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Twice the scale, now how about the motor?

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Twice the scale, now how about the motor?

Old 02-26-2010, 02:04 PM
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Quitty
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Default Twice the scale, now how about the motor?

If I double the size of an airplane, by what factor do I need to increase the power to keep it flying? Also could someone provide me with mathematical reasoning behind your statement?
Old 02-26-2010, 02:10 PM
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BadSplice
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Default RE: Twice the scale, now how about the motor?

I think it depends on the airplane. My understanding is that if you double the dimensions (wingspan, length, etc) the total volume of the airplane will increase by a factor of 8. The question becomes how light you can build that larger structure, and what type of flying you want it to be able to do. What I would suggest is to look at airplanes that are similar in size and design to what you have in mind, and see what it takes for them to fly.
Old 02-26-2010, 02:15 PM
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Quitty
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Default RE: Twice the scale, now how about the motor?

I have thought of that. This plane would be used for mostly level flying, no loops or rolls, and my goal is to increase the size to increase the payload for a much longer flight.
Old 02-26-2010, 04:35 PM
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Default RE: Twice the scale, now how about the motor?

It's strictly related to the weight. If you can double the size and keep the weight down to only double instead of 8 times then you only need double the power to achieve the same climb. However since you're squaring the frontal area and wetted surface there will be a big increase in the power needed to maintain level flight. It'll be a blend of the power needed to reach the new flying speed as well as to combat the increase in section drag. If you were able to only let the weight double the flying speed would actually not change. Or rather it may well reduce a little due to the improvement in Reynolds number of the wider wing chord which would allow the slightly slower speed. So the only required increase would be in the frontal area and wetted surface drag.

More realistically your weight will fall somewhere between the max of 8 times higher suggested by the simiple scaling factor and the much harder to achieve mere doubling that would only come from doing a complete structural re-design. Where the final numbers would land up is totaly up in the air.... sorry, bad pun

Models climb based on watts per pound for electrics. This factor is pretty common over a fairly wide range of sizes from all I've seen. It pretty much stands to reason that to maintain level flight also requires a fairly consistent value of watts per pound assuming that it's a design that is more like a sailplane or other smaller fuselage and generous wing area style model.

I can see from this thread and the other one that you're keen on really trying to nail down this issue with pure numbers. While I'm sure it can be done there's no real overall formula that will do it down to the last picowatt. There's just too many variables to nail it down that tight. Frontal area and wetted surface gives us a good impression but if you achieve minimal frontal area and wetted surface with shapes that promote poor airflow and result in large turbulent wakes then you hurt the design more than if you use a simple but clean shape. And we just do not have any equations commonly available for describing or avoiding this sort of issue. Sailplanes get around the problem by making their fuselage as skinny as possible while staying clean. A cargo carrying model doesn't have that luxary. So we come back to basics and the idea that a shape that uses an airfoil for the side and top view is going to generate a smoother airflow without any gross separation bubbles at the expense of a little more wetted surface.
Old 02-26-2010, 04:47 PM
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Jim Thomerson
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Default RE: Twice the scale, now how about the motor?

The general idea is that if you double the linear dimensions, both weight and power needed will go up as the cube. An application of scale effect, or the square-cube law. I can't think of the name (starts with a B) of the airplane design which has an airfoil shaped fuselage with twin tail booms, stab and elevator, and regular wings. That would be something to think about for weight lifting.
Old 02-26-2010, 04:52 PM
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Default RE: Twice the scale, now how about the motor?

Jim you're thinking of the Burnelli style aircraft.

http://www.aircrash.org/burnelli/chrono1.htm

From what I read and what common aerodynamic sense tells me these were mostly a waste of material. The fuselage is such a low aspect ratio that the vortex flow around it would have reduced or eleminated much of the lift while generating a lot of drag. It's far better to make the fuselage as slippery as possible and let the wings do their job.

The only exception to this would be to make the design a pure flying wing and thick enough that there's room for whatever payload is needed.
Old 02-26-2010, 05:47 PM
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Default RE: Twice the scale, now how about the motor?

Quitty,

For a solid body, the mass increases eight times when the dimensions increase twice.
For a model airplane, having so many cavities, that proportion should not apply, I believe.

I have compared two electrical RTF models sold by Tower, in order to obtain a more practical proportion.
They come with radio and motor, just RTF.

http://www3.towerhobbies.com/cgi-bin...&I=LXXJS8&P=RF
http://www3.towerhobbies.com/cgi-bin...=LXSGY1**&P=RF

Wingspans = 68.5†/ 44†= 1.55 scale factor
Lengths = 56†/ 36.5†= 1.53 scale factor
Weights (minimum) = 112 oz / 25 oz = 4.48 scale factor
Weights (maximum) = 136 oz / 28 oz = 4.85 scale factor

Sorry, I couldn’t find any RTF models with scale factor of two for dimensions.
Old 02-26-2010, 07:34 PM
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Default RE: Twice the scale, now how about the motor?

