dlevi67

I disagree, as you would expect. The analogy is not an analogy, but it is a completely true statement. The force with which the car will move forward is exactly equal to the torque at the wheel divided by the wheel radius - you are welcome to buy your own dynamometers and verify this. Given that for all practical purposes the radius is constant, torque is exactly proportional (if not scalarly identical) to force. This BTW is also true vectorially.

If you really insist, the "correct" equation in angular terms is M = Jε (or T = Iα, depending on where you come from), where M = torque, J is the moment of inertia (rotational mass) of the body, and ε is the angular acceleration.

In this particular case, the only difference between the two equations is a scalar - namely the wheel radius, and I feel entirely justified in skipping this in the name of simplicity, and to illustrate the concept using terms that are familiar to more people.

BTW your "bizarre" equation was probably P = mv, i.e. Momentum = mass x velocity, which is the first integration in time of the F=ma equation. And F=ma is really a differential equation using vectors, so it can refer to any type of force, including one that varies in intensity and/or direction, of which a circular motion is a special limit case. In any case, an accelerated motion is not generally a uniform one (unless you want to consider a particular case in which acceleration is perfectly constant). So who is giving erroneous analogies here?
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Aside: What on Earth does "TMI" stand for in this context? Too much information? Where is the "too much"? Perhaps in this post?

geokr1

I agree. Without getting into differential equations, think about this....the BMW engineers, who have nothing better to do all day than play with their dynamometers, put the automatic shift points at redline because that's where it belongs. You're paying for that expertise...so....sit back and enjoy the ride!

cobradav

Yes he and friends did discuss this and MORE in these threads.

http://forums.e60.net/index.php?showtopic=...3&hl=G-Tech ~ post 293 and up

http://forums.e60.net/index.php?showtopic=...6&hl=G-Tech ~ post 31 and up

And we certainly came to much the same conclusion that dlevi67's clear and simple explaination provided. Znod came at it from the more experimentation side with some theory thrown in for good measure. Several of us tried to validate the findings thru experimentation as well.

aybeesea

Probably not. http://www.google.co.uk/search?hl=en&client=firefox-a&rls=org.mozilla%3Aen-US%3Aofficial&hs=n7G&q=%22p+%3D+mf%22+newton%27s+laws&btnG=Search&meta=
Just nomenclature.

ABC

znod

The idea is to minimize the decrease in road torque when shifting (or maximize the increase). Check the musing out on Thread1 and Thread2. You'll have to search around a bit, but there are 4 or 5 posts on these threads applying optimal shift theory. And, optimal shift theory says that redline is not always optimal in any given gear or car. Unfortunately, the Step doesn't give us the chance to find out what is optimal experimentally. Most of my calculation suggest that redline, or close to it, is optimal for the 545i Step in all gears.

aybeesea

I see. Fair enough.

Torque represented by force. Not properly analagous then.

ABC

dlevi67

From Merriam-Webster online
Main Entry: anal?o?gy
Pronunciation: &-'na-l&-jE
Function: noun
Inflected Form(s): plural -gies
1 : inference that if two or more things agree with one another in some respects they will probably agree in others
2 a : resemblance in some particulars between things otherwise unlike : SIMILARITY b : comparison based on such resemblance

I think it's pretty clear that torque in a rotational system that transfers the rotational motion into a (roughly) rectilinear one is force... and viceversa. I'm not sure what is more analogical than this. In fact, it's proper duality, not just an "analogy". And I think I pointed out the reason for not using the "correct" rotational equation in my previous post...

BTW - Do you think pistons rotate? Or that combustion and expansion generate "torque" directly?

dlevi67

Yep. New one (for me) to add to the baggage.

fünf dreißig

You also need the engine and drivetrain RPM's. You can have a bunch of torque at a low RPM but if your wheels aren't turning fast, you are not accelerating fast. Unless you have a lower gear (higher ratio) ring and pinion, but then you loose out on top end.

heezy545i

I was actually granny-shifting a little shy of 6000rpm. Not sure how I won....