frontal area (A)
 

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

E.G.: in Reason with me before I destroy a classic

Skewbe says:

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Responses to Skewbe from that thread, below...

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For those of us who are not code jockeys, I actually found a program that will do this for you. I'll dig it up again if someone wants it.

Yo Metro,

I have an idear for your idear :D.

A small laser level would hug the body more tightly as long as it was square to the wall, no?

It would render it a two-person job but would definitely be more accurate than shadows. The beam offset on mine is only 3/16". The difference could be calculated if yer into it, but is insignificant enough to be ignored altogether.

2 points on the digital photo/pixel counting method:

Other ways of getting this info about your car...

Drive through a big snowbank and measure the hole. ;-)

So... Typically you can find the cD value for almost any car on the market... That hasn't been modified :p

For an unmodified car, you should be able to infer it from torque and gearing (that is, in 4th you're making X torque and in 3rd you're making X torque at a higher rpm). So you should be able to get a function of rpm and torque... Then use that function at different speeds (different rpm)... and I've lost my train of thought...

But in theory, you should be able to calculate cDA from something like that... Hrmm, you might need to know acceleration though... iono, it seems like more work for a less accurate result. But if you really want to infer it, you'll have to get a better derivation than that :p

:)

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

There's an easier way. Just move back, way back and crop. The perspective in the center 1/3 of a 50mm lens is the same as, say a 100mm lens. It's an old portrait photographers' trick (people generally look better with a 135mm lens on a 35mm camera), if you don't have the right lens with you, just move back and crop. Using a higher pixel count should get you pretty darn close.

You would have to move back the same amount using a flash light or laser pointer to get results with the same level of distortion.

Now if you had two metros, and used one as a guide for the pointer and the other as a template to be measured you could decrease the distance a great deal because the beam is not originating from a single point, the beam (if you did it accurately enough) would be square with the template.

But I think you should drive through a snowbank... and post a video. :D

An excellent illustration, and I like the use of binoculars :) More people have those than telephoto lenses certainly. Rifle scope might help too.

And another good tip there: "If you can see the rear tires in the photo, it's a sign the zoom isn't strong enough. "

That's interesting - didn't know that.

Well, only if you were planning to fix the light/laser at a single point while tracing the shadow.


That would definitely be the most fun.

Here's another method:



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

Great Cesars ghost, If the cardboard is uniform, you could measure it's area and weigh it, then trim it and weigh it again, and figure out the area removed that way, arrgh.

That could work.

You could do it with a laser, but it would drive you and your assistant nuts, especially if you don't have an assistant.

On level ground, put a blank canvass in front or behind your car. The canvass could be the drywall at the back of the garage or cardboard or anything for that matter as long as it is a flat surface and large enough.

The someone at the other end shines the laser at the edge of the cars surface, where the laser disappears, the assistant marks a dot. The laser has to stay parallel and level the whole time. The level part is easy, just mount it on a 4' level. The parallel part would be tougher, but you could draw parallel lines on the ground and use a jointed parallelogram base for the level. Just make sure it always in line with grid lines.

It would be a ton of work, but you'd get a nice profile on the canvass that could be measured pretty easily!

Well I'll be!

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.)

I am impressed by the talent displayed in these posts. My way is pretty simple-minded...

I did a google image search for a Beetle (my car). Most cars have pictures on-line that are straight-on front views. I got the height and width from car dimensions. Then, I printed the car picture onto a sheet of graph paper stuck in my printer. I counted the number of squares in the image and used horizontal and vertical scale factors to get the area. Yes, different scale corrections were needed since the picture was distorted by somebody to make it look more sexy.

The number I got: 23 square feet for my 2003 New Beetle.

So, I have a technical question-- should the area under the car be counted as part of the frontal area?

Now, why do we need the frontal area? ANS: drag coefficients are routinely published but frontal areas are not. You need CdA to calculate the drag.

Measuring CdA directly (measuring the drag) is a fairly easy thing to do. Start with the easy formula--

F = m a = CdA 1/2 rho V^2 + Crr m g

Rho is air density. You can get that with the help of the airport-- they can give you pressure and temperature and may have the density as well. In metric units, it will be about 1.2 kg /cu.meter. V is the speed of the car in meters per second: mph x .447 = meters /sec. m is the mass of the car in kilograms. 1 kg = 2.2 pounds. Crr is the tire rolling resistance coefficient, which you will find out in the calculation. And, g is the gravity constant, about 9.81

Take your car out to a level, straight section of road when there is no wind or traffic and no cops are around. Take a stopwatch or something like runners use. Go as fast as reasonable, say 80, shift to neutral and start coasting. Start the watch when the speed crosses 75, then click it at 70, 65, 60, 55, 50, ..., 25, 20, 15, well, maybe 10. Do that both directions about three times and average the numbers. Then, carefully check your speedometer and correct the gage readings to true speed. Now you have a good set of numbers.

Make a graph of speed versus time. Take your car to an accurate truck scale and find out how much it weighs. Have the scale operator do it both with you in the car and out. The difference should be close to your correct weight.

Okay, the slope of the curve is the car's acceleration, a = F /m. Draw a straight line tangent to the curve at a very high speed, say, 60, and at a very low speed, say, 20. (Don't worry about where the straight line touches the curve, just read the speed where it does.)

Now you have all the stuff you need to calculate CDA, which will be in square meters.

Can you guess a value for either CdA or Crr? CdA will be around 0.7 sq.m. Crr will usually be in the range from 0.012 to 0.007, depending on the quality and condition of your tires and their pressure.

You might plug all your numbers into the equation at the low speed tangent, with a guess for CdA = 0.7 and calculate the only remaining unknown, Crr. (The answer isn't sensitive to your guess for CdA at low speed.) Then, plug that into the high speed case and calculate the CdA. (Which isn't sensitive to Crr at high speed.) Go around one more time, plugging in the new CdA, etc., and the calculated numbers should begin to "converge," repeat themselves. And, then you have both the CdA and the Crr for your car.

The numbers for my car:

Crr = 0.0065
A = 23 sq.ft.
Cd = 0.30

I have very low rolling resistance tires and I have a drag reducer to bring down my Cd. There are pictures at www.max-mpg.com

Ernie Rogers

^^
That's similar to this - but the goal was finding cD and cRR
https://www.instructables.com/id/Meas...t-of-your-car/

Some of us don't have a stock cD :p

Nope -- that doesn't count. Interactions down there will be included as part of cD ;)

What devilry is this planimeter? You can integrate an arbitrary shape into an area with a simple skidding wheel? That's pretty cool!