Determining WS for a desired weight

[Viper Pilot]

How do you determine the WS of a model if you have a target weight ? ?

I plan on building an Arup S2 (photo attached).

I have a target weight of 2 1/2 lb AUW, including landing gear (3/32" piano wire and small wheels).

Can't find a formula anywhere . . . maybe it doen't exist.

Help please.

Viper :confused: :confused: :confused: :confused:

[Ollie]

The plane is a very low aspect ratio flying wing. The airfoil you choose should be reflexed so that you can achieve pitch trim. Such airfoils do not produce very high maximum lift coefficients. That means that the wing loading should be about 25% lower than normal. Which in turn means that the wing area should be about 25% bigger than normal for the weight of the model. Make the span as big as you can consistent with your target weight and your ability to design a structure that is strong enough yet meets your weight target.

The reason you can't find a formula is that there is none. There are a wide range of possible answers which depend on the purpose of the model and its expected performance envelope.

[Trizza]

Viper, this would be my process:
- Choose a desired wing loading, and estimate the AUW (as you have)
- Divide the AUW by the desired wing loading, which gives desired wing area
- Take a top view of the plane and figure out its area (call this A), measure its span and call it S.
- calculate k, where k = (S*S)/A (ie area divided by span squared)
- multiply the desired wing area by k, and take its square root. This gives the span you should aim for.

Make sense? If I've made a boo boo in the maths please point it out. I was just working it in my head there.

Theres a few different methods for finding wing area. My favourite is to trace around the top view from a 3-view in AutoCAD, convert it to a Region, and use commands (I think its called measure) to find its area. I then just use a linear dimension to find its span, and use the above process.

[Ollie]

Trizza's process makes sense to me.

Pick a plane that has the desired speed range that you are looking for. Reduce that plane's wing loading by about 25% to allow for the lower maximum lift coeficient of a reflexed airfoil and use that as an input to Trizza's calculation process. You will come very, very close to picking the right size plane for the performance you want.

Handling is another matter. The lack of sweepback will make it somewhat different than a low aspect ratio delta as far as dihedral effect is concerned. Otherwise the handling will be similar to a delta.

[Viper Pilot]

Originally posted by Ollie
. . . . . Handling is another matter. The lack of sweepback will make it somewhat different than a low aspect ratio delta as far as dihedral effect is concerned. Otherwise the handling will be similar to a delta.

Would dihedral and/or washout be needed for this type of wing.

How much of each??

This is very interesting stuff ! ! !

Viper

[Ollie]

The aspect ratio is so low that the whole wing is operation in its own tip vortex and the flow is three dimensional rather than the two dimensional flow that is forced in airfoil wind tunnel measurements. What you can count on is that there is a lot of downwash over the wing due to the tip vortices. This downwash produces a very large induced angle of attack that delays stall way beyoud the stalling angles on high aspect ratio wings. Because the whole wing is wing tip so to speak, the concept of tip stall kind of merges with the general concept of stall. For this reason, I wouldn't bother with washout.

It may not be necessary to have sweepback or dihedral with enough vertical tail area to keep it from yaw instability. If you want yaw to roll coupling you could use two or three degrees of dihedral.

[Viper Pilot]

Originally posted by Trizza
. . . . . . .calculate k, where k = (S*S)/A (ie area divided by span squared) . . . . .

Conflict here:

does k = (S*S) / A

or k = A / (S*S) ? ? ? ?

Viper

[Trizza]

Viper,
Sorry about that I wrote it wrong afterwards. Either way will work it just changes the way you do the final calculation. To make it consistent with the final step, use k = (S*S)/A. Otherwise you divide desired area by k to get squared span.

Its safest just to ignore that bracketed comment after the calculation.

Good luck with it mate and be sure to post pics :D

[Viper Pilot]

Trizza, Thanks for the update!! By my calculations (including the extra 25% suggested by Ollie) comes out to very near the 36" WS that I guessed using the SWAG system.
Originally posted by Ollie
. . . . It may not be necessary to have sweepback or dihedral with enough vertical tail area to keep it from yaw instability. If you want yaw to roll coupling you could use two or three degrees of dihedral.
Ollie,

I found an article on the internet that says Dr. Snyder (designer of the S2) actually had some anhedral in the wing. The airfoil he used was a modified M-6, which has some reflex built in.

This is getting way too complicated now, and I think I'll just use a Clark Y with no dihedral. What do you think??

Viper

[Trizza]

Viper - I think you'd probably be best with a flying wing airfoil. They are designed to have a low (or zero!) pitching moment so that the horizontal stab is not needed.

You're only going to find out by trying something, so go ahead and try whatever you like. If it doesn't work, try something else!

[Ollie]

The Clark Y has a lot of mean line camber which results in a very large negative (nose down) pitching moment. It will take a very large up-elevator neutral position to bring the plane into pitch trim. The large up-elevator neutral position will transform the Clark Y for the center wing panel into a reflexed airfoil. The required neutral position of the elevator will leave very little additional up-travel available before the elevator stops acting like an elevator and starts acting like a speed brake.

You just can't escape the need for a low mean camber, reflexed airfoil like the M6. Low camber results in the need for less reflex which, in turn, will allow much better pitch control response.

The Saracen series of tailless designs by Bill Evans very successfully uses a slightly modified NACA five digit airfoil with about one or two percent mean camber. The high point of the mean camber is much farther forward than most other airfoils. This NACA airfoil is modified with a very slight reflex to achieve the desired pitching moment characteristics that you need.

[Viper Pilot]

Good info, guys.

I'll use the M6 airfoil, then, to avoid the above mentioned problems.

Not really a problen there, since there are going to be only 16 rib sections.

Thanks for the help. I'll keep you posted.

Viper

[Trizza]

MH 60 and MH 45 are also meant to be very good flying wing airfoils. Optimized for models, they have a zero pitching moment for most angles of attack.