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Ok, I wanted to get a concrete answer to this question so I emailed a physics professor and here is what he said:
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Hi Alfred,
Replies inserted into the body of your text below:
----- Original Message -----
Sent: Sunday, May 09, 2004 10:19 AM
Subject: Re: Moments of inertia
| Thank you for taking the time to answer my question.
| Can I ask you a couple more questions and then I won't
| bother you again?
|
| I know that it's only by experiment that we know that
| forces obey the laws of vector addition so is the
| equation for the effective moment of inertia that you
| sent me also shown to be true only by experiment or
| can it be proven mathematically?
REPLY: The basic laws of physics are based on experiment, including vector addition and moments of inertia. I derived the formula that I sent you from these basic laws.
|
| Also, someone on a bulletin board that I'm a member of
| asked if when a car with known crankshaft horsepower
| is placed on a chassis dynamometer to measure the
| drive-wheel hp, is the hp loss through the drive-train
| a constant value or will the chassis hp measured
| always be a constant percentage of the crankshaft hp.
| I'm not a physicist or engineer so the best
| explanation that I could come up with was that if the
| car performs two back-to-back chassis dynamometer runs
| with the transmission in the same gear for each run,
| then the drive-train and chassis dyno drum system
| will have a certain moment of inertia that is the same
| for each run and if the hp is measured each time at
| the same rpm (say 5000), then the equation
|
| Angular acceleration = Power / [(moment of inertia) *
| (angular speed)]
|
| would show that increasing the crankshaft hp by a
| certain factor would increase the angular acceleration
| of the chassis dynamometer drum by the same factor
| (since the moment of inertia and speed remain constant
| for the two runs) and therefore the chassis dyno hp
| reading would always be (disregarding friction) a
| constant percentage of the crankshaft hp.
|
| Am I on the right track with this answer?
REPLY: I understand your answer and it may be correct. I would
prefer, however, to answer along the following lines. In most cases, friction is proportional to the velocity (or rotational velocity in the case of gears); e.g. wind-resistant on a moving car increases with the speed of the car. Thus, if speed of the crankshaft were unchanged when the power is increased
(e.g. starting to go up a hill, but the car is kept at constant speed
by pressing on the accelerator), then the friction should be unchanged and the "percentage of the crankshaft hp" should decrease; i.e. more efficient transfer of power.
Bob.
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