Understanding Torque

[mikeinatlanta]

Read the article and IMO it draws conclusions not fully supported by the data, but still contains relevant information in regards to shift points.

This closely relates to a motorcycle project I'm currently working. The bike is being prepped for the Texas Mile. Once the basic prep work is complete it will get a series of dyno runs.

IMO, the relevant data for acceleration is torque to the wheel. In order to determine best shift points we'll take a measure of the raw data torque output at the wheel for each gear. An overlay of that data for all gears will show very clearly which gear provided maximum torque at any given mph. Of course after first gear peak you have a continuing falling torque curve. Shift point is the point at which the falling torque in one gear is matched by the next higher gear's torque.

Basic example would be that you don't want to shift out of third if it is putting down 110 lb torque when fouth at that mph only gives 105. In this case you would hold third until the falling rate hit 105 and then shift to fourth. This method ensures that you are always in the gear that puts maximum torque to the ground. Calculating hp is irrelevant to determining best shift point with this method.

All that said, the comment about flat torque curve giving low average is absurd. I'm assuming he misspoke and meant that a flat torque curve gives a lower peak, not average.

[eschaider]

Your observation and assessment and every example you used is spot on, Mike.

You are being kind when you suggest that his comment should be interpreted as a flat torque curve gives a lower peak, not average. It simply does not. Flat is flat and if he is talking torque, essentially the same torque at all rpms is not a lower peak it is the same everywhere.

If he was implying that a flat torque curve yields lower hp this is also a canard. HP is torque x rpm divided by 5252 (HP= TQ*RPM/5252). When torque is flat increasing RPM provides a linear increase in HP exactly proportional to the increase in RPM.

What we have with this guy is someone that read a few articles (maybe even books) collected some data (not clear if it is empirical or actual) used an XL spreadsheet to make some pretty graphs and began proslytizing his own version of the physical sciences as applied to a fictional performance for a vehicle in his mind.

Like most unschooled and uninformed shotgun approaches, some of the pellets come close to the mark but most fly far afield. Same thing here. This guy missed the mark by a country mile but the story sounded good and the graphs sure seem to support his argument. This is exactly how urban legend gets started.


Ed

[Gaz64]

Originally Posted by eschaider

Your observation and assessment and every example you used is spot on, Mike.

You are being kind when you suggest that his comment should be interpreted as a flat torque curve gives a lower peak, not average. It simply does not. Flat is flat and if he is talking torque, essentially the same torque at all rpms is not a lower peak it is the same everywhere.

If he was implying that a flat torque curve yields lower hp this is also a canard. HP is torque x rpm divided by 5252 (HP= TQ*RPM/5252). When torque is flat increasing RPM provides a linear increase in HP exactly proportional to the increase in RPM.

What we have with this guy is someone that read a few articles (maybe even books) collected some data (not clear if it is empirical or actual) used an XL spreadsheet to make some pretty graphs and began proslytizing his own version of the physical sciences as applied to a fictional performance for a vehicle in his mind.

Like most unschooled and uninformed shotgun approaches, some of the pellets come close to the mark but most fly far afield. Same thing here. This guy missed the mark by a country mile but the story sounded good and the graphs sure seem to support his argument. This is exactly how urban legend gets started.


Ed

This is the best response I have read yet.

Could not have summed it up better,

Gary

[patrickt]

Originally Posted by Gaz64

This is the best response I have read yet.

Could not have summed it up better,

Gary

OK, so is this then "fake news?"

[eschaider]

The comment Gary is making is about my commentary not the original article although you can infer relative to the original.

We work hard for our dollars and do not need to be mislead into faulty thinking processes that waste those dollars on frivolous parts excursions that are initiated because of false information promoted as the real McCoy.


Ed

[patrickt]

Originally Posted by eschaider

The comment Gary is making is about my commentary not the original article although you can infer relative to the original.

We work hard for our dollars and do not need to be mislead into faulty thinking processes that waste those dollars on frivolous parts excursions that are initiated because of false information promoted as the real McCoy.


Ed

Well as busy as Tom K. is, and as knowledgeable as he is, why would he go to the trouble of posting it here, considering he posts so rarely anymore?

[olddog]

Torque is the rotational equivalent to Force, in linear motion.

