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      05-02-2011, 05:27 AM   #1
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Peak in gear acceleration is not quite at peak torque...

OK if you are not interested in the math and engineering subtleties of vehicle acceleration performance stop reading here. If you have participated in any of the very lively discussions and debates about hp vs. torque read on...

There have been many threads here on this forum discussing one or more of two key points about vehicle acceleration. I just wanted to point out a minor correction to one of them that many here, myself included, embraced as absolutely true. I'm not so sure why I preiously missed all of the contributing corrections. Probably because it is true for all practical purposes but ultimately just not 100% correct and accurate. Just in review those statements are:
  1. Peak acceleration at any given speed occurs at peak power.

    Read between the lines - you need to get to a gear and rpm combination such that you get as close to peak hp (obviosuly without an over rev). The thing folks typically misunderstand here is that you do not downshift for more engine torque, you downshift for more engine power which in turn means maximizing wheel torque.

  2. Peak acceleration in any given gear occurs at the rpm/speed where the engine is producing peak torque.

Much discussion has been had as to the seeming contradiction among these statements. However, they are absolutely consistent if you think them through carefully. Or make some spreadsheets...

Statement #2 is the one that needs some clarification and refinement.

When you write down the long equivalent of F=ma for a car, #2 seems somewhat obvious. The shape of the acceleration curve basically follows the shape of the engine torque curve (gearing just multiplies the torque with some scale factors). However, as written it is only strictly true for a car with lossless tires and in a vacuum. Wow talk about a useless physics problem... lossless tires and driving in a vacuum... Granted these effects are fairly minor but they do affect the results. The equation to use here is again just basically F=ma:

a ~ T - Lt - Ld

I've left out some constants (mass terms) and units to keep it simple but basically the acceleration is proportional to the engine torque minus loss terms for both tires and drag. Do note that this is in any given gear - and of course if you "get" point #1 above you will know that there is a slightly modified version of this equation for each gear - and that is exactly why you can't claim that "torque is everything" for acceleration. In each gear the speed vs. rpm curve is different and thus these "corrections" are also gear dependent. Furthermore drag varies with the square of vehicle speed. In other words statement #2 is actually closest to being entirely correct in 1st gear where speeds are low enough that tire and aero losses are very small. In 1st gear in any normal car the corrections are indeed truly small enough to ignore completely (on the order of 1%).

Just running some off the cuff real numbers in 7th gear in the E9X M-DCT the correction for the drag term alone amounts to only about 500 rpm (i.e. the true peak acceleration is about 500 rpm lower than that predicted by the simpler statement, 3000 vs. 3500 rpm). The effect of tire losses is significantly smaller as those losses are only about 1/3rd - 1/4th of the aero losses at this speed (around 80 mph). So again when thinking about acceleration performance this "rule" #2 is accurate enough to still make it very useful just not quite 100% accurate down to the finest level of detail and getting the exact true speed/rpm where you will have peak acceleration.

Statement #1 could also use a minor correction but not quite for the same reasons, i.e. not due to the power lost to tires or drag. At any given (fixed) speed the only choice becomes which gear. For cars with very linear power curves each lower gear will result in a higher engine power. Here the tire and drag power losses are constant and the drivetrain losses are never high enough at higher rpms to overcome the large extra amount of power made by a downshift. However, for more typical power curves that climb linearly, taper off, peak and then decline (think just for example 2008 LS3 Corvette) you can generally find a speed where two gears will produce the same engine power (this is the same as having drive power curves cross). Here the lower gear will obviously provide more wheel torque and thus more acceleration. Thus "rule" #1 actually does not quite fully cover this somewhat ambiguous case.

Well, hopefully some will find my Sunday night (uh Monday morning...) ramblings interesting or useful...
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Last edited by swamp2; 05-03-2011 at 02:46 AM.. Reason: Minor typo
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      05-02-2011, 06:14 AM   #2
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You should've seen the look on my face after I finished reading your post. Well the nausea and dizziness didn't help
I'm interested in this subject however, I'll wait for the English translation.
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      05-02-2011, 09:39 AM   #3
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Good post swamp!

