Scaling down a real airplane

[dtrip]

SUPPOSE that
1) I want to build a real airplane.
2) But I first decide to build it as a model to see if it flies and
how fast.

Now SUPPOSE that for the airplane I have the following requirements:

1) Some given geometry G (i.e. "shape" of the airplane).
2) Power = 100 HP
3) Total weight = 500 kg
4) Wing area = 20 m square meters. This derives directly from (1)
above.
5) Stall speed = 20 m/sec

Suppose the scale of the model is 10 times smaller. So I should have:

1) The geometry will be the same, scaled down 10 times. Thats easy.
2) Power = ???
3) Total weight = ???
4) Wing area will be derived from (1) above, thus 100 times smaller
than original (if each dimension is scaled by 10 => area scaled by 100).
5) Stall speed = ??

What should I put in (2) and (3) to have a reliable test ?
What should the model's stall speed be, to be confident that the real
airplane will have a stall speed of at least 20m/sec ?

I hope you understand my question.

Thanks in advance,
Dimitris

[HugePanic]

keep in mind:

if you have a length-factor f:

all areas go f², all masses go f³!

but: the masses will be completely different! this depends from you building technique.
best is to find a compareble existing model aircraft that fit's best to yours.

stallspeed is hard to calculate, because its hard to get the correct needed information.
there is another threat open here, that gives you all the formulas here.

[dtrip]

Thanks for your reply,

No no no, you have not understood. Building technique should not affect
the weight. We are using the small model to test the real airplane.

So we dont necessarily need a nice flying lightweight model. We need the
exact copy of the orginal. If the original is heavy, underpowered, or too fast,
we want the model to be also heavy, underpowered or too fast.

What is the thread you are talking about ? Could you post a link ?

[JetPlaneFlyer]

'If' it were that simple then the weight should be the 10^3 (1000) times less for the model. The power should be reduced by the same factor so that you end up with the same power/weight ratio. On the face of things this would give a stall speed of: √0.1 x full size stall speed = 6.3m/s.
Unfortunately the real world is not so simple; you are flying in 'full scale air' which means that the Reynolds number is much lower for the model than for the full size aircraft. This means the model will perform in a very different way to the full size even if you could scale everything down exactly. The biggest impact is that the much reduced Reynolds number will mean that the Cl (lift coefficient) of the model wing is considerably lower than the full size, so the model's stall speed will be higher than the prediction in my first paragraph. Also airfoils that perform well at full size may be poor at the lower flying speeds expected for this model.

Also the flying speed wont look scale; if you want a truly scale looking flying speed (2m/s) then you would have to build a 50 gram model :rolleyes:

[HugePanic]

What is the thread you are talking about ? Could you post a link ?

http://www.rcgroups.com/forums/showthread.php?t=789635

[BMatthews]

I think you'll find that stability and general handling will scale well. However the weight and stall speed will be harder to scale well. I'd say that for those areas just stick to generally acceptable wing loadings for each size.

[JetPlaneFlyer]

The model will fly in a more full scale like manner if you make it big... 1/5th or 1/4 scale will give flying characteristics much closer to full size than a 1/10th scale model.

[vintage1]

You should, for aerodynamics eval., design it to fly at the square root of the scale flying speed.

i.e. 1/4 scale= 1/2 speed.

Fly at the same or very similar watts per pound.

The weight will be whatever wingloading it needs to be to get the above scaling is stall speed.

The model will need to be viewed via a 1/2 speed slow motion camera to 'look like' the same as the full size.

Such a model always looks too fast to a casual observer, and for real scale appearance work you try to make it slower and lighter, but the above is strictly correct in terms of aerodynamic loading.

[JetPlaneFlyer]

You should, for aerodynamics eval., design it to fly at the square root of the scale flying speed.

Vintage,
You are of course correct, I forgot about the square root in the stall speed calculation...Doh! (I'll correct my original post to reflect this)

Dtrip, in the case of your 1/10th scale model this would mean scale flying speed was: square root 1/10 x 20m/s = 0.316 x 20m/s = 6.3m/s. This ignores any Reynolds number considerations

if you wanted to have a truly scale looking flying speed i.e. 2m/s, then you would have to reduce weight by a factor of 10 cubed (10,000) which would give a model weight of 50 grams... :rolleyes:

Bottom line is it would be best to build the model as light as humanly possible.

[vintage1]

The trouble is you can't have it all ways.

