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David Mellor23/02/2018 17:24:31
485 forum posts
99 photos

As far as I can tell, you are exactly right, Jez.


The basic maths (cubic wing loading) we've been discussing here was first worked out by Galileo nearly 400 years ago.


Biologists also use it to work out comparative structural parameters of skeletons - like the mice and elephants example you mention.  (Comparative anatomy in evolution).


But with animals, the structural materials are always the same - bone (or cartilage in cartilaginous fish). Different animals have evolved different ways of using the same material. So a bone isn't a material - an individual bone is actually a structure in its own right (bird bones being very different to those of land mammals, for instance) and a skeleton is a system of individual sub-structures.


I think model planes also can be thought of as systems of sub-structures, rather than a single structure.


But, unlike biological systems, model planes use a wide variety of structural materials rather than just one or two structural materials. 


So instantly you can see that model airplanes have the potential to be actually more complex than biological structures.  Thats because there are more materials available to a plane-designer than are available in nature to build viable animal structures.


So, we may use glass, resin, carbon fibre, steel, aluminium, hard-wood, softwood, polymers, papers etc all in the same structural system.   Things like rods, tubes, boxes, wires, beams and so-forth are all sub-structures in their own right.


I think design rules for model plane structures, therefore, may be harder to pin down than some of the aerodynamic "rules".  


I suspect most model planes may be over designed in that they aren't using materials as efficiently as biological systems  which have had millions of years of evolution testing their designs to destruction.


Edited By David Mellor on 23/02/2018 17:55:02

Jez Saunders23/02/2018 17:36:12
109 forum posts

Thanks David, not really into the maths but going to your models of equal wing loading but different inertia characteristics problem it most be the difference in mass ? Perhaps the mouse and elephant example could be applied here ?

John Stainforth23/02/2018 21:16:29
148 forum posts
37 photos

David et al,

I also plotted empirical data of engine size (cc) versus aircraft wingspan and weight for some fullsize and model planes:



The size of engine does go up roughly cubically with the wing span, and roughly linearly with aircraft weight. The slope of the line in the last plot is roughly 1.3 cc per lb of aircraft weight. The power of piston engines increases linearly with swept volume very roughly at about 1 hp per 10 cc (although 2-stroke engines are quite a lot better than that), so the line in the second plot also represents about 0.13 hp/lb, which lo and behold is about 100 W/lb -again about the same as a Boeing 747! The more powerful models and fullsize piston planes have about twice that power to weight ratio.

Scaling of physical laws is indeed and intriguing subject.

David Mellor23/02/2018 21:19:08
485 forum posts
99 photos

Great stuff, John. It will take me a while to get into that, but it sure looks good!


Denis Watkins23/02/2018 21:28:25
2489 forum posts
126 photos

Many many years ago John, my dad and I graphed our relatively small planes and the average in cubic inches was

Almost exactly your 1.3cc/lb, at .08cu inches/lb

Whereby a 6lb model was flown on a.46 2 stroke, in round figures, 6 x .08 = .48

This data came about from just 5 models

So I find your work and Davids quite amazing.

David Mellor24/02/2018 08:08:22
485 forum posts
99 photos

Ok... puzzle over. I get it now. And it is remarkably simple.

But, before giving the explanation (next post), we should perhaps stop and remind ourselves that this thread is about designing RC model aircraft.

So a critic might well ask what the graphs and equations have to do with the design process and making informed design decisions.

So lets answer those questions first, and explain the answers subsequently.

Answers: - Imagine you have designed a successful RC model plane. If you were forced into describing it, but could choose only one single number (a ridiculous situation, but bear with me), what would it be? The answer is that cubic wing loading (C) conveys more information as to how the plane will fly than any other number (such as just the weight, or just the wingspan or just the airfoil designation).

But now suppose the game changes slightly and you are allowed to describe the plane using two numbers rather than one. What would they be? There is no point in choosing Weight and Wing Area (or wingspan) because those two numbers are already "embedded" in C which automatically also embeds the correct cubic relationship (thats what C is and why it is so useful).

