Different ways to measure/calculate frontal area (A)

[MetroMPG]

This has come up in a few threads, decided to start a dedicated one.

The old trick was to photograph the car with a telephoto lens, cut the car out of the photo & weigh the cutout vs. the cutout + the rest of the photo. Using a known measurement on the car in the photo, area can be derived using the proportion of the photo's weight.

A more modern method is to take a digital photo, trace the car's outline & use a pixel-counting program to get the image vs. vehicle proportions.

The problem is, you need a very strong telephoto to make this work. 3x optical isn't enough (I already tried, and it was quite off, when comparing the known length of the front plate to the length of a wiper blade by counting pixels.)

I think a more accurate (but harder) way to do frontal area is to back the car up to a wall, then take a strong flashlight far away and point it at the car. Trace the outline of the shadow on the wall. Then photograph it and do the pixel counting.

EDIT: ideally you would use the sun at sunrise/set, but good luck finding such a wall/unobstructed sightline.

[MetroMPG]

Using a laser level has also been suggested as a way to trace the vehicle outline.

[MetroMPG]

2 points on the digital photo/pixel counting method:

1) I've already tried this, and can confirm that there's way too much distortion with a 3x optical zoom.

Solution: stick the lens of the camera against a binocular lens. I tried this, and think I can make it work. (Focus is the difficult part - I have a somewhat fuzzy image from my first attempt.)

2) Photoshop can do the pixel counting part, once you've made it a 2-colour format. In Photoshop 7.0...

> Image > Histogram

[MetroMPG]

Or make a big one of these:

[MetroMPG]

Here's a good illustration of the amount of error you'll be dealing with if you use a camera without enough optical zoom to measure frontal area:

Images resized so the width of the hood between the headlights is the same in both pics...



Left: 2x optical zoom

Right: 2x optical zoom shot through one side of a pair of binoculars from about 150 ft further away. (Sorry, don't know the power of the binocs).

If you can see the rear tires in the photo, it's a sign the zoom isn't strong enough. You can make out about 1 inch of the inside of the rear tire in the right pic, which isn't bad, considering the rear track is a total of 1 inch narrower than the fronts anyway.

If I could get a crisply focused version of the right pic, I think it'd be good enough to use the outline-and-pixel-counting method.

[MetroMPG]

HOWEVER: someone told me that you can just move waaaay back, and keep the vehicle in the center of the lens where there is much less distortion.

That's interesting - didn't know that. So I should try the binocular thing again, but don't try to fill the view right up? Go back another 150 feet and keep the car in the middle of the view? I'll have to sort out getting it to focus properly first - or it'll just be a fuzzy blob.


If I were doing the light-at-a-distance-trace-the-shadow-on-a-wall method, I'd do something like: move the light source a measured amount to keep it as perpendicular as possible to the wall where that area of the shadow is being traced:

[MetroMPG]

Here's another method:

1) position the car parallel and close to a wall
2) make a second cardboard "wall", 90 degrees to it, at least half the width of the car
3) roll the car back and forth through the cardboard wall, trimming as you go
4) photograph the results (edit - no telephoto lens required, since you're taking a pic of a flat surface) & do the pixel counting thing

eg:



Hey, I'm not saying it's practical/easy - or more fun than punching the car through a snowbank. Just an idea.

[MetroMPG]

You could also measure the cutout with a planimeter.

[MetroMPG]

I just took a pic with the 2x optical zoom from waaaaaaay back, and sure enough there's far less perspective distortion in the image than in the pic above where I filled the frame with car @ 2x.

There's still more than the binocs + 2x version, but much less than the 2x photo above (you can't see as much of the rear tires).

So... if folks have a digital camera with a lot of resolution, this may be another option: max out the optical zoom, and go waaaaay down the road before taking the pic. Then crop the resulting image.

Mine's only 2MP, so it won't really work. To get the rear tires to disappear in the image, the car is only about 50 pixels wide in the resulting image

So I will have to stick with the binoculars + camera method.

[MetroMPG]

2x optical zoom, from close up, medium & faaaar away. Look at the rear tires in each to see diminishing perspective "distortion". (Or the apparent height of the roof line.)