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Torque, Horsepower, and RPM


110_USA
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Trying to understand a bit more about engines and the like and found myself in a conundrum.

"Why is it that the relationship between Torque, Horsepower, and RPMs isn't linear, in engine terms?"

Allow me to explain.

Torque x Engine Speed / (arbitrary number) = "Horsepower" or Force x Speed = Work

So if you increase torque at a given rpm, horsepower increases; and if you increase rpm at a given torque, horsepower increases.

So why is it that and engine spinning at say 5,000rpm might produce less torque (and or horsepower) than that very same engine spinning at say 2,500rpm?

I would think that all the bits are going twice as fast and therefore have twice as much inertia, so certainly it should produce more torque (if not twice as much); in a direct relationship to RPMs. But I'm wrong, and don't know why.

Does it have something to do with the compression ratio and combustion rate of the fuel? In which maximum torque would be where the fuel burns completely just as the piston reaches the lowest point of its stroke?

( I apologize that it isn't Land Rover/Defender oriented but I thought someone might be able to enlighten me. )

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The keyword is efficiency. The entire engine is designed for a maximum efficieny in a determined power band (cfr for example the power bands stated for after market camshafts). If you are below the optimum, power will be lower because the engine does not operate in the ideal design scenario, if you exceed the optimim, losses will become greater and reduce available power.

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Max torque ( as measured) is a function of engine design, particulary the Cam lobe profile, combustion chamber, compression ratio, and timing. However, the timing should alway be set to MBT (Minimum Best Timing ......... which really means the minimum timing to give the best torue). All torque measurements are usually made on a dyno (rolling road).

I guess in the terms of the thread then we need a little understanding here…………..this is what I recently posted in the RR section in reply to a V8 query....

HP (or BHP – Same thing) is a calculation of ‘work done’ and torque is a measured quantity that is part of the HP calculation.

HP = Torque x 2 Pi x RPM / 33000 or to put it in common engineers language,

Horsepower = Torque x rpm / 5252.

Torque = Horsepower x 5252 / rpm

(5252 is derived from 33000 / 2Pi) ….. ok, if you want to be precise then the figure is,

5252.113122032546080373164191293 :rolleyes:

Torque is the force that that is produced at the flywheel and then transmitted by various means the wheels. Just like we think of pulling or pushing forces, torque can be considered to be a twisting force.

So…….. when somebody says that their engine produces 300bhp, it sounds really impressive ……….. but maybe not, because the next question would be ‘at what RPM’ ?

When the guy says 6000 rpm , then you just smile and walk away, because you now know that your engine which produces 250bhp @ 4000 rpm is a more powerful as it produces more torque.

300 x 5252 / 6000 = 262ft/lbs

250 x 5252 / 4000 = 328ft/lbs

As a pure calculation of power that is fine, but it is not the whole story ;) . The meat of the story is the way in which the torque is produced which gives the ‘torque curve’ when plotted against rpm and the only way of doing this is with a dyno.…………..

On my 3.9 the max torque is produced at 2700 rpm, however, the torque curve shows that it is producing more torque at 1400 rpm than it is at 4500rpm.

In ‘off road’ use we need the engine to produce as much torque as possible at low rpm. If this could be replicated throughout its capable rev range then this would make a very powerful engine, however, it is generally understood that if changes are made to achieve low rpm performance, then the torque produced at higher rpm suffers. Naturally the larger the displacement then the better the torque is at the lower rpm, however, within reason a smaller displacement engine can be tuned at the lower rpm band to produce similar levels of performance as its bigger brother within a given rev range.

The key areas here are in valve timing, and inlet / exhaust design.

:)

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Ian

I wondered where the 5252 came from, now I sort of understand but where does the 33000 come from. I understand that it is the constant in the equation but it must/should have a reason? But where/how is that number derived?

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One HP is a definition of the ‘rate of doing work’…………. The definition of one mechanical horse power is the rate of doing work at 33,000 ftlb/min or 745 watts.

i.e 1hp = 33000 ftlb/min ………… you have to thank James Watt for sussing out that one.