The next most useful number you could choose to describe your plane is Power Loading (Z). And because power loading is the same for the same type (warbird, trainer, powered glider etc) of aircraft at any size, the number Z gives a near-perfect description of what the plane's performance envelope is likely to be.

So...... knowing C and knowing Z more or less define the plane and what it is designed to do. Therefore the design process can start by fixing just these two numbers.

In the next post I'll go back to the explanation of why the size of engine (strictly speaking, the power) follows a simple cubic relationship to wingspan - precisely and exactly matching the graphs presented by John. It turns out that I can do this using what appear to be the simplest of all equations in model flying........and they are elegant.

David Mellor24/02/2018 08:19:50
485 forum posts
99 photos

Here's an explanation of why power loading (Z) has a cubic relationship to wingspan.

We will use the two most useful numbers that exist to describe the behaviour of a plane (any plane, actually, but lets stick to models for now).

C = W divided by (S raised to the power 1.5)

and Z = P divided by W

Therefore, if we multiply C by Z we get the product CZ, noticing that W cancels out altogether giving us:-

CZ = P divided by (S raised to the power 1.5)


David Mellor24/02/2018 09:12:24
485 forum posts
99 photos

Some may say that the relationship between C and Z is hard to imagine, or hard to relate to.

It isn't, and you are already familiar with it.

Here are some "standard" numbers for C and for Z and the graph of C versus Z .

C = 2 OPCF for light foamies

C = 3 OPCF for light powered gliders

C = 4 or 5 OPCF for slow fliers

C = 6 or 7 OPCF for trainers (not the ones on your feet, they can fly, though, with large enough Z)

C = 9 or 10 OPCF for aerobats

C = 11 to 13 OPCF for scale warbirds (exactly matching the Spitfire case we talked about)

C = 15 OPCF for pylon racers and anything super-fast

C = 16 + OPCF for jet turbines

Z = less than about 35 Watts per pound makes powered flight/ROG difficult

Z = 50 Watts per pound for really slow flyers and vintage designs

Z = 80 Watts per pound for light powered gliders and slow flyers

Z = 100 Watts per pound for general hacks and knock-about designs

Z = 120 Watts per pound for sport planes

Z = 150 Watts per pound for aerobats

Z = 180 Watts per pound for 3-D

Z = 200 + Watts per pound for v. fast turbine jest and Elon Musk's rockets......


David Mellor24/02/2018 09:25:15
485 forum posts
99 photos


These graphs of C versus Z tell us a lot about materials and structures that designers have used over the years and how that is changing in recent time.

One thing you can see on the graph is that most RC models traditionally made from balsa/ply and powered by internal combustion engines (IC) tend to all fall along the "mainstream RC" line. Thats because the aircraft structures made from traditional materials tend to have similar weight penalties and have done for decades.

But lighter, non-traditional materials such as Depron and carbon fibre can make structures that are lighter than those built with traditional materials yet remain adequately stiff.

Coupled with powerful, lightweight batteries (it is the battery that supplies power, not the motor - the motor merely converts it from electrical to mechanical power) has the effect of rotating the line of C versus Z anti-clockwise on the graph.

A good example is the Precision Aerobatics "Addiction" which uses brilliant design to transfer structural loads through ultra-light balsa/carbon composite sub-structures.


What is so powerful, in design terms, is that the designer can use the C versus Z relationship to design his (or her) plane using materials and structures appropriate to the flight-task..

And for fans of TLAR (that includes me), you can simply plot the values for C and Z on the graph to see how it compares with all other RC aircraft - irrespective of wingspan.  The steeper the gradient, the higher the content of exotic materials (like carbon) is likely to be.


Edited By David Mellor on 24/02/2018 09:50:33

supertigrefan24/02/2018 17:29:20
49 forum posts
1 photos

Any advice on CAD programs for designing and printing?

