[rajeev k]

The following formula applies here.
Power = 2x3.14xNxT divided by 4500, where N is the RPM and T the torque.
Therefore RPM x Torque is a constant which means Torque drops if RPM increase for the same power.

[Shreyas Aterkar]

Harbir, Thanks a lot and hats off to you! Amazing information. Relating theory to practice is what makes this thread brilliant. Torque and BHP are two very common things that people ask and the way you have explained it is brilliant. Rated this thread 5 stars.

This was a refresher of the physics that I had learnt years back and never applied. You have put it very well. ALso as requested by noopster, would be great if you could answer the question on torque produced by diesel engines vis-a-vis the same by a similar capacity petrol engine.

[AlphaKilo]

Fantastic one Harbir.

Can you detail more on "rolling resistance" in relation with power and torque? I didn't see it anywhere in your posts/probably you left it out for the ease of understanding or for the sake of simplicity. Now that you have explained the basics, can we go deeper?

Originally Posted by noopster

why diesel engines generate more torque than petrols of the same displacement?

@noops, I believe the answer for your diesel vs. petrol question is that, diesel inherently has higher energy density than petrol = more energy released during explosion. (Harbir, correct me if I am wrong)

[gostel]

Originally Posted by noopster

why diesel engines generate more torque than petrols of the same displacement?

@noopster, may I add my guess-work? Diesels have a higher compression ratio. This means their pistons travel a greater length, which in turn means the crank has a greater radius. Now greater radius means greater torque IIRC. Just let me know if I am right.

@harbir, great explanation and great thread. OK, so I did understand your equation about force goes like (power / velocity) so if there is a cap on power then as velocity rises force drops. However, I wish to know why is there a cap on the max power? For example, if the max power happens at say 4k rpm why does higher rpm not give more power as we are expending more fuel per unit time. What are the factors for this drop? Thanks.

[Harbir]

Everyone, I have created some slides to explain the subject in some detail, attached as a PDF. It may seem complex to those not technically minded, but its as simple as a complete and thorough explanation of Power, torque, gearing, acceleration, and top speed as is possible. If you take the time to read and think through the text and absorb the charts, it should be fairly straight forward to understand.

If folks don't have the patience or the interest, its perfectly understandable, but those interested should find this a definitive lesson on the subject.

This is over 40 hours of spreadsheet and slide creation work, so I hope its appreciated.

This is of course just what I thought of and I do not claim that it is textbook perfect, so if there are physics errors, I would appreciate your bringing them to my attention, so I can correct them for my own benefit and for those of the readers.

[Harbir]

mods - These are some additional comments. I apologize for the second post in a row, but I would prefer it were not merged with the previous one because I want that to stay in the record as about ONLY the pdf attached to it.

Originally Posted by noopster

Harbir- can you explain in your trademark "Physics for Dummies" style why diesel engines generate more torque than petrols of the same displacement?

There are two parts to the answer to this question. One is relatively straight forward, one is anything but that.

The simpler part is this: There are aspects of engine design that by their nature will lead to a high torque output, regardless of the fuel used. Diesel engines, due to the necessities and/or limitations of the fuel have those characteristics and thus create large torque.

THe first, obvious one, is the compression ratio:. A high compression ratio causes high combustion chamber pressure at ignition relative to the pressure at the lowest point of the power stroke. This large pressure variation equates to how much work is done by the expanding gas on the piston (and thus by the piston to drive the load connected to the crankshaft). THe greater the work done (energy transfered) by the expanding gas, the greater the torque at the crankshaft.

Valve timing: Valve timing has an effect on cylinder filling during the intake stroke. At low RPM, you want to leave the intake valves open as long as possible. The moving column of fair has inertia, and will keep flowing into the cylinder even when the piston has slowed to a stop at the bottom of the stroke and is about to start moving upwards. This effect is so strong that many engines will leave their intake valve open even after the piston has already started moving up. Even when the piston starts moving up, the air flow continues into the cylinder just by the momentum of the flowing air, cramming that last bit of extra air in. However, as the RPM rises, the piston rises too fast and quickly overcomes the momentum of the incoming air column, and starts to push the air back out of the piston from the intake valve. This is what variable valve timing aims to bypass. Leaving the intake valve open longer at low revs, and closing them sooner at high revs (something similar happens on the exhaust valve side as well).