Back in the stone age, Uglug was the biggest and strongest man around. A rich man was paying people to carry stones from the river to the top of a mountain, to build a stone house. Uglug pushed on a huge bolder all day, never budging it, while the smaller men carried smaller rocks up the mountain. At the end of the day, the smaller men were paid according to the rocks they moved. Uglug was furious, when the rich man wouldn't pay him. Uglug argued he was twice as big as anyone else and he had worked hard. The rich man explained that he had not accomplished anything, as the bolder was still in the same spot.

If I push on a huge bolder with all of my might, I might be able to put 200 or maybe even 300 pounds of Force on the bolder. If the bold does not move, I did no work, on the bolder. However if I push with much less force on a smaller rock and move it a long distance, I have done work. Work is Force times Distance.

W = F * D

When you factor in the time it took to move the rock that distance, you can calculate the Power require to do the Work. You can generate more Power by moving a light rock, a long distance, in a short time, verses moving a heavy rock, a short distance, over a long time.

Hp is the rotational equivalent to Work per unit of time, in linear motion.

So Torque, like force, accomplishes no work, if there is no rotation. When you pull on a wrench and the bolt does not turn, you have accomplished nothing. On the other hand, if you apply a Torque and the object rotates, you have done work, and when you factor in the time it took to rotate an angular distance, you can calculate the Power expended. Or in the case of an engine, the power generated.

So folks listen carefully here. You do not have to calculate the torque to the wheels in each gear at every rpm and graph it, to figure out which gear will give more acceleration at a given speed. If you know the Hp at every rpm (if you know the torque at every rpm then you know the Hp it is simple math) and you know what rpm you will run, in each gear, at a given speed, it is simple to calculate the Hp the engine will make, at a given speed, in each gear. Whichever gear allows the engine to make the most Hp, at that speed, is the gear that will accelerate the vehicle at the highest rate.

Maximizing Torque does not yield maximum acceleration! Maximizing Hp yields maximum acceleration! I cannot shout that loud enough. Hp is the measurement of work per unit of time. It is the the measurement that everyone is trying to figure out, but they do not understand it and ignore it!

Peak Hp always happens well past peak torque, at considerably less torque. Get your rpm at peak Torque in 4th gear, floor it and feel the acceleration. Now get your rpm at peak Torque in 4th gear again, only this time shift down to 3rd gear and floor it. Much more acceleration, right? Yep, and you accomplish it with the engine making less Torque, but more Hp. There's your proof. You've done it a thousand times.

Torque is just rotational force. If nothing moves, all the force in the world will do no work. Work moves your car from point "A" to point "B". Power is the distance per unit of time. If you want to get from point "A" to point "B" in less time, increase the Power. Hp is rotational Power. Folks they understood this in the 19th century. That is why they figured out how to calculate Hp in the first place. They wanted to compare the work a horse could do, to the work an engine could do. Here we are in the 21 century with every learning aid and google at you fingertips, and most people still do not get it.

[eschaider]

Originally Posted by patrickt

Well as busy as Tom K. is, and as knowledgeable as he is, why would he go to the trouble of posting it here, considering he posts so rarely anymore?

The only person who can answer that question, Patrickt is in fact Tom K.

If I were to hazard a guess it was because he believed it might be helpful and perhaps did not critically read the author's work.


Ed

[eschaider]

Originally Posted by olddog

Torque is the rotational equivalent to Force, in linear motion.

You are close to the mark olddog. The actual definition of torque is the cross product of the vector by which the force's application point is offset relative to the fixed suspension point (distance vector) and the force vector, which tends to produce rotational motion.

Originally Posted by olddog

... If I push on a huge bolder with all of my might, I might be able to put 200 or maybe even 300 pounds of Force on the bolder. If the bold does not move, I did no work, on the bolder. However if I push with much less force on a smaller rock and move it a long distance, I have done work. Work is Force times Distance.

W = F * D

You are correct.

A more precise definition of work is, a displacement of the point of application in the direction of the force.

However we were talking about torque and horsepower not work.

BTW the less force example on the smaller rock for a longer distance is essentially the F-1 engine model. If I take a typical 750 HP F-1 engine that operates at 18,000 rpm that engine only makes 218 ft/lbs of torque.

Now that F-1 engine's 750 HP output is really impressive but if you put that into a Cobra and put a 482" FE that only made 650 HP into another Cobra which one do you think would have the better driving experience? The difference is torque.

