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Scaling Plans

There are many reasons to scale a 3 view drawing, magazine plan, or full size model plan up or down. 

 

Scaling to a new wingspan or other dimension

Perhaps you have a different size engine that you'd like to use, or the plan you have is much bigger or smaller than what you usually build. I have scaled a few designs to fit some ready made wheels. Models can also be scaled to fit bubble canopies such as those available from SIG. 

Example: Scaling a model for this purpose is relatively easy - just multiply all dimensions by the scale factor. 20" wingspan model is to be scaled to 24". Divide 24" by 20" to get the factor: 1.2.

Every dimension on the plan can be multiplied by 1.2 to allow the plan to be redrawn, which is a labor-intensive project and one that can introduce many errors. Scaling ribs, formers and curved outlines this way can also be less than precise - see notes below about a better method.

 

Scaling to a new area

When trying to scale a model up or down to a new area, the problem is that we cannot just multiply the dimensions by the area increase. For example to go from 400 square inches to 500, we'd like to just multiply by something - in this case 1.25, which is the change in area.

But, because we are looking at area, we need to look at square root to find the answer. An example may illustrate this better. Imagine a square box 2" on a side, which will have an area of 4 square inches. Now, think about a box with an area of 5 square inches. What are the dimensions of the new box? We can find that by taking the square root of 5, which is 2.2360679" on my pocket calculator. We can check this by multiplying 2.23 etc by itself, to get 4.99999996 square inches - pretty close to 5.

So, while we could have tried 2.5" [or 1.25 times the original 2" side], we can see that this wouldn't work. The method that works is to take the new area divided by the old, then take the square root of that ratio. 

Example: 5 square inches / 4 square inches = 1.25 [this is a ratio, with no units]; square root of 1.25 is 1.1180339. Then multiply the old side dimension of 2" by 1.1180339 to get 2.2360678", darn close to our first approach. 

So, to scale up a design 25% in area, multiply all dimensions by 1.1180339.


The method works for scaling down, also. To go from 5 square inches to 4, we do much the same thing. 

Example: 4 square inches / 5 square inches = .8 ; square root of .8 is .8944271. So, we multiply the original dimensions by .8944271. 

2.2360679" {the old side dimension} X .8944271 = 1.9999997, which is for all practical purposes 2". 

 

A better solution to making a scaled plan

 
One can scale a design by hand to get the new size, and in the 'olden days', many of us did just that, scaling and drawing plans on butcher paper, brown wrapping paper, or even drawing right on the workbench top. As noted, the process is error prone as well as tedious. One needs a bit of drawing skill and a collection of french curves to produce accurate results. Scaling curved parts can be done by drawing a grid of pencil lines, say 1/4" apart horizontally and vertically over the part. On another piece of paper, draw a new grid with the lines separated by 1/4" times the scale factor. Then, eyeball style, start making marks on the new grid where edges cross grid lines or intersections. Connect the dots and you can produce a scaled part.

However, there is a more practical method: go to a blueprint shop with a big engineering Xerox - ask them to scale the original drawing. What they will want to know is the factor, thus for our first area example, we ask for a print at 1.1180339 . Their machine doesn't have that many decimals, but they can probably do 1.118 .
In the scale down area example, ask for a print at .8944271; probably .894 is what you'll get.

You'll pay about $1.25 / sq ft of finished print on plain white paper, but this is a real time saver. It is possible to go much bigger, too - a small 3 view up to a 5' wing, for example, but you get to pay for the paper in the intermediate steps as the big machines won't do that much in one shot. With a small 3 view or just a few parts, a practical method is to do the initial scaling on the self-service machines, which often will go up to an 11" X 17" sheet. This will save some money.

Also, this whole process is an optical blow-up, so lines and lettering tend to get wider and blurred a bit. Scaling down makes lines get narrower. Another thing to be concerned about, is that the math and the optics seem to drift a bit with multiple setups - so it's worth checking the numbers for the final shot. I have adjusted the factor on final shots just a tiny amount to get just the wingspan I was after.

 

Another solution

Your blueprint/copy shop may have a large scanner that will accept the plan to be scaled. The same size/scale considerations we've discussed apply here - with 2 differences. (1) As a scanned, then printed/plotted product, the new plan can have lines that are no wider than the originals, making for clearer images. (2) Some scanned images may print out with jagged edges on curved parts - ask for a sample first, then discuss scan/print resolution with the operator.