I realize that both 1 and 2 practical have value, but as of late I have really come to embrace #1 as the one with the most eye-opening impact. One thing it really hammers home is that there are only 6 (with 6MT) or 7 (with DCT) different speeds whereby an M3 can actually accelerate with all the power potential of the S65. This of course applies to all other cars (and powered vehicles for that matter) too obviously.

Now, if we had a CVT, we could get all the power at any speed (well, any speed in the CVT's range).
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      05-02-2011, 03:20 PM   #4
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This wording doesn't sit quite right with me: "Peak acceleration at any given speed occurs at peak power."

I would say: Peak acceleration occurs in whatever gear that gets you to peak power (i.e. RPM) in the shortest amount of time.

For example, if the M3 makes peak power at 8000RPM, and your car is at a steady 8000RPM, then you're not accelerating anymore. Your speed is what ever it is, but Acceleration is 0.

Does this make sense to you guys?
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      05-02-2011, 03:27 PM   #5
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Quote:
Originally Posted by mkoesel View Post
Good post swamp!

I realize that both 1 and 2 practical have value, but as of late I have really come to embrace #1 as the one with the most eye-opening impact. One thing it really hammers home is that there are only 6 (with 6MT) or 7 (with DCT) different speeds whereby an M3 can actually accelerate with all the power potential of the S65. This of course applies to all other cars (and powered vehicles for that matter) too obviously.

Now, if we had a CVT, we could get all the power at any speed (well, any speed in the CVT's range).
Thanks.

However, the conclusion that for each gear there is one speed at which you get maximum in gear acceleration follows directly from statement #2 not #1 . The other interesting result from this is that for pretty much all cars, when in a WOT run through the gears, you are never at this "magic rpm" in each gear (except in 1st gear if starting from a low or zero speed). Again in the M3 it is about 3000-3500 rpm (again slightly speed/gear dependent). You actually do not want to ever hit peak in gear acceleration. Why - you are too busy "hanging out" at or near max power (Point #1)! Instantaneous acceleration is only important for that very small instant of the maximum push in the back feeling. Staying at or near peak power over an extended period of time (at the lowest possible gear for the longest period of time) is what leads to maximum overall acceleration.

The regular caveats apply to the important of a high peak torque for 0-60 (or 0-less than 60) times. Is surely is important here. In such contests you spend an appreciable amount of time at and near the rpm of peak torque and you actually use peak torque. Either way power/weight ratio as opposed to torque/weight (and 2WD vs 4WD) still gives you a reasonable estimate of 0-60.
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      05-02-2011, 03:34 PM   #6
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Quote:
Originally Posted by sameh View Post
You should've seen the look on my face after I finished reading your post. Well the nausea and dizziness didn't help
I'm interested in this subject however, I'll wait for the English translation.
The post is really directed to all those involved in the nitty gritty details of the power vs. torque debate in many prior threads. We all embraced #2 as pure gospel and it is only "almost" correct.

I used as few formulas as needed with all of the gory detail left out. Tried to keep it all in English rather than formulas. Just think more about both points, #1 and #2. If you understand both and why they are not inconsistent you definitely get it. "It" meaning what really matters in automobile performance, torque vs. power, instantaneous acceleration vs. overall acceleration, torque multiplication by gearing, etc. i.e. all of the key basics.
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      05-02-2011, 03:54 PM   #7
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Quote:
Originally Posted by raiste View Post
This wording doesn't sit quite right with me: "Peak acceleration at any given speed occurs at peak power."

I would say: Peak acceleration occurs in whatever gear that gets you to peak power (i.e. RPM) in the shortest amount of time.

For example, if the M3 makes peak power at 8000RPM, and your car is at a steady 8000RPM, then you're not accelerating anymore. Your speed is what ever it is, but Acceleration is 0.

Does this make sense to you guys?
This is almost the same way of saying it. However, the problem is that this does not drive home the point and the understanding of hp vs. torque. Those that argue the importance of torque generally refer to point #2 as "proof" of some sort.

