mlb - here's the Torque Horsepower answer -math and all- much more
10-05-1999, 07:30 AM
#1
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mlb - here's the Torque Horsepower answer -math and all- much more
mlb, I'm continuing our discussion of torque vs horsepower here as a new post. Horsepower is a calculated value where as torque is a real rotationl force. On the dyno we don't measure HP, we measure torque and calculate horsepower.
But we need to understand the math before we go any farther, you probably do, but for others on the forum here goes.
Some time ago a man named Watt (of steam engine fame) observed that the the average horse could lift 550 lbs one foot in one second, thus performing work at a rate of 33,000 foot lbs per minute. He published this info, and stated that 33,000 foot pounds per minute of work was equivalent to one Horse Power, everyone else said OK. We need to measure units of force from a rotaing crankshaft which is defined as foot pounds of torque. A foot pound of torque is the twisting force necessary to suport a one pound weight on a weightless horizontal bar, one foot from the fulcrum. Now if we rotate that weight one full revoution against a one pound resistance, we have moved it a total of 6.2832 feet (Pi * a 2 foot circle), and have done 6.2832 foot pounds of work.
So Watt said 33,000 foot pounds per minute was equivalent to one horsepower. If we dived 6.3832 foot bls of work we've done into 33,000 foot lbs per minute of work,we come up with the fact that one foot lb of torque at 5252 rpm is equal to one horespower. Therefore the following formula applies for calculating HP form torque.
Horsepower = Torque * RPM / 5252
This is not debatable, it's the way it is.
It's interesting to note that below 5252 rpm any motor's torque will be higer that horsepowrer and above 5252 rpm horsepower will always be higher than torque. When you look at a graph of HP and Torque there lines always cross at 5252rpm. If you make alot of torque but it's at low rpms then you can move a small moutain. If you make alot horsepower but only at high rpm , you'll have an engine that will scream when wound up but be lethargc around town. An example of alot of torque but low HP is a water wheel. It can generate 2600 fts lbs of torque but only can reach 12 rpm for a modest 6hp. Well I think I'll stop now, and let someone else continue; there is alot more to talk about, how engines make torque what causes changes and the HP vs torque trade off. If you want to go farther with this I will be happy to participate. JIM
But we need to understand the math before we go any farther, you probably do, but for others on the forum here goes.
Some time ago a man named Watt (of steam engine fame) observed that the the average horse could lift 550 lbs one foot in one second, thus performing work at a rate of 33,000 foot lbs per minute. He published this info, and stated that 33,000 foot pounds per minute of work was equivalent to one Horse Power, everyone else said OK. We need to measure units of force from a rotaing crankshaft which is defined as foot pounds of torque. A foot pound of torque is the twisting force necessary to suport a one pound weight on a weightless horizontal bar, one foot from the fulcrum. Now if we rotate that weight one full revoution against a one pound resistance, we have moved it a total of 6.2832 feet (Pi * a 2 foot circle), and have done 6.2832 foot pounds of work.
So Watt said 33,000 foot pounds per minute was equivalent to one horsepower. If we dived 6.3832 foot bls of work we've done into 33,000 foot lbs per minute of work,we come up with the fact that one foot lb of torque at 5252 rpm is equal to one horespower. Therefore the following formula applies for calculating HP form torque.
Horsepower = Torque * RPM / 5252
This is not debatable, it's the way it is.
It's interesting to note that below 5252 rpm any motor's torque will be higer that horsepowrer and above 5252 rpm horsepower will always be higher than torque. When you look at a graph of HP and Torque there lines always cross at 5252rpm. If you make alot of torque but it's at low rpms then you can move a small moutain. If you make alot horsepower but only at high rpm , you'll have an engine that will scream when wound up but be lethargc around town. An example of alot of torque but low HP is a water wheel. It can generate 2600 fts lbs of torque but only can reach 12 rpm for a modest 6hp. Well I think I'll stop now, and let someone else continue; there is alot more to talk about, how engines make torque what causes changes and the HP vs torque trade off. If you want to go farther with this I will be happy to participate. JIM
10-05-1999, 08:56 AM
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when do you shift ?