To build a plane that is twice as big, you multiply every dimension by the square root oftwo. This is 1.414. If you multiply every dimension by 2 you will have a plane 8 times as big as the original. You must also include the height in the formula for the volume. Nearly all the drag is created by the wings. The fuse contributes a lot of parasite drag. Drag increases as the square of the speed. If you fly at 50mph with the original size plane and then double the size using 1.414, the drag will increase 4 timesif you fly at 50mph. With an increase of 4 times for drag, you will need 4 times the power to fly at the same speed.

Wedge
Old 02-27-2010, 06:05 PM
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Default RE: Twice the scale, now how about the motor?

Quitty,
Over the past several years I worked out a scientific way to scale aircraft parameters in order to build a sensibly realistic model.

The outcome is: there IS NO hard and fast rule. It depends upon what weight you choose to build and that determines how fast it will fly. Once you choose a weight everything else falls into place mathematically.
All this eventually appeared as a series of magazine articles in the issues June to September 2009 of the British magazine R/C Model World, published by Traplet. The first of the four articles had all the theory and equations to prove my main point - there is no such thing as Scale Speed. There is one weight that gives a model that can fly its own length in the same time as full size (but most modellers would say it is too light and floaty). At quite a different weight the model will fly turns and loops whose radius is in scale (but for practical purposes they are a bit heavy).

So we compromise by choosing a weight in between.
Don't worry Quitty, I'm getting to your answer

The final (fourth) part of my series in September '09 R/C Model World featured a spreadsheet that runs in Excel, with instructions how to use it. You input basic information about a full size and it spits out useful data in a whole range of scales. You can download the spreadsheet from the R/C Model World website
http://www.rcmodelworld.com/ (click "Features", sixth item down)
or from my club's website (under Alasdair's Aerodynamics)
http://www20.brinkster.com/gvmac/

ANSWERS
Eventually. I decided that making a model bigger or smaller is no different to making a model of a full size so I tried the Spreadsheet and it works. You have to choose a new WIX (Weight Index, a scaling term I made up) and Scale Factors - that's the number you divide by to get the model's wingspan (4 for quarter scale).

To make a twice size model you need a scale factor SF = 0.5
And from experience I found that a WIX of 2.5, give or take a little, gives realistic results. By that I mean models of a different size that fly pretty much like the original, and are practical to build and fly.

I input figures from one of my own models, and with a WIX of 2.5 if you
DOUBLE the wingspan, you get
Four times the Area,
5.65 times the weight,
1.415 times the wing loading,
1.18 times the flying speed
and you need 5.9 times the power

All the figures relate to each other on the premise that you are flying at the same lift coefficient with both sizes of model.

As has been pointed out, increasing the Reynolds Number gives a little performance bonus.

You asked for the mathematical reasoning, well it's all in the articles and if you download the spreadsheet you can check out the math and play with the answers. Adjust the numbers in blue to see "what if..."
Old 02-27-2010, 07:37 PM
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Default RE: Twice the scale, now how about the motor?

There's another issue here as well. If this is to be a purely practical plane to carry a given load to do some job and you want it to do so with the least power used so you can fly for longer then you're far better off to design the model from scratch. Things like what is a good chord to achieve a reasonable reynolds number for the small one will result in a larger chord than you need for the double size. At that point you're better off to increase the chord only slightly and use the higher efficiency of the higher aspect ratio along with the moderate area increase to achieve your increase in efficiency. But as soon as you do this you find you need to alter the fuselage and stabilizer as well. And since you don't want to slavishly copy the internal structure of the smaller model in any event you may as well just given in to the reality of the situation and start afresh.
Old 02-27-2010, 10:23 PM
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Default RE: Twice the scale, now how about the motor?

To build a plane that is twice as big, you multiply every dimension by the square root of two. This is 1.414. If you multiply every dimension by 2 you will have a plane 8 times as big as the original. You must also include the height in the formula for the volume.
Do you see the contradiction? For the first statement to match up with the second you would increase the size by the cube root of two. So for an airplane with double the volume you increase the linear size by 1.260, however if you want double the area, then 1.414 is correct.

Nearly all the drag is created by the wings. The fuse contributes a lot of parasite drag.
If you actually do a numbers work up, you would find that the wing only contributes about 30% of the total drag in un-accelerated flight. A fuselage contributes about the same. However if producing a large amount of lift (high g turn or slowed up for landing) then the induced drag adds a significant amount of drag to the total.

