Ask Mr. Fishwrench:
When Do We Get to Crash?

Ah, crud! I deleted my e:mail folder, and I had some good ones in there. One that really stands out was an Ask Mr. Fishwrench question. It stands out because I have to do math to answer it - I hate math. Do I need to understand geometry to pick the best fishing line for today's quarry? No. Do I need to understand calculus to shave a quarter-second of my Rockingham lap time? Probably not. So, why in carnation would someone ask me a math question? Because it's a good question - that's why.

Because I don't have the e:mail anymore, I'll have to take some liberties with the question. It went something like this:

"Dear Mr. Fishwrench, My Hero and My Idol, A Man I Hope to Never Have to Face on the Track, and a Fisherman Above All Others -" (no, really, the question opened like this)

"Lets say that the Fishwrench, Hopkins Auto Body, Tim's Snowplowing Figure 8 and Hobby Stock cars are on the track at the sametime, being driven by Tim Lewis doing they're respective routes. Assuming they start at the same time, and that John Lebens is nowhere around, how many laps would it take until they collided with each other?"

Racewaytim73@..."

Dag - good question. The simple answer would be the cars would crash at the start/finish line upon taking the green flag. They start the race at the same point on the track, but in different directions. But, that's too easy. I'm sure our reader was looking for an answer more in-depth. So, being the good guy I am, here's a mathematical view of the question posed.

In order for my little brain to figure this out, I've had to make some assumptions, and take some liberties with the track size and shape. I've turned the oval into rectangle, and made assumptions that the turns on each end of the track are of equal distance, as well as the front and back straight-aways. If I would have stuck with the oval shape, but I'm sure I would have had to use Pi (¶) somewhere in my formulas, and quite frankly, I hate the concept of ¶. Twenty-two divided by seven - the problem with no solve. Years of human and super-computer calculations, and we still don't know where ¶ ends. To most, it's thought of as 3.14, but that's an absolute - ¶ is no absolute. Strung out number after number, there is still no end to ¶. That boggles the mind, and makes me uneasy. I'm pretty sure there is something dark and demonic about ¶. It probably originated in Ostrander, OH somewhere. But, I digress.

Raceway Park is the local track of Shakopee, MN. It's 1/4 mile in length, with 12 degree banked turns. Hobby Stock cars exceed speeds of 60mph, while the featured Figure-8s hover closer to 40mph. Geez - 40mph, 60mph, .25 miles...ugh. Of course, the English ruler makes math a nightmare for all whom work it. Mathematicians everywhere praise the metric system - easy to use, easy to convert, 10-base numbers. Water boils at 100 and freezes at 0 - what could be easier? Conversion to kilometers puts our quarter mile track at 4/10ths of a kilometer. Now you're probably thinking, "great, genius, now the math just got harder because of a fraction." Hardly so - 4/10ths of a kilometer easily converts into 400 meters - nice round number. Converted into metric values, Tim's Hobby Stock car goes 96.5kph, or 1,608m per minute. His Figure-8 car would run in the neighborhood of 1073m per minute. Whew - my first math problem for the day is solved, and I didn't have to use ¶.

Knowing how fast the car goes, it's important to also know the distance around the track. I've broken the track up into four parts - turns and straight-aways. From geometry, we know that the perimeter of a rectangle is equal to two times the length plus the width. Written mathematically, we get the following formula:

P=2(L+W)

The perimeter of the track is 400 meters. My challenge is to then figure out the distance of each straightaway and the distance around the turns...ugh. To make my life a little easier, I'm going to assume that the distance around a turn is half the distance of the straightaway. Thus, I get the following mathematical equation:

P=2(L+.5L) or converted, P=3L

Someone get me some ice, my head is killing me!

Knowing the perimeter of the track is 400 meters, we can now safely say the following:

400=3L

Get the three away from the L, and you get the following answer:

L=133.33, or 133 for simplicity sake. The result gives us our distance down a straightaway - 133 meters. That means the distance through a turn is 67 meters, rounded up to the nearest whole number. Let's check the equation...

