Who's Good At Math? (Need An Upscaling Size Formula To Build Design Larger)
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Who's Good At Math? (Need An Upscaling Size Formula To Build Design Larger)
Here's the deal. I've got some free foamie plans off the net that are using a 400 motor and Sub A batteries. I want to build the same plane only using a 540 motor and Sub Cs. I'm going to base this upscale formula on the Challenger and Extreme since they are the exact same plane with the only difference being size. The Challenger uses a 400 motor and Sub As. The Extreme uses a 540 and Sub Cs. This should be helpful to arrive at a formula since the foamie uses the same motor and packs as the Challenger, and the Extreme uses the 540 and Sub Cs I want to upscale the foamie size to. The Challenger has a 42" wing. The Extreme uses a 55" wing. What is the size increase percentage from the smaller wing to the larger? Based on this, what size should the 36" foamie wing be increased to in order to match the increased size ratio? A good example of the math involved to show how you arrived at the answer would be helpful. This way I can apply the same formula to the other dimensions of the formie to increase their size to proper proportion. I plan to keep the foam size the same thickness the same size as the original (1 and 1/2"), but will add carbon rods for support. Am I missing anything else I'll need to convert over? For instance, can the wing foil (structure of the wing to give it lift) remain the same as the original or would I have to change that too? Thanks for any help.
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RE: Who's Good At Math? (Need An Upscaling Size Formula To Build Design Larger)
Well, going from 42" to 55" requires a 131% increase (55 divided by 42). Applying that to the 36" wing results in a 47" wing span. (36 times 1.31) However, I think you may want to look at square inches of wing area rather than wing span as a guide. Do you know the square inches of each of the three wings involved?
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RE: Who's Good At Math? (Need An Upscaling Size Formula To Build Design Larger)
If I understand you correctly, you want to use a 540 motor and sub C batteries in an enlarged 36" foam design. You have selected the likes of the Extreme because you know it flys with a 540 and sub Cs.
If this is the case, then you really should size the foam design to the wing area of the Extreme.
Bringing in the Challenger with a 400 was unnecessary.
As Chad indicated, you need to determine the wing area of the 36" foamie and the wing area of the Extreme. With that information, you can scale the foam airplane to the larger wing area, and the span may not be 55".
If you don't know how to get the wing areas, you can post a scale drawing of the planform of the 36" and 55" wings, and the wing areas can be estimated.
feihu
If this is the case, then you really should size the foam design to the wing area of the Extreme.
Bringing in the Challenger with a 400 was unnecessary.
As Chad indicated, you need to determine the wing area of the 36" foamie and the wing area of the Extreme. With that information, you can scale the foam airplane to the larger wing area, and the span may not be 55".
If you don't know how to get the wing areas, you can post a scale drawing of the planform of the 36" and 55" wings, and the wing areas can be estimated.
feihu
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RE: Who's Good At Math? (Need An Upscaling Size Formula To Build Design Larger)
Understand your question but I think it's two ways to skin the same cat. Since the Challenger & Extreme are the exact same plane except for size and weight with the bigger 540 & Sub Cs, the square inches of the wing area has already been accounted for by the designer. I think that regardless of basing my increased size ratio on the length of the wing or it's square inches I'd still come up with the same ratio of increase. Others helped me figure out that the size ratio from 42 to 55" is 1.3 (42x1.3=55"). So, I would then multiply every dimension of the foamie by 1.3 to arrive at the new sizes. Based on this, 1.3x36 (foamie wing size)=46.8" for the new foamie wing size. Since the foamie wing is wider than the other wings, this should compensate for it's shorter length by design. Hmmm...does make me wonder though, should I also multiply the wing width by 1.3 or will this do funky things to the square inches of the wing surface. To clearify, should only the wing length be increased or should it's width be also?
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RE: Who's Good At Math? (Need An Upscaling Size Formula To Build Design Larger)
Length and width should be increased. If you increase only the span and not the chord you end up with less square inches and increased aspect ratio. Probably not what you want.
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RE: Who's Good At Math? (Need An Upscaling Size Formula To Build Design Larger)
Critter, when you scale a design up as you want to do you scale ALL of it up. The span, chord length, etc. If you decide to start fudging a dimension here and there then you are getting into designing and you need to make these changes knowing what and why you are doing them.
The 55/42=1.3 was just an example. But I can see why you are using it. But to determine if this is the way to go you need to also consider the aspect ratio of the Challenger and the foamy.
A lot of what you make your final size will also depend on how you want to build this new enlarged foamy. The Depron that works at 36 inch span isn't going to hold up at the new size. The need for a stronger material and a totally new structure will determine if you can make the model to the weight you want at 47" span or if you can make it larger to suit the system you have.