If you fly at 50mph with the original size plane and then double the size using 1.414, the drag will increase 4 times if you fly at 50mph. With an increase of 4 times for drag, you will need 4 times the power to fly at the same speed.
Actually the drag is less than 4 times as great due to better Reynold's numbers due to the increased size.
Old 02-27-2010, 11:35 PM
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Default RE: Twice the scale, now how about the motor?

Thank you for the links, Alasdair.

Very interesting work!
Old 02-28-2010, 04:19 AM
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Default RE: Twice the scale, now how about the motor?

Lnewqban, thank you.

BMathews is right to say that designing for purpose, from scratch, should produce the better model.
But as I understand it we started from "I like my Super Wotnot, I want a bigger one, so how much power etc??"

HighPlains. That is true, the things that do not change with size though are the coefficients. That why they were invented so why not use them? That's why in my spreadsheet I assumed that the aerodynamics would be copied, lift coefficients would be the same regardless of size and drag coefficients would increase a tiny bit as Reynolds number reduced &vv.
This should produce a model that is "in character" with the original.

Some day I'll go public with my Model Resizing spreadsheet.

Old 02-28-2010, 07:07 AM
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Default RE: Twice the scale, now how about the motor?

Looks at how the size, weight and power needed goes up on the different sizes of the same plane, in this case a Super Sportster.

Super Sportster .20 engine 48" span weight 3.5 pounds
Super Sportster .40 55" span weight 5.5
Super Sportster .60 61" span weight 6.5
Super Sportster .90 72" span weight 11.5
Super Sportster 2.0 82" span weight 13.5
Old 02-28-2010, 10:00 AM
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Default RE: Twice the scale, now how about the motor?

to cut to the chase-
as th model gets smaller it has to get increasingly lighter
As it gets larger - it has to have increasingly greater power
asign numbers as it suits .
The B19 and the B36 were classic examples of how the need for power increases far more than suspected. Even by real honest oto god degreed aeronautical engineers.
on 4 ounce foamies indoor areobatics - a few grams of weigh can wreck performance.
Old 02-28-2010, 03:12 PM
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Default RE: Twice the scale, now how about the motor?

Great examples RMH. The B36 looks twice the size of the B29. They put on two extra engines but in the end had to put on FOUR extra jet engines on the thing!
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Old 02-28-2010, 07:53 PM
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Default RE: Twice the scale, now how about the motor?

As BMatthews stated very early- power to weight is your answer.
Old 04-03-2010, 06:27 AM
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Default RE: Twice the scale, now how about the motor?

Take a piston engine and double the size of everything, twice the bore and twice the stroke, and you end up with 8 times the displacement.

I once built a 2/3 scale version of a .40 size sport plane and used the cube rule to determine engine size. This resulted in me using a .15 glow engine. It worked out quite well.
Old 04-04-2010, 02:00 PM
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Default RE: Twice the scale, now how about the motor?

Quitty, if you're still out there it would be polite to reply with some comments, concerns or at least a thankyou. Otherwise it seems like we're typing for no reason.
Old 04-04-2010, 02:16 PM
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Default RE: Twice the scale, now how about the motor?


ORIGINAL: BMatthews

......it would be polite to reply with some comments, concerns or at least a thankyou. Otherwise it seems like we're typing for no reason.
This statement applies to so many threads, that it should be made part of RCU Policies!!![sm=thumbs_up.gif]
Old 08-08-2013, 01:14 AM
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[h=2]Twice the motor, now how about the scale?[/h]
Old 08-08-2013, 02:58 AM
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As stated back in 2010 it all related to weight, hence power/weight ratio. On any given scale weight is going to be the main factor when making considerations of power, drag comes into play yes, but is nothing compared to the weight issue.

Bob
Old 08-10-2013, 02:03 AM
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Originally Posted by mberme
Twice the motor, now how about the scale?
Increase scale by roughly 26%, e.g. if you have a 1m wingspan model with a .25 glo engine and want to scale it up to fit a .50 size engine you make it 1.26m span.
Old 08-11-2013, 05:49 PM
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Power = Drag x Velocity
Drag = Weight / (Lift Drag Ratio)

So if your aircraft size is doubled (wing span double = 4 times the original wing area), the weight could be 4 times the original (assuming same wing loading).
Assuming your Lift Drag ratio is the same, same cruise speed (same wing loading), then the power required will be 4 times.
Old 08-12-2013, 03:09 PM
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I have a scale model of a twin-engined plane, which uses an 90mm EDF (1750W apx). If I use two 90mm EDF. I multiply the size of the original one by.......?

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