Scaling down a plane?

[Frank B]

I plan on scaling down one of my existing models to half the size. How do I calculate the figures for the new plane (thrust, pitch speed, wingloading etc.) if I want the same flying characteristics as the original plane?

I guess the top speed should be halved, but that's about what I can figure out.

Do I just scale down the profile, or will this result in too thin an airfoil?

[Dick Huang]

Frank,
You state:
"I plan on scaling down one of my existing models to half the size."
Just multiply the liner dimensions by 0.5. for example if your current wing span is 50 inches and the wing chord is 10 inches your 100% wing area is 50*10=500 in². your half size model will have a span of 50*0.5=25 in and wing chord of 10*0.5=5 in;the new wing area is 25*5=125 in². or 1/4th of the 100% size. Are you sure this is what you want to do? Use a program like Moto-cal to determine the performance of this 125 in² model.

Dick Huang:confused:

[Frank B]

Dick,
Yes, I want a plane half the size of the original.

What I am not sure about are the figures needed to get the same performance as the original (so that it flies in the same manner and feels the same).

All measurements will be 50% of the original. This means (as you state) that the wing area will be 25%, but what about the weight? My logic tells me that it should be 1/8 (12.5%) of the original, as the plane is scaled down in three dimensions (the volume is reduced to 1/8). This would give the new plane half the wing loading of the original.

Maybe the real figures will help:

Original:
Wing span: 56 in
Wing area: 490 sq.in
Weight: 78 oz
Wing loading: 22.9 oz/sq.ft

New plane:
Wing span: 28 in (50%)
Wing area: 122.5 sq.in (25%)
Weight: 9.75 oz (12.5%)
Wing loading: 11.45 oz/sq.ft (50%)

This new design seems to fit the measurements of other small planes, so they could be the right calculations? or are they?

And then there is the performance. The original has a climb rate of 1280 ft/min. What do I aim for with the new plane? 50%, 25%, 12.5% or?

I would like the new model to have the same (apparent) performance as the original.

[Ollie]

The airfoil will have a larger coefficient of drag in the smaller size because of scale effect (reynolds number). At the lower reynolds number of the smaller model, thinner airfoils will be more efficient. Also, to allow for the increased drag coefficient, the power loading (gross weight / engine displacement or gross weight / watts) should be somewhat higher.

For the model to have the same apparent (visual) size after one minute of climb the rate of climb should be 640 feet per minute. Similarly, the trimmed airspeed in level flight should be half for the smaller model if it is to appear to take the same amount of time to traverse the sky at a distance that results in the same visual impression as the larger plane.

[Frank B]

Thanks a lot Ollie,

Half the climb rate and half the top speed. images/icons/icon14.gif

I will play around with MotoCalc to find a suitable power setup for those numbers.

When you suggest that I use a thinner airfoil, do you mean thinner than the 50% I will get by just scaling it down? The original airfoil has a thickness of 12%, should I use 10% or even 8% instead?

Have I got the weight right?

[Ollie]

For the smaller model an airfoil whose thickness is 8% of the chord will work better than an airfoil whose thickness is 12% of the chord. Where weight is concerned, you just have to meet the power loading objective.

[Frank B]

OK, I will use an airfoil thickness of 8%. images/icons/icon14.gif

Doesn't the wing loading (and total weight) matter? Does a heavier plane fly in the same way as a lighter one if it just has more power to compensate? Surely the sink rate must be greater.

[vintage1]

Originally posted by Frank B
Thanks a lot Ollie,

Half the climb rate and half the top speed. images/icons/icon14.gif

I will play around with MotoCalc to find a suitable power setup for those numbers.

When you suggest that I use a thinner airfoil, do you mean thinner than the 50% I will get by just scaling it down? The original airfoil has a thickness of 12%, should I use 10% or even 8% instead?

Have I got the weight right?

If you keep the watts-per-pound at a similar level the performance when scaled will be similar.

Some rough guidelines - gappy where my knowledge is gappy.
10-15W GWS IPS. 6-9 oz AUW.
20-30W Speed 280, 8-10oz AUW
30-50W Speed 300 10-14 oz AUW
50-80W Speed 400 14-22oz AUW
80-120W speed 480 18-27oz AUW
150-250W speed 600
250-350W buggy motor.

That's for cheapo brushed motors.

In general a brushless is the 'next size up' e.g. a 300 class brushless really puts out 400 class power.

weight ought to scale as the third power of the linear dimensions: In practice it doesn't quite, because you tend not to e.g. build a 20" Boeing out of tinfoil :-) There is a tendency for wieght to NOT go down as fats as dmensions would indicate, so small models tend to fly faster than linear scale speeds would indicate.

