Redline vs. gearing.
02-24-2009, 05:11 PM
#21
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Originally Posted by ace123,Feb 24 2009, 05:48 PM
If you have a 200hp@5kRPM car (car A) vs a 200hp@10kRPM car (car B), car A has twice the torque as car B. But at their peak RPM, they will accelerate exactly the same, assuming all else equal.
Physics of power and acceleration:
(assuming i did it right from memory, that is...)
P = F * V
P = power
F = force (lbs of thrust)
V = velocity
F = m*a
F = force (lbs of thrust)
m = mass of car
a = acceleration of car - this is what we are interested in
Substituting,
P = m*a*V
Rearranging,
a = P / (m*V)
So using this simple model, (instant, not average) acceleration depends only on power of the car, the mass of the car, and the current speed of the car. This ignores drag and lots of other things, but it shows the trends very clearly.
Average acceleration over a time, such as 1/4 mile or a segment of track, is going to depend on the average power of the car and the average speed of the car, assuming the mass doesn't change.
Notice that torque is not directly considered, and gearing is not either. But these are still critical--and that's because Power = Torque * Gearing, as shown above. But if you have a lot of torque, you'll generally have high average power all the way through the RPM range, so you'll also have good acceleration regardless of what RPM your car is at. That's why high TQ is desirable. Our cars, on the other hand, have to get revved up to make power.
Cliffs:
Power transferred to the ground is what accelerates the car, so power rules all as it's the product of the others. If power is the same, the RPM doesn't matter--the higher RPM car has lower TQ if they make equal power. It's like 2*3 or 3*2--they're both 6.
Physics of power and acceleration:
(assuming i did it right from memory, that is...)
P = F * V
P = power
F = force (lbs of thrust)
V = velocity
F = m*a
F = force (lbs of thrust)
m = mass of car
a = acceleration of car - this is what we are interested in
Substituting,
P = m*a*V
Rearranging,
a = P / (m*V)
So using this simple model, (instant, not average) acceleration depends only on power of the car, the mass of the car, and the current speed of the car. This ignores drag and lots of other things, but it shows the trends very clearly.
Average acceleration over a time, such as 1/4 mile or a segment of track, is going to depend on the average power of the car and the average speed of the car, assuming the mass doesn't change.
Notice that torque is not directly considered, and gearing is not either. But these are still critical--and that's because Power = Torque * Gearing, as shown above. But if you have a lot of torque, you'll generally have high average power all the way through the RPM range, so you'll also have good acceleration regardless of what RPM your car is at. That's why high TQ is desirable. Our cars, on the other hand, have to get revved up to make power.
Cliffs:
Power transferred to the ground is what accelerates the car, so power rules all as it's the product of the others. If power is the same, the RPM doesn't matter--the higher RPM car has lower TQ if they make equal power. It's like 2*3 or 3*2--they're both 6.
02-24-2009, 09:33 PM
#22
Originally Posted by tarheel91,Feb 24 2009, 08:11 PM
Formulas are correct according to physiscs. However, if this is true, why don't we just look at average peak horsepower, that is, make a graph plotting the greatest amount of horsepower vs. velocity (because obviously, you can go the same speeds in multiple gears with different amounts of power), integrate it from v1 to v2, and divide by v2-v1? That seems like it would give a much more accurate idea of a car's ability to accelerate.
On the OP's topic, by assuming the cars have the same power, you automatically assume the cars accelerate the same. My aim was to help show some of the math that ties redline/RPM/gearing and torque together through power. Maybe I should have focused more on comparing redline to gearing instead of focusing on power, but what can you do...
02-25-2009, 05:33 AM
#23
Originally Posted by TheDonEffect,Feb 24 2009, 07:29 PM
But to take it a little further, bigger engine does have more friction to overcome, but the higher revving engines I would imagine has the same issue as well due to the piston speeds, plus the greater amount of energy lost at TDC and LDC since it hits those areas more.
Piston speed + crank mass + flywheel mass = inertia problem.
Originally Posted by DavidM,Feb 24 2009, 07:31 PM
In your scenario the 5th gear will accelerate a lot slower than 1st gear simply because of it's multiplier ratio (eg. 1st is geared to ~40mph, and 5th is geared to ~130mph).
Unless your 1st and 5th gear ratios are exactly the same, the difference in acceleration between 1st gear at 5000rpm and 5th gear at 1000rpm will be massive ...it will be in a magnitude of 5x the difference.
Unless your 1st and 5th gear ratios are exactly the same, the difference in acceleration between 1st gear at 5000rpm and 5th gear at 1000rpm will be massive ...it will be in a magnitude of 5x the difference.
If the 200hp motor (~100tq at this RPM) was in first gear at 5000rpm, it would not accelerate any faster if in fifth gear at 1000rpm with 200hp (~400tq at this RPM), because it has the exact same power available
Does that make more sense? I should have stated that before. I just made those numbers up to make my point, so don't expect them to be accurate
A little explanation to help others visualize this "multiplier" factor. The cylinders in one cycle create a set amount of power at any given time, lets imagine a consistant 5tq per "explosion" cycle. At 10rpsecond, it makes 50tq in a second. At 50rpsecond it makes 250tq. So its obviously more complex than my simple statement is letting on.