Also your statement is not quite true. I think what you mean to say is "peak overall acceleration". That is a key distinction. At a fixed speed the statement I have given is correct. It is basically equivalent to simply saying one should downshift as far as possible without an over rev. However, for cars that have power curves shaped much differently than the M3, say a 2008 LS3 Corvette, things are a bit different. With such a power curve it is not linear or nearly linear up to redline like in the M3. It is linear at low to mid rpm, then drops off, peaks out and turns downward. For such a power curve you should actually use the highest rpm portion of it actually operating below peak power for the best overall acceleration. Even though your power is lower than peak power the acceleration in the lower gear is so much higher than in the higher gear you win out overall. In this way your statement does not cover such cases. And actually most cars power curves look more like an LS3 than the M3.

Statement #1 (maybe not entirely obvious) includes the idea that you are in a rolling start drag race and got fully WOT from the given fixed speed in question.

Statement #2 sort of assumes a WOT trip all the way across the tach range in one particular gear. You record the acceleration as a function of time then pick out the rpm of the peak acceleration. If instead starting from a rolling condition the engine and or turbo spin up will affect the results.
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Last edited by swamp2; 05-03-2011 at 02:32 AM..
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      05-02-2011, 03:58 PM   #8
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Hmm. The problem with statement #1 is that unless we change the gearbox, acceleration at a defined speed will stay the same, since peak acceleration will always be done in the lowest gear possible.

I would say your analysis of statement #1 is correct, however I'd like to add to the statement that it is conditional on how much traction is available. You are also correct that friction plays a role, but as speeds increase, drag becomes exponentially greater, and therefore a real factor as speeds climb.
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      05-02-2011, 09:39 PM   #9
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Swamp,
I agree with your statements, But your title conflicts with #2, correct? Assuming you are in the right gear for peak acceleration.

Title:
Peak in gear acceleration is not quite at peak torque...

#2
Peak acceleration in any given gear occurs at the rpm/speed where the engine is producing peak torque.
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      05-03-2011, 02:24 AM   #10
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Quote:
Originally Posted by e1000 View Post
Hmm. The problem with statement #1 is that unless we change the gearbox, acceleration at a defined speed will stay the same, since peak acceleration will always be done in the lowest gear possible.
That is not a problem with the statement. A limitation perhaps but fairly minor. Just abstract one level further and realize that we are talking about ANY speed. You can also imagine the rule being applied to two cars both beginning at the same speed - a basic rolling drag race. The one with that can develop the most power (well best power to weight actually) will initially out accelerate the other. Once the speeds become appreciably different you can't use the exact same rule/formula. For this you need a full dynamic time domain simulation.

Quote:
Originally Posted by e1000 View Post
I would say your analysis of statement #1 is correct, however I'd like to add to the statement that it is conditional on how much traction is available. You are also correct that friction plays a role, but as speeds increase, drag becomes exponentially greater, and therefore a real factor as speeds climb.
Absolutely, should have stated the first assumption on traction. Sort of felt it was obvious/implied but it wasn't. Also as far as friction you mean losses right? I am talking about dissipation in the tire itself from its cyclic deformation. Some of that mechanism is certainly frictional but we are not talking about tire on road friction.
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      05-03-2011, 02:26 AM   #11
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Quote:
Originally Posted by GotM View Post
Swamp,
I agree with your statements, But your title conflicts with #2, correct? Assuming you are in the right gear for peak acceleration.

Title:
Peak in gear acceleration is not quite at peak torque...

#2
Peak acceleration in any given gear occurs at the rpm/speed where the engine is producing peak torque.
Yes, the conflict was the point. The whole was to show that prior forum "gospel" (i.e. statement #2 as written) is basically correct but that tire losses and drag offer a small correction to the rpm prediction of the statement.
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      05-03-2011, 08:15 AM   #12
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Quote:
Originally Posted by swamp2 View Post
Thanks.

