Computing Surface area with Photoshop

[mclarkson]

I'm not actually sure where this ought to go, but I decided that scratch builders would probably be the most interested. Please let me know if it belongs elsewhere.

Computing the area of a plane’s wings (or other surfaces) can be complicated, involving lots of geometry and assorted arithmetic. This method requires none of those. (Well, okay ... maybe a little bit of simple math.) It works with any shape, no matter how convoluted. Here’s how to do it:

Load a plan into Photoshop.

IMPORTANT NOTE: Even though your plans may be in grayscale, and we will be working in black-and-white, Photoshop must be set to RGB color mode for this to work. (Image / Mode / RGB Color)

Let’s say we have this wing.


Using whatever method works best for you – I generally select an area with the ‘magic wand tool’ and fill it with the foreground color – convert it into black and white, where white is the wing and black is the background. Make sure these colors are pure, 100% white and black. This is crucial!


Now, from the menu, choose Filter / Blur / Average. This will turn the entire image into a solid rectangle of gray:


All that remains is to measure how light or dark the resulting gray is.

1. Click the foreground color swatch on the toolbar to bring up the Color Picker dialog box.
2. The cursor changes to an eyedropper tool. Click anywhere in the gray rectangle.
3. In the Color Picker dialog, find the brightness value. In the image below, it reads 34%

Now we’re ready to make the final calculation. Let’s say the original plan – the entire sheet – is 24″ tall by 20″ wide. That’s 20×24 = 480 in^2, or 480 square inches. Photoshop tells us that, in our example, 34% of those pixels were white (that’s why our resulting gray had a brightness of 34%). That means the surface area of the wing, itself, is 34% of 480 in^2 or 163.2 in^2.

This method isn’t just useful for wings. Let’s say these rough plans for a plane are to be printed at 28″x16″


Converting them to black and white, then averaging them…



…yields a brightness of 59%. 28×16 = 228, the area of the plans. 59% of 228 is 134.5. So the surface area of all the parts on that plan will be about 134.5 square inches (134.5 in^2). I happen to know that Dollar Tree foam weighs 0.19 grams per square inch with the paper on. That means that all the parts on this plan, when cut from Dollar Tree foamboard, will weigh approximately 0.19 * 134.5 (25.5) – grams.

[Larry3215]

Thats a very 'nerdy' way to do it - I like it!

have you checked your results on a simple plan form - say a rectangle and circle of known dimensions - to see just how accurate the results are?

[mclarkson]

I have checked it on several simple plans - white circle on black square, white triangle on black square, etc. etc. etc.

It seems to be dead on the money. The attached, for example, works out to 72%.

It's a circle inscribed within a square. The ratio of the surface area of a circle with diameter N to the surface area of a square of side N is about 78% (78.54).

Then there's a little square, 1/16th the area of the big one. 1/16 is 6.25%. 78.54 - 6.25 = 72.29. Photoshop reports 72%.

[mclarkson]

I just completed my first real world test today - cutting plane parts for which I had previously calculated the surface area and weight - and it came out dang near perfect!

[JetPlaneFlyer]

That's really ingenious, but given the very high cost of Photoshop and the contrived and long-winded method to measure area might it not be a lot easier/cheaper to measure area directly in a free CAD program such as Draftsight?


The procedure is pretty simple:

1. Import image file into CAD.
2. Check the scale by measuring a few key dimensions and scale the image if not correct.
3. Trace around the object you want to measure.
4. Do an enquiry on area.

ok, so CAD software takes a while to learn but it's no harder than Photoshop, and learning CAD will be a lot more useful if you are a scratch-builder. It's just a case of the right tool for the job.

[cyclops2]

I run a piece of string around the perimeter. Divide the length by 4.

Multiply the number by itself.

So far so good.

Yes. I am VERY old.

[mclarkson]

That works pretty well if your wings are rectangular (which most wings are. )

I never meant to imply that this was the way to compute surface area; it's just a trick I thought of that I sometimes find convenient and wanted to share. A lot of people have an old version of Photoshop sitting around.

For me, it's a way to take something like this:


and quickly see that, say, with a 24" wing span, that plane would have about 147 square inches of wing surface. With a 48" wing span, the wings will weigh just shy of 4 ounces if I make them out of Dollar Tree foam with the paper on, etc. etc.