Friday, May 22, 2009

Carl 2 Long

Carl 2 Long
Or is NASCAR too short, again?

So, Carl 2 Long was found to have had an oversize engine, 358.17 cubic inches, over the allowed 358.000 as per the NASCAR rule book.
Not to be insulting but Carl Long is a back marker, something like 63rd in points the last time I checked; the 46 car wouldn’t be a threat to pull an upset win if you spotted them 17 cubic inches, much less 0.17 cubes.
It’s math time, students. First of all 0.17 above a limit of 358.000 is 0.04748 %, or less than half of one-tenth of one percent. If you weigh 180 lbs and take two quarters in change out of your pocket, you will weigh less (about 0.047 %), but it doesn’t mean you’ll suddenly be running the wheels off of Lance Armstrong in a bicycle race.
And how would you measure this difference?

The number we want is the total displacement of the pistons in the engine (the volume that is swept by the pistons moving up and down inside round tubes called cylinders), which are inside the engine block.

The idea is simple: measure the distance a piston moves, called the stroke, and multiply it by the area of the cylinder, remember that algebra thing?

However, since we measure diameter, we use

and area becomes

The area is pi times the square of the diameter of the cylinder all divided by 4; easy enough. But the level of precision required is not so easy.

A standard piece of notebook paper is approximately 0.0025” to 0.0035” thick, depending on the quality of the paper, the humidity and temperature of the room and if you’ve touched the paper. The make or break measurement for Carl 2 Long is on the order of 0.0005”, or one-fifth the thickness of one sheet of paper.

Now think of measuring out a ribbon that is to be three and a half feet long, 42,” and cutting it precisely to 42.000” in length, 41.999” is too short, 41.001” is too long. What does that look like? If you’ve measured out a length that is precisely 42.000” in length, see the arrow in the picture.

You must now cut it to precisely that length, and a line is drawn where the cut is to be made. If you cut to the left of that line, it’s too short, if you cut to the right it’s too long, you must cut right down the middle of that pencil line, the line itself is too wide to help, it is 0.0197” in width. You must measure to a level of precision that is one-sixteenth the width or thickness of this line.

In machine shops there are tools, called dial calipers, which have a precision of 0.001” (a tape measure at best has a precision of 0.0625”, too crude by a factor of 62).
Shown here we’re measuring the diameter of a piston from an RC car.

Imagine yourself to be a dutiful NASCAR inspector: does this piston have a diameter of 0.735” or 0.736”? The dial indicator is in between. If your call is 0.735” then Carl 2 Long must be renamed as Carl The Legal; and if your call is 0.736” then Carl 2 Long is a cheat and a liar. Notice the indicator doesn’t have another level of precision, so we can’t say precisely if it is 0.735” or 0.736.” The precise number is something between those two values. Now you the honest, diligent inspector, must make a judgment call.
To be really thorough, the inspector should measure each of the eight cylinder diameters and strokes (not just one and then multiply by 8). The dial in our one example seems slightly over the rule limit of 0.735”. But the next one might be slightly under, and the total of all 8 cylinder measurements would still meet the rule.
Just for laughs say that the engine which Carl 2 Long ran had a stroke length of precisely 3.250000000” allowing a piston diameter of 4.187066887” inches to meet the 358.000 cubic inch limit (never mind that this level of precision is down to counting individual molecules and there’s no way to do so).
But, just as in the example above, when you measure the piston diameter, it seems to be between 4.187” and 4.188”. Look at the dial in the picture above, if you say you’re going to “round up” and call that dimension 0.736” or, 4.188” in our example, then Carl 2 Long gets shorted 200 Large (street slang for fined $200,000). If you think the dial is slightly less than half way between the two lines and you round down to 0.735” (or 4.187” in this example), then Carl The Honest has been unfairly taken to the cleaners.

On the one-hand, NASCAR publishes a finding which purports to have found an overly large engine, but without any supporting data. What measurements were taken, by whom, using what piece of equipment? The NASCAR rule is 358.000 cubic inches but they only report 358.17 cubic inches, this alone is too crude a measure by a factor of 10. To put this in perspective it is the difference between 1/10th scale RC cars and real, full size cars.
Measurements at this level are very demanding, and now the consequences have been made very painful ($200,000 in fines and parked for 12 races), but so far the published reports don’t support the charges against Carl Long.
There are other micrometer calipers which can measure precisely down to 0.0001” but there’s no published supporting paper indicating that this was done.

In the world of technical experts who testify in liability trials, the case NASCAR has made public seems particularly weak and ill-founded at this point. Perhaps they have better data. For the sake of credibility this would be an excellent time to produce the numbers.

No comments:

Post a Comment