BTW: All squaddies are rated at zero HP …………..mainly because I have never seen them do any real work. :P

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Thanks for that.

As for 0 HP squaddies. I won't argue that fact. But the word squaddie is so crude :o . Can you not find a nicer word to descibe us layabouts :P:P

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Right you two. That's enough :o:o . We are drifting O/T from the original question. You coukld always start a new thread beratng your uniformed friends. Who defend your liberty :P

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Thats a really good explanation. However, something bothered me in viewing torque/bhp graphs when I realised that bhp was calculated from torque - and that was how come the two curves didn't follow the same profile a bit closer ?

Here's a couple of samples:

http://www.dynospeed.co.uk/images/bmwk1200.GIF

http://www.dynospeed.co.uk/images/ZX10R.gif

Is it just that the BHP curve has been smoothed a bit ? I do see "Smoothing: 5" on the top-right of the graphs, but surely all the ones I've seen over the years haven't been done that way ?

Here's another (blue, torque - red BHP)

http://www.kometmotorsports.com/main/page_...dyno_graph.html

As you can see in the latter, peak torque is reached much quicker than BHP and it persists for longer. So how come peak BHP doesn't follow the same profile ?

*curious*

(In case anyone's wondering - the holes early in the power curves on the bikes are typically meant that way, to help them pass emmissions and volume levels - a power commander would "fix" these artificial holes)

edit: and another thing. Growing up on a farm, I've driven plenty of tractors over the years, and can pretty much guess the horsepower of a tractor just by looking at it. Typical here:

http://www.tractordata.com/td/td800.html

That's one my father had, but you can see that the engine produces peak 64lb/ft torque (albeit at 1400rpm) and 81hp. This really doesn't seem like a lot, but you'd expect to be able to get a hell of a lot more than that out of a 4 litre engine. How come these things are powered so low ?

OK, it might take a few more revs to get a motorbike engine to produce 64lb/ft, but it's still not a hell of a lot more. And yep, we know who would win in a pulling competition between both. What am I missing here (apart from "traction/gearing - and lots of it!") - how come a tractor isn't fitted with, for example, a rover v8 or the TDV8 from a Range Rover? Why wouldn't it be suitable given it produces more power for a few more revs ? Help me out here :)

editedit: yep, I know the tractor also has to power the PTO and hydraulics etc, but still...

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ooh we can have a good argument about this one

think about it this way; take your engine out of the car and hang it over a mine shaft, dangle a winch rope off the end of your crank nose, so that when the engine starts the rope is wound upwards.

torque is the amount of weight that the engine will just start to lift

power is the number of times it will lift that weight in a certain time. This is why things like water wheels have ginormous torque and about 1hp. They go really slowly but with a huge amount of force.

engines produce more torque at low revs because there is more time to suck a bigger air and fuel mix into the cylinder- ie the piston is going up and down in the cylinder slower. Mor fuel/air= bigger bang= more power.

At higher revs the pistons are moving quicker and the time frame allowed to suck in air and fuel is that much smaller- so for every revolution of the engine you are actually getting less power. BUT because the engine is doing way more revolutions per minute you end up doing more work. So you might get 20% less power from each revolution of the engine but the engine is revolving 6 times faster so you get more work done (ie more BHP).

The relationship between "power" (torque) and "work done"(BHP) is based on time, which is aways constant.

For those that followed BBCs reasoning above, the figure of 33,000 is mentioned. This is the figure that James Watt came up with. Watt needed to be able to rate the power output of his steam engines in order to advertise them. He decided that the most sensible unit of power to compare them to was the rate at which a horse could do work. He tested the ability of a variety of horses to lift coal using a rope and pulley and eventually settled on the definition of a "Horsepower" as 33,000 foot pounds per minute.

in actuatlity he found his horses could work at only 22,000lb/ft/min, butbeing a careful type he added 50% just in case any of his potential customers had really powerful horsies!