If the approach speed looks right, in a turn, the model will be hopelssly 'flat in the bank'.. if you make the model fly aerodymaically correct, it looks hoplesssly fast in the approach.

AS far a convincng scale models go, they all fall somewhere betwen linear scale speed and root scale speed.

You can get the loops to look right with an excess of power, and hope that overbanking and opposite rudder will make for wide turns that look OK.

Unless you video the thing and low it down that way ;)

[HugePanic]

what would happen when you treat a real AC like a model...

-you cant throw a "real" airplane! even holding it in a hand would damage the fuselage and break all frames.

-when throwing, for example a airliner, it would loose all its engines!

-loops would sacrifice the wings

-putting the fuselage in your trunk, would "shorten" the landinggear
..
.


All this would happen to a real scale-build model.... :o

[Brandano]

I think if you start to take reynolds numbers in consideration you will find that the smaller flying surfaces will be too far from the full size to be really representative of its performance. Better build it as big as humanly possible. I think that in wind tunnel models the windspeed is arranged so that the reynold numbers are comparable to the actual flight envelope of the plane. Building a scale model of the plane has its merits, but it's only halfway there compared to a wind tunnel analysis, at least as far as the performance is concerned.

[Bobber Bob]

Hi Folks...

Rather then munipulating the airspeed in wind tunnels they raise the density to bring the Rn in line with the actual full sized aircraft (a pressure tunnel). This not always done, as most of the W/T testing is done at whatever pressure happens to be in the test section at the time (but this can be varied to some extent, without outright pressurazation of the W/T).

Another "trick" that is used, for airliner sized models is to figure where the airflow would go turbulent all by itself (on the full sized aircraft), and apply "trip strips" at that point, to more closely simulate the airflow.

The point for "trip stripping" is that below a certian Rn, the airflow is always laminer, and above a certian point, it is always turbulent.

Finding out the point to apply the T/Ss, is just doing the Rn calculation with all the givens in the W/Ts test section, and then the only variable is the length of the airstream's travel over the surface of the aircraft.

Stability and control W/T models, are built very accurately to the finished, full sized aircraft. They may use some "fanagle factors" to bring the data in line, but the models are accurate, and a lot of the models that I built/tested, were around 10 % scale.

I hope the above is of some use...

A retired Wind Tunnel model maker...

Bob Reynolds
. "ComeUpHere"

[dtrip]

Thank you all for great description. Now I get it. I was influenced by the
pioneers of RC, who built and flew AM models to test real aircraft (I think it
was the British during WW-2 or something ?). I thought there was a 1-1
analogy of model-realsize attributes. Now I see its not that simple.

PS: In case you re wondering, the task is to decide wether a 10m single-seater
hanglider could maintain flight powered by 1000 Watts of solar energy. Im not crazy
or rich enough to try in reality, but I would be interested to try in RC (solar cells
need not be used for the model, as long as it is similarly underpowered). Needless
to say, there is no access to wind tunnels or similar professional equipment.
Provide some idea if you want, I will read with interest. Thanks again.

[Brandano]

I think that the easiest way would be to get a motorized hang glider, get its weight to tally with that of the electric equipment and then measure the minimum power required to mantain level flight (better if it can mantain a shallow climb, though). Shouldn't be too hard if the engine has known power curves. You should also consider that a model will most likely not fly at the same temperatures the fullsize does, or dissipate engine heat in the same way, so the actual power you can get from the system might be different from that you can measure on the bench. Incidentally, most watt-hp converters found on the web give me 1.34 odd HP for 1000 watts (with minimal variations whether referring to electrical HP, Boiler HP, British HP etc... ). Doesn't look like much. But there's been hyperlight planes flying on 400 watts, maybe a clean rigid wing design can manage it. Btw, gliders regularly fly on solar power :)

[JetPlaneFlyer]

the task is to decide wether a 10m single-seater
hanglider could maintain flight powered by 1000 Watts of solar energy.

Certainly it could not if it weighed anything like the 500KG noted in your first post :rolleyes:

The Solar Challenger http://www.donaldmonroe.com/solar_challenger_photography weighed only 90Kg and had a span of 14M and produced about 2600W from it's solar cells.

Human power aircraft can fly on about 300W but these dont have to carry all the extra weight of solar cells and electric motors. The human power Gossamer Albatross was about 30m span and weighed only 32Kg.

