Scaling down models

I have been thinking about scaling down the Trivial Pursiut, to a size suitable for an conventional 46 engine (Stalker 46).
Do anyone have any good "on the thumb" rule for this. For example; 80% of an 60 size model to suit a 46 engine???

Appreicate your comments.

Valle
Uppsala
SWEDEN

As a quick approximation, the wing area scales directly with engine displacement for equivalently tuned engines.

Weight, however should vary as:

Weight = (constant) * wingspan * wing area

Calculate the constant from the original size as:

(constant) = Weight / (wingspan * wing area)

and then use that constant in the first equation to calculate the weight of the new model.

>I have been thinking about scaling
>down the Trivial Pursiut, to
>a size suitable for an
>conventional 46 engine (Stalker 46).
>
>Do anyone have any good "on
>the thumb" rule for this.
>For example; 80% of an
>60 size model to suit
>a 46 engine???
>
>Appreicate your comments.
>
>Valle
>Uppsala
>SWEDEN

Scaling can be tricky. I once scaled a model figuring it for converting from over 700 sq. inches to 500. To do this I divided the desired sq inches of area by the existing, 500/700 = ~71.4% This was an error as I wound up with a ~375 sq. inch wing area. There's one more thing to do and that is find the sq root of the sum which winds up being ~84.5%.

I don't know what the area on the TP is, but would estimate it to be ~700 sq inches. The Stalker .46 should handle 625 sq inches with ease. You do want the wing loading to be decent. 625/700= 89.2857142%. the square root of that is ~94.5%. In this example, using 80% to scale a 700 sq inch wing would result in a less than 500 sq inch wing, which a Fox .35 or even a .29 would handle with ease.

I would figure on using 94 or 95% as the scaling factor for what you want to do.

Best of luck with your project.

I think the TP runs around 650 sq inches. Maybe a little larger but not much. You could shorten the span by about 2 to 3 inches and leave the wing alone other than that. Take off 1" on the stab span and leave the rest alone. Build the rest of the model right from the numbers on the plan. Maybe shorten the nose by about a 1/4" ot maybe a 1/2" but not any more than that.

Cutting out 2-3 inches of wing span can reduce the area as much a 30 inches, I think. Maybe not that much but maybe more. You would have to do the numbers. One thing that will be different is the wing sweep will be slightly more. But to the casual observer and maybe to the high techy guy looking at it it wont be noticeable.

One thing is for sure. Get Teds angle on it before you change it.

Also 95% sounds about right from the above post. 80% and the foil will be way to small to carry the weight.

This is an interesting thread. I think that Larry is on a good track, using what I think has been called "wing cube loading". If someone can produce the original figures, I'd be interested in this method's predictions.

Generally accepted scaling theory says that power required is proportional to the 3.5th power of the scale factor. If the actual power used in C/L stunt were proportional to displacement (which is doubtful), then the linear scale factor would be the 3.5th root of (46/60) = .927. Then area would be (650?) x (.927)^2 = 558. But I suspect that the well-behaved stunt engine is operating lower on the power curve in an area of good torque, but where the engine also reacts constructively to aerobatic forces. Here the respective outputs would be closer. So does anyone know a good approximation of the power produced by these two engines as operated in a stunter?? It would be interesting to know whether this theory gives realistic results in the C/L-constrained environment.

To anyone who uses Excel spreadsheet program, I'll be happy to send a couple of files. One compares various scaling formulae, the other has a whole bunch of planes compared by my favorite two techniques.

Scaling is tricky, because there really ain't no such thing. You can only scale models to meet a few selected criteria. Those are chosen for your particular purpose. For example, in a wind tunnel, you want to scale to get the Reynolds number the same. In models, you want the flight to appear to be the same. These two have VERY different results!

The one I outlined in the message above, is theoretically correct based on two assumptions:

1. The plane flies "x" wingspans forward in one second
2. The plane can pull a "y" wingspan radius loop at that speed.

These criteria mean that the planes appear to fly identically relative to their own size.

Given those, and the basic formula for lift, you can show the above is correct. I dealt with the whole derivation in an article in Model Airplane News a few years ago. I have that scanned in as jpeg files too. Don't know the legality of distributing copies of the article, even for free.

The Excel files are mine, and happily will go to any and all.

