How do you scale thrust?

[Frank B]

If I want to scale an existing model up or down, what is the formula for scaling the thrust, so that the new model will have the same apparent performance.

(The weight is scaled by the scalefactor^3)

[Mike Taylor]

thrust to weight ratio should stay the same.

[Frank B]

Thanks Mike.

[vintage1]

Don't forget to scale the pitch speed accordng to the stall speed as well.

Not sure how that varies - some fractional power I think.

[Frank B]

Good point Vintage, but then the question is: How do you scale the stall speed? Should a 1/10 scale model have 1/10 the stall speed (and top speed) of the full scale plane?

[Ollie]

http://www.charlesriverrc.org/articles/design/ibtherkelsen_scalespeed.htm

[Mike Taylor]

Frank,

It is interesting that this question has come up this week. A couple of days ago I got the latest issue of RCMF, and today MA came. Both have articles on this subject. It seems that this is of interest to others as well...

[vintage1]

Good point Vintage, but then the question is: How do you scale the stall speed? Should a 1/10 scale model have 1/10 the stall speed (and top speed) of the full scale plane?


If only one could, but one would need to scale the air as well. And gravity.

In general the stall speed and general aerodynamics work out if the speed of the model and time, are both reduced by the square root of the scale factor :-)

Take a 1/12 scale WWI plane. Maybe stalls at about 40mph, top speed of 120mph.

And imagine a model that flies at 6-8mph, and has a top speed of 10mph, and stalls at 4mph...flyng outside in any sort of wind...

Realistically, it will stall at maybe 12mph, and fly in the mid twenties and maybe just make 35mph or so flat out.

Now that plane will behave in terms of geometric flight path, angle of bank for a given scale turn etc, as the full size does, but its visual speed will be about three times higher than it ought to be (i.e. how fast does it from from a dot to a plane) . Slowed down with a slomo camera by 3:1 it will be almost totally realistic..

So you can't win. It either is impossibly slow, but looks scale in level flight, but has compeletly unlikely flight dynamics, or it flys dymaically correctly, but altogether at a smaller 'time' scale..

If you go by the weight=scale cubed
area = scale squared
then I think speed is square root scale.

[Frank B]

OK, I see. Altering time and gravity wasn't excatly something I learned in high school. :)

Do you scale guys then have some general rules for which speeds to aim for, like 1/3 of the full size, or do you just try to make the planes as light (and slow) as possible? I guess the flight dynamics ought to count more than the speed of the plane.

[Mike Taylor]

You get what you can. I like micros, but there are a lot of micros smaller than mine. Matt Keenon's 4" SE-5 flies at a scale speed of about 400 mph (~8 mph at a 1/48 scale). However, his 7" P-47 flies at closer to 20 or 30 mph, or somewhere well over a scale mach 1. On the other hand, these are so great to see fly at this size that you sort of forget about its scale speed - you just stand there slack-jawed, amazed that they fly at all...

[Frank B]

Vintage, when you scale the speed by the square root, do you then get the speed where the flight dynamics are the same?

[roger75]

:D Hi Frank,
Amongst the model flyers Ive known, the general consensus is "You can not scale nature" airfoils scaled from full size aircraft do not work at scales less than 1/4 scale
The P 51 laminar airflow does not work at scales smaller than 1/4 scale, at larger scales the "scale effect" has much less effect and scale flight charactaristics are more easily achieved

[Frank B]

1/4 scale, that's big. I can't have such a model with me on my bicycle. :)

I will just aim for making my model as light as possible.

[JMP_blackfoot]

Vintage, when you scale the speed by the square root, do you then get the speed where the flight dynamics are the same?
Roughly, yes.

But the "easiest" is to think that TIME is accelerated by a factor of the square root of scale.
I once read that this is how the film makers do when using scale models. They run the camera faster by a factor of (square root of scale) when shooting the film.
Once you've accepted this idea, the rest falls together.

The scale distance is then covered in the full-scale time divided by the square root of scale.

Your scale prop rpm is also multiplied by the square root of scale, which figures if you realise that over the scale distance it must have made the same number of revolutions as the full-size prop, but in a shorter time. (As an example, if full-scale rpm is 3000, your 1/20th scale model should turn its scale prop at 13400 rpm, which IMHO sounds realistic)

Using this concept of accelerated time, the flight dynamics are the same (except for the fact that aerodynamic properties of your airframe suffer somewhat from scaling down), even your take-off and landing distances should be the same.
Power required should be close to 1/scale^(7/2).

[Frank B]

Excellent answer JMP_blackfoot. It is actually easier to grasp, when you think of it as speeding up the time.

Your last info: power = 1/scale^(7/2). Does this meen that the weight also should be 1/scale^(7/2) instead of 1/scale^3, to keep the power to weight ratio the same? Or am I confusing this with thrust to weight ratio?

[JMP_blackfoot]

The weight should be multiplied by the scale^3. Since the speed is multiplied by the root of the scale, and the power by scale^(7/2), it turns out that the thrust is multiplied by the scale^3, same as the weight. Thrust/weight remains the same. So does acceleration during the take-off run, but since time is multiplied by the root of the scale, your take-off distance comes out scale!
It can be calculated that the scale loop radius will give the same g's as the full-size, etc... (inasmuch as one could ensure that the smaller wing is able to supply the same lift and drag coefficients :confused: )