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Midterm on torque vs. acceleration

To: sol%hoosier@cs
Subject: Midterm on torque vs. acceleration
From: mit-eddie!cs.utah.edu!mjb%hoosier@EDDIE.MIT.EDU (Mark Bradakis)
Date: Fri, 9 Mar 90 00:57:28 -0700
Thiose of you who found Jim Muller's torque and horsepower text too boring
or intimidating feel free to toss this message as well.  Those of you who
managed to stick with the entire missive may have noticed the ending example.
In that Jim mentions that the Triumph Competition department, under Graham
Robson, got an 1147 cc Spitfire to do 140 mph.  Then Jim mentions a more
streetable car with a six cylinder engine, which you all know as the GT-6.

Well, to further elaborate on Jim's discussion, here's a question.  Suppose
you have a wide variety of cars from which to choose a street prepared
autocross machine.  Which of the two cars will accelerate faster, GT6 or the
Spitfire?  Which of the two cars will be a killer machine in the 5 to 45 mph
range?  Now you can guess why I just happen to have the following info
on line.


Theoretical acceleration (a = F/m) can be approximated by the equation

            Torque(r) * Gear_Ratio * 12
   G(R) =  -----------------------------
             Weight (lbs) * Tire_radius (inches)

For this example, let's say both cars are using 13" wheels with Hoosier
Autocrossers, 225/45/D13, diameter of 20.7".  The Spit runs a rear axle
ratio of 4.1, the GT6 has 3.89 screws in the back.  The gearbox values are:

       Spit   GT6

1     3.50   2.65
2     2.16   1.78
3     1.39   1.25
4     1.00   1.00

The as raced weight of the Spit would be, say, 1650 lbs, the GT6 would be
2100.  Notice that the value of G changes with the RPM of the engine.  So,
let's assume some possible values of torque:

Torque     Spitfire   GT6

2000.0      71
2500.0      78  128
3000.0      83  128
3500.0      88  128
4000.0      89  131
4500.0      86  137
5000.0      83  141
5500.0      79  138
6000.0      74  134
6500.0      67  128
7000            120

Feel free to ignore all this, and worry about more mundane things like bugs
in your teeth, oil spots in your driveway, and so on.

mjb.


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