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What is cubic wing loading????

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What is cubic wing loading????

Old 10-02-2003, 06:53 AM
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Scoubidou
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Default What is cubic wing loading????

Hello
Can you help me to calculate the cubic wing loading of this plane:
Extra300L
Wing area=890sqin
Weight=10.5lbs
Wing span: 72''
1) What is the formula?
2) What is good or bad cubic wing loading for aerobatic IMAC plane?

Scoubidou
Old 10-02-2003, 10:17 AM
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Rodney
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Default RE: What is cubic wing loading????

The formula is Weight of model in ounces divided by the wing area in sq. Ft raised to the 1.5 power. In your case 10.5 times 16 devided by 6.18 raised to the 1.5 power which, if my math is correct is equal to 10.9. This should be a reasonably good flyer but will have to land slightly fast. A value of 7 would be a real floater.
Old 10-02-2003, 10:26 AM
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David Cutler
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Default RE: What is cubic wing loading????

Interesting.

Why is the result of the calculation raised to the 1.5th power? I can understand doing that if it's needed to weight a factor, (like, for instance the fourth power law applied to the distance in gravity calculations) but if you do it after all the other calculations have been completed, all it does is create a different range of numbers to use as standards.

I mean, why not multiply by 12756? or divide by 37465? or raise to the 18th power? Providing it's always done, the result will still create a range of numbers that, if you always use the same calculation, will be meaningful when compared with each other.

-David C.
Old 10-02-2003, 11:45 AM
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Scoubidou
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Default RE: What is cubic wing loading????

I tought i was good in math? You gave me the 'wing loading formula' wich is weight/wing area:
Wing loading=168oz/6.18sqft=27.18oz, not bad for aerobatic.

What about the CUBIC wing loading now What raised to the 1.5 power mean?

Scou
Old 10-02-2003, 11:59 AM
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JimTrainor
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Default RE: What is cubic wing loading????

The equation is:

Weight^2 / Area^3

Which is identical to :

Weight / Area^(3/2) = Weight / Area^1.5

^ means "raised to the power"

... so you see where the cube comes from.

And.. as Rodney stated, weight in ounces and area in square feet if you want to compare your result with the number he gave (e.g. 7 is a floater).

Perhaps someone else can chime in and explain why it is meaning full to begin with??? I've read some explanations that make sense but I've never sat down and thought it through myself.
Old 10-02-2003, 12:36 PM
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erjpilot
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Default RE: What is cubic wing loading????

Scou:
The wing loading calculator I use is from the mini-iac website. It is an excel spread sheet and it works very well. The link is below. If it doesn't work it is on www.mini-iac.com under site services then downloadables then excel files. In the excel program it has a paragraph that explains what good cubic wing loading is for an aerobatic plane. I put the numbers in that you listed and the cubic wing loading is 10.93 which is a bit on the high side, but smaller planes usually do have a higher wing loading for their size than the larger scales. 8-10 is listed as good for IMAC style planes. Hope this helps, Travis

[link]http://www.mini-iac.com/pages/services/download_wing_loading.asp[/link]
Old 10-02-2003, 02:28 PM
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Tall Paul
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Default RE: What is cubic wing loading????

Why 1.5 power?
Makes the answer look "scientific".
Otherwise there's no reason for it.
Old 10-02-2003, 02:48 PM
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Default RE: What is cubic wing loading????

Seems to me I've seen stuff where the airfoil thickness is taken into account in calculating the wing volume.

From what I see here it's only considering the AREA rather than the actual wing volume. The forumula here is just covering the basics wing area loading with chocolate to come up with a number that does not properley consider the actual wing volume. Granted the resulting number means something but it's no more sifnificant than the basic wing loading since the third dimension to make it cubicly related isn't there.

There's more out there than I haved time to find just now but perhaps someone else can back me up on this.
Old 10-02-2003, 03:03 PM
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Montague
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Default RE: What is cubic wing loading????

Actually, the 1.5 power thing is based on some valid stuff. The idea is to calculate the weight spread over the volume of the wing instead of the area. So, to truely calculate the volume loading of a plane, you take (wingspan) * (average area of a wing rib).

But wing ribs are hard to measure for area.

However, if you make a base assumption that everyone is using pretty much the same airfoil with pretty much teh same thickness, then, and only then, you can compare two models of different sizes buy just raising the area to the 1.5power. So, if you want to compare two IMAC planes, it works. If you compare an IMAC to a Cub, it doesn't. Compre two cubs, and it works again.