Jim,
Good post, thanks. Now, here are is my questions from a practical point of view:
1. When do you shift for maximum accelration from a standstill to say 60 MPH ? At the RPM point where maximum torque is achieved or always at redline ?
Good post, thanks. Now, here are is my questions from a practical point of view:
1. When do you shift for maximum accelration from a standstill to say 60 MPH ? At the RPM point where maximum torque is achieved or always at redline ?
10-05-1999, 09:10 AM
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Re: when do you shift ?
There will be a point past the peak horsepower where the horsepower in one gear at the high rpm will equal the horspower in the next gear at the lower rpm. That's when you shift for maximum acceleration. The exception to this rule is if you hit redline before that point is reached. In that situation, you shift at the redline (or maybe a little past). For what it's worth, at least one manufacturer I know of tests their engines for 24 hours straight at redline without failure before they officially set where the redline really is, so I wouldn't worry too much about driving all the way up to redline.
10-05-1999, 09:58 AM
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A cars acceleration exactly matches its torque curve.... MORE
From the driver's perspective, torque RULES. Any given car (or motorcycle), in any gear, will accelerate at a rate that exactly matches it's torque curve. Another way of saying this is that a car will accelerate hardest at it's tourque peak in any gear, and will not accelerate as hard below or above that torque peak. Torque is the only thing a driver feels, and horsepower is just a sort of esoteric measurement in that context. 173 pounds of torque will accelerate yoy just as hard at 2000 rpm as 4000 rpm in the same gear, yet per the formula, horsepower is doubled. Thus horsepower isn't particularly meaningful from a driver's perspective.
In contrast to a torque curve (and the matching pushback into the seat), horsepower rises rapidly with rpm, especially when torque is also climbing. Horsepower will continue to climb, however, well past torque peak. Only when the torque curve really begins to plummet, faster than rpm is rising, will HP fall.
SO where to shift? If we could just stay with the torque peak, bit we can't; most torque curves fall off after a slow rise. Engines like the TT's or the Honda VFR750 have wide flat torque bands, when they start to fall off you want to grab a gear to keep your drive going. There is no reason to run your engine to red line if you are past your torque peak and want maximum acceleration. Of course if you are in top gear at Spa and want to 'top end' the McLaren chasing you (as if this was possible) just keep your foot in it. A car will accelerate pasts it's torque peak, just not as fast. JIM
In contrast to a torque curve (and the matching pushback into the seat), horsepower rises rapidly with rpm, especially when torque is also climbing. Horsepower will continue to climb, however, well past torque peak. Only when the torque curve really begins to plummet, faster than rpm is rising, will HP fall.
SO where to shift? If we could just stay with the torque peak, bit we can't; most torque curves fall off after a slow rise. Engines like the TT's or the Honda VFR750 have wide flat torque bands, when they start to fall off you want to grab a gear to keep your drive going. There is no reason to run your engine to red line if you are past your torque peak and want maximum acceleration. Of course if you are in top gear at Spa and want to 'top end' the McLaren chasing you (as if this was possible) just keep your foot in it. A car will accelerate pasts it's torque peak, just not as fast. JIM
10-05-1999, 10:11 AM
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minor dissagreement....
Your analysis is correct on torque vs. horsepower (my mistake in the other post), but Your shift point is still wrong.
Let me make up some numbers for simplicity:
assume peak torque of 200 at 4000 rpm.
assume shifting costs you 2000 rpm.
if 4100 rpm is still 190 ft/lb but 2100 rpm has only climbed to 170 ft/lb then you keep revving.
Eventually you get to 4300 rpm and 180 ft/lbs and dropping. If you shift now, you are at 2300 rpm, 180 ft/lbs and rising.
In this example you would shift at 4300 rpm which is PAST the torque peak. You should always shift past the torque peak until that point of equilibrium where your available torque AFTER the shift is equal to the torque BEFORE the shift. Otherwise you shift out of 200 ft/lbs and into 170 when you still would have had 190 available.
