I’m planning on teaching a high school level class on the math used in cars. Right now, my options are wide open as far as topics go. I’ll probably start with something simple like fuel economy and progress through displacement, and so on. I would like ideas on topics that I might include. I’d welcome any and all ideas.
Thank you,
Don
Math class
A driver goes around a 1mile race track. He averages 30 mph for the first lap. How fast must he go the second lap to average 60 mph for the two laps?
(This is a trick question. The answer is amusing and it starts a good lesson on rate, time, distance problems.)
There are a bunch of examples that could be used, depending on the level of the class:

calculate the relationship between vehicle speed and engine speed based on gear ratios and the diameter of the tires.

calculate the displacement of an engine based on bore, stroke, and number of cylinders.

convert engine displacement for cubic inches to liters to cc’s

convert torque values from ftlbs to nm

calculate the relationship between power, torque, and engine speed (rpm)

calculate the compression ratio of an engine based on bore stroke and the area left in the cylinder at top dead center

show that the motion of a piston approximates a sin/cos (and show why it is not an exact relationship).

show the relationship between displacement, velocity, acceleration, and jerk using piston motion (approximated as a sin/cos) if you are covering basic differential calculus

calculate the efficiency of a vehicle driving up a hill based on the energy content of the fuel used and the potential energy gained by climbing the hill
calculate how much energy is lost to friction for a car coasting down a hill by comparing the original potential energy with the final kinetic energy
 calculate the expected increase in tire pressure as the temperature of the air increases (use ideal gas law and assume a constant volume)
Plenty more…
… nope, not even close to 90 mph, but traveling back in time a few seconds might help. (;
Craig,
The first few were what I was starting with, some great ideas in the second half, especially if I do a Gearhead Math B. That’s the stuff I am looking for .As far as the 3090 debate, maybe Einstein was wrong and the speed of light is no big deal. 186,000 mi/sec, it’s not just a good idea, it’s the law.
Don
I did a paper for my high school physics class (I think it was physics) about math used in cars. If I can find it, I’ll have more ideas (it was about 10 years ago I wrote it… don’t even know if I still have it.)
Give them a lesson on the stoichiometric ratio and do the world a huge favor by teaching them that one cannot squeeze 85 MPG out of a car by using acetone or a hydrogen generator.
;(
You could get the class to unravel the 60 + 60 question.
How many wheel revolutions in a mile.
What determines the load a wheel will bear before the rim hits the ground.
Does a windscreen gather more or less rain if the car is moving or stopped.
Will increasing the tyre diameter improve or lessen you MPG, What about your breaking and acceleration?.
Which provides the greater acceleration, Torque or Power?
Which are better in the dry, Bald or ribbed tyres, which in teh wet. What to choose for mud & why.
Could you use brakes to move a vehicle sideways?.
Does an electric starter/wiper/wondow motor use (flow) more or less current when stalled than running. Why.
Are car electrics a car AC or DC or Both?.
Would you get a tan inside a closed (saloon) car, how about sunburn… why, why not?
Why does McPherson strut?.
What are Eddy Currents and where may may they flow in a car. (might need an older car for that one)
If you put a free floating Hydrogen baloon in a (closed and not tethered nor stuck to the floor, ceiling, etd) car or van , and accelerate rapidly, will the baloon move to the rear of the vehicle, the front of the vehicle, vertical, down, or stay as it is.
Find the Center of Gravity of a vehicle. What is it and why is it important.
Bert has a pickup with 31" tires; he wants to install 33" tires to impress the ladies. The factory rear end ratio is 3.42:1. What should his new gear ratio be to compensate for the larger tire size?
You might show them how much it costs to borrow money at 8% interest for a $20,000 loan over a 4 year period. You could vary the interest rate and the period of the loan. I used this example to show that the amount paid in interest would buy a lot of gasoline at today’s prices. Another good problem is to have them convert displacement in cubic inches to cubic centimeters or vice versa. I’ve had a lot of students that don’t understand volume measurement.
There is also the measure of electrical power in watts. Watts = volts x amperes and one can see that to maintain the same amount of power, if the voltage is increased, the amperage is decreased. I remember pondering over this in the 1950’s when we had a 12 volt system on the Buick and a 6 volt system on the Dodge. The 6 volt system had heavier gauge battery cables. Finally, you might explain the difference between resistance in series circuits R(total) = R1 + R2 + . . . + Rk and the resistance in parallel circuits 1/Rtotal = 1/R1 + 1/R2 + . . . + 1/Rk. I have often explained this by showing that you have one path through the resistances in a series circuit so that adding a resistance increases the total resistance, while in a parallel circuit, adding a resistance provides another path and decreases the total resistance.
This may be nitpicking but the watt is not a unit invented to measure electrical power, it is simply a metric unit of power.
One Newton of force X one meter per second = one Watt.
The reason that amps X volts = watts is because the watt is used to define the volt.
All electical units are metric so don’t say that the US doesn’t use the metric system.
Topics:
The relation of horse power to acceleration
Distance traveled between recognition of a hazard and application of brakes.
Distance traveled for g’s of deceleration i.e. braking distance
Kinetic energy of vehicle a various speeds.
How doubling velocity quadruples kinetic energy.
The deceleration g’s experienced in a collision.
The deceleration experienced by a belted and air bag deployed driver, a belted driver, and an unrestrainted driver.
The deceleration experienced by a car as it hits a solid object.
Get into the 60 vs 60 collision question; the 120 vs wall collision; and 60 vs wall collision.
Calculate the conversion of miles per gallon to horse power used to drive a car.
Calculate the air drag of a car going a various speeds and the power consumed in air drag.
Hope that helps
I like word problems where there is an “obvious” but wrong answer. For example: A small airplane has a cruise speed of 75 mph. The pilot heads for a destination that’s 100 miles away against a 25 mph headwind that lowers his ground speed to 50 mph, however, when he makes the return trip, that same wind now is a tailwind and his ground speed is 100 mph. What is the moving average speed for the round trip?
Throw in some useless information too. A drag racer puts a longer swingarm on his motorcycle to lengthen the wheelbase. This makes it necessary to replace his 110 link drive chain with a 130 link chain. Before the modification, the final gear ratio was 2.5:1 What is the new gear ratio?
A skilled machinist who makes miniature engines as a hobby builds an accurate 1/4 scale working model of a 327 cubic inch Chevy V8 engine. What is this engine’s displacement?
As extra points question for the honor students, What’s the gear ratio of this planetary gear set when the center gear is the input, the outer ring gear is stationary, and the planet carrier is the output.
Problems concerning scale are fun, such as the displacement of BLE’s 1/4 scale 327 cubic inch engine.
Why did the 50 foot tall woman, whose heart was healthy when she was 5 feet, die of a heart attack? (It wasn’t because she had been a race car driver.)
Math and logic: If you double the gear ratio in your car, will your car go twice as fast? Or, 1 1/2 times as fast?