Originally Posted by olddog

When you factor in the time it took to move the rock that distance, you can calculate the Power require to do the Work.

Complete agreement again.

The text book definition is, power is the rate of doing work, the amount of energy transferred per unit time.

Originally Posted by olddog

You can generate more Power by moving a light rock, a long distance, in a short time, verses moving a heavy rock, a short distance, over a long time.

Not quite as much agreement here, but close. The power is not generated by moving the rock in this instance, rather it is consumed by the action of moving the rock. The distinction being the difference between generation and consumption.

Originally Posted by olddog

Hp is the rotational equivalent to Work per unit of time, in linear motion.

HP as its naming convention suggests is Power. One HP can be expressed in watts as 745.xx watts or 745.xx newton meters/ second or as we more often hear about it, as 33,000 foot pound-force/minute and it is work per unit time.

Originally Posted by olddog

So Torque, like force, accomplishes no work, if there is no rotation. When you pull on a wrench and the bolt does not turn, you have accomplished nothing. On the other hand, if you apply a Torque and the object rotates, you have done work, and when you factor in the time it took to rotate an angular distance, you can calculate the Power expended. Or in the case of an engine, the power generated.

Complete agreement.

Originally Posted by olddog

So folks listen carefully here. You do not have to calculate the torque to the wheels in each gear at every rpm and graph it, to figure out which gear will give more acceleration at a given speed. If you know the Hp at every rpm (if you know the torque at every rpm then you know the Hp it is simple math) and you know what rpm you will run, in each gear, at a given speed, it is simple to calculate the Hp the engine will make, at a given speed, in each gear. Whichever gear allows the engine to make the most Hp, at that speed, is the gear that will accelerate the vehicle at the highest rate.

Somewhat of a simplification but in general correct for n/a engines.

Where the surprise comes in, is the flat torque curve engines whether electric or supercharged. The supercharged engines will have a power curve that looks like a straight line moving upwards at a 30˚ or 45˚angle (pretty potent engine). Because the area under the power curve continues to grow as the engine speed is increased there is no obvious shift point. With these flat torque curve engines you want to shift before destructive engine speed costs you engine internals.

An interesting observation that some drivers, who are used to n/a engines, make after their first driving experience with a supercharged engine is that it never seems to stop pulling. That driver sensation is a direct result of the essentially flat torque curve that produces the essentially straight line power curve angling upward at 30˚ or 45˚.

In the case of the n/a engine (as we have all experienced) you will actually want to shift beyond not just your peak torque but also peak power to get the benefit of the most area under the power curve to accelerate the car. Again this is because you are looking to optimize the area under that power curve (not torque) that you use to apply power to the wheels.

The electric cars like Tesla have no transmission so the concept of shifting gears does not translate well for them.

Originally Posted by olddog

Maximizing Torque does not yield maximum acceleration! Maximizing Hp yields maximum acceleration! I cannot shout that loud enough. Hp is the measurement of work per unit of time. It is the the measurement that everyone is trying to figure out, but they do not understand it and ignore it!

Actually what you are looking for again is the area under the power curve not just maximum power. The maximum acceleration will be provided by choosing shift points and gear ratios that bracket the horsepower curve capturing the greatest area under the curve, gear change to gear change.

With a n/a engine the torque curve will be concave downwards. Eventually the power curve will also nose over and decline. The optimum shift point is the point at which the area under that power curve in each gear is maximized.

With a supercharged engine the torque curve will be essentially flat with an ever so slightly downwards concave curve. Production supercharged engines, like my BMW for instance, have a very pronounced termination of their flat torque curve — I suspect for warranty expense reasons. Performance supercharged engines, like the one I built for my Cobra, simply go until they break or you get scared.

The flat torque curve of the performance supercharged engine makes selecting shift points a no brainer compared to their n/a brethren.

The torque side of the story is down two more answers.

Originally Posted by olddog

Peak Hp always happens well past peak torque, at considerably less torque.

This is predominately true for n/a engines not so for performance supercharged engines.

Originally Posted by olddog

Get your rpm at peak Torque in 4th gear, floor it and feel the acceleration. Now get your rpm at peak Torque in 4th gear again, only this time shift down to 3rd gear and floor it. Much more acceleration, right? Yep, and you accomplish it with the engine making less Torque, but more Hp. There's your proof. You've done it a thousand times.