If you take the time to compare two planes with the same wing area, but one has a 9% thick airfoil, and the other a 18% thick airfoil, you know that wing area loading isn't enough to predict things like low speed handling. But if you do something to factor in the airfoil thickness, you can get a better comparison. That something is volume loading using the acutal volume of the wing.

The 1.5 thing is an easy short hand for a special case, that's all. But it does work, for a quick and dirty number in it's intended limited scope.
Old 10-02-2003, 03:05 PM
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Rodney
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Default RE: What is cubic wing loading????

This is a formulae that was first (at least to my knowledge) proposed by a gentleman named Reynold's (no not the one who developed Reynold's number) who used to write for Model Builder. It is very good and a much better indicator of performance than just wing loading. For instance, if you try to fly a 1/2 a model with a wing loading of 18 oz./sq.; ft., you will have a lead sled that will probably be unflyable but, a 1/4 scale job with that wing loading will float forever. Wing volume loading is way of normalizing all sizes of models to have a good idea of how they will perform. If you do not believe this, just calculate the wing volume loading of as many planes as you can that you have flown and then compare the results. You will find that those with a 7 to 10 WVL will be the best performers regardless of actual size. You might also check out those that were dogs to fly to see where they fit in the evaluation.
Old 10-02-2003, 03:08 PM
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Montague
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Default RE: What is cubic wing loading????

Actually, I read an article about acutal volume loading, using the actual volume of the wing instead of the "shortcut" quite a while back. I don't know if it pre-dates the stuff you mention. And I've long since lost my source citation.
Old 10-02-2003, 05:16 PM
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Scoubidou
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Default RE: What is cubic wing loading????

Gentlemen,
Thanks for all information . I don't care who is wrong or right but by sharing our experiences, knowledges and challenging each other, we do the most important thing, WE LEARN!!

I have used the IMAC calculator (thanks erjpilot) and the formula (JimTrainor) and both give the same result of 10.9 cubic wing loading on my Extra 300. My goal is to build a nice IMAC plane with a 2.5 pounds gas engine in the nose to fly a lot at low cost. 10.5lbs is the lightest possible to do with that plane with full CF hardware and other modifications.

Now i have 2 questions:
1) Can flaperons or spoilerons reduce the landing speed on that plane?
2) If it can, i assume the flaperons will reduce the landing speed by 25%? which inconvenience having 10.9 cubic wing loading?


I am not a 3D pilot but a patttern-IMAC addicted. The only 3D stuff for my flying style is the knife edge and torque rolls.
Scou
Old 10-02-2003, 06:30 PM
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Default RE: What is cubic wing loading????

Francis Reynolds, writing for the old Model Builder magazine, did originate one of the cubic loading formulas. And he had 2 versions of the formula.

The problem is that wing loading does not work when comparing airplanes of different sizes. Reynolds was making an attempt at creating a formula that would cut across size.

His original formula did include a variable for average wing thickness. This was later replaced by his less complex formula using the weight divided by the area and the square root of the area. This is area to the 1.5 power. The result was pounds per cubic foot. He claimed this formula worked just as well as the more complex one.

Another modeler, who was more sailplane oriented, used a formula that was weight divided by the area and the span. This one favored longer wings.

Reynolds also showed his Reynolds Performance Factor, which factored together cubic loading and power. The problem with this formula, in my opinion, was in 2 areas. First, the answers were in very small decimals. I feel that when the average modeler sees a number like .00013, his mind zones out. Second, the smaller value was better than the greater value. This may be fine for wing loading, but when you start adding in power, we tend to think of bigger is better.

Since I wanted to use the formula, I went into it, and disregarding units, revised it so the larger the number, the better and the answers came out in numbers like 75, 100, 150. Sizes we normally understand. I called this revised formula the Aircraft Performance Rating, or APR. Both Reynolds' formula and mine require you to enter a factor for the engine. This is a judgement area and it can influence the answer.

I will be glad to supply the formula to anyone and I have it done in Visual Basic on CD. I compiled it on a computer running Win 98SE, so I am not sure if it likes Win XP or not.

A couple of examples follow: EF = eng factor WL=wing loading. CL=cubic load, APR=acft perf rating
750 sq in 7.5 lbs .46 EF=1.2 WL 23.04 CL 10.10 APR 72.90

750 sq in 5.0 lbs .46 EF=1.2 WL 15.36 CL 6.73 APR 164.03

750 sq in 7.5 lbs .914s EF=.85 WL 23.04 CL 10.10 APR 51.64
Old 10-02-2003, 08:23 PM
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LouW
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Default RE: What is cubic wing loading????