For example, a 1/10th scale WWI machine OUGHT to maybe fly at 1/10th full scale speed. say stalling at 5mph and top speed of (gasp) as much as 12mph. In practice its more likely to stall at 12, and fly at 25-30mph.

Unless you build it really flimsily, take care not to walk too fast with it, and only fly it in flat calm conditons...

In general, its probably easier to build so that the speed scales as the square root of the scale factor. That puts our 1/10th WW1 model in practical territory with - say - a 16mph stall and 40mph top speed.

[Frank B]

Vintage1,

OK, so at least in therory my 1/8 (12.5%) of the weight is correct. I think it must be possible in practice as well (the original is rather heavy).

My example of a model with a wingspan of 28" and a weight of 9.75 oz should not be a problem. I have another 28" plane that weighs only 4.8 oz (not brushless). This should give room for the power needed.

[Frank B]

I have just done some calculations in MotoCalc and found a good power system for my little plane:

Motor: Hacker B20 18L
Gear: 4:1
ESC: Phoenix 10
Prop: 10x8
Accu: 2xET-1200

To meet the weight limit of 12.5%, the airframe (incl. servos and receiver) must weigh 5.8 oz. That should be possible.

The climb rate is actually the same as the original. It is hard to get it down to 50%. Well, I think there is something called "half throttle", I wonder if my transmitter can do that :)

The top speed is around 50%.

Now after a closer look:

The watts-per-pound are the same as the original, so this apparently gives the same climb rate (it is not scaled down). Changing the prop to a 9x7 gives half the climb rate (and still half the top speed), but now the watts-per-pound are only 66% of the original.

Also, the stall speed is 70% of the original, not 50%, that surprises me. A 12% airfoil only gives a slightly lower stall speed than an 8%. The model would have to loose 5.4 oz in total weight to have a stall speed of 50%, that's impossible :confused:. A weight of 1/16 (6.25%) would give half the stall speed.

This is obviously more complicated than I thought at first. I will play around some more with MotoCalc, perhaps try a smaller motor. Maybe the stall speed isn't that important. After all, this is a sports plane, and who flies such a thing at stall speed? :p

[AndyKunz]

MotoCalc isn't 100% accurate. They still build 100% prototypes to test on, you know, and that's after running multi-million-dollar CAD packages to analyze performance prior to cutting the first piece of aluminum (or graphite).

Your model by rules of thumb is in the ballpark with the 8% airfoil. Sounds like a pylon racer.

It'll be lots of fun. Go for it. Remember - it's only two or three sheets of balsa at that size.

You have to fly it to know for sure.

Andy

[Ollie]

If you want to lower the stall speed at the expense of inverted performance add one percent of mean line camber to the 8% thick airfoil. Another approach is to employ full span flapperons.

[Al-Parkflyer]

How scale do you really want to go.
Most of the "scale planes" are semiscale anyway.
You may find that by giving up a little bit of scale appearance can improve the performance noticeably. One effective way is to, let say, increase wingspan and chord by 15 % . This automatically lowers you wing loading for about 30% depending on how light is your wing structure. This will lower the stall speed. Lowering the stall speed you can also reduce the pitch speed and still be able to fly comfortably. By lowering the pitch speed you can improve the thrust for same setup or go for ligther power system. If you do not insist on inverted performance or on perfectly axial rolls, use more cambered airfoil, etc.
Compromise and find your sweet spot. :)

[Frank B]

Thanks a lot for all the good answers.

Perhaps I should have stated this more clearly before: My aim is not to get a precisely scaled down version. It's more that I like the flying characteristics of the original, and would like to have a smaller plane which feels the same in the air.

It could be that I'm totaly wrong in my assumption that a smaller plane with the same characteristics must be an excact downscaled version of the original. Maybe a smaller one must have longer wings to feel the same? I don't know.

By the way, the plane I want to scale down is a Supra 40 (you can see it in my avatar).

Originally my main concern was if the small version would have enough power to fly like the real thing. Now I can see that this is not a problem. The small one will easily outperform the original. My setup with the Hacker and a 10x8 prop will draw only 6.8 amps static (on only two Li-Pos). If I give it three Li-Pos and aim at 10 amps static (9.5x7 prop), it will go vertical at 2930 ft/min. I think I can live with that. :D

A 9x9 prop gives it a top speed of 65 mph (nearly the same as the original).

I will definitely start building this plane.