However, the conclusion that for each gear there is one speed at which you get maximum in gear acceleration follows directly from statement #2 not #1 .
Hmm, ok.

In any case, speed is a necessary side effect of acceleration, so when accelerating, the constraint "any given speed" will cover every speed from where you start accelerating until where you stop accelerating. My point in stating (what I suppose is obvious) is that, for me, it makes the most sense to think about power at speed and then pick the right gear to achieve the best result for your current speed. I.e. you don't do the opposite - pick a gear hoping to get to that perfect RPM to achieve the best acceleration for that particular gear.

I.e. this part:

"...you do not downshift for more engine torque, you downshift for more engine power which in turn means maximizing wheel torque."

Is what is most important.
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      05-03-2011, 10:58 AM   #13
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Quote:
Originally Posted by swamp2 View Post
Yes, the conflict was the point. The whole was to show that prior forum "gospel" (i.e. statement #2 as written) is basically correct but that tire losses and drag offer a small correction to the rpm prediction of the statement.
Made me smile.

Of course you're correct, but the "small correction" is obviously gear dependent, as you've stated, but also may be not-so-small based on the shape of the torque curve. I'd postulate that an S2000 in fifth would have a significant difference between theoretical and actual, based on the fact that the peak is so "soft", with gentle ramps before and after.

None of this actually matters, of course (hence the smile), since we're all searching for the power (and not the torque) at the drag strip or on a road course, but it's still interesting.

The other (and tiny) modifier is that as you make more torque, wheel slip increases, meaning some of the thrust is lost to heat.

OK, that's a dimple on a pimple on a flea's left nut, but hey, just thought I'd bring it up.

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      05-03-2011, 11:49 AM   #14
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Love these knowledgeable threads.
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      05-03-2011, 12:54 PM   #15
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Quote:
Originally Posted by swamp2 View Post
That is not a problem with the statement. A limitation perhaps but fairly minor. Just abstract one level further and realize that we are talking about ANY speed. You can also imagine the rule being applied to two cars both beginning at the same speed - a basic rolling drag race. The one with that can develop the most power (well best power to weight actually) will initially out accelerate the other. Once the speeds become appreciably different you can't use the exact same rule/formula. For this you need a full dynamic time domain simulation.



Absolutely, should have stated the first assumption on traction. Sort of felt it was obvious/implied but it wasn't. Also as far as friction you mean losses right? I am talking about dissipation in the tire itself from its cyclic deformation. Some of that mechanism is certainly frictional but we are not talking about tire on road friction.
Correct. If that was the intent of the statement then I agree. However, I fear people may read it and think that peak power for a set speed can be manipulated without changing gear ratios.

I think a more accurate statement would be "Peak acceleration occurs at the point where a given powerplant produces peak power (torque) while utilizing the shortest (numerically highest) possible gear ratio"

Speed is an afterthought in this discussion since it is a simple byproduct of engine rpm and gear ratios.

Quote:
Originally Posted by Wall$treet View Post
Swamp I have read your great informative posts on this topic on other threads as well and its good stuff. However I think you need to be more specific when you say the word torque. Most people just look at engine torque and neglect WHEEL torque as the force which accelerates the car. As I have mentioned before a real easy conceptual way to understand things is that engine torque and RPM's both create power from the engine. The gearing transfers that power to the wheel in multiples based on gears and that creates wheel torque to accelerate the car.

At lower RPM's, the engine torque is more important since RPM's are not high enough to create power. That is why the m3 is a bit slower off the line. At high revs it is a combo of engine torque and RPM's. Even though engine torque declines after 7k, the increasing RPM's more than make up for that and overall net power continues to increase until 8300. Then after that the car is at the limits of its camshafts and setup, thus you do nto make infinite hp with higher revs. The peak HP is when the wheels of the car are turning with the most torque force and acceleration
you were right until you got to the second paragraph.
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      05-03-2011, 04:49 PM   #16
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Quote:
Originally Posted by bruce.augenstein@comcast. View Post
Made me smile.
Good!