Cubic wing loading is an empirical "rule of thumb" with little theoretical basis, but it seems to work for comparison of similar model aircraft of different size.

Yes flaperons will reduce landing speed. I think your assumption of a 25% reduction is quite optimistic. Something on the order of 10% is more likely. Spoilerons won't reduce landing speed, but both will increase approach angle which will make landings a bit easier.
Old 10-02-2003, 08:33 PM
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David Cutler
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Default RE: What is cubic wing loading????

A
The equation is:

Weight^2 / Area^3

Which is identical to :

Weight / Area^(3/2) = Weight / Area^1.5
Ah! I understand now!

However the above isn't true. You are mixing apples and pears. If the Weight has to be squared and the Area has to be cubed, then their relationship to each other is changed in the final result (the Area, in this case, has a greater effect on the result due to its 'boost'). You can't mix the exponents like that.

Put it this way:-

If weight = 4 and Area = 2 then :-

Weight^2 / Area^3 = 16/8 = 2

and Weight / Area^(3/2) = 2^1.5 which is about 2.8

-David C.
Old 10-02-2003, 09:20 PM
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JimTrainor
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Default RE: What is cubic wing loading????

Your right. It would have to be:

W^2/A^3 = (W/A^1.5)^2

.... so I don't have a clue what I'm talking about

I'll have to study all the above posts...
Old 10-02-2003, 09:21 PM
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Tall Paul
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Default RE: What is cubic wing loading????

And there's no direct relationship between weight and area.
Stick and paper construction to foam, same sized plane, vastly different weights.
Old 10-02-2003, 09:39 PM
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Ed_Moorman
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Default RE: What is cubic wing loading????

It would be weight in pounds divided by area to the 1.5 power.

The 1.5 power of area is area times the square root of area. Area is in square feet. The square root of area would be in feet. Multiply these and you get feet cubed.

Dividing the 2 gives pounds per cubic foot.

If you want the conversions figured out, the formula would be:

CL = 27648*pounds/square inches/square root of sq in.

Ex: 1000 sq in & 10 lbs

CL = 27648*10/1000/sqr(1000) = 8.74 lb/cu ft
Old 10-03-2003, 08:13 AM
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Default RE: What is cubic wing loading????

Read this definition for the cubic wing loading

[link]http://www.genesis-rc.com/wacoymf5/wing%20loading.htm[/link]

I also saw a show on history channel yesterday talking about a similar relationship with respect to jet engines. The size of engines decrease as a power of 1/2 while the weight goes down as a power of 1/3rd while miniturizing engines.

I am not sure what to make out of this but it is interesting nevertheless.

Also David Cutler is correct about the powers. and the units (standard system) of this mysterious number is (lb/cu.ft.)^2 (not exactly cubic loading).

my 2 cents

e=mc2
Old 10-03-2003, 09:21 AM
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JimTrainor
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Default RE: What is cubic wing loading????

In my attempts to understand where area to the power of (3/2) came from, I did some more math.... sorry

This page talks about scale and it's relationship to speed, area, mass, etc:
http://jmquetin.free.fr/tips5e.htm

It concludes, and has a small graph, showing that wing loading is propotional to the square root of weight as model scale varies.

Starting with that I did the following:

W=Weight A=Area r=scale factor
prop = "is propotional to" or "varies with"

W/A prop W^(1/2) (wing loading is proportional to square root of weight)

Also, weight is proportional to the cube of scale and area is proportional to the square of scale, so we can also say that wingloading is proportional to the scale:

W/A prop r
hence
W prop Ar

So that means:

W/A prop (Ar)^(1/2)

square both sides

W^2/A^2 prop Ar

so

W^2 / A^3 prop r

Let's decide we don't like look of that, so take the square root of both sides:

W / A^(3/2) prop r^(1/2)

The cubic wing loading is proportional to the square root of the scale ratio.

So perhaps who ever came up with cubic wing loading liked the fact that they had a number that looked something wing loading ad was related to the scale factor of the plane.

But... I don't how you'd go from that to a conclusion that planes of differing scale will fly equally well if the cubic wing loading is that same. Actually, I come to the opposite conclusion. One shouldn't look for a constant cubic loading at all... one should look for cubic wing loading to increase with the square of the scale factor.

... time do get back to making a living.



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