about the graphical method I used. I drew two options for him and he used the small one. even as small as it was it still slowed the plane down well without needing much pitch trim. A small TE flap produces a lot of induced drag by messing up the lift distribution. You can also use a lower surface split flap (this is not a spoiler as it does not decrease lift) to add a lot of drag.

#### Aerowerx

##### Well-Known Member
...remember the NACA graph I posted here? Washout moves the curve up and to the right ie more planes fall on the stable side of the curve. However it would take a huge amount of twist to eliminate the possibility of stall so the goal is to make it fairly docile.
Yes, I remember it. It seems to indicate that sweep and aspect ratio are fighting against each other. If you want a higher aspect, then you need less sweep. Since I am looking at BSLD, there will be a fair amount of twist. Do you have any idea just how far it will move "up and to the right"? With XFLR5, I have been looking at aspects of around 8-10, to reduce drag. Sweeps of 20-30 degrees. Not good according to the chart, but this is with a twist of about 4-5 degrees (root to tip).

Power-on cruise should be at the AoA of minimum drag. Since sweep decreases lift coefficient...
Hmmm. So is increasing the area a good way to compensate for the loss of lift coefficient? I have written an Excel spreadsheet to calculate the BSLD twist. Works pretty good. XFLR5 somes pretty close to my desired cruise speed when I get the CG at the right place, but the coefficient of lift has been coming out lower than predicted.

#### Norman

##### Well-Known Member
HBA Supporter
Do you have any idea just how far it will move "up and to the right"?
Not a clue.

With XFLR5, I have been looking at aspects of around 8-10, to reduce drag. Sweeps of 20-30 degrees.
30 degrees and AR=10 would be begging for flutter unless you use a very thick airfoil at the root and/or a long root chord. Model gliders can get away with it because of the low speeds (true airspeed NOT indicated) and altitudes plus they benefit from viscose damping due to the low Reynolds number.

is increasing the area a good way to compensate for the loss of lift coefficient?
Yes

#### Aerowerx

##### Well-Known Member
Norm, can you, or do you know someone who can, summarize the recommendations of Nickel?

I know there is a lot of information in that book, but I am having trouble figuring out just what he recommends. I thought he said that 30 degrees was good if the other parameters were selected carefully. This came from a chart he had--can't remember the page number without looking it up.

##### Well-Known Member
30 degrees and AR=10 would be begging for flutter unless you use a very thick airfoil at the root and/or a long root chord. Model gliders can get away with it because of the low speeds (true airspeed NOT indicated) and altitudes plus they benefit from viscose damping due to the low Reynolds number.
Carbon skin? Even with a layer or two I'd be amazed if critical speed would be below 200-250 kts.