Thursday, May 28, 2009

Dover Monster tamed by math

Dover Monster Mile

The track that grabs cars as they exit the turns 2 and 4, and chews them up (crashing the cars against the outside wall)

In an interview Elliott Sadler described driving the Dover track as feeling like an amusement park roller coaster ride, however, he didn’t seem to realize he'd explained the car crushing feature of the Dover “Monster.”
It’s all about transitions, from the banking in the turns to the banking along the straight-aways. The track is 1 mile around (measured 30’ inside the outside wall, NASCAR rule), and has 24 degree banking in the turns (same as Atlanta and Charlotte—Lowe’s—) and 9 degrees on the straights; but as the track is only two-thirds size of the other two, the radius of the turns is smaller.
This photo (taken in the stands from Turn 1) shows how the track looks in person, along with section lines drawn into the picture to illustrate important points in the turn.

This cartoon sketch exaggerates the track but shows the idea, at section 1 the track is still banked at 24 degrees, by the time one gets to section 5, the banking is down to 9 degrees, as a result the runs uphill from the apex to line 1, over a crest (line 3) and then it is literally a down-hill run at the end of the turn exit (line 5).

In the traditional car chase scene over the hilly streets of San Francisco the hills are so steep that the cars literally are flying after they crest the hill. This is because the car drops at the acceleration of gravity, 32.2 ft per second per second; but if the road is dropping away more quickly relative to the forward speed of the car, then it goes air borne.
One can imagine in this sketch that if the car is moving slowly it stays on the ground, but at high speeds it does not. If one knows the curve of the hill it is easy to calculate the maximum speed that will still have the car on the ground, or conversely, the minimum speed to get it air borne (this is the essential calculation for stunt teams in doing ramp jumps).
Relative to the track at Dover, the crest of the hill for the drive path of most race cars occurs at about section line 3. Now if we look at the vertical profile of the drive path of the race car around the turn, it becomes more apparent what the effect is.
The car doesn’t need to actually become air borne to significantly change the handling of the car.If the car is still turning, the driver hasn’t straightened out yet, and the tires are pushing at their maximum side thrust to keep the car from sliding sideways, then unloading the car just a little bit, due to the road dropping away too quickly, results in the car seeming to “jump” sideways (and often into the wall).
The spring rates in a NASCAR Sprint race car are on the order of 300 lbs per inch, so if the racetrack drops away just 1 inch too much (the car continues on its arc as in the San Francisco car flight illustration, but the wheels follow the road) then the frictional load on the tires is decreased by 1200 lbs (300 lbs per inch of spring x 1 inch elongation of the spring x 4 wheels = 1200 lbs reduction in wheel load on the ground).

The teams which have 7 post rigs can predict the wheel loads for any given drive path on any track for which they have an accurate survey. It then requires a crew chief and driver to talk to the race car engineers to understand the relationship between drive path and ability of the car to turn at any given speed.

Consider an entire turn.

At point A the driver is at maximum speed from accelerating down the straight-away, and this is their lift point, the spot where they get off the throttle and onto the brakes to slow the car. As the car turns in, point B, the car is slowing and the driver is turning more to the left. By point D the car is at it slowest and the driver has turned the wheel to the maximum for this curve. From point A to D the car has been literally going down-hill due to the banking. At point D the car starts going up-hill, the driver starts accelerating and decreasing the turn of the steering wheel. As the race car exits the turn, through points E, F, and G, it is accelerating and going up hill, all the while decreasing the amount of turn in the steering wheel, the car is straightening out for the run down the next straight.

However, if by point G the car is still turning, and running as fast as the tires will allow without sliding, then as the car crests the hill at G and starts down towards section line 4, the wheels will partially unload and the car will suddenly slide sideways towards the wall: it actually appears to “jump” sideways.
Watch for TV views from the vantage point of looking down the straight-away towards a turn and see how often a car “jumps” sideways to get crunched by the Dover Monster.

Some drivers can learn intuitively what the drive path is that will allow them to defeat theDover Monster, but it’s a slow process; much easier and quicker if you have a good engineer.

All the big teams with 7 post rigs and race car engineers can calculate the path and show the driver where it is and at what speeds (engine RPM) they can negotiate the turn. The 7 post rig also allows the team to evaluate different set-up combinations, springs and shocks, for a given track, before they ever leave their race shop. This is in part why the well funded teams are the only ones that win, with the exception of a weather fluke as last week in Charlotte (Lowe’s).

Just having sophisticated equipment such as a 7 post rig is in itself not sufficient to win races, the crew chief must be technically astute enough to understand and utilize the information which engineers can provide; this is the essential skill of some one such as Chad Knaus (for the 48 car), Steve Letarte (for the 24 car) and Alan Gustafson (for the 5 car) in the Hendrick operations.

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.