Originally Posted by ace123
...
Originally Posted by tarheel91,Feb 24 2009, 10:11 PM
That seems like it would give a much more accurate idea of a car's ability to accelerate.
02-26-2009, 02:31 AM
#24
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If the 200hp motor was in first gear at 5000rpm, it would not accelerate any faster if in fifth gear at 1000rpm with 200hp, because it has the exact same power available. Does that make more sense?
If I'm not mistaken, you're saying that there is same acceleration in 1st gear at 5000rpm as in 5th gear at 1000rpm when there is exactly the same power at 1000 and 5000rpm.
If that's what you're saying, then my original post still stands as this is very wrong. The 1st gear will have exponentialy more acceleration than 5th gear in this situation/scenario.
It's no different to looking at any (real) car and comparing the acceleration in 1st gear at 5000rpm to 5th gear at 5000rpm. Afterall, at 5000rpm you always have the same power, but the acceleration will be significantly inferior in 5th gear due to the gearing ration being significantly taller in 5th.
Bottom line is that unless the 1st and 5th geat are exactly the same (ie. reach exactly the same speed), then there will be different acceleration within each gear even if the power delivered by the engine is exactly the same.
Am I still misundertanding what you're trying to say?
If I'm not mistaken, you're saying that there is same acceleration in 1st gear at 5000rpm as in 5th gear at 1000rpm when there is exactly the same power at 1000 and 5000rpm.
If that's what you're saying, then my original post still stands as this is very wrong. The 1st gear will have exponentialy more acceleration than 5th gear in this situation/scenario.
It's no different to looking at any (real) car and comparing the acceleration in 1st gear at 5000rpm to 5th gear at 5000rpm. Afterall, at 5000rpm you always have the same power, but the acceleration will be significantly inferior in 5th gear due to the gearing ration being significantly taller in 5th.
Bottom line is that unless the 1st and 5th geat are exactly the same (ie. reach exactly the same speed), then there will be different acceleration within each gear even if the power delivered by the engine is exactly the same.
Am I still misundertanding what you're trying to say?
02-26-2009, 04:22 AM
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Originally Posted by ace123,Feb 24 2009, 10:33 PM
It would give a better overall picture of average acceleration than what my post described, yes. Expanding the physics model to account for drag, gearing, shift times/delays, tire slip, and so on could further improve the model. Someone on the board did it in Matlab a while ago and got their model to correlate quite well to real results--predictions were within a few percent of what people were seeing at the drag strip.
On the OP's topic, by assuming the cars have the same power, you automatically assume the cars accelerate the same. My aim was to help show some of the math that ties redline/RPM/gearing and torque together through power. Maybe I should have focused more on comparing redline to gearing instead of focusing on power, but what can you do...
On the OP's topic, by assuming the cars have the same power, you automatically assume the cars accelerate the same. My aim was to help show some of the math that ties redline/RPM/gearing and torque together through power. Maybe I should have focused more on comparing redline to gearing instead of focusing on power, but what can you do...
Surely they've already thought of it, and it wouldn't be that difficult.
02-26-2009, 04:48 AM
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Originally Posted by DavidM,Feb 26 2009, 06:31 AM
It's no different to looking at any (real) car and comparing the acceleration in 1st gear at 5000rpm to 5th gear at 5000rpm. Afterall, at 5000rpm you always have the same power, but the acceleration will be significantly inferior in 5th gear due to the gearing ration being significantly taller in 5th.
Bottom line is that unless the 1st and 5th geat are exactly the same (ie. reach exactly the same speed), then there will be different acceleration within each gear even if the power delivered by the engine is exactly the same.
Am I still misundertanding what you're trying to say?
Bottom line is that unless the 1st and 5th geat are exactly the same (ie. reach exactly the same speed), then there will be different acceleration within each gear even if the power delivered by the engine is exactly the same.
Am I still misundertanding what you're trying to say?
You're comparing a a real car, and assuming that it's the same model car.
So yes, in real life with the same car, 1st will probably accelerate faster than 5th.
However, if an engine makes 200hp at 5000 rpm in 1st and a separate engine makes 200hp at 1000 rpm, then they should both accelerate the same. 200hp is 200hp.
Your answer may be attributed to the fact that the scenario of 200hp@5,000rpm = 200hp@1,000rpm is very rare in real life.
To make 200hp at 1,000rpm the engine would have to produce 1,050.4 lbs of torque at 1,000rpm...I know of no engine like this.
02-26-2009, 06:07 AM
#27
Originally Posted by DavidM,Feb 26 2009, 07:31 AM
Am I still misundertanding what you're trying to say?
Originally Posted by ts80,Feb 26 2009, 09:48 AM
However, if an engine makes 200hp at 5000 rpm in 1st and a separate engine makes 200hp at 1000 rpm, then they should both accelerate the same. 200hp is 200hp.
