Well I hate to say this but I was a straight "D" student in math. That means my teachers passed me because they felt sorry for me, not because I understood what they were talking about! LOL
I think I understand what you guys are saying though. Take the wing area I want, divide it by the large wing area and that gives me a percentage number to use to shrink the original large plan. And if the large model was a good flier, the reduced model should also be a good flier. Is this basically correct?
Not quite.
When dealing with wing areas, you are dealing with squared numbers. 620 square inches divided by 700 square inches = .8857 squared. You have to remove the sq. from the answer, and you do that by using the sq. root of the number, which in this case is .9411239.
I have the availability to have my computer find the area of an object. Here's a practical example using this principle. I'll use at least 3 decimal space as the cad program is accurate to 17 decimal spaces, just to show how accurate it is.
Gordan's Tony has a wing area of 743.321 sq inches, and a span of 63.901 inches. It's designed for a .72 or larger engine.
I want to scale one for an OS .46LA. I've seen this engine doing a great job powering a plane with 640 sq inches.
So I want to scale the Tony down to 640 sq inches, I don't know what the span will be because this will not be a lineal scaling job.
I have to find the scaling factor that will give me the square inches I want, then I can measure the span.
640 sq inches divided by 743.321 sq inches = .861....inches squared.
I need to get rid of the inches squared portion of the answer, so I find the square root, which = .9279012. (I'm going to use all the decimal places here because I want the exact square inches after all is done.) This is my scale factor.
Now going back to my Cad program where I had the computer figure the wing area, I can use the scale command, and use .9279012 as the scale factor.
The computer now resizes the wing using this information.
I do another inquiry for area, and the computer measures the new wing at exactly 640 sq inches. The span now measures 59.294 inches. The new wing is now 4.607 inches shorter, but the area is a little over 103 sq inches less.
In my earlier example, I may not have been clear on one point. That 60 I referred to was not the wing span. it has no place in figuring using sq inches of area. it referred to the engine size, a .60 engine related to a .40 engine. They were only used to illustrate the size airplane normally utilizing the wing areas noted.
I use the example of the Tony showing that the math works, and the Cad program shows the figures to be correct.
So simply put.
Take the area you want, divide it by the area you have, find the square root of the answer, and you have your scale factor, using the area (Inches squared).
If all you are concerrned about is a lineal distance, such as wing span, then it's simpler, but may not reflect exactly what you think it does.
Take the span you want, and divide it by the span you've got. No squared numbers, so no square root to arrive at the scaling factor. A clean and simple linear scaling.