Another item.... When you scale up a design like this there are two key elements. There's the linear scaling as you've seen above where you multiply the span, length and all deminsions by a simple 1.3 factor. But when you enlarge a surface like this by a linear scale factor the AREA of that surface goes up by the square of that same factor. So the wing would go from 36 to 47" span but the wing area would go up by 1.3 x 1.3 = 1.7, or often shown in type as 1.3^2 = 1.7 because we can't type in a superscript "2". So the wing area of the 36 inch model will actually be 1.7 times the increase when blown up to the 47" span.
So the thing to do would be to find out the wing area of the Extreme and compare that to the wing area of the 1.3 times foamy. If they are close then you're good at 47" span. If it's off by more than about 10% you need to make some decisions about which way to change and in light of how you will build it and how you want the model to fly when it's finished.
The 55/42=1.3 was just an example. But I can see why you are using it. But to determine if this is the way to go you need to also consider the aspect ratio of the Challenger and the foamy.
A lot of what you make your final size will also depend on how you want to build this new enlarged foamy. The Depron that works at 36 inch span isn't going to hold up at the new size. The need for a stronger material and a totally new structure will determine if you can make the model to the weight you want at 47" span or if you can make it larger to suit the system you have.
Another item.... When you scale up a design like this there are two key elements. There's the linear scaling as you've seen above where you multiply the span, length and all deminsions by a simple 1.3 factor. But when you enlarge a surface like this by a linear scale factor the AREA of that surface goes up by the square of that same factor. So the wing would go from 36 to 47" span but the wing area would go up by 1.3 x 1.3 = 1.7, or often shown in type as 1.3^2 = 1.7 because we can't type in a superscript "2". So the wing area of the 36 inch model will actually be 1.7 times the increase when blown up to the 47" span.
So the thing to do would be to find out the wing area of the Extreme and compare that to the wing area of the 1.3 times foamy. If they are close then you're good at 47" span. If it's off by more than about 10% you need to make some decisions about which way to change and in light of how you will build it and how you want the model to fly when it's finished.
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RE: Who's Good At Math? (Need An Upscaling Size Formula To Build Design Larger)
Critter:
Here are some things you might consider.
Generally, a 540 motor is slightly more powerful than a 400 motor (depending on the armature wingings) and therefore can fly a larger airplane. The 540 direct drive motor can fly an airplane with a wing area of ~ 200 sq. inches if you want speed, or the 540 geared motor can fly an airplane with a wing area of 500 (and upwards) if you want a floater.
By not knowing what your foamy design is, (fast, aerobatic, conventional, trainer, or sailplane), and whether you plan to use a direct drive or geared 540 motor, it would be difficult to assign a wing area. Because the 540 flys with the Extreme wing does not mean that your foam design with the same wing area will have the same flight and handling characteristics; it could be better or it could be worse.
To come up with your foam wing with a desired wing area is not a big math problem - in fact it boils down to two equations with two unknowns.
Once you come up with the desired wing - then your scaling factor becomes linear - and every part of the foamy will use this scale factor for your 540 motor size airplane.
Whether or not the wing structure can remain the same depends upon the structure itself.
feihu
Here are some things you might consider.
Generally, a 540 motor is slightly more powerful than a 400 motor (depending on the armature wingings) and therefore can fly a larger airplane. The 540 direct drive motor can fly an airplane with a wing area of ~ 200 sq. inches if you want speed, or the 540 geared motor can fly an airplane with a wing area of 500 (and upwards) if you want a floater.
By not knowing what your foamy design is, (fast, aerobatic, conventional, trainer, or sailplane), and whether you plan to use a direct drive or geared 540 motor, it would be difficult to assign a wing area. Because the 540 flys with the Extreme wing does not mean that your foam design with the same wing area will have the same flight and handling characteristics; it could be better or it could be worse.
To come up with your foam wing with a desired wing area is not a big math problem - in fact it boils down to two equations with two unknowns.
Once you come up with the desired wing - then your scaling factor becomes linear - and every part of the foamy will use this scale factor for your 540 motor size airplane.
Whether or not the wing structure can remain the same depends upon the structure itself.
feihu
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RE: Who's Good At Math? (Need An Upscaling Size Formula To Build Design Larger)
See what you are getting at. I'll check the surface area of the Extreme and post the numbers. The stock 36" foamie wing surface is 252 square inches, I think. It's a 7x36 inch wing. As far as strength goes I plan to use carbon tubes in the wings and body of the foam build. Have lots of experience with using those to strength a Stryker body with a brushless motor and lipos. The stock 540 (non-geared motor) and prop the Extreme uses push it along nicely and that plane weighs around five pounds or so. I'd figure as long as the weight remains about the same the motor should push it along fine without the need to be geared.