Edited By supertigrefan on 24/02/2018 17:30:00

Rick Tee25/02/2018 09:33:42
286 forum posts
20 photos

I use QCad here, basic 2D Cad. If you register for a fee it will print drawings on multiple pages. CAM is also available.

supertigrefan25/02/2018 12:59:52
49 forum posts
1 photos

Is it 'CAD Dummy' friendly?

Jez Saunders25/02/2018 13:17:28
109 forum posts

As supertigrefan says ? Also which is the best online tutorial ?

Rick Tee25/02/2018 16:11:27
286 forum posts
20 photos

Plenty of help out there, a quick google of qcad tutorials brought up a good few links. I didn't find it particularly difficult to learn YMMV. I think there is a thread on here about various CAD programs, many though are not cheap. If you want 3D FreeCad is erm free, I've not really taken a good look at it yet as I find 2D is fine for my needs. I've looked at some others like Turbocad but they are either above my budget or gave me a headache. frown

Oh and QCad has a free version so you can play all you like before spending any money. smiley

Edited By Rick Tee on 25/02/2018 16:12:55

supertigrefan26/02/2018 11:20:33
49 forum posts
1 photos

Can you import airfoils into QCad?

Rick Tee26/02/2018 12:25:53
286 forum posts
20 photos

I have done with dxf files exported from Profili.

Nigel R26/02/2018 16:02:10
911 forum posts
229 photos

"A good example is the Precision Aerobatics "Addiction" which uses brilliant design to transfer structural loads through ultra-light balsa/carbon composite sub-structures."

I would point out that you will also find guys knocking up 3D planes with the same WCLs (~4 oz/cuft) and using those traditional materials we all know and love - balsa, ply, film type covering - without using carbon fibre covered laser cut latticework.

David Mellor26/02/2018 16:22:18
485 forum posts
99 photos

Yes, I do too, Nigel. I use Depron with small amounts of 1/64" ply (top and bottom as spar caps).

I've designed & built several 3-D planes at well under 4 OPCF.

One of the lowest-loaded aircraft I made was a 40" diameter Nutball with a 750 mAh battery and a 1300kv Blue Wonder motor. It weighed 21.25 ounces, had a wing area of 8.73 square feet and a cubic wing loading of 0.82 OPCF. Great fun, and even flew in a bit of wind, but anything more than 6 mph wind was too much for it.


David Mellor26/02/2018 16:41:02
485 forum posts
99 photos

I found an old video of that 40" Nutball (the one at 0.82 OPCF cubic wing loading), and my old data sheets for it.

It originally had a BL 2220/07 motor and was very lively indeed, being so light. That gave it 184 Watts per pound on an aeronaut 11 x 6 folding prop (in lieu of landing gear).

The one in the photograph above (with the BL 2220/07 swapped out for the lighter, weedier BW1300 motor) was designed as a duration "floater". It would stay up for well over an hour on a 2600 mAh battery. Incredibly boring to fly, though.

Here it is in action (or rather, inaction), a few years ago.

Nigel R27/02/2018 09:14:31
911 forum posts
229 photos

"Yes, I do too, Nigel. I use Depron with small amounts of 1/64" ply (top and bottom as spar caps).

I've designed & built several 3-D planes at well under 4 OPCF."

Neat composite.

The only trouble with loadings that low is their ability to handle wind. It's really into indoor territory at that point. Or, as you say, wind speed in the very low single digits. Personally I find most anything under about 7 or 8 oz/cu ft to be a light winds type affair. And would look to something pushing 12 oz/cuft for a breezy day.

Coincidentally, I have 2 models flying regularly right now, a flyweight depron 3d at around 4.5 oz/cu ft, a small but quite lardy biplane at 12 oz/cu ft, and now the sport/trainer I've just finished at 7 oz/cu ft. Gives pretty good coverage of most flyable weather.

I'm right with you on the cubic wing loading, it's the single most useful 'what if' tool for our purposes.

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