[Brandano]

Plus the weight of the pilot, remember... :). I don't think that either could fly much out of ground effect either. If you got the sun available, what's wrong with using the thermals?

[dtrip]

Incidentally, most watt-hp converters found on the web give me 1.34 odd HP for 1000 watts (with minimal variations whether referring to electrical HP, Boiler HP, British HP etc... ). Doesn't look like much.

Yes I know its not much, but keep in mind we want to have a level flight
with 1kW. Not take-off.

The 1000 Watts needed for level flight, I derived from:
1 m2 of solar cells produces 150 Watts of electricity
A 10m wingspan hang glider has a wing area of about 10-15m2.
Thus covered with cells will give about 1500-2250 Watts.
Lets say 2000 Watts, its a fair middle value.

Now the airplane will have a motor of 5 kW and a battery. Thus it will be
taking off quite easily. Once in the air, if it can maintain flight with 1 kW,
it can use the remaining 1 kW to recharge the battery.

I know there are wonderful brilliant solar gliders and pure gliders.
But I need a solar hang-glider that can take-off in a short space and
keep flying safely close to the ground for big distances. For hobby,
for crop spraying, fence checking, police, etc. Motorless aircraft can
not approach the ground, and solar gliders need A LOT of space to take
off.

PS: No it would definitely not be 500 kg total weight. The glider weights
about 25 kg, plus 75 kg the human = 100 kg. Allow another 100kg for
seat, motor, battery, propeller and perhaps payload ---> 200 kg AUW.

PS2: As gliders have proven, it CAN be done. The problem with the hang
glider is that it produces rather high drag. High drag is a big
problem when you are so greatly underpowered.

[JetPlaneFlyer]

You’re not going to do it with a conventional hang glider, as you point out there is too much drag giving too low a glide ratio.
The aircraft parameters you describe sounds very like the Solar Challenger, unless solar cells have come on leaps and bounds in the last 20 years (maybe they have?) then it's going to be hard to come up with anything that performs much better or is a lot more practical than the Challenger. Also note that a VERY lightweight pilot is required. The 90KG weight I quoted for the Challenger INCLUDED the pilot!.... Jockeys only need apply. The idea of carrying useful payload for crop dusting or police work would not be possible unless you can come up with some huge advance in technology compared with the Challenger.

Adding a battery may help give better take off performance but it will act as ballast for the rest of the flight and mean even more solar power was required to maintain level flight.

Bottom line... Look at the specs and performance of the Challenger, this aircraft is a very good benchmark of what can be done with the sort of power levels you predict.... If you want better load capacity and/or better performance you are going to either need a system that generates much more power than the Challenger team had to work with (2600KW), or something much more aerodynamically efficient, or a bit of both.

You are not going to get better performance from 'nowhere'.

[dtrip]

You’re not going to do it with a conventional hang glider, as you point out there is too much drag giving too low a glide ratio.
The aircraft parameters you describe sounds very like the Solar Challenger, unless solar cells have come on leaps and bounds in the last 20 years (maybe they have?) then it's going to be hard to come up with anything that performs much better or is a lot more practical than the Challenger. Also note that a VERY lightweight pilot is required. The 90KG weight I quoted for the Challenger INCLUDED the pilot!.... Jockeys only need apply. The idea of carrying useful payload for crop dusting or police work would not be possible unless you can come up with some huge advance in technology compared with the Challenger.

Adding a battery may help give better take off performance but it will act as ballast for the rest of the flight and mean even more solar power was required to maintain level flight.

Bottom line... Look at the specs and performance of the Challenger, this aircraft is a very good benchmark of what can be done with the sort of power levels you predict.... If you want better load capacity and/or better performance you are going to either need a system that generates much more power than the Challenger team had to work with (2600KW), or something much more aerodynamically efficient, or a bit of both.

You are not going to get better performance from 'nowhere'.

You are right on all these, but on the other hand people have flown with
say, 200 Watts (human powered). Examples were mentioned above, and
also check out the MIT Daedalus here (Crete-Santorini, 119 km over 4 hours):

http://en.wikipedia.org/wiki/MIT_Daedalus
and here:
http://www.youtube.com/watch?v=l131fSveof8

Of course this is not a hang-glider and this makes a whole lot of difference.
But if we multiply the MIT Daedalus with x5 power, x5 drag and x3 lift and weight,
then we are closely to what Im talking about.

Im not saying it will work. Im saying that Im not convinced it doesnt work.

