Cubic Wing Loading

[Craig Toutolmin]

I would like to know if this is an accurate formula for scaling up aircraft.

http://www.aei.ca/~genesis/wacoymf5/wing%20loading.htm

Thanks for any info,

Craig

[Ollie]

I think the formula would be dead wrong to apply to the design of dynamic soaring aircraft.

The aerodynamic performance of dynamic soarers is determined by lift to drag ratio, not by wing volume loading.

The structural performance of dynamic soarers is limited by the fact that for a given structural configuration and material, strength goes up as the square of the linear dimension but weight goes up as the cube of the linear dimension. In other words small structures have better strength to weight ratios than large structures.

Dynamic soaring sites limit the size of the oval flight path by the physical size of the site itself. Beyond a certain size and wing loading the aircraft will be too large for the site.

L/D improves slowly with reynolds number (size times speed) but not as fast as strength to weight ratio decreases.

At the best L/D the induced drag is exactly half the total drag of the aircraft. Induced drag reduction is a very high priority so a relatively high aspect ratio is required. High aspect ratios demand strong and stiff wing spars. Profile drag reduction demands thin airfoils, which limit spar strength and stiffnesss. Reduction of aircragft weight that is not distributed along the span according to the lift distribution, must be minimized to limit the bending load on the wing spar.

The best configuration from a structural and aerodynamic point of view might be an unswept flying wing with an elliptical lift distribution and an elliptical mass distribution. There would be no spanwise bending load on the wing at any airspeed and radius of turn. Little of the strucrure would have to be devoted to the wing spar and structural objectives could be aimed at flutter control and chord wise stiffness. The remaining problem is to make such an aircraft's attitude visible to the pilot at all times so that it could be efficiently piloted without adding excessive appendages and their parasitic drag. Another problem is to distribute the mass fore and aft so that the plane balances ahead of it neutral point without concentrating the mass spanwise. A slight sweep forward would help to solve the mass distribution but would, in turn, put great structural demands on the torsional stiffness of the wing.

[Craig Toutolmin]

Hi Ollie,

I was hoping you would respond. Yes, this is a DS project. I have encorporated many of the suggestions in your post already. Unswept (straight 25% chord), high aspect ratio (15), thin foils (8.5%-8%), weight distribution in the wings (in the LE for mass balancing of the tip panels) and a massive spar (and sub-spar) - using your spar bending moment calculation from the Charles River site.

There are many sites that do not require the little, tight, more destructive patterns for DS. Cape Blanco, Kiona Butte and two sites in the Bay Area are examples that support a more subtle approach to DS. Bigger circles with lower lift coefficients and higher wing loadings generate speed in a more easily flown flight pattern. The planes the cracked 180 at Blanco were either fully ballasted (Scott's 2V) or had relatively high DS wingloadings of 18+.

Using the cubic loading calculation to scale up an 80", 22.5 oz/ft^2 plane to 124" would result in a wing loading of approximately 34 oz/ft^2. The 80" plane is the fastest plane of its size and has endured abuse for over a year. I want a similar feel of weight and glide in the larger plane. Is this even a possiblility? I do have a 100" alternate that is complete. Right around 100" seems to be current balance point of efficiency and strength. The 124" plane is almost complete and I'm going to be very close to that wingloading.


Craig

[Ollie]

If the best balance between efficiency and strength is at around 100 inches for present designs, and you want to go to 124 inch span, then you need to reduce the mass that is concentrated near the center line. Lighten the tail, the fuselage, the radio gear, the nose weight that are the masses that causes the bending load on the wing spar when doing high G turns. You want to move as much of that mass out along the span as possible so that the mass is where the lift is. When you do that you reduce the bending load on the wing spar and some of the structural limit on size is lifted. The mass that you can't move out along the span must be reduced by other means. You could lengthen the nose moment so that less lead in the nose is needed. You could design tails and tail booms the have better strength and stiffness to weight ratios. For example, the tail boom should be an all carbon fiber tube of the proper diameter, wall thickness, fiber orientation and taper to reduce weight to a minimum for the anticipated load and stiffness requirements.

BTW, to achieve maximum DS speed the plane must be flown at the best L/D which for most airfoils and high aspect ratios results in a coefficient of lift somewhere in the range of 0.6 to 1.0. I don't think wing loading enters into the maximum speed criteria except through the back door of the weight of the structures necessary for strength and stiffness.

[Craig Toutolmin]

Your explainations give me a good mental picture of what I need to know. I'm in the process of getting the tail lighter.