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er, sorry Puggers old chap, I have to challenge you on one small point there:

......... is based on time, which is aways constant.........

Definately incorrect in my experience - between the hours of 8am to 6.30pm Monday to Friday time passes at a geological rate. That is until you actually need more time to finish something. At these moments time passes at warp speed.

Outside these hours time passes at an increasingly rapid rate as you approach midnight on Sunday. :P

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Thats a really good explanation. However, something bothered me in viewing torque/bhp graphs when I realised that bhp was calculated from torque - and that was how come the two curves didn't follow the same profile a bit closer ?

Here's a couple of samples:

http://www.dynospeed.co.uk/images/bmwk1200.GIF

http://www.dynospeed.co.uk/images/ZX10R.gif

Is it just that the BHP curve has been smoothed a bit ? I do see "Smoothing: 5" on the top-right of the graphs, but surely all the ones I've seen over the years haven't been done that way ?

Here's another (blue, torque - red BHP)

http://www.kometmotorsports.com/main/page_...dyno_graph.html

As you can see in the latter, peak torque is reached much quicker than BHP and it persists for longer. So how come peak BHP doesn't follow the same profile ?

*curious*

(In case anyone's wondering - the holes early in the power curves on the bikes are typically meant that way, to help them pass emmissions and volume levels - a power commander would "fix" these artificial holes)

edit: and another thing. Growing up on a farm, I've driven plenty of tractors over the years, and can pretty much guess the horsepower of a tractor just by looking at it. Typical here:

http://www.tractordata.com/td/td800.html

That's one my father had, but you can see that the engine produces peak 64lb/ft torque (albeit at 1400rpm) and 81hp. This really doesn't seem like a lot, but you'd expect to be able to get a hell of a lot more than that out of a 4 litre engine. How come these things are powered so low ?

OK, it might take a few more revs to get a motorbike engine to produce 64lb/ft, but it's still not a hell of a lot more. And yep, we know who would win in a pulling competition between both. What am I missing here (apart from "traction/gearing - and lots of it!") - how come a tractor isn't fitted with, for example, a rover v8 or the TDV8 from a Range Rover? Why wouldn't it be suitable given it produces more power for a few more revs ? Help me out here :)

editedit: yep, I know the tractor also has to power the PTO and hydraulics etc, but still...

El Puggo pretty much has it spot on ................. more rpm = more work in a given time frame = more BHP (but that does not equal faster acceleration as that is a pure funtion of torque :rolleyes: )

As Escape mentioned earlier, torque figures are almost a measure of the engines efficiency at any given rpm. BHP will always rise steadily with rpm as it is a measure of work done, and higher rpm means you are doing more work per minute ;) ........ if you consider the mathmatics then this will always be the case until the torque begins to drop significantly. With any of the graphs posted you should be able to perform the above caculations and get the right answers on the graph...........the dyno uses eactly the same calcs to produce the BHP graph ;)

With regard to tractors............ lets not confuse gearing with torque................... gearing down is a torque mutliplier !

If you wanted a tractor that had a top speed of 100mph+ and was still able to pull a plow through a clay soil at 2mph then yes, fit a TDV8, however, if you want a reliable machine that is not stressed and will run forever then keep the mechanicals very simple and then use gearing to give you the torque required a the wheels.............. gearing down is a torque multipler, but you cant have the best of all worlds ........... whats the top speed of a tractor ?

Here is another dyno run ................ my engine this time..............measured at the wheels (to measure at the flywheel an engine dyno is preferrable).

gallery_269_31_73756.jpg

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Thanks BBC, that clears the tractor bit up.

Re your graph, how come the power curve looks smoother than the torque curve (given it's just a mathematical transformation) ? Is it just a smoothing applied to the BHP figures ?

(Sorry to go on, I'm naturally curious :))

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Thanks BBC, that clears the tractor bit up.

