If you've visited my site you can see that I mostly build small aircraft. I've often wanted to scale up some of my designs but I actually have very limited experience with larger aircraft and am not sure what is a good wing area for engines larger than say a .60.

I have run the numbers several times and think that the best method is #1. The wing areas differ quite a bit depending on the method used. I'm wondering which of these methods is actually the most valid.

In this example I am scaling a 450 square inch wing having a .15 2-cycle to an unknown area wing having a 1.5 2-cycle.

==========

Method 1 - Use the ratio of the cube root of the engine displacement to the square root of the wing area. This is my normal method.

.15 ^ 1/3 = a = .5313
1.5 ^ 1/3 = b = 1.1447

450 ^ 1/2 = c = 21.2132
area ^ 1/2 = d = ?

a / c = b / d

.5313 / 21.2132 = 1.1447 / (area ^ 1/2)
.0250 = 1.1447 / (area ^ 1/2)
area ^ 1/2 = 1.1447 / .0250
area = 45.7880 ^ 2

Wing Area = 2097 square inches

==========

Method 2 - Use the ratio of the 2/3 root of the engine displacement to the wing area.

.15 ^ 2/3 = a = .2823
1.5 ^ 2/3 = b = 1.3104

c = 450 square inches

a/c = b/area

.2823 / 450 = 1.3104 / area
.0006 = 1.3104 / area
area = 1.3104 / .0006

Wing Area = 2184 square inches (pretty close to method 1)

---------------

Method 3 - Find wing area per cubic inch displacement

450 / .15 = 3,000
area / 1.5 = 3,000

Wing Area = 1.5 * 3,000 = 4,500 square inches (Yikes!!)

I think that you would be better off playing with power & wing loading, rather than using displacement as the key determinant. Generally, specific output drops with increasing displacement, as does engine power/weight ratio. Larger engines usually don't make the ponies like little engines, but as the forces rise with increasing power, the necessary mechanical strengthening to ensure integrity adds weight faster than power goes up. Additionally, model wing-loading can increase rapidly as size goes up -- again due to the need to maintain structural integrity.

Why not look at some well known models that would fly well with a 1.5 2 stroke. Here are some examples from the Tower and Horizon Hobbies web sites

Sig Rascal 110 1522 in^2
Lanier Stinger 1344 in^2
Dynaflight Decathlon 1237 in^2
H9 Ultra Stik 120 1210 in^2
H9 P51 1.5 1039 in^2
Sig Extra 300XS 990 in^2

Sounds like 2000 in^2 might be usable, but a real floater. Probably 450 square inch wing with a .15 2-cycle is a floater, too.

4000 in^2 is too high. The balsausa 1/3 J3 Cub has 3051 in^2 and the recommended engines are 2.0 - 4.0 2 strokes.

Carl

This would be a good way to do it, but you can't believe the numbers provided by manufacturers regarding power output and I don't have the equipment to find the watt output of an engine.

I've found that as a model gets larger it's easier to make it lighter. I've also found that a lot of designers WAY overdesign models when they start getting bigger. For example, a friend recently built one of the big guy's Extra kits. It has a 6' span and 1/2" pine spars! It would have been fine with 1/2" balsa and a heck of a lot lighter.

The engine sizes I used were just examples. I'm not looking for an answer to that specific problem but just the best way to solve it. Many of my designs have nothing comparable available commercially and I'm not sure I want to trust what someone else thought was "right" for a given engine. I'd rather just know how to figure it out. So far my first method seems to be the best.

What I'm actually asking is a way to do it empirically - not just finding something similar that may already be available.

By the way, my design Great Gonzo has 580 or 670 inches of wing depending on configuration. It flies on a .15 but could fly on much less. As I recall, I figured a Greater Gonzo having a 1.08 engine would have about a 120 inch span which would give it roughly 2,500 squares. I could be remembering that wrong. I did the math in a German hobby shop trying to explain to the owner the 2/3 root thing. I didn't speak German and he didn't speak English. I was mainly trying to get the concept across and doing the math in my head.

I doubt you will find a universal scaling law that works for all types of models. I would use scaling laws as a guess. If there are no similar planes for comparison, then build a prototype and be prepared to make lots of changes. I also agree with britbrat, engine displacement is not a reliable predictor of engine power and any theoretical scaling law would use power or thrust.