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RE: Who's Good At Math? (Need An Upscaling Size Formula To Build Design Larger)
OK, did a little digging and found the following information on the Extreme's wing...It's surface area is 2.203 square feet. The wing is 55" long and roughly 6.75" wide...it tapers to an angle near the tips which makes it slightly less wide in those areas. The stock foamie wing is 36" long by 7" wide with (I think) a surface area of 252 square inches. So, if I just multiply the foamie wing's length and width by 1.31 will that put me in the ball park of where I want to be. Note that I'm not trying to match the surface area of the Extreme. I want the foamie's surface area to remain in proper proportion to it's probable 1.31 increase in dimensions or whatever you guys settle me on. Thanks.
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RE: Who's Good At Math? (Need An Upscaling Size Formula To Build Design Larger)
If you know the existing wing area and the new area wanted the formula is to divide the square root of the smaller wing into the square root of the larger wing. All angles and aspect ratios will remain the same.
Ray
Ray
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RE: Who's Good At Math? (Need An Upscaling Size Formula To Build Design Larger)
Critter:
Ray's method above is fine. sq rt 317.23 / sq rt 252 = 1.122 as the scale factor.
Here's another way:
The Extreme wing area is 2.203 sq ft which is 317.23 sq inches.
The stock foam wing is 36 span by 7 chord.
The following calculations are to make a wing of area 317.23 sq in and have the same proportion span to chord of the stock foam wing; and come up with a scale factor for all proprotional parts as well:
From your given information, the aspect ratio of the stock foam wing is s/c or 36/7 = 5.28
Calculating a 317.23 area wing,
Eq. 1 s x c = 317.23
Eq. 2 from the aspect ratio, s = 5.28 c
Substitute Eq. 2 back into Eq.1, we get 5.28c x c = 317.23
Solve eqs for c, we get 5.28c^2 = 317.23; and c^2 = 60.08
c = sq root of 60.08 which is 7.75, and the span is 5.28 x 7.75 = 40.92 inches (use 41)
The new wing with the same proportion of the stock foam is then 41x7.75.
And the wing area is now 41 x 7.75 = 317.75 sq inches.
Using the chord (optional), the scale factor of 7.75/7 = 1.107 THIS IS YOUR MAGIC NUMBER 1.107
Now take the dimentions of any part of the stock foam airplane and multiply by 1.107
Good luck on your up-scaling.
feihu
By the way, if you use 1.31 as your scale factor, then your span would be 47.16 in; chord 9.17, and area 432.46sq in.
See the difference? Of course you can use this if you want a larger plane.
Ray's method above is fine. sq rt 317.23 / sq rt 252 = 1.122 as the scale factor.
Here's another way:
The Extreme wing area is 2.203 sq ft which is 317.23 sq inches.
The stock foam wing is 36 span by 7 chord.
The following calculations are to make a wing of area 317.23 sq in and have the same proportion span to chord of the stock foam wing; and come up with a scale factor for all proprotional parts as well:
From your given information, the aspect ratio of the stock foam wing is s/c or 36/7 = 5.28
Calculating a 317.23 area wing,
Eq. 1 s x c = 317.23
Eq. 2 from the aspect ratio, s = 5.28 c
Substitute Eq. 2 back into Eq.1, we get 5.28c x c = 317.23
Solve eqs for c, we get 5.28c^2 = 317.23; and c^2 = 60.08
c = sq root of 60.08 which is 7.75, and the span is 5.28 x 7.75 = 40.92 inches (use 41)
The new wing with the same proportion of the stock foam is then 41x7.75.
And the wing area is now 41 x 7.75 = 317.75 sq inches.
Using the chord (optional), the scale factor of 7.75/7 = 1.107 THIS IS YOUR MAGIC NUMBER 1.107
Now take the dimentions of any part of the stock foam airplane and multiply by 1.107
Good luck on your up-scaling.
feihu
By the way, if you use 1.31 as your scale factor, then your span would be 47.16 in; chord 9.17, and area 432.46sq in.
See the difference? Of course you can use this if you want a larger plane.
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RE: Who's Good At Math? (Need An Upscaling Size Formula To Build Design Larger)
WOW! Now that's what I call some number crunching. Thanks a bunch for all that info and I can now procede with the build. Two more quick questions...So you are saying I can use the 1.31 upscaling factor if I want a bigger plane. This would, I would think, make the plane glide better but slow it down? I'll probably just go with your numbers as I don't really want a plane that'll glide a bunch...my Extreme does that for me. I want more power and decent speed which I would guess the numbers you provided would do better at. Found out the COG point of the stock foamie (can't remember but think it's 1/3rd back from the leading edge of the wing), so if it is I just go 1/3rd back on the new wing size? Also, the plans have no mention of how many degrees (or whatever) the wing airfoil should be cut to create lift. Is there a standard number for this on any plane or do I have to find that out? Thanks again!