Re your graph, how come the power curve looks smoother than the torque curve (given it's just a mathematical transformation) ? Is it just a smoothing applied to the BHP figures ?

(Sorry to go on, I'm naturally curious :))

The smothing of the BHP curve is a function of the mathmatical equation (in terms of 'work done')......................

ie. 225ftlb @ 2700 rpm = 115.5 bhp ................................... if you have a significant drop in torque as you reved slightly higher, then the rpm will make up for more work done ........... ie a drop of say of 15ftlb over 200rpm ................... 210ftlb @ 2900 rpm = 116bhp. ............. the torque has dropped by 15 but within 200 rpm the BHP is up by just 0.5 ;)

The above goes a long way to explain why just knowing the BHP curve of your engine is of no real use................... the important facts are the actual torque produced and at what rpm................ then you can adjust your driving style to get the most from it :ph34r:

Ther classic circuit racing comment is,

Understeer is when you hit the wall with the front of the car and ... Horsepower is how fast you hit the wall, torque is how far you take the wall with you ;)

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ie. 225ftlb @ 2700 rpm = 115.5 bhp ................................... if you have a significant drop in torque as you reved slightly higher, then the rpm will make up for more work done ........... ie a drop of say of 15ftlb over 200rpm ................... 210ftlb @ 2900 rpm = 116bhp. ............. the torque has dropped by 15 but within 200 rpm the BHP is up by just 0.5 ;)

And that's the missing piece in my jigsaw. Finally, I understand this stuff - thanks for that :)

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Right you two. That's enough :o:o . We are drifting O/T from the original question. You coukld always start a new thread beratng your uniformed friends. Who defend your liberty :P

...and then watch it disappear as it gets deleted for being OT ...rather like some of the chat in this thread :rtfm:

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Some great explanations there puggers and BBC.

The tractor thing is interesting and I thought I'd add a couple of my own thoughts on it. Firstly, the tractor engine won't produce large amounts of power because it doesn't need to - given that a lot of work is done at a single speed having a wide power band isn't an issue. You just want to have peak torque low down to make life easier (no slipping clutch) and to increase the longevity of the engine (its revs that tend to kill engines). The reason for the low torque will be because the engine design is simple and robust to keep costs down, increase reliability and make it more tolerant to abuse/lack of maintenance. However, it will produce all its torque right at tickover (as opposed to a bike engine which produces it at high rpm). This would mean that you'd have to rev the nuts off a bike engine before engaging the clutch even if the gearing was right - not good.

As far as what is best IMHO you want a torque curve that's as flat and as wide as possible. This means that you need to look at all the figures to get an idea of how the engine performs. The 'perfect' engine would be one with peak torque at low rpm with a power figure at a high rpm which corresponds to a very similar torque figure. Few engines can do this with the best I know being some of the Chevy LS series engines and the Honda K20a (2l VTECi lump found in the Civic Type R). The latter is particularly impressive in supercharged trim and could be interesting in a light weight trialer.

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Thanks everyone for the explanations, it all helped out a bit.

The 'perfect' engine would be one with peak torque at low rpm with a power figure at a high rpm which corresponds to a very similar torque figure.

I've heard that electric motors provide 100% torque, 100% of the time. (or at least so near it, it might as well be)

Will be interesting when engines become generators and drive trains disappear.

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The beauty of an induction motor over a combustion engine is only realised when you use a Frequency Inverter so you can alter hundreds of parameters for example you can alter :

Torque Boost

Acceleration

De-acceleration

Speed via the change in frequency ( pole pairs/frequency*60=output speed)

PID

DC Injection Braking

I could go on for ever on this topic.

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Sorry to dredge this one up again, but this article is really simple to follow and might clear up any remaining gray areas (if anyone still has any :)): http://auto.howstuffworks.com/horsepower.htm

For a comparison between a caterpillar engine and a wild car with the same horsepower output, check this out as well:

http://science.howstuffworks.com/fpte5.htm

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