>This is an interesting thread. I
>think that Larry is on
>a good track, using what
>I think has been called
>"wing cube loading". If someone
>can produce the original figures,
>I'd be interested in this
>method's predictions.
>
>Generally accepted scaling theory says that
>power required is proportional to
>the 3.5th power of the
>scale factor. If the actual
>power used in C/L stunt
>were proportional to displacement (which
>is doubtful), then the linear
>scale factor would be the
>3.5th root of (46/60) =
>.927. Then area would be
>(650?) x (.927)^2 = 558.
>But I suspect that the
>well-behaved stunt engine is operating
>lower on the power curve
>in an area of good
>torque, but where the engine
>also reacts constructively to aerobatic
>forces. Here the respective outputs
>would be closer. So does
>anyone know a good approximation
>of the power produced by
>these two engines as operated
>in a stunter?? It would
>be interesting to know whether
>this theory gives realistic results
>in the C/L-constrained environment.
>
>SK

Serge, I don't think in our applications, a direct scale factor can be equated, comparing engine size to airplane size. Way too many variables. For instance, My Pathfinder 40 ( the full fuse version) has over 650 sq inches. It's powered very nicely with an OS .40fp. Some people would power it with a larger engine. I've seen stunters in this size powered with PA .65's. Using a factor such as your example, I haven't done the math, so I'm guestimating, I should have a ~500 sq inch stunter for the fp.

Now, my particular fp has been massaged and is probably stronger than the norm, and the PA .65 is a tank and can be operated at about any power level, so we have some extremes or limits to look at.

Any rules of thumb I've been taught to use are the following.

A good flying Nobler would weigh in at ~38 oz's I believe the area on a Nobler is ~530, so 530/38= ~14 sq inches to the oz.

That's the standard of performance based on a known good flying setup I've been taught to use. I try to match my wingloading to this number on any design.

A Fox .35 running 4-2-4 will haul such a loaded plane ~the size of a nobler just fine. But, power is addictive, and if we can add more engine and keep the same or better loading I'll go for it.

A decent running .40 will handle a plane with 600 to 650 sq inches as long as the loading is in this range. heavier loading = bigger engine. .46 to .60 4-2-4 can go up to ~700 sq inches depending on the power available. .40 and up Piped engines seem to hover around 650 to 700 sq's regardless of the engine size.

I haven't yet formed too much of a rule for 4 strokers yet. They seem to be able to handle heavier loadings and larger sized planes relativly easily. Time will tell as we learn more about them in our use.

The plane I'm building at this time is for a Saito .72 and has 733 sq's. We figure that the loading should come out right at that size, and the engine is capable of handleing the drag a plane that size will have.

I've rambled a bit and apoligise for it.

The formula, should one be developed, should include more than the area/engine factor ^2. Perhaps additional factors relating to the loading and drag should be included. Mybe even a "fudge" factor after all is figured to allow for a range.

Just some thoughts from an admitted math challenged student of the art.

>I have been thinking about scaling
>down the Trivial Pursiut, to
>a size suitable for an
>conventional 46 engine (Stalker 46).
>
>Do anyone have any good "on
>the thumb" rule for this.
>For example; 80% of an
>60 size model to suit
>a 46 engine???
>
>Appreicate your comments.
>

There's not really a rule. All 60's aren't created equal. A 40VF will fly a full-size Trivial Pursuit well enough to fly at the highest levels. A Stalker 40 wouldn't. For instance, the Trivial Pursuit was designed to fly with a 46VF. A Stalker 46 is not anything like the same power.

Based on past experience, if you do anything I would suggest a slight scale-down to 600-615 square inches. This is about the size of the TP's immediate predecessor, the Temptation, which IMO, was the pretty much the ultimate ST46 model (close race with the Imitation). Since the original TP is about 650, that's about 97% scale of linear dimensions.

The reasoning: most of the ST46 airplanes were WAY too big for modern performance, and before the demise of 4-2 break as a competitive system, ST46 airplanes were shrinking. The TP has a very thick airfoil, and will fly well at 55-60 oz for 615 squares. This will be easy to hit with average skills. The Stalker is probably weaker than the average ST46 (although I bet it's more consistent because of the superior cylinder/piston).

