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# Area for lift coefficient calculations for Grid Fins?

## Area for lift coefficient calculations for Grid Fins?

(OP)
Hi All,

I have some test data from a wind tunnel for several designs of grid fins with minor design tweaks. I'm trying to plot the aero efficiency (C.L / C.D) to compare them, but I feel like my resulting values aren't quite making sense. Compared to some studies I've looked at, my drag coefficients are in the right ballpark, but my lift coefficients are way low, and I'm thinking it's the area values I'm using.

For for the lift coefficient, would the area be Fin Length * Fin Depth? Effectively, the planar area of the side view of the fin? Or would it be the sum of control surface area on one "side", i.e. 2 * Cell Width * Cell Depth * No. of cells? Also, when changing the AoA, would you account for that in the area value used to calculate the lift coefficient? For my drag coefficients, I have been using the planar area of the top view (looking down through the lattice) and do account for the change in projected area with a cos(AoA) added into the mix, and my values are roughly aligning to the studies I mentioned.

Any input greatly appreciated - thanks in advance!
Replies continue below

### RE: Area for lift coefficient calculations for Grid Fins?

Cd (and Cl) is based on the area assumed (as circular as that sounds). Eg for a wing, drag (and lift) is based on wing area, S. Particularly if you're going to cal Cl/Cd then I thin kit makes sense that they are based on the same area. What data do you have ? force balance results ??

### RE: Area for lift coefficient calculations for Grid Fins?

The area used for conventional Cl is the area that could intercept the oncoming flow - I suppose you could do the same with the grid fin - use the nominal plan view area and ignore the depth or take the entire wetted area if you want to account for the depth. I don't think it will scale quite as well as a conventional wing there are more complex interactions in the flow.

### RE: Area for lift coefficient calculations for Grid Fins?

(OP)
That's what I figured, use the same area for both. Like I mentioned, the Cd's I was calculating using the plan view / flow facing planar area seemed to be on point. I've been using the same area for the Cl, but my Cl / Cd values are coming out much lower than the studies I was looking at, which have comparable flow regimes (mach number, Reynold's number, and general grid fin design), leading me to believe I was using the wrong area for the Cl calc and therefore getting a lower Cl / Cd value. I had seen some videos and articles where it looked like calcs done for a traditional airfoil used the plan view area to calculate Cl, and the front area used to calculate Cd, and thought something similar may apply here. I suppose as long as you're consistent with how you do the calcs from from one test case to the next it should allow for a fair comparison between them all? I'll likely stick with my current calcs based on your responses... I'm not an aero engineer and I'm kind of figuring this out as I go, so I appreciate the pointers!

### RE: Area for lift coefficient calculations for Grid Fins?

"for a traditional airfoil used the plan view area to calculate Cl, and the front area used to calculate Cd" ... that doesn't sound right !

as 3DD suggested I'd use the planform of the fins (maybe the planform of one fin *number of fins ?).

### RE: Area for lift coefficient calculations for Grid Fins?

Frontal area for Cd is used on cars, not airfoils. When compressibility is a factor the interference between the elements of the grid will become much more noticeable.

Seems like an aero engineer would be useful on your project.

### RE: Area for lift coefficient calculations for Grid Fins?

(OP)
We most certainly could use an AE - I've been trying to make that case haha. But doing what we can for now. I'll stick with the planform area as everyone has mentioned. Thanks all for insight!

### RE: Area for lift coefficient calculations for Grid Fins?

Have you reviewed Biplane wing theory verse your test data?

### RE: Area for lift coefficient calculations for Grid Fins?

(OP)
I have not, but I can look into it. Anything part of it in particular that would be valuable? Or any resource that you'd point to?

### RE: Area for lift coefficient calculations for Grid Fins?

Over the years, I've noticed that AIAA [in the ARC] had several published papers on Grid Fins... along with several university thesis from all over... and a bit from NASA.

A quick glance show how complex this topic gets...

What airspeed range: Subsonic, transonic, supersonic, hypersonic?

What materials: composites, aluminum, titanium, steel/CRES/HRA.

What size/purpose: small/handheld tactical, large(er)/transporter tactical, ballistic missile, space-launch, emergency escape, etc...?

Probably lots of proprietary stuff that is sensitive/classified/trade-secret.

Devil-is-in-the-details.

Regards, Wil Taylor
o Trust - But Verify!
o We believe to be true what we prefer to be true. [Unknown]
o For those who believe, no proof is required; for those who cannot believe, no proof is possible. [variation,Stuart Chase]
o Unfortunately, in science what You 'believe' is irrelevant. ["Orion", Homebuiltairplanes.com forum]

### RE: Area for lift coefficient calculations for Grid Fins?

(OP)
Complex indeed! I've been through a fair share of research docs at this point, and while I'm getting more comfortable it still makes my head spin from time to time. I can provide some of the details you've asked about though...

-We operate in the subsonic range, ~M0.1 to 0.3.
-Our materials are not set in stone, but at the moment we're utilizing 3D printed Nylon 12; longer term we may looking into glass filled injection molded Nylon or potentially Bulk Molding Compound carbon fiber.
-Fins are in the range of 1 sqr ft of planar area, though that's still changing depending on how developments go. We are in the transport / logistics space of applications.

I hate to backtrack, but with regard to the area used for Cd and Cl calcs, is it typical that the area value is changed with each change of AoA? Or is the 0° AoA plan area used regardless of the AoA value? I had been opting for the former so far. Obviously, the projected area of a thin, flat surface relative to the flow is going to decrease with increases in AoA, so I'd been multiplying in a cos(AoA) to approximate that change (not perfect since there is some thickness to the grid fin but close enough for our purposes).

### RE: Area for lift coefficient calculations for Grid Fins?

A single area is used so the calculations make sense. In most applications the area of a wing doesn't change during airfoil selection. The area is used to normalize the graph. Since a grid fin isn't acting like a wing pick an area that you would use to represent all possible grid fins. I would use the wetted area as this would account for changes in thickness as well as planform.

### RE: Area for lift coefficient calculations for Grid Fins?

(OP)
Gotcha, okay makes sense. Thanks 3DDave!

One other thing I forgot to mention; we have also been exploring Cascade Fins, which are an offshoot of Grid Fins where the lattice density is reduced and they align 0/90 rather than ±45. A few studies have shown they have about twice the aero efficiency for subsonic speeds, and can be increased beyond that if the cross members are shaped like airfoils, which is far easier to do with Cascade Fins than Grid Fins.

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