Cascading Wings: Do they really increase lift by 300%?

Question

Cascading Wings for Ultralights: Do they really increase lift by 333%?!?!?

The classic NACA 650-18 airfoil has a Clmax of 1.5 according to airfoiltools.com ( a modified 650-18 is used on the Zenith 701).

Add non-slatted flaps, and the Clmax jumps to about 2.2.

What if one arranges the wing in a cascading fashion as shown below? Javafoil shows the Clmax jumping to 5, that’s an increase of 333% over the plain wing!!!

Not by just adding the same planform, but dividing the original chord by 4, so the a/r ratio is 4 times the original....

So that the quadplane is 400% more efficient than the original monowing, less a quadplane inefficiency of about 50%, so that the quadplane is still 200% more efficient than the monowing(maybe).

This probably only works ( if at all ) for very slow speeds (Re 300-800k) where the form drag and induced drag is very low.

I understand Javafoil uses Xfoil, which I’m told is a robust airfoil performance prediction program and is accurate up to an AOA of +/-20 deg.

Alternately, I’m told the VLM method (XLFR) is good up to only a Clmax of 1.5, +/- 20 deg.

So…. the million dollar question is… is a Clmax of 5 realistic, or is this beyond the scope of Javafoil/xfoil, even though the AOA is only about 8 deg….?

Ultralight Design Data:

See charts and tables below.

Flaps: 20% chord, 50 deg deflection

Wing Loading:51kg/m>2

Aspect Ratio: 7

Atmospheric conditions: Standard

Wing configuration: see chart below

Gap(vertical): 50%

Stagger(horizontal): -10%

Therefore biplane ( not multiplane) lift efficiency as per the table below should be: .26/.34=76% efficiency vs mono wing (Is this correct?) ( ignore the big green arrow, it's from the source I found the table)

Reynolds #: 880k

or......

is there a glitch in the software as per the comment below:

and the Clmax is about: climax 5 / 4 wings = 1.25

given the Clmax for a monowing is 2.2, and a biplane at 50% gap is 22% less efficient, a quadplane with 4 wings can easily be 40-50% less efficient, giving a clmax of about 1.3, which is close to the clmax of 1.25 above.

So what is the likely Clmax, 5 or 1.25?

Answer 1

The software appears to be taking the net plan area or shadow area of the overlapping stack as its area, but is adding the individual lifts of each wing. If you add the individual areas too then the calculation should show a fall in Clmax due to interplane losses. I'd call it a bug, however I do not know the software so perhaps it is a "feature". It depends on whether you regard your stack as one wing or four.

Answer 2

What if one arranges the wing in a cascading fashion as shown below? Javafoil shows the Clmax jumping to 5, that’s an increase of 333% over the plain wing!!!

Not really. As per the previous answer, you get this figure for a non-dimensionalized unit chord. Please also notice your drag increases accordingly as well.

Not by just adding the same planform, but dividing the original chord by 4, so the a/r ratio is 4 times the original....

So that the quadplane is 400% more efficient than the original monowing, less a quadplane inefficiency of about 50%, so that the quad-plane is still 200% more efficient than the mono-wing(maybe).

Here taking non-dimensional parameters are a little deceiving. Probably you can get a better picture by dimensionalizing the above with dynamic pressure and Area. Then you will see there is no much gain from staging.

This probably only works ( if at all ) for very slow speeds (Re 300-800k) where the form drag and induced drag is very low.

Lower the Reynolds number higher the form drag will be. Also for a given weight and area, lower the speed, higher the induced drag will be.

I understand Javafoil uses Xfoil, which I’m told is a robust airfoil performance prediction program and is accurate up to an AOA of +/-20 deg.

Javafoil does NOT use Xfoil. As a background info;

There are 2 ways to handle boundary layer flows for 2D panel method. First method is calculating the potential flow solution first and then apply that solution to the boundary layer flow because BL flow is governed only by the outer potential flow. But the BL thickness alters the shape of the body hence this method is not very accurate. One way to deal with it is running the solution in iterations until the solution converges. But especially on separated flows such a laminar separation bubbles or stall this method doesn't provide accurate results.

Second method is to simultaneously solve both boundary layer flow and potential flow. This overcomes to shortcomings of the first method.

Xfoil uses the latter method and Javafoil uses the former method.

Alternately, I’m told the VLM method (XLFR) is good up to only a Clmax of 1.5, +/- 20 deg.

VLM method in XLFR does not take the boundary layer into account si Clmax is something that is not known to it. What it does is calculate potential flow solution and then get the drag values by interpolating 2D airfoil results. XFLR5 uses xfoil as its 2D flow solver and I believe it could be taken for granted that it gives accurate results in the normal airfoil operating regime.

So…. the million dollar question is… is a Clmax of 5 realistic, or is this beyond the scope of Javafoil/xfoil, even though the AOA is only about 8 deg….?

It depends on how your non-dimensionalize your forces. I would check the dimensional data for better clarity as per above.

Also as a complete side note, high Clmax airfoils are not the best for general use. Imagine such high Clmax is possible (lets say via direct boundary later manipulation such as suction). Before one might see the stall, there might be myriad of other problems one might come across on control for example due to greatly reduced dynamic pressures on the surfaces. As per my limited understanding specifically designed high Clmax airfoils such as S1223 only makes sense for area constrained designs.