Thanks,

Craig

[Sail 'n Soar]

You want to move as much of that mass out along the span as possible so that the mass is where the lift is. When you do that you reduce the bending load on the wing spar and some of the structural limit on size is lifted.

That may minimize the moment at the root, but that is the worst thing you can do for maneuverability.

At the best L/D the induced drag is exactly half the total drag of the aircraft.

That is true with a constant CDo, but if CDo is a function of CL, the best L/D does not occur where CDi = CDo.

[Ollie]

Yes, design is about finding a balance between conflicting objectives. How much maneuverability are you willing to give up for reducing the load on the wing spar? If you can reduce the mass concentration enough by other means you won't have to redistribute the mass along the lift distribution.

At best L/D the Di=Do+Dp in level flight but that doesn't apply to a circle of constant size as the airspeed and angle of bank increase. I'm sorry for my wrong assumption.

[Craig Toutolmin]

Roll inertia is not a bad thing for DS if your only concern is top speed. The plane is easier to fly with a little weight in the tips. It is less easily upset in the often turbulent conditions. I'll just have to deal with landing the best I can.

"The structural performance of dynamic soarers is limited by the fact that for a given structural configuration and material, strength goes up as the square of the linear dimension but weight goes up as the cube of the linear dimension."

This is a great piece of information relating to the original question about cubic loading. It will be interesting to see how the size of future designs find the strength/weight limit.

Craig

[Sail 'n Soar]

"The structural performance of dynamic soarers is limited by the fact that for a given structural configuration and material, strength goes up as the square of the linear dimension but weight goes up as the cube of the linear dimension."

Craig, This relationship includes a number of false asumptions for models. First, the cube relationship for weight assumes the object's weight varies with its volume. This is generally not the case. Most of our models include a stressed skin (D-tube, etc.) and/or spars on or near the surface, and a lower density filler (foam or air.) The weight of the "payload" radio, batteries, etc., are one of the design variables and definitely do not follow the model dimension cube rule. For the structure itself, the weight will go up with the area, or square of the linear dimension, times the thickness of the outer skin and weight of the spar. For single a solid spar going from top to bottom - not the most efficient design, the length and height will go up linearly, but the width need not. Thus, the weight will go up as the square of the linear dimension times the width, and the strength will also go up with the square of the linear dimension times the width - a wash.
For a stressed skin design, the strength will go up with the cube of the linear dimension - area times height - times the skin thickness, i.e. with the fourth power - as long as the skin has something to prevent the compression side from buckling, including a thicker skin. In other words, the strength can go up FASTER than the weight!

At best L/D the Di=Do+Dp in level flight but that doesn't apply to a circle of constant size as the airspeed and angle of bank increase. I'm sorry for my wrong assumption.

Olie, Please run some real numbers. You can derive your equation easily for Do+Dp = constant (AE 101). But they are not constant. Do is strongly dependant on CL. Unless you have a relatively low aspect ratio, you cannot achieve a sufficiently high CL to achieve Di = Do + Dp at the sort of Reynolds numbers we fly.

Chose your favorite airfoil, take the CL vs. CDo curves at REDUCED RE (RE*sqrt(CL) = constant), and choose an honest Dp. For an absolutely minimalist fuselage things might work out, but I doubt it. Since we are talking about soarers, please use an AR of at least 7, preferably higher. Make a table of CL vs. CDo+CDp and I wager you will find L/D max at CDi less than CDo+ CDp unless you have chosen a high lift foil, in which case your efficien operating envelope will be small and/or you will not have accounted for the excess drag of operating a high lift foil at lower CL's near the outer wing panels.

[Sail 'n Soar]

Unless you have a relatively low aspect ratio, you cannot achieve a sufficiently high CL to achieve Di = Do + Dp at the sort of Reynolds numbers we fly.

Should have dropped that line! :o
Correcting myself, with the newer foils, a narrow fuselage and a low drag stab, the resulting CL's can be less than 1 at CDi = CDo + CDp, but that is most likely not going to be the condition for best L/D if you calculate CDo(CL) @ RE*sqrt(CL) = constant because the reduced CD will generally grow relatively fast due to both the lower RE due to lower flight speeds at higher CL's and because the min CD at constant RE is probably at a lower CL than the CL for CDi = CDo + CDp.

[Ollie]

Sail and Soar,

I accept your challenge to run some real numbers. Will David Fraser's Sailplane Design program using Selig's wind tunnel test data be acceptable to you? What airfoil, aspect ratio, tail area, tail moment arm, span, fuselage diameter, gross weight and wing weight would you propose? After we settle the L/D question I propose to design a spar for the plane to handle 50G's and another spar for a similarly configured plane twice the size also to handle 50 G's. Then we can discuss the results.