This one can be deceiving. In fact you do accelerate harder in third gear than you do in fourth but what you are forgetting is that you are using the mechanical advantage of the transmission's third gear to multiply the torque going to the rear tires. The transmission basically augments the reduced torque the engine has at higher engine speeds while allowing you to realize the benefits of the increased power available at higher engine speeds.

Lets assume we have tires that can hook up in this next example. Lets also assume our engine peaks its power at 6500 rpm. If I stage the car and leave in fourth gear the car will launch but not particularly impressively.

If I do the exact same launch but start in first gear the car will feel like a land based missile. The difference is the mechanical advantage that first gear provided increasing the torque the rear tire saw at launch.

This phenomena is exactly what plagued the Subaru WRX when it was used as a daily driver rather than a race car. Similar story, although not as pronounced for the Honda S2000 cars.

In Cobra replicas the original argument between big block and small block engines (before small blocks got big displacement) was founded in the difference of not just low speed torque but torque everywhere in the engine rpm range. Even in the big block corner the reason for the stroker cranks is the increased displacement and increased everywhere torque that makes the cars so attractive to the driver. Increased torque everywhere will always provide increased power everywhere

Originally Posted by olddog

Torque is just rotational force. If nothing moves, all the force in the world will do no work. Work moves your car from point "A" to point "B". Power is the distance per unit of time. If you want to get from point "A" to point "B" in less time, increase the Power. Hp is rotational Power. Folks they understood this in the 19th century. That is why they figured out how to calculate Hp in the first place. They wanted to compare the work a horse could do, to the work an engine could do. Here we are in the 21 century with every learning aid and google at you fingertips, and most people still do not get it.

There is absolutely no question about more power bringing more thrills but the impact of torque should never be forgotten or misunderstood. Again, just stage your car in fourth gear at the next stop light Grand Prix. The effect will not be as impressive as if you use first gear and its torque multiplication — no matter how close to your peak horsepower rpm you launch at in fourth gear.


Ed

[mikeinatlanta]

Originally Posted by olddog

Torque is the rotational equivalent to Force, in linear motion.

Back in the stone age, Uglug was the biggest and strongest man around. A rich man was paying people to carry stones from the river to the top of a mountain, to build a stone house. Uglug pushed on a huge bolder all day, never budging it, while the smaller men carried smaller rocks up the mountain. At the end of the day, the smaller men were paid according to the rocks they moved. Uglug was furious, when the rich man wouldn't pay him. Uglug argued he was twice as big as anyone else and he had worked hard. The rich man explained that he had not accomplished anything, as the bolder was still in the same spot.

If I push on a huge bolder with all of my might, I might be able to put 200 or maybe even 300 pounds of Force on the bolder. If the bold does not move, I did no work, on the bolder. However if I push with much less force on a smaller rock and move it a long distance, I have done work. Work is Force times Distance.

W = F * D

When you factor in the time it took to move the rock that distance, you can calculate the Power require to do the Work. You can generate more Power by moving a light rock, a long distance, in a short time, verses moving a heavy rock, a short distance, over a long time.

Hp is the rotational equivalent to Work per unit of time, in linear motion.

So Torque, like force, accomplishes no work, if there is no rotation. When you pull on a wrench and the bolt does not turn, you have accomplished nothing. On the other hand, if you apply a Torque and the object rotates, you have done work, and when you factor in the time it took to rotate an angular distance, you can calculate the Power expended. Or in the case of an engine, the power generated.

So folks listen carefully here. You do not have to calculate the torque to the wheels in each gear at every rpm and graph it, to figure out which gear will give more acceleration at a given speed. If you know the Hp at every rpm (if you know the torque at every rpm then you know the Hp it is simple math) and you know what rpm you will run, in each gear, at a given speed, it is simple to calculate the Hp the engine will make, at a given speed, in each gear. Whichever gear allows the engine to make the most Hp, at that speed, is the gear that will accelerate the vehicle at the highest rate.

Maximizing Torque does not yield maximum acceleration! Maximizing Hp yields maximum acceleration! I cannot shout that loud enough. Hp is the measurement of work per unit of time. It is the the measurement that everyone is trying to figure out, but they do not understand it and ignore it!