Maybe crop dusting is too much. But an IR camera or CB-size radio, or a
laptop computer, are not too much of a payload for any real-size craft.

PS: Unfortunately solar cells are still 150 Watts per square meter (=10.75 sq ft).

[vintage1]

Actual power to maintian altitude is easily calculated from the weight, times airspeed times drag to lift ratio..with appropriate constants throwm in.

Double that for prop/drive train losses and you get the answer that seems to work in reality.

Its something like 6-10W/lb for a slow low drag affair.


IIRC as little as 3W/lb is theortetically possible.

[macboffin]

IF you can get a solar powered single seat aircraft flying reliably, It will be fragile and slow.It will not tolerate windy conditions, especially near ground induced turbulence nor will it be able to position it accurately enough for "crop spraying or police duties" except when there is zero wind.
A very clean aerodynamic design might hack it, from carbon fibre and kevlar for weight considerations, (Very expensive of course!). Seriously, the current state of the art as regards aerodynamics, structural materials, motors etc, and of course the weight and cost of solar cell material relegates this concept to science fiction.
As to a flying proof of concept model, I doubt if you could build it light enough at a tenth scale. I suggest you do some more sums and detailed design analysis at full scale and see what realistically is possible.And of course, source and cost all materials and equipment.

[dtrip]

macboffin hi and thanks for replying,

you are right about the real aircraft being so weak that it will not handle any significant wind, even if it flies. This is something I hadnt thought about. :(

Anyway, about building the model lightweight enough, I can currently build (have not, but have weighted the materials) a "hang-glider with v-tail brushless airplane"), similar to the one posted previously, with a wing area of 1.12 m2 and a AUW of about 500 gr. This is made of wooden sticks, "thin tent fabric", and the AXI brushless system I use in my Fidget 3D airplane (about 120 Watts on 1050 3s LiPo and 10x4.7 APC prop). Tail fins (v-tail) will be depron with carbon strips.

This results in a wing loading of 500gr/1.12 m2 = about 17 oz/12 sqft = 1.41 oz/sqft.
Even if my calculations are dramatically wrong (which I doubt) and the wing loading
doubles, it will still need ballast to fly controllably.

So Im not sure I understand what you mean by "building it lightweight enough".

[dtrip]

Actual power to maintian altitude is easily calculated from the weight, times airspeed times drag to lift ratio..with appropriate constants throwm in.
Double that for prop/drive train losses and you get the answer that seems to work in reality.
Its something like 6-10W/lb for a slow low drag affair.
IIRC as little as 3W/lb is theortetically possible.

Wow! Thanks, very useful !

[vintage1]

I am trying to get my head round this one..stall speed is the square root of wing loading, and so the lighter it is the slower it is..and so what you ned is the lowerst piossible wing loading AND the highest lift to drag ratio..those do NOT normally go together.. high L/D ratios mean long thin wings, and those are structurally weak ...and tend to be heavier..

Ther is a complex mix of optimaisations here..if you make a stubby large wing, you can get a lower wing loading, but at the expense of a poorer L/D ratio...somehere in there is an optimal shape, but thats also constrained by strictural strength, and weight...something keeps nagging me that a sort of medium aspect ratio with an ellipitical planform, deep chord where strength is meeded in the middle tapering out to either slender tips or maybe raptor winglets..might be the best choice.


I.e. copy an albatross or an eagle..whichever.. :D

[Brandano]

Something like... this perhaps?

http://www.petworks.co.jp/~hachiya/opensky/

[vintage1]

I don't think I could have drawn a better picture than that.

Won't catch me riding it tho.

[Brandano]

Oh I agree, probably it would enter an uncontrollable tumble if you sneeze. The full size has been test-glided though, there's a few videos of both the full size and a scale model on youtube. The only pluses I can see in that configuration is the low drag and the fact you can open a parachute while flying one, at a lower altitude when compared to a deltaplane.

[creyes123]

Correctly scaling down a full-size aircraft is surprisingly difficult. If you go strictly by the rules of aerodynamics, the model will appear to be flying too fast. When Hollywood makes a movie with flying model airplanes, they slow down the film when they play it back. To get rid of the time warp factor, you have to make it very light - probably impractical.

My free online calculator (www.RCAdvisor.com (http://www.RCAdvisor.com)) includes a scale calculator. The calculator lets you use a slider to see the exact trade-offs involved. As far as I know, my approach is unique and I've received many compliments on it.