msauve

wRPM=Wheel RPM
eRPM=Engine RPM
wT=Wheel torque
eT=Engine torque
wHP=Wheel power (arbitrary units, simply ignoring a constant to make formulas simpler)
eHP=Engine power
GR=drivetrain gear ratio
Z=current roadspeed

Car1, 1' radius tires. Givens: wT=1000, GR1=Y
wRPM1 = Z/(2pi)
eRPM1 = wRPM1 * GR1
eT1 = wT1/GR1 = 1000/GR1
wHP1 = wRPM1 * wT1 = (Z/(2pi)) * wT1 = 1000Z/(2pi)
eHP1 = eRPM1 * eT1 = (wRPM1 * GR1) * (wT1 / GR1) = ((Z/(2pi) * GR1) * (wT1 / GR1) = ((Z/(2pi)) * wT1) = wRPM1 * wT1 = wHP1
->
wT1 = 1000
wHP1 = 1000Z/(2pi)
eT1 = 1000/Y
eHP1 = wHP1 = 1000z/(2pi)
Acceleration force = wT1/1' = 1000

Car2, 2' radius tires. Givens: wT2=1000, GR2=Y
wRPM2 = Z/(4pi)
eRPM2 = wRPM2 * GR2
eT2 = wT2/GR2
wHP2 = wRPM2 * wT2 = (Z/(4pi)) * wT2
eHP2 = eRPM2 * eT2 = (wRPM2 * GR2) * (wT2 / GR2) = ((Z/(4pi) * GR2) * (wT2 / GR2) = (Z/(4pi) * wT2) = wRPM2 * wT2 = wHP2
->
wT2 = 1000
wHP2 = 1000Z/(4pi)
eT2 = 1000/Y
eHP2 = wHP1 = 1000z/(4pi)
Acceleration force = wT2/2' = 500

Comparisons:
wT1 = wT2
wHP1 = 2wHP2 = eHP1 = 2eHP2
eT1 = eT2 = 1000/Y

You proposed changing the gear ratio of car 2, to give it more accelerating force. We'll call it car 3:
GR3 = 2 * GR2
wT3 = 2 * wT2
Acceleration force, car 3 = wT2 * 2 = 500 * 2 = 1000
They're travelling the same speed and have the same size tires, so
wRPM3 = wRPM2
->
eRPM3 = wRPM3 * GR3 = (wRPM2) * (2 * GR2) = (wRPM2 * GR2) * 2 = eRPM2 * 2
->
eRPM3 = eRPM2 * 2
eHP3 = wHP3 = wRPM3 * wT3 = wRPM2 * wT2 = eHP2

To when you doubled the acceleration force on car 3, you doubled the engine RPM and doubled the power, car 3 is now putting out twice the torque, and the same HP as car 2 and the engine is running at twice the speed of car 2's engine.

smallTTs

Bollocks - This is a great English word with many excellent uses. Technically speaking it means ********* but is typically used to describe something that is no good (that's bollocks) or that someone is talking rubbish (he's talking bollocks). Surprisingly it is also used in a positive manner to describe something that is the best, in which case you would describe it as being "the dog's bollocks". Englishmen who live in America take great delight in ordering specialised registration plates for their cars using the letters B.O.L.L.O.X. Good eh?

I'll take it that you meant "the dog's bollocks"; thank you for the compliment. I blush.

While it has been a slice of life trying to communicate with you, we don't seem to be in the same universe. The good thing is our cars don't give a sh*t what we believe about how they work; they just do their thing.

On another physics subject: what are your views on the "Planck length", the smallest fundamental length in physics? Should we fund a particle accelerator large enough to study this? It would be a big sucker, wouldn't it? Quite a bit larger than the aborted SSC.

msauve

Your apology is accepted.

smallTTs

I thought we were comparing equal vehicles with drive wheels of 1 ft and 2 ft radii with equal engine speed at a given mph. That requires the larger tired car to have more gear ratio. I thought that's what I said. ["If you doubled the final drive ratio in your example, force at the road would again be equal, and if polar moment and weight of things didn't change, both vehicles would accelerate the same."]

Doubling the gear ratio for the big tires doubles the torque at the wheels, but keeps the acceleration FORCE(your words) at the road the same (Force = torque/tire radius). Of course the hp at the wheels is the same because the larger, slower turning wheel has exactly twice the torque and exactly half the rpm.

With the SAME gear ratio, engine speed in the big tired car will be 1/2 that of the small tired car at any given road speed...obviously. Other than saying the small tired car will then accelerate faster than the big tired one, there's not much left to compare. Again acceleration FORCE = torque/wheel radius.

So what exactly is accelerating the car? the "acceleration force" which you calculated so well from torque? or, quoting you, "As I said, it is power which determines acceleration." Which is it? torque(work) or power(work/time)?

We may have confused each other somewhat. It is my wish that any of our casual readers not be confused. Certainly the cars aren't confused by our combined rhetoric.

FWIW, you remind me a lot of a fellow who posted here a few years ago. I think the chip on his shoulder fell off and he faded away. Who's to know. Enjoy your life.

smallTTs

??

msauve

"I thought we were comparing equal vehicles with drive wheels of 1 ft and 2 ft radii with equal engine speed at a given mph."

No. They could NOT be "equal vehicles" if they drove wheels at different speeds at the same engine RPM. The gearing would be different.

And it would be IMPOSSIBLE for wT2 = 2 x wT1, as the explicitly stated conditions were that they were equal.

Everything is equal except what is explicitly stated otherwise. That's SOP.

For the THIRD time, torque is NOT WORK. It is a force. A force is the potential to do work, it is not work itself. If you know any electronics, a direct analogy is that Volts (electromotive force or potential) == Torque (mechanical force), Amperes (Current) == RPM (speed), and Watts (Power) == Horsepower. Work is accelerating a car, or moving it uphill - in British units, work is measured in foot-pounds (not pounds-feet, which is torque)

AHA! That's where you're confused - ft/lbs vs lbs-ft. One is work, the other is a force (torque). Work is raising X pounds Y feet. Force is a linear force of X at the end of an arm Y feet from the center of rotation. (car mechanics often incorrectly refer to torque as ft/lbs, but physicists take care to clearly differentiate between the two) They are two ENTIRELY DIFFERENT things, despite having confusingly similar units.

...as I was saying, work is foot-pounds. In electrical terms, work is watt-hours.

NexxTT

and that can be confusing.....to us or to students (if you teach). (If you teach, perhaps that is why students aren't learning as you wish.) ;-)

msauve

It's easy to write simple explanations, if you can ignore the facts.

smallTTs

;-) :

NexxTT

YOU'RE FULL OF BULL****!!!








Your own bull****.