Peak Hp always happens well past peak torque, at considerably less torque. Get your rpm at peak Torque in 4th gear, floor it and feel the acceleration. Now get your rpm at peak Torque in 4th gear again, only this time shift down to 3rd gear and floor it. Much more acceleration, right? Yep, and you accomplish it with the engine making less Torque, but more Hp. There's your proof. You've done it a thousand times.

Torque is just rotational force. If nothing moves, all the force in the world will do no work. Work moves your car from point "A" to point "B". Power is the distance per unit of time. If you want to get from point "A" to point "B" in less time, increase the Power. Hp is rotational Power. Folks they understood this in the 19th century. That is why they figured out how to calculate Hp in the first place. They wanted to compare the work a horse could do, to the work an engine could do. Here we are in the 21 century with every learning aid and google at you fingertips, and most people still do not get it.

You make some good points, however, just a bit misguided in the real world.

You see, our friend Uglug is much smarter than what we give him credit for in our story meant to substantiate a theory in the village of Internet. You see, he comes from a village called Reality. When he pushes on that big rock (mostly to impress the ladies) he quickly realizes that it isn’t moving and continuing along that path will most certainly result in an embarrassing stall. No, our friend Uglug stops pushing the big rock and picks up a smaller one, however, the smaller one is just too small to make best use of his genetic advantage (torque).

Uglug does some testing and finds the perfect size rock to allow him to bring the greatest tonnage to the top of the hill (peak horsepower), but upon looking at the quarry, he sees that there are very few rocks in his perfect size, he then has to evaluate which rock size range will give him best advantage over the little fast guys. Some are a bit smaller and some a bit bigger than his best size. This spread is what we hot rodders see as the spread between transmission gears. The smaller we keep that spread (close ratio tranny) then the better we will be able to perform work, but this quarry only has a wider spread available (street tranny) so Uglug must find the optimum range, not just the single optimum size.

Back to our reality. Unless running a CVT, we spend almost 100% of our time either above or below peak hp. The torque curve both before and after peak hp. combined with transmission spread tell us the optimal shift point for best acceleration. In real testing, peak hp will be found in every gear, you may hit it just after shifting or maybe just before shifting, or maybe in the middle. It all depends on the torque curve in that area. Does torque fall off quickly after peak? Maybe builds quickly to peak and then holds. Do you hit peak hp 100rpm before the rev limiter? Only the dyno can tell us everything we need to know.

That said, yes, you can get close calculating shift points with a single gear pull and math, but simply knowing peak will never be sufficient, you must know the curve. That said, consider that the single gear/math method completely eliminates factors such as MOI of rotating parts and differing frictional losses in each gear. You are already on the dyno, why would you bother with a math approximation when all you have to do is change gears and see the facts?

EDIT: Here is the factory dyno chart for my motor (MSTR). Note how torque falls off rapidly immediately after peak hp. My speculation is that this curve will require me to shift immediately after hitting peak hp, but with such a flat curve I won't know until I test.

[Dominik]

I pressed "like" already before I even read the article.

In the 90s I had a 496 with a very flat torque curve and corresponding "low" hp.
My limitation were the tires.

No bike in the 90s could keep up from standstill to 160 mph. Not even a Duc 996 with power upgrade. A 900 cc Ninja with 160hp had NO chance. Well, it had no torque ;-)

[patrickt]

Funny how none of our professional engine builders want to even touch this thread.

[DanEC]

Best to sit this out and let the Mechanical Engineers and Physics guys exhaust themselves on this. If the tires spin and the motor pulls I'm happy.

[eschaider]

Mike, olddog and a few others seem to catch the gist of this.

If we use his dyno graph and select the data for the white and blue curves the white curve intersects the Y-axis at 100 ft/lbs of TQ at 8100 rpm. If you use the formula for HP, the HP at that point in the pull should have been 100*8100/5252 or 154 HP. When you check the HP trace it is showing 154 HP.

Torque is a proxy for engine volumetric efficiency. As engine volumetric efficiency begins to nose over with increasing rpm so to will torque — in absolute lockstep. Your transmission gears selection for acceleration (drag racing) should be chosen to straddle the peak horsepower point on the engine's power curve to capture the greatest area under the curve if you want to optimize the vehicle performance.