To derive a linear scaling factor, decide your New area, which should be about 610 square inches (glad Mr. Buck agrees). Find the area of whatever design you wish to scale up/down, say 650. Your math assignment is to multiply 610 x 610 and divide that by 650 x 650. You've just squared both areas and divided the new by the old. Now take the square root of the result, and you have the scale factor for linear dimensions. If you are scaling down, the factor will be below 1.0, and if scaling up, above 1.0. In this case, .938461538. Steve

>To derive a linear scaling factor,
>decide your New area, which
>should be about 610 square
>inches (glad Mr. Buck agrees).
>Find the area of whatever
>design you wish to scale
>up/down, say 650. Your math
>assignment is to multiply 610
>x 610 and divide that
>by 650 x 650. You've
>just squared both areas and
>divided the new by the
>old. Now take the square
>root of the result, and
>you have the scale factor
>for linear dimensions. If you
>are scaling down, the factor
>will be below 1.0, and
>if scaling up, above 1.0.
>In this case, .938461538. Steve
>

I'll readily admit that I'm math challenged, but I think you've made an error Steve.

By squaring the areas and then dividing them, and then taking the square root, you have the same number you would have if you hadn't squared them in the first place.

610/650 = .93841538

The square root of .93841538 = .968742245

I'll bet you will get less wing area using your method, in fact, I think I'll fire up the Cad system and check what the area would be.

The PF 40 wing is 650.916 sq inches If I scale it at .93841538 I get 573.268 sq inches. If I scale it at .968742245, I get 610.860 sq. inches.

Sorry for all the numbers in the examples, but I found this out the hard way and built a plane I thought was 500 sq inches that wasn't. It now hangs on the wall as it's too heavy, ( I didn't simplify the structure) and the wing is too small, so the loading is way too high. Nice looking plane though.

So Steve, ya gonna be at the Regionals?

LAST EDITED ON May-08-02 AT 10:54 PM (CST)

Good catch, Mr. Miller! Ok, so divide 610/650 and take the square root. It shouldn't be that easy, should it?

NW Regionals? Yeah, I's s'posed to add stunt scores or somet'n. Plan to arrive Wed. nite, do setup/registration Thursday, then some kind of stunt chores I hope, like sit in a lawnchair and eat donuts. Steve

LAST EDITED ON May-09-02 AT 02:21 AM (CST)

If the engine to be used has been chosen for a scaled down (or scaled up) design, the desired wing area should be determined next. Larry Renger gives one approach on how to do this. Another method would be to consider the size (wing area) of other designs that use that or a similar engine and establish the wing area accordingly.

The calculation to determine the multiplier or factor (F) to scale the new dimensions is simply the square root of the ratio of the new design wing area (N) to the original design wing area (S).

Or, for the way these computers recognize such things:

F = (N/S)^0.5

An example will show how this works.

Let's say that we have a Whatzit with a wing which has a 10 inch chord and a span of 40 inches for an area of 400 square inches. Now we want a new Whatzit with the same configuration but with 300 square inches. Our scaling factor will be

F = (300/400)^0.5 = 0.866 (This is the square root of 0.75)

So the wing will now have a chord of 8.66 inches, a span of 34.6 inches and an area of 300 square inches. Multiply every dimension by the scaling factor and you will have an 86.6% Whatzit where the wing area is 75% of the original.

Now you can go to Kinko's, set their big printer at 86.6% and have the drawing almost instantly. (But you have to be careful with the Kinko's machines. The factor is not always exact and there will be some distortion or difference in the verticle and horizontal dimensions.)

(Apologies to the designer of the Whatzit, if there is one.)

LAST EDITED ON May-09-02 AT 06:53 AM (CST)

Valle,
I have written an Excel spreadsheet program which can be used to scale an airplane up or down. What you do is to input the dimensions from the "original" then input the "scaling factor" and the program returns all the new dimensions. The program asks for diminsions such as wingspan, chord, tip, LE sweep, flap chord, flap tip, flap length, nose moment, tail moment, fuse height at the LE, stab span, stab chord, stab tip, ...etc...you get the picture. I'll be glad to email it to anyone who would like a copy. It has several columns for the scaling factor so you can compare the different sizes. Works pretty slick. It also has a "worksheet" that you can print out and then write down all the dimensions from the original design. These can be taken off a set of plans or a real model can be measured. It's a lot easier to input the data from the worksheet into the computer because the "worksheet" numbers are in the same order as to the data that has to be entered. If you, or anybody else is interested in a copy, I'll email it to you.

LAST EDITED ON May-09-02 AT 07:47 AM (CST)

Thanks for the offer! I'd like to see your Excel files. Now that M.A.N. has forsaken most forms of model airplanes, it lacks my full sympathy regarding proprietary use of its authors' submissions.

