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.