Since diesel fuel burns slowly, combustion proceeds slowly and diesel engine do not rev very high. At high revs, the fuel just doesn't burn fast enough to complete combustion before the piston reaches the bottom of the power stroke. Since diesels are never going to rev hard, valve timing is optimizing for low RPM running, instead of being compromised for a good performance across a wide RPM range. This enables diesel engines to always get more air crammed into the cylinders during the intake stroke than would an otherwise identical petrol engine that had its valve timing set for a broad RPM range. This extra air charge can burn more fuel, releasing more energy to drive down the piston, meaning more torque.

Intake plenum design: This is related to the point above. At low rpm, to promote maximum cylinder filling, you want the incoming air to have as much momentum as possible. You can do this by designing an intake plenum that has long air pathways. that gets more air moving towards intake valve, meaning greater inertia in the air column, and better filling. At higher rpm, long intake paths become an obstruction to high volume air flow as the friction goes up, choking the intake plenum. Again, as with valve timing, if the car doesn't have a variable intake plenum length, compromise has to be sought to make for efficient filling across a wide rev range. Since diesel engines will never rev as high as petrols, Intake plenum runner length is optimized for low speed cylinder. Better filling = more energy released = more force on the piston and higher torque.

These design features, if applied to petrols, will and does cause them to also produced large torque at slow to midrange speeds, even though they can obviously not go so high with on the compression ratios.

There are other such design decisions around optimizing low and high speed running. Since diesels don't run at high rpm, these design decisions can be tilted in favor of strong low to midrange torque.

It has been said that the greater torque is due to the greater energy density of diesel fuel. this is not correct. Diesel fuel actually has slightly less energy than petrol on a mass basis. It is a denser fuel than petrol by volum, but energy per gram of fuel is a little lower. Since fuel metering in the engine is determined by mass, not volume (even though the metering device may be measuring volume, the appropriate amount of fuel to be injected is measured by mass. Diesels appear more fuel efficient than petrols because we buy and measure it by volume not mass.), the energy content of the fuel itself cannot produce higher torque.

Now comes the difficult part. This is the part that is not straight foward and requires fairly advanced understanding of thermodynamics to figure. Diesels engines operate thermodynamically according to the Carnot cycle. This is different from petrol engines that run on the otto cycle. Understanding what they are, how they differ, how and why their energies differ takes very thorough knowledge of thermodynamics. Suffice to say, it has do with the mechanics of thermodynamic expansion, and understanding that requires knowledge of concepts such as isoentropic expansion and isothermal compression.

Suffice to say, the carnot cycle is the most efficient process for converting thermal energy into mechanical work. Given exactly the same amount of energy released by combustion, the Carnot cycle puts more of it to use than the otto cycle, leaving more of the energy captured mechanically, rather than dissipated as heat from the engine's cooling system. Greater mechanical energy shows up as higher torque.

The Carnot cycle is also the true reason for the greater efficiency of diesel engines. Diesel fuel is more dense than petrol, so while its energy per kg is about the same as petrol, its energy per litre is greater since there are more kg per litre. It is an accident of history that liquids are sold by volume, not weight. If we we bought diesel on a kilogram basis rather than on a litre basis (as we do with LPG and CNG), we would find the efficiency difference between diesel and petrol much smaller (a litte less than half of what it is). And the difference that would remain would be due to the greater efficiency of the carnot cycle in converting thermal energy to mechanical power.

So in summary you can thank the higher compression ratio, the low rpm design optimization, and the carnot cycle for the greater torque output of diesel engines.

Originally Posted by AlphaKilo

Can you detail more on "rolling resistance" in relation with power and torque? I didn't see it anywhere in your posts/probably you left it out for the ease of understanding or for the sake of simplicity. Now that you have explained the basics, can we go deeper?

It is the force opposing the motion of the car in friction and other mechanical forces. When you drive, you are having to overcome friction in the transmission, differential, wheel bearings etc all of which provide a force counteracting the force the engine creates at the contact patches. A simple way to comprehend this is to imagine a tire rolling. As it rolls, it distorts so that the potion under the wheel becomes distorted. that take effort.

See the pdf posted above for more clarity

Originally Posted by gostel

I wish to know why is there a cap on the max power? For example, if the max power happens at say 4k rpm why does higher rpm not give more power as we are expending more fuel per unit time.

Please see the pdf attached in the previous post.