For a road race application you want to select gear ratios that complement the vehicle's exit speeds from the various turns on the road course in such a manner as to again capture the greatest area under the curve. Once you are exiting the turn, not in the turn, you are once again in what amounts to a drag race and it is area under the curve and torque applied to the tires that accelerate the vehicle.

Because drag racing is a different type of contest than road racing you can make some generalizations that tend to be pretty close to the mark. One is that torque essentially accelerates the car and is a primary contributor to elapsed time. The other is that quarter mile trap speed is a pretty good proxy for horsepower.

For every day drivers torque at the axle is what we are most frequently presented with and associate with performance. When you have a lazy acceleration you can crutch the car's performance by going to a taller rear gear, i.e. 3.31 to a 3.73. The taller rear axle ratio mechanically leverages the engine torque to provide more twisting force (torque) at the axle/tire for increased vehicle acceleration. The ratio change has no effect whatsoever on engine power only torque — you experience it's effects as increased acceleration or an increase in the driver seat of the pants dyno numbers.

When we get away from all the fancy words this is actually pretty simple stuff that, surprisingly most of us already have a fairly good intuitive feel for. Don't set aside / ignore your personal experience for urban legend. You will do yourself a disservice.



Ed

[olddog]

Well for once, I'm discussing with some people who understand this subject. Eschaider I appreciate most all of your points. Many were things I were thinking and just didn't want to take the time to go into. I was intending to get people who do not understand this to see a simplified example that they could understand, so yes a lot of detail was left out. I truly appreciate you filling in more detail.

The only point I think you may have missed that I was getting at, was the 3rd verses 4th gear acceleration. I set the example up so the car was going at the same speed in both cases. Yes 3rd gear gives you more torque to the wheels by the lower ratio, but the point is you do not have to calculate the torque to the wheels. At any given speed, the gear that allows the engine to make the most power is the gear that will yield the most acceleration. Precisely because power is a measure of work over time.

I have been working 70 hr weeks and just don't have the time to spend on making sure I have every technical detail stated correctly. If I was writing a book expecting to be paid, I would have put much more effort into it.

Anyways thanks for the help. It was appreciated.

[mikeinatlanta]

Originally Posted by Dominik

I pressed "like" already before I even read the article.

In the 90s I had a 496 with a very flat torque curve and corresponding "low" hp.
My limitation were the tires.

No bike in the 90s could keep up from standstill to 160 mph. Not even a Duc 996 with power upgrade. A 900 cc Ninja with 160hp had NO chance. Well, it had no torque ;-)

Lots has changed with modern bikes. A current liter class sport bike is good for about 80 lb peak torque. Looking at the graph you can see the MV4R makes that just off idle, and carries over 100 all the way to the rev limiter. BTW, it is a Katech developed pushrod V4 based largely on LS architecture. Long live the pushrod.

[olddog]

Mike,

Just a quick thought on the dyno chart. When torque drops off a cliff on top end, I would first suspect you are loosing control of your valves.

That does make determining your shift point more challenging. You may want to give up a bit of acceleration for longevity of the engine.

[mikeinatlanta]

Originally Posted by olddog

Mike,

Just a quick thought on the dyno chart. When torque drops off a cliff on top end, I would first suspect you are loosing control of your valves.

That does make determining your shift point more challenging. You may want to give up a bit of acceleration for longevity of the engine.

Agree, however, the manufacturer claims it's purely cam profile. Have to give it a look on the dyno with my own eyes and see what we have. As flat as the curve is, I can see shifting just after hitting peak hp, but we'll see.

EDIT: Bike has LS rockers, Ti valves, Ti keepers, Ti retainers, hydraulic lifters, and beehive springs. I read that the beehive springs tend to give up softly. Anyone have any experience pushing beehive springs to their limit? How do they behave at the limit?

[olddog]

There was a link to a video some years back that showed a valve spring through a dyno pull. It was all over the place and never lost control keeping the valves closed. I cannot remember what type of spring it was. If that is typical, I have no clue how they last.

[jon@harrison.ne]

As a PhD in Mechanical Engineering I can't resist commenting on this statement by Old Dog, who otherwise made a lot of correct statements. HP is simply one commonly used unit of power and has nothing to do with whether it is produced in linear or rotational motion. For example, a solid rocket engine has no rotational parts, in fact it has no moving parts of any kind, but it sure can have a lot of power, which we can express in HP, watts, Btu/min.,....