Does this make ANY sense?
Let me make up some numbers for simplicity:
assume peak torque of 200 at 4000 rpm.
assume shifting costs you 2000 rpm.
if 4100 rpm is still 190 ft/lb but 2100 rpm has only climbed to 170 ft/lb then you keep revving.
Eventually you get to 4300 rpm and 180 ft/lbs and dropping. If you shift now, you are at 2300 rpm, 180 ft/lbs and rising.
In this example you would shift at 4300 rpm which is PAST the torque peak. You should always shift past the torque peak until that point of equilibrium where your available torque AFTER the shift is equal to the torque BEFORE the shift. Otherwise you shift out of 200 ft/lbs and into 170 when you still would have had 190 available.
Does this make ANY sense?
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10-05-1999, 10:33 AM
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You make perfect sense - consider this- MORE
You are 100% correct and that is why it is so important to understand your engine's torque curve. I have not seen a dyno graph on the TT but they spec it out as 173ft lbs 1950rpm to 4700rpm. With a flat torque band like this, you don't have to worry about your gear change dropping you below 'the power band'. It would be fun to get together at the strip (after doing our own dyno graph) and see what tines we could produce using different shift points. My thinking is to shift the TT right after torque peak (4800)to get the best acceleation. This is not the answer with all cars as you pointed out.
10-05-1999, 10:52 AM
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NOW we agree! :-) (more)
If the TT's curve is wider than the rpm drop from shifting, then it should be very easy to get maximum acceleration from this car...it's simply easy for most people to get 98% out of it. That's probably why so many people are having so much fun in it!!
10-05-1999, 11:58 AM
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Don't forget the gearing >>>
I think that you know this but, you want to shift when your torque at the wheels drops to a point where shifting into higher gear gets you better acceleration (forget torque at the crank for a minute, don't forget the essential torque multiplication to the wheels that is responsible for allowing you such quick acceleration rates).
If you shift at 4,800 you may drop into a place where torque at the crank is better or equal to where the torque at the crank was in the previous gear, but the torque reaching the ground may still have been superior in the lower gear and you may be better off holding this gear to take further advantage of the greater multiplication to the road, giving your car better acceleration.
If the torque drop off is steep at 4,800, then shift, but if it's gradual, allowing the horsepower peak the occur MUCH later, then hold that lower gear until you reach the hp peak in that gear, then shift (which if the gears were selected properly will drop you into the meaty range of the engines torque curve).
The Mustang GT and Cobra have just about identical peak torque figures, but the Cobra engines torque trails off, whereas the GT's torque drops into non-existence. The Cobra can hold his revs past the torque peak to take advantage of the multiplication of torque to the rear wheels afforded in the lower gears, while the GT must shift. The ability to hold the lower gears longer get the Cobra better acceleration.
In the end, however, horsepower only tells you what the top speed will, and torque tells you how fast you're gonna get there... all other things being equal.
But you know this already.
-EJS
If you shift at 4,800 you may drop into a place where torque at the crank is better or equal to where the torque at the crank was in the previous gear, but the torque reaching the ground may still have been superior in the lower gear and you may be better off holding this gear to take further advantage of the greater multiplication to the road, giving your car better acceleration.
If the torque drop off is steep at 4,800, then shift, but if it's gradual, allowing the horsepower peak the occur MUCH later, then hold that lower gear until you reach the hp peak in that gear, then shift (which if the gears were selected properly will drop you into the meaty range of the engines torque curve).
The Mustang GT and Cobra have just about identical peak torque figures, but the Cobra engines torque trails off, whereas the GT's torque drops into non-existence. The Cobra can hold his revs past the torque peak to take advantage of the multiplication of torque to the rear wheels afforded in the lower gears, while the GT must shift. The ability to hold the lower gears longer get the Cobra better acceleration.
In the end, however, horsepower only tells you what the top speed will, and torque tells you how fast you're gonna get there... all other things being equal.
But you know this already.
-EJS