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RE: Who's Good At Math? (Need An Upscaling Size Formula To Build Design Larger)
Critter:
If you use a 1.31 scaled up plane, you would have a 47.16 in span and a wing area of 432.46 sq inches. You now have a larger plane and also a HEAVIER plane; so now the wing loading comes into play. Wing loading is the weight of the airplane divided by the wing area and is expressed as ounces per square foot. So the wing loading of the new airplane depends on the weight of the structure and all the parts such as the radio, servos,motor and battery. But because you have a heavier plane, you also have a larger wing area - so the wing loading could be the same, or even less than your stock foam model. The lower the wing loading, the better the flyability. You can you compare wing loadings between your stock foam and the Extreme to get an idea of their flyability characteristics; but even with the same wing loading, different designs will fly differently.
The CG location would not change; so the CG of 1/3 back will apply to your new wing.
Also, I don't understand your question regarding "degrees wing airfoil should be cut to create lift". Your up-scaling should be an exact duplicate of the original in terms of shape and location as shown on your plans.
feihu
If you use a 1.31 scaled up plane, you would have a 47.16 in span and a wing area of 432.46 sq inches. You now have a larger plane and also a HEAVIER plane; so now the wing loading comes into play. Wing loading is the weight of the airplane divided by the wing area and is expressed as ounces per square foot. So the wing loading of the new airplane depends on the weight of the structure and all the parts such as the radio, servos,motor and battery. But because you have a heavier plane, you also have a larger wing area - so the wing loading could be the same, or even less than your stock foam model. The lower the wing loading, the better the flyability. You can you compare wing loadings between your stock foam and the Extreme to get an idea of their flyability characteristics; but even with the same wing loading, different designs will fly differently.
The CG location would not change; so the CG of 1/3 back will apply to your new wing.
Also, I don't understand your question regarding "degrees wing airfoil should be cut to create lift". Your up-scaling should be an exact duplicate of the original in terms of shape and location as shown on your plans.
feihu
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RE: Who's Good At Math? (Need An Upscaling Size Formula To Build Design Larger)
What I mean is the plans show the curved leading edge of the wing that I think you call the "airfoil" which creates the lift. However, there is no mention at measurements to cut this curved leading edge in degrees or otherwise. So, is there some form of standard curve that I'm supposed to use?
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RE: Who's Good At Math? (Need An Upscaling Size Formula To Build Design Larger)
Critter:
I have no idea of what your stock foam airplane looks like, or the foam used in its construction - so it leaves me at a loss to make any comments.
I know that some foam wings are cut to specific airfoils, some are just a curved piece of 3/16 or 1/4 sheet foam, and some are just plain flat sheet foam with a fold-over leading edge, and some have molded foam to specific airfoils. But on park flyers, the airfoil is not that critical and thats why you see these kinds of construction. Is there some way you can post a photo or sketch of the airfoil from your plans?
If you have a copier, you can just copy from your plans and enlarge 1.12 or whatever scale factor you choose. Otherwise you might revert to the old hand method of drawing "graph paper" squares over the copy of the airfoil, then draw another set of graph paper that has 1.12 x larger squares, and fill in the squares for your airfoil.
One point I might add - since you're enlarging the foam wing from 36 to 41 inched (only 5 inches longer) you might be able to use the same foam material as the plans but with some added strength such as carbon fiber if needed.
feihu
I have no idea of what your stock foam airplane looks like, or the foam used in its construction - so it leaves me at a loss to make any comments.
I know that some foam wings are cut to specific airfoils, some are just a curved piece of 3/16 or 1/4 sheet foam, and some are just plain flat sheet foam with a fold-over leading edge, and some have molded foam to specific airfoils. But on park flyers, the airfoil is not that critical and thats why you see these kinds of construction. Is there some way you can post a photo or sketch of the airfoil from your plans?
If you have a copier, you can just copy from your plans and enlarge 1.12 or whatever scale factor you choose. Otherwise you might revert to the old hand method of drawing "graph paper" squares over the copy of the airfoil, then draw another set of graph paper that has 1.12 x larger squares, and fill in the squares for your airfoil.
One point I might add - since you're enlarging the foam wing from 36 to 41 inched (only 5 inches longer) you might be able to use the same foam material as the plans but with some added strength such as carbon fiber if needed.
feihu