Josh -
This torque misunderstanding has bugged me for a long time. I had been thinking that, over the winter dead time, I would start a flame war by publishing a rant about this whole topic (You need to keep everybody excited when you can't race!) If it would have helped you, I'm sorry I didn't get around to it.
Your analysis using the only two numbers available - HP at peak and torque (and indirectly HP) at peak sort of confirms my point (wish I'd thought of that!) I would quibble with a couple of things. You say that the transmission ratio gaps are about the same for all cars, so that the number of shifts is about the same for everyone. But then you turn around and say that the high reving (shorter-geared) car increases its revs faster and thus has to shift more. Obviously, it can't be both. The first statement is the correct one. The reason the second statement is erroneous points to the main shortcoming in you analysis. The short-geared/high reving car increases engine speed faster, but not car speed. If one car shifts at 6000 with a 3.40 final drive and another shifts at 9000rpm car using a 5.10 final drive, they'll be shifting at exactly the same car speed (trans gears and tires diameter being equal).
Similarly, when you look at the power band, you need to consider the effective rev range not as a specific number of rpm (3000 in your example), but as a percentage of your maximum rpm. In other words, because of the differences in revs at which cars operate, the high reving car needs to have a broader hp range, at least as expressed in rpm. As in the example above, if your 9000 rpm car needs a 3000 rpm rev band, the 6000 rpm car needs only a 2000 rev band because of the longer gearing.
Since your analysis is based on absolute rpm instead of a percentage of the peak, it makes the low reving cars look a little worst than they actually are. A further and related problem is that the low reving cars tend to have a greater rpm variation between hp peak and torque peak, so your slope (hp/ 500rpm) is based on a broader range of absolute rpm than for the high reving cars. And if you again account for rpm as a percentage of peak this problem is exacerbated. Bottom line - the way your analysis is done makes the low rev cars look considerably worse than they actually are. If you could account for both these factors, I suspect you'd find that the power bands are fairly similar for all the cars.
That gets me back again to my original point - horsepower is what counts. I've heard all those torque mottos before. Just remember mine - "You can multiply torque. You can't multiply horsepower." (Not that it's original with me - I think it's Paul van Valkenburgh).
This torque misunderstanding has bugged me for a long time. I had been thinking that, over the winter dead time, I would start a flame war by publishing a rant about this whole topic (You need to keep everybody excited when you can't race!) If it would have helped you, I'm sorry I didn't get around to it.
Your analysis using the only two numbers available - HP at peak and torque (and indirectly HP) at peak sort of confirms my point (wish I'd thought of that!) I would quibble with a couple of things. You say that the transmission ratio gaps are about the same for all cars, so that the number of shifts is about the same for everyone. But then you turn around and say that the high reving (shorter-geared) car increases its revs faster and thus has to shift more. Obviously, it can't be both. The first statement is the correct one. The reason the second statement is erroneous points to the main shortcoming in you analysis. The short-geared/high reving car increases engine speed faster, but not car speed. If one car shifts at 6000 with a 3.40 final drive and another shifts at 9000rpm car using a 5.10 final drive, they'll be shifting at exactly the same car speed (trans gears and tires diameter being equal).
Similarly, when you look at the power band, you need to consider the effective rev range not as a specific number of rpm (3000 in your example), but as a percentage of your maximum rpm. In other words, because of the differences in revs at which cars operate, the high reving car needs to have a broader hp range, at least as expressed in rpm. As in the example above, if your 9000 rpm car needs a 3000 rpm rev band, the 6000 rpm car needs only a 2000 rev band because of the longer gearing.
Since your analysis is based on absolute rpm instead of a percentage of the peak, it makes the low reving cars look a little worst than they actually are. A further and related problem is that the low reving cars tend to have a greater rpm variation between hp peak and torque peak, so your slope (hp/ 500rpm) is based on a broader range of absolute rpm than for the high reving cars. And if you again account for rpm as a percentage of peak this problem is exacerbated. Bottom line - the way your analysis is done makes the low rev cars look considerably worse than they actually are. If you could account for both these factors, I suspect you'd find that the power bands are fairly similar for all the cars.
That gets me back again to my original point - horsepower is what counts. I've heard all those torque mottos before. Just remember mine - "You can multiply torque. You can't multiply horsepower." (Not that it's original with me - I think it's Paul van Valkenburgh).
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