Quote:
Originally Posted by bruce.augenstein@comcast. View Post
Of course you're correct, but the "small correction" is obviously gear dependent, as you've stated, but also may be not-so-small based on the shape of the torque curve. I'd postulate that an S2000 in fifth would have a significant difference between theoretical and actual, based on the fact that the peak is so "soft", with gentle ramps before and after.
Run the numbers! Tire losses are probably the only hard part to get at luckily CarTest handles this.
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      05-03-2011, 04:54 PM   #17
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Quote:
Originally Posted by Wall$treet View Post
At lower RPM's, the engine torque is more important since RPM's are not high enough to create power. That is why the m3 is a bit slower off the line.
0-60 in 3.9 seconds is not exactly sluggish off the line. However, I agree in principle that peak engine torque is somewhat important in 0-60 times.

Quote:
Originally Posted by Wall$treet View Post
The peak HP is when the wheels of the car are turning with the most torque force and acceleration
Uh, no. Completely wrong. Torque is not force they differ by the radius of application (tire radius here). Also peak hp is always simply given by the dyno it is independent of gearing and vehicle speed. That is part of why it is more useful. Read points #1 and #2 again and think about them more to understand when peak torque, peak instantaneous acceleration and peak hp occur.
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      05-03-2011, 05:01 PM   #18
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Quote:
Originally Posted by e1000 View Post
Correct. If that was the intent of the statement then I agree. However, I fear people may read it and think that peak power for a set speed can be manipulated without changing gear ratios.
Correct, at a given speed, you can only change power by changing rpm and hence by changing gear.

Quote:
Originally Posted by e1000 View Post
I think a more accurate statement would be "Peak acceleration occurs at the point where a given powerplant produces peak power (torque) while utilizing the shortest (numerically highest) possible gear ratio"
But that is not correct. Peak INSTANTANEOUS acceleration in any gear is at the rpm of peak engine torque (again with corrections discussed here). You are trying to combine the statements somewhat and they can not be.

Now peak OVERALL acceleration occurs simply by maximizing power at every point in time. You can do that typically by staying in any given lower gear as long as possible.

Think about it some more. When driving aggressively (i.e. for maximum OVERALL acceleration) in an M3 you are almost always above 5000 rpm. The peak INSTANTANEOUS acceleration in any gear is way down around 3000-3500 rpm! In most sporty engines you simply never "use" peak torque nor do you hit peak instantaneous acceleration. Odd but true.
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      05-03-2011, 07:08 PM   #19
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Quote:
Originally Posted by Wall$treet View Post
Actually ya, torque is the force accelerating the wheels of a car and this is what gives it thrust. There is engine torque and whee/tire torque which is the actual force putting power to the ground. Torque simply means applied force at a vector angle different than the lever/tire in this case.

And nothing in my 2nd pararaph was incorrect. It breaks down to simply 3 inputs into dictating wheel/tire torque which accelerates the car. RPM, engine torque and gear multiplication. They are not all equal inputs but they are the 3 inputs that dictate what makes the car move and how fast. Minus drag, friction, parasitic losses etc for simplicity.
not to be a dick, but actually almost everything in your second paragraph was wrong. using the hypothetical example of a car with no driveline loss in a vacuum, peak acceleration in any gear occurs at the peak engine torque.
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      05-03-2011, 10:27 PM   #20
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Quote:
Originally Posted by swamp2 View Post
Think about it some more. When driving aggressively (i.e. for maximum OVERALL acceleration) in an M3 you are almost always above 5000 rpm. The peak INSTANTANEOUS acceleration in any gear is way down around 3000-3500 rpm! In most sporty engines you simply never "use" peak torque nor do you hit peak instantaneous acceleration. Odd but true.
The problem with this statement is that it is only true for 1st gear, and that's precisely why I added the part about acceleration being traction limited. If peak torque of the S65 truly comes at 3000rpm, it theoretically is the max instantaneous acceleration the M3 is possible of IF AND ONLY IF the tires don't break loose.... and we all know if traction control is off, they will most certainly be roasted to a pulp.