400=2(133+67). Add 133 and 67, and the end result is 200. Multiply that times two, and the answer is 400. Yes, the formula worked, and at now time did I have to use ¶. I'm liking this.

Now for the tricky part. The Figure-8 car doesn't follow the same path as the Hobby Stock. Instead of using the straight-aways, the Figure-8 cars run diagonals across the track, sometimes meeting sheet metal to sheet metal in the "X". That means, another distance has to be calculated - the distance of the Figure-8 car diagonal. Enter the Pythagorean Theorem. We've just moved from Geometry 101 into Trigonometry 201. Lucky for us, I took our oval track and turned it into a rectangle with four right angles. Slap a diagonal in there, and you've got yourself two triangles, each being congruent and each being right triangles. Sorry about the techno math-geek stuff. I just had to justify my use of the Pythagorean Theorem. Everyone's heard of it, but it is not often that we get to apply it to our everyday racing lives.

A2+B2=C2, where C2 is our hypotenuse, or rather the diagonal that the Figure-8 cars drive down instead of the straight-aways. In this equation, the distance through turns one and two will be represented by A, and the distance down the straights will be B. Therefore (I love math - you get to use a lot of 'Therefores'):

1332+672=C2, and the result is 22178=C2, or 149 meters rounded to the nearest whole number. This tells me that while the Hobby Stock is running 400 meters each lap of the race, the Figure-8 is running a whopping 432 meters.

Doing some more fancy-pants type conversions, I was able to ascertain that the Hobby Stock can complete a lap in about 14.9 seconds on a really good day, assuming there is no other traffic on the track, and a constant tail-wind is blowing the car up to 60mph. The Figure-8 car can turn a lap in 24.1 seconds. Sure, I didn't really have to do a lot of math to figure this out - I could have just called Tim Lewis and asked. But, that would require the use of a phone, and I hate phones almost as much as ¶.

Now the question becomes, where will each car be on the track at any given time? Hell, I don't know. But, I can make some more assumptions to make this formula trickery I'm doing a little more believable. For simplicity, I've rounded the cars lap times to 15 seconds for the Hobby Stock and 24 seconds for the Figure-8 car. Six checkpoints have been created on each track. Their approximate times, assuming a constant speed, at each location have been calculated. At two of the six checkpoints, there is no chance of the cars colliding, as the cars are not sharing any of the track. The Hobby Stock is going down the straightaway, while the Figure-8 is heading toward the X. At two other checkpoints, referenced as turns three and four by Hobby Stock drivers, the Figure-8 car is moving in the same direction as the Hobby Stock. This means there is only one area on the track where the cars can meet in opposite directions - checkpoints one and two. For the Hobby Stock class, this would be turns one and two. Figure-8 drivers know these as turns three and four.

To determine when a crash is most likely, lap times at these locations must be calculated for each car. The Hobby Stock will make its first pass through these turns between 2.5 and 5 seconds, while the Figure-8 car won't be there until 20 seconds into a run. The table below the approximate lap time of each car passing through this area.

As you can see, the first point of impact is a mere 20 seconds into the race. The Figure-8 car is near completion of its first lap, while the Hobby Stock car is burning through its second. Things don't look much better for the Figure-8 car on lap two, as the Hobby Stock takes it head on during its 4th lap of the day. Another 5 laps tick by the for the Hobby Stock car before it finds the nasty side of a Figure-8 grill, when it exits turn three of only its fifth lap. Through a 20-lap feature, the cars manage to tangle three more times. Of course, this assumes neither car has become incapacitated and was able to maintain a constant speed throughout all these sheet-metal rubs and head-on pile-ups. In any event, neither car is going to be looking real well at the end of the day. All this and John Lebens never made it onto the track.

Through assumptions, guesses, and crooked math, we were able to determine that indeed a Hobby Stock and Figure-8 car will meet head-on at Raceway Park running their respective courses. Of course, I don't really trust my math, and I made way too many assumption to be comfortable with. For that reason, look for Tim Lewis in the #73 Hobby Stock, as he races newcomer Gene Gruber in the #18 Figure-8 car this upcoming 2003 racing season. I'll be the guy with the camera.

Math...don't try this at home.

Mr. Fishwrench