The Pit Area

Welcome to the PIT AREA! Strap on your power tools (our unique mathematical notation and the units we use) lift the hood and dive in! There are many points in this hummer to check out. Need to get your bearings, a map, take a breather, refuel or maybe you found a bolt you just can't crank? This is the place to come. The information, concepts and experiments developed in this manual will take some mental strength and stamina to fully grasp. A pitstop now and then in this Pit Area can only improve your race through it all.

Modeling Your Grand Prix Race

1. Real Answers From The Models

   Why should you bother to understand or use mathematical models of the Grand Prix race? Here are some of the answers we found by using them.

   1. What is the speed limit?
   2. What is the slowest possible time?
   3. Can a slower car win?
   4. What is the worst source of friction?
   5. Does cutting the tread help?
   6. What is the best place to put the weight?
   7. Can a Grand Prix car pop a wheelie?
   8. Can lower weight win a race?
   9. Does wheel weight matter?
   10. Are there advantages to lifting a wheel or two?
   11. What is my "scale" speed and time?



2. Answers From Experiment

   Each experiment uses a simple homemade device to demonstrate or measure important properties of your car.

   What is your car's tread friction?	A simple ramp can give you an idea of your wheels' tread friction coefficient. Use it to get performance estimates from the model.
   What is your car's axle friction?	A simple ramp can give you an idea of your car's axle friction coefficient. Use it to get performance estimates from the model.




3. Development Of The Race Model - Straight and Narrow

   Follow the step-by-step creation of the race model. See how this complex, physical activity can be captured "on paper". Understand the limitations of mathematics to express it and why computers are essential tools in science.

   1. Virtual reality Now we see but a poor reflection as in a mirror; then we shall see face to face. Now I know in part; then I shall know fully, even as I am fully known. 1 Corinthians 13:12

      Modeling creates a kind of virtual reality. Though a shadow of reality, it amplifies your ability to understand what is going on and how to turn it to your advantage.

   2. Brothers, think of what you were when you were called. Not many of you were wise by human standards; not many were influential; not many were of noble birth. But God chose the foolish things of the world to shame the wise; God chose the weak things of the world to shame the strong. He chose the lowly things of this world and the despised things--and the things that are not--to nullify the things that are, so that no one may boast before him. 1 Corinthians 1:26-29

      Before the "invention" of the wheel, man was confounded daily by the weakest macroscopic force in the universe - gravity. But it wasn't long before he learned to "bend" the rules and have some fun with it.

      The gravity of the situation at Pisa	Check out Galileo, the first Italian racer.
      Warp space and time	See how Galileo did it centuries before Einstein even thought about it!
      Virtually a track	Discover what a mathematical track looks like.
      Static "cling"	Find out what the catch is.
      Playground slides	One way you can really relate to your car.

   
   
   
   3. Your first antigravity device: This was the appearance and structure of the wheels: They sparkled like chrysolite, and all four looked alike. Each appeared to be made like a wheel intersecting a wheel. As they moved, they would go in any one of the four directions the creatures faced; the wheels did not turn about as the creatures went. Their rims were high and awesome, and all four rims were full of eyes all around. Ezekiel 1:16-18

      Wheels? Sure! With wheels, man has reached a kind of orbital escape velocity and may never come down to earth again!

      Wheels in wheels	Round, like a circle in a spiral, like a wheel within a wheel...
      Wheels spinning	Never ending nor beginning on an ever spinning reel...
      Wheels rolling	Like a snowball down a mountain...
      Wheels and friction	Running rings around the moon...

   
   
   
   4. Reaching for the sky: As they were walking along and talking together, suddenly a chariot of fire and horses of fire appeared and separated the two of them, and Elijah went up to heaven in a whirlwind. .. And Elisha saw him no more. .. 2 Kings 2:11,12

      Does a mathematically modeled car have anything in common with the chariot that swept up Elijah?

      It's all in relationships	Your car drawing virtually comes to life.
      Follow your heart	Your car's nose is first, but its "heart" stokes the fire.
      Ride horses of fire	Add those antigrav devices to your virtual car.
      Disappear into thin air	Complete the model with energy that does just that!

   
   
   
   5. Subliminal images: "Don't be afraid," the prophet answered. "Those who are with us are more than those who are with them." And Elisha prayed, "O Lord, open his eyes so he may see." Then the Lord opened the servant's eyes, and he looked and saw the hills full of horses and chariots of fire all around Elisha. 2 Kings 6:16-17

      A few physical effects are mentioned in this section for completeness. You won't see them in the race model proper. This will open your eyes.

      Seeing is believing?	What would really happen at the sudden bend in the model track?
      Look up to the hills	How much energy does it take to correct your car's attitude?

   
   
   
   6. Summary of the race model

      All this is for your benefit, so that the grace that is reaching more and more people may cause thanksgiving to overflow to the glory of God.

      2 Corinthians 4:15

      For those on a "fast track" through this manual, here are the highlights of the mathematical model of the race.




4. Drift Means Bumping Into Things

   Some aspects of the Grand Prix race are dominated by a kind of randomness. This section explores these fascinating nooks and crannies. You'll get a feeling for how much CHANCE is involved in the Grand Prix game.

   Straight and narrow is the road to the finish line	Consider alignment before, during and after each race.
   Collisions are always full of dynamic events	Bumping into things dissipates energy that could be spent on forging ahead.
   Bouncing back has its problems	Find some elastic limits.
   A wayward car is a grief to its racer	Inelastic limits are quite different.
   Reducing Drift	How can drift be minimized.

Resources

1. How Does Your Car Measure Up?

   One step at a time. These carefully designed worksheets lead you through steps to estimate your car's characteristics and performance.

   Worksheet for car CM	Find out from design drawings where your car's center of mass is.
   Worksheet for car MI	Find your car's moment of inertia "on paper".
   Worksheet for wheel MI	Model your wheels.
   Worksheet for static friction	Find your car's static tread and axle friction coefficients. If you do this well, you may not need to measure your kinetic tread and axle friction coefficients, just use these.
   Worksheet for wheel/track friction	From a model and measurement below, find your wheels' kinetic tread friction coefficient.




2. Equipment To Build

   Here's how to make simple devices needed to measure and solve for some characteristics of your car that can't be hounded out purely on paper. There's one to help insure the best race possible too.

   Jig to space wheels in a race (racer spacer)	Use this one at the start of a race to give your car the best chance of going straight.




3. How to evaluate the model

   Symbolic analysis of the model yields many answers about the race, but for answers in feet and inches at the finish line, the model must be evaluated. Here are two ways to evaluate the model. One is for those of us who still like to use calculators, while the program is for those who want answers without the possibility of messing up a calculation. If you use the program, please read through the first link to make the measurements of your cars and track you will need for the program. Other wise, feel free to experiment with the input values keeping in mind the cautions mentioned in the user's manual.

   Run your virtual race using the Race Model	A simple guide to using the model equations.
   Simulate your race on your PC	A free DOS program that provides detailed race results on smooth transition tracks.