In all other gears, 3000rpm in that gear (for example 3rd) will be inferior to a higher rpm in a lower gear (2nd) simply due to the multiplication factor of the shorter gear (numerically higher) delivering a greater ammount of resultant torque to the wheels. The alternative is partial throttle acceleration, meaning the torque curve is artificially limited by the driver to match the thresholds of traction, thereby changing the point of peak power.

In the end, we are saying the same thing. I just want to make things clear so others don't get the wrong idea.

Lots of people get the relationship between HP, torque and gearing all wrong. Remember folks, torque is multiplied through the gearbox, horsepower is not.
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      05-03-2011, 10:39 PM   #21
e1000
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Quote:
Originally Posted by Wall$treet View Post
Actually ya, torque is the force accelerating the wheels of a car and this is what gives it thrust. There is engine torque and whee/tire torque which is the actual force putting power to the ground. Torque simply means applied force at a vector angle different than the lever/tire in this case.

And nothing in my 2nd pararaph was incorrect. It breaks down to simply 3 inputs into dictating wheel/tire torque which accelerates the car. RPM, engine torque and gear multiplication. They are not all equal inputs but they are the 3 inputs that dictate what makes the car move and how fast. Minus drag, friction, parasitic losses etc for simplicity.
You always do so well in your first paragraph and then follow it up with something that isn't quite there.

Wheel torque is what moves a car. PERIOD. Engine TQ x gearing = wheel torque. Whether an engine does this at 500 rpm or 5000 rpm, as long as the resultant wheel torque figure is the same, the (point) acceleration will be identical. Small detail with this is, due to gearing, the speed at which this acceleration is happening may be different.
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      05-04-2011, 02:04 AM   #22
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Quote:
Originally Posted by e1000 View Post
The problem with this statement is that it is only true for 1st gear, and that's precisely why I added the part about acceleration being traction limited. If peak torque of the S65 truly comes at 3000rpm, it theoretically is the max instantaneous acceleration the M3 is possible of IF AND ONLY IF the tires don't break loose.... and we all know if traction control is off, they will most certainly be roasted to a pulp.
Hardly. It is not just true for 1st gear. Run the calculations in a spreadsheet if you can show otherwise.

The issue of traction is an obvious exception and one that brings enough variability to the problem that there becomes no real definitive answer. However, let's discuss just a bit. Though is does depend on temperature of the tires, surface and generally the maximum friction available in the surface. If you launch carelessly or in a show boating fashion sure in 1st you can have your tires spinning well through 3000 rpm and above. On the other hand it can also be quite the opposite with a good full hookup around that rpm. Also do note that the torque curve for the M3 is VERY flat - about 90% of peak torque available from 2500 rpm all the way to about 8000.

Quote:
Originally Posted by e1000 View Post
In all other gears, 3000rpm in that gear (for example 3rd) will be inferior to a higher rpm in a lower gear (2nd) simply due to the multiplication factor of the shorter gear (numerically higher) delivering a greater ammount of resultant torque to the wheels. The alternative is partial throttle acceleration, meaning the torque curve is artificially limited by the driver to match the thresholds of traction, thereby changing the point of peak power.
What will be inferior? Not counting the corrections for aero and tire losses the statement is true. Now those corrections can be larger than I thought (see a following post) however the approximation becomes worse in higher gears not lower gears. You MUST clearly state whether you are speaking about in a given gear or at a given speed and then whether you are talking about peak values at the crank or at the wheel. Lastly you must clearly specify instantaneous or overall (perhap including overall across gears).

Quote:
Originally Posted by e1000 View Post
In the end, we are saying the same thing. I just want to make things clear so others don't get the wrong idea.
I'm not at all convinced we are saying precisely the same thing. I have chosen my words carefully and precisely and stand by them as written.

Quote:
Originally Posted by e1000 View Post
Lots of people get the relationship between HP, torque and gearing all wrong. Remember folks, torque is multiplied through the gearbox, horsepower is not.
Here we agree!

Cheers.
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