With due regard for the valid points made in submissions below, I'd still like to know some approximate power or torque figures for the .60 and .46 engines in question - in their state of tune and at stunt-useful RPMs. Mental or mathematical models often fall short of fully modeling complex phenomena, just as the mental models used by many expert modelers do. Sometimes, however - and I believe we've all seen this - such over simplifications (even wrong interpretations!) still point in the right direction. It's good to learn how close certain mathematical models can come to predicting actual performance in varied circumstances.

John's point about wing loading (a parameter inherant in your own method) is well taken and seems a prime factor in engine choice, but once chosen, the wing engine combination should be scalable. Weight at least seems a usual consideration in trimming. As you say, scaling is full of contradictory requirements that make it impossible to create a model that scales accurately in all ways. Still, if any mental or mathematical model comes close enough, dependable "fudge factors" (sometimes responsive to other parameters - like loadings, propellor dia./pitch, etc.) can make them useful. I just like to know how far we miss - for future reference.

Thanks Kieth for the additional clarification. Aint this fun?

John

LAST EDITED ON May-09-02 AT 11:05 AM (CST)

deleted. remove access denied.

>(Apologies to the designer of the
>Whatzit, if there is one.)

Riley Wooten?

I still have one.

Crist:

I'd appreciate a copy of your spreadsheet.

[email protected]

Thanks in advance.

L.

LAST EDITED ON May-10-02 AT 08:44 AM (CST)

LAST EDITED ON May-10-02 AT 08:17 AM (CST)

One reason I was happy to see this question raised - past a general interest in such things - is that I'd like to tailor an original design to the LA or FP .25 engines. So far I have neither power nor weight data and can only go on ball-park estimation. I have been told that these engines might be a good match for some classic period (500+ sq. in.) stunters that were originally powered by Fox .35's, if run at high RPM on low-pitched props. Set up otherwise, perhaps a 400 - 450 sq. in. area/45" - 48" span would be more appropriate. Are there any opinions out there?

Thanks to Larry Renger for the fascinating spreadsheets. 'lots of food for thought there on this topic.

SK

P.S. (Edit):

A friend on this list gave a viable approximation relating displacement to model weight: W = 100D + 2. For example, the weight of a stunter employing a .25 engine would be about 25 + 2 = 27 oz. This allows use of Larry's method. Opinions?

>One reason I was happy to
>see this question raised -
>past a general interest in
>such things - is that
>I'd like to tailor an
>original design to the LA
>or FP .25 engines.

The only recent "modern" design of which I'm aware that is specifically tailored to the LA 25 is Mike Pratt's Primary Force. It is an advanced profile flapless design, available as a laser cut semi-kit, that several folks on this forum are building. As built by Mike it is a really slick and attractive ship, wish I was building one, and worthy of consideration by all whether or not you're interested in exploring the flapless question. Take a look at it; http://home.mindspring.com/~mikeypratt/index.html

Darwin-

Thanks for reminding me. I actually HAVE one under construction. Since mine gets an FP .35, I had forgotten that Mike's flew on the .25! That and the wide variety of spans and areas used for equal displacement engines re-emphasizes the need to scale to the particular make/model engine in a given displacement class and its mode of operation.

Thankyou all for you valuable inlays to this thread. I hav been unable to check in for a while and was surprised when I saw al your answers.
It took me some time to read it all through.

It seems that Wing area in relation tom engine power is a good way to go. Of course this is when you keep the same airfoil etc.

After doing some Calculations myself, I have come to the conclusion that around 93% will be the right size. I have not yet decided if I should use the Stalker 46 or a Moki51. But I think that size will suit both engines.

Once again thankyou for your valuable thoughts.

Valle

>Thankyou all for you valuable inlays
>to this thread. I hav
>been unable to check in
>for a while and was
>surprised when I saw al
>your answers.
>It took me some time to
>read it all through.
>
>It seems that Wing area in
>relation tom engine power is
>a good way to go.
>Of course this is when
>you keep the same airfoil
>etc.
>
>After doing some Calculations myself, I
>have come to the conclusion
>that around 93% will be
>the right size. I have
>not yet decided if I
>should use the Stalker 46
>or a Moki51. But I
>think that size will suit
>both engines.
>
>Once again thankyou for your valuable
>thoughts.
>
>Valle

Good luck Valle with you project. It will be nice to see how it comes out when fiished.

I think you should know that I have a friend who flies a full sized Trivial pursuit on a ST .51 with no problems as far as available power goes. If you're planning on using the Moki, which I, never having seen one run, but told that they are a quality and powerful engine, believe is on par with the ST, you may want to follow my friends example and build it full size for that engine.