Try looking at the article on scaling in Model Aviation DEC 2004. The author derives a power scaling of L^3.8, using hovering requirements, probably not what you want. He has based the scaling on the assumption that the prop diameter is 20% of wing span, I doubt that that is universal. He immediately quotes a different scaling law for aerobatic planes. I'm sure you could derive a scaling law for many different parts of the flight profile -- hover, take-off, cruise, top speed, etc and they would all be different. I would think the requirements for a powered glider would scale quite differently from that of a sport plane.

Looking at other models is not just trusting what someone else thought was right. I have some idea how the models quoted fly and it tells me more than the three scalings using engine displacement. I understand the desire to create something new and different, but that doesn't mean you shouldn't learn from what others have done.

Carl

I agree. None of what we design any more is truly original. It's just rearranging old concepts. I'm really just looking for something to get me in the ballpark.

My main problem with most designs is that they are over designed having more structure than necessary and heavier than necessary. I keep building lighter models and have yet to have one fail no matter what I did to it which tells me I can make them still lighter. That's the main reason I don't want to simply follow conventional designs, but I do agree they get me in the ballpark.

What I'm really trying to avoid is simply guessing.

"Well this one with the .15 has 400 inches of wing. Maybe it should have 3,000 for the 1.5." I've designed a lot of planes and don't mind cutting off parts and making new ones. At the same time I want to be close enough on the first attempt that I can't get much useful information from it.

How about this. The BalsaUSA 1/3 Cub is designed for a 2.0 to 4.0 2-stroke with a 3051 in^2 wing area weighing 30 to 35 lbs. A wing loading of 40 to 46 oz/ft^2. Make it 30% lighter it should fly fine with a 1.5. We know how a Cub flies and we should have a pretty good guess how a Cub 30% lighter should fly.

30% lighter ==> 21 to 24 lbs ==> 28 to 32 oz/ft^2. Does that sound like the flight characteristic you want for your Super-Giganto Gonzo, if yes then try 3000 in^2 and a target weight of 21 lbs.

Actually, I'm considering scaling [link=http://airfieldmodels.com/gallery_of_models/rc/thwing!/index.htm]Thwing! for my 1.60 four-stroke twin[/link]. Seriously.

Look at the Delta Vortex [link]http://www.btemodels.com/[/link], lots of good info on large delta wings and then look at [link]http://www.btemodels.com/beastpop.html[/link]

Carl

I figure a Super Duper Greatest Gonzo with a 10' wing should weigh no more than 12 lbs. Let's see....

8 oz. / sq. ft. = target wing loading

12 x 16 =192 oz
192 / square feet = 8

24 square feet (3456 square inches)

aspect ratio of 5.8 / 1

s/c = 5.8
s x c = 3456

c = 3456 / s
s / (3456 / s) = 5.8
s ^ 2 / 3456 = 5.8
s ^ 2 = 20,000
s = 141 inch span.
c = 24

actual area = 3384

OK, I can't build that at 12 lbs probably so I guess I'll have to settle for a higher wing loading.

I've seen that. One guy asked me to build one and never got back to me. Thwing! is way cooler though and will probably have a much lower wing loading.

I think you can get away with a heavier wing loading in the larger scale.

Yea, the beast at 42 lbs is a monster. It would be cool to have a big Thwing!

Have you read the MA Dec 2004 article Page 43? Might be worth a look. Maybe some of the Aerodynamics guys can comment on various scaling laws. Sounds like something that could go in the FAQ.

By the way you have an excellent website. I have learned much from previous visits.

Carl

Yes. A larger model can have a higher wing loading and fly like a smaller model with a lower wing loading. But I want to see how light I can make it even if it won't come back down.

I read it but don't remember what it said now. It's all the way across the room and too much effort to get to. Easier to sit here and ask questions.

Thanks.

I would try to take some clues from the Delta Vortex. It's wing loading is about 13.5 oz/ft^2 at 8 lbs and should not fly insanly different from your Thwing! with 9.5 oz/ft^2 at 1.6 lbs. Assuming your twin 1.6 has about 40% more power than a 91 four-stroke, then you should select a target weight around 11 lbs.

The tougher part is, how big a wing can you make and hit the 11 lb?

Carl

Depends on how much the retracts weigh. I'm good about building to a maximum weight. I normally beat the weight by 10-20%. I start my designs by choosing a size, powerplant and wing loading and do whatever it takes to stay below that.

I can't imagine building a wing that would weigh 11 lbs. I'm not sure what the engine weighs but I think it's a little over 3 lbs.

I'm thinking a 3-blade carbon prop so I can keep the gear as short as possible. Maybe twin pipes on the engine.