I gave my copy of Sailplane Design to a flying buddy because my computer no longer runs MS DOS programs. It will take me a few days to access the program so, I hope you will be patient with me.

[Sail 'n Soar]

How about using Mark Drela's numbers for Allegro-Lite.
at 16oz loading,
AR = 11.7
W/a = 4.9oz/sq ft
L/D,max = 20 @ CL = .5

Then CDi + CDo + CDp = .5/20 = .025

assume e = .98 (should be at least that high for Mark's wing plan)

Then CDi = .5^2/(Pi*.98*11.7) = .007
and CDo + CDp = .018

Therefore, at L/D max for Allegro, CDi <<CDo + CDp

even with e = .96 (constant cord wing, no washout)

CDi ~ .007
CDo+ CDp ~.018

For this case study the CDi is so much less than the CDo +CDp at max L/D, I don't think you really need to run the numbers. But if you would like, here is a good source of airfoil data:

http://www.nasg.com/afdb/search-airfoil-e.phtml

BTW, per Mark's calculations, that 8.73% root foil/ 11.7 AR wing can take 150 g's at the 16 oz weight, with his carbon capped spar.

OK, guess I've beaten that dead horse enough.

[Ollie]

Sail 'n Soar,

Thanks for setting me straight.

Dead Horse

[Craig Toutolmin]

"For a stressed skin design, the strength will go up with the cube of the linear dimension - area times height - times the skin thickness, i.e. with the fourth power - as long as the skin has something to prevent the compression side from buckling, including a thicker skin. In other words, the strength can go up FASTER than the weight!"

Bending loads are a big problem. How do bending loads increase with span? Can this strength that increases faster than weight increase as fast as bending load too? More span = more speed = higher loads in addition to the geometric problem. Right now a stock 60" plane is almost impossible to break. A custom built 3M is a roll of the dice whether it will hold - most have failed.

Craig

[Sail 'n Soar]

Originally posted by Craig Toutolmin
"For a stressed skin design, the strength will go up with the cube of the linear dimension - area times height - times the skin thickness, i.e. with the fourth power - as long as the skin has something to prevent the compression side from buckling, including a thicker skin. In other words, the strength can go up FASTER than the weight!"

Bending loads are a big problem. How do bending loads increase with span? Can this strength that increases faster than weight increase as fast as bending load too? More span = more speed = higher loads in addition to the geometric problem. Right now a stock 60" plane is almost impossible to break. A custom built 3M is a roll of the dice whether it will hold - most have failed.

Craig

At a constant wing loading (W/A=constant) and CL, bending loads go up with the wing area times the span. For a constant aspect ratio this results in the bending loads increasing with the cube of the span. More span relates to more speed only if the wing loading goes up - and that is a design choice.

You need to ask yourself when and why the 3M is the roll of the dice. I would guess you are looking at lower AR designs for your 60" plane and significantly higher AR's for the 3M, in addition to likely heavier construction. If you designed the 60" planes to the same AR, wing loading, and similar design practices, the 60" span planes would result in the same roll of the dice.

I mentioned Drela's Allegro-Lite in an earlier post. Per his discussion, Mark's wing was designed to take the loads at max winch speeds, resulting in designing to a max 150# and a root bending moment of 1400 in-lbs. He designed to a set of requirements. The real issue is that many times we design by feel and experience without defining the requirements and running at least a few numbers. For those who don't have the background, best approach is to copy someone else's successful design.

[Ollie]

See:
http://members.tripod.com/douglasturner/id27.htm

Acording to Joe Wurts' analysis, the maximum speed attainable by dynamic soring is determined by the strength of the wind shear and the L/D of the plane.

"It turns out that the wing loading drops out of the equations. "

Dr. Drela comes to the same conclusion by another method of analysis.
See Dr. Drela's analysis of dynamic soaring at the Charles River web site.

[Sail 'n Soar]

So that's what DS is? Some of us flat-landers are disadvantaged.
In any case, seems to call for sticking with lower aspect ratio/modest L/D designs. From the write-up, the key is knowing something about the wind shear statistics of your chosen site, and then designing to them - or controlling your enthusiasm!:) Of course, with a stall speed of ~29 and a top speed ~299+, you are dealing with a 100+ g design goal. Can be done, but carefully. Long, thin wings also become flutter prone, further increasing the challenge.

[Ollie]

For the current state of DS speed see all nine pages of:
http://www.shredair.com/album/dsfest5.html