Your answer may be attributed to the fact that the scenario of 200hp@5,000rpm = 200hp@1,000rpm is very rare in real life.
To make 200hp at 1,000rpm the engine would have to produce 1,050.4 lbs of torque at 1,000rpm...I know of no engine like this.
Your answer may be attributed to the fact that the scenario of 200hp@5,000rpm = 200hp@1,000rpm is very rare in real life.
To make 200hp at 1,000rpm the engine would have to produce 1,050.4 lbs of torque at 1,000rpm...I know of no engine like this.
If you think about it that way it isn't too hard to imagine it being possible. diesel dyno I know its hard to compare diesel to petrol, but when talking about gears its all relative.
02-26-2009, 09:09 AM
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My perspective:
To maximize performance you would want the gearing that gives you the most average horsepower over the distance covered, assuming zero time for shifts.
If I were to select gears for a car and I wanted to maximize both acceleration and top speed, I would:
1. Select a top gear that allows the engine to run at horsepower peak at the speed that the car was drag limited at that amount of horsepower.
2. Select a first gear that allows good off-the-line acceleration and quick access to the horsepower curve.
3. Split the remaining ratios between the two where the lower gears have slightly larger split, since dropping down some additional RPM upon the shift won't hurt so much at a speed where inertia is the primary obstacle to overcome and drag is not high. That leaves you smaller gear splits at high speed where drag comes more into play and you want to stay as close as you can to the optimal part of the powerband.
If the width of the powerband between the low RPM engine and the high RPM engine are about the same and the power output is about the same then the acceleration should be about the same. The only real difference I see is that the lower RPM engine will probably make the car a little easier to launch. After that it shouldn't matter.
To maximize performance you would want the gearing that gives you the most average horsepower over the distance covered, assuming zero time for shifts.
If I were to select gears for a car and I wanted to maximize both acceleration and top speed, I would:
1. Select a top gear that allows the engine to run at horsepower peak at the speed that the car was drag limited at that amount of horsepower.
2. Select a first gear that allows good off-the-line acceleration and quick access to the horsepower curve.
3. Split the remaining ratios between the two where the lower gears have slightly larger split, since dropping down some additional RPM upon the shift won't hurt so much at a speed where inertia is the primary obstacle to overcome and drag is not high. That leaves you smaller gear splits at high speed where drag comes more into play and you want to stay as close as you can to the optimal part of the powerband.
If the width of the powerband between the low RPM engine and the high RPM engine are about the same and the power output is about the same then the acceleration should be about the same. The only real difference I see is that the lower RPM engine will probably make the car a little easier to launch. After that it shouldn't matter.
02-26-2009, 09:30 AM
#29
Hmm, to clarify a little more to clear up the gearing murkiness just to be sure we're on the same page:
both cars will reach the same MPH at the end of each gear, meaning in first they'll both hit, say, 25mph when they hit their optimal shifting point (assuming it's redline which is usually the case), 60mph in second, etc etc, so the higher revving engine will have shorter gearing but a higher redline, but at the end of first it'll hit the same speed as the car with the taller gearing and lower redline.
both cars will reach the same MPH at the end of each gear, meaning in first they'll both hit, say, 25mph when they hit their optimal shifting point (assuming it's redline which is usually the case), 60mph in second, etc etc, so the higher revving engine will have shorter gearing but a higher redline, but at the end of first it'll hit the same speed as the car with the taller gearing and lower redline.
02-26-2009, 07:22 PM
#30
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To restate some things already said before:
The 200hp, 1000rpm engine produces 1050.4 lb-ft of torque. If we assume that engine speed is good for 30mph, and it has average size tires, the overall gearing needs to be about 2.8:1.
The 200hp, 5000rpm engine produces 210 lb-ft of torque. If we assume that engine speed is good for 30mph, and it has average size tires, the overall gearing needs to be about 14.3:1.
1050.4 times 2.8 is 3001.
210 times 14.3 is 3001 as well.
Meaning, the two cars produce the EXACT same torque after the gearing, and therefore the exact same forward thrust, and the exact same acceleration.
Apply this to the real world, and the S2000's 9000rpm 240hp engine is rather comparable to any other 240hp engine no matter what the redline. (Obviously factors such as torque curve shape and the car's actual gearing has a big effect on this.)
The 200hp, 1000rpm engine produces 1050.4 lb-ft of torque. If we assume that engine speed is good for 30mph, and it has average size tires, the overall gearing needs to be about 2.8:1.
The 200hp, 5000rpm engine produces 210 lb-ft of torque. If we assume that engine speed is good for 30mph, and it has average size tires, the overall gearing needs to be about 14.3:1.
1050.4 times 2.8 is 3001.
210 times 14.3 is 3001 as well.
Meaning, the two cars produce the EXACT same torque after the gearing, and therefore the exact same forward thrust, and the exact same acceleration.
Apply this to the real world, and the S2000's 9000rpm 240hp engine is rather comparable to any other 240hp engine no matter what the redline. (Obviously factors such as torque curve shape and the car's actual gearing has a big effect on this.)