[Harshal.Bhosale]

Originally Posted by Harbir

There are two parts to the answer to this question. One is relatively straight forward, one is anything but that.

The simpler part is this: There are aspects of engine design that by their nature will lead to a high torque output, regardless of the fuel used.
.
.
.
So in summary you can thank the higher compression ratio, the low rpm design optimization, and the carnot cycle for the greater torque output of diesel engines.

Succinctly explained, thanks a lot. I got to know more about the practical application of these concepts (power torque etc) from this thread than from my entire IC Engine subject which I had studied in my 2nd year!

Originally Posted by Harbir

It may seem complex to those not technically minded, but its as simple as a complete and thorough explanation of Power, torque, gearing, acceleration, and top speed as is possible.

Terrific. That was quite enlightening, especially all the graphs. True, complex for some, but for those who do have a slight background knowledge, that pdf is the ultimate piece of literature to relate the theoretical concepts to everyday driving! !

[sarathlal]

Originally Posted by Harbir

Everyone, I have created some slides to explain the subject in some detail, attached as a PDF.....
This is over 40 hours of spreadsheet and slide creation work, so I hope its appreciated.

This is of course just what I thought of and I do not claim that it is textbook perfect, so if there are physics errors, I would appreciate your bringing them to my attention, so I can correct them for my own benefit and for those of the readers.

Brilliant, and thanks a lot for taking lots of your private time to bring up something that T-BHPians will cherish. Though this one liner is not adding any value, this comes straight from heart. There are lots of aspects about the machines we love, that I could take from this thread. Thanks for sharing!

[Harbir]

All, I see I made some typos in the first couple of slides. thats what you get from not proof reading. Here it is attached again. if a moderator could delete the previous file (and perhaps substitute with this one, that would be great).

[spkingsley]

Originally Posted by noopster

Holy pistons Batman, that was quite an explanation!

(and to think it was my post on the AT thread that triggered it off!)

Harbir- can you explain in your trademark "Physics for Dummies" style why diesel engines generate more torque than petrols of the same displacement? The explanations I googled up (most leading to Team BHP) all spoke of bore and stroke and made my eyes glaze over.

Saw a long answer... I will attempt a shorter one.
Torque = Force x distance; force is the explosive force above piston and distance is the crank throw (which is half the stroke).
Since the displacement is same...the stroke can be same
So the difference can be only in the force..combustion pressure
Petrol engines this pressure is 30 - 40 bar
Diesel engines it is upward of 80 bar and reaches more than 120 bar in turbocharged engines
I hope the answer is clear...

[d3mon]

Originally Posted by Harbir

All, I see I made some typos in the first couple of slides. thats what you get from not proof reading. Here it is attached again. if a moderator could delete the previous file (and perhaps substitute with this one, that would be great).

Hi Harbir, that's a really awesome pdf. Even though I thought I was familiar with the concepts of power and torque and how they relate to top speed and acceleration, your detailed analysis has provided several interesting nuggets of information that I had never thought about earlier.

There's one thing that I'd like to point out about your pdf - in the last slide, you mention that the excess power in each gear is wasted as heat while cruising in lower gears. This is not correct, since while cruising, the engine is not producing the MAX possible torque at that RPM, and hence, not producing the MAX power AT THAT cruising RPM. If we're cruising with zero net acceleration, the engine would be producing EXACTLY the same amount of power as is required for that speed in any gear, otherwise, we'd start accelerating!

The fuel efficiency calculation requires a lot more parameters than what you've considered in your current model and I think you should simply delete that last slide as it'd require an analysis of how the ECM controls the engine at partial throttle inputs, which is well beyond the scope of this discussion.

Thanks again and cheers for producing this awesome doc.

[Harbir]

Very true. I wasn't happy with that slide but I'd run out of patience and interest by the time I got to it. I was thinking about how I was saying something quite ridiculous, that the car would be producing ~2.5 times power in 4th than in 6th while cruising at 80. If it was it would be accelerating. and it would consume 2.5 times as much fuel (assuming constant thermodynamic efficiency). That was wrong, but frankly, it had been a week since I was working on this, it was 2 in the morning, and I just didn't care anymore. I wanted to make the point about higher fuel consumption, and thought this illustrated the point even if the physics wasn't right.

I contemplated what modeling power vs throttle opening vs speed would involve (a 3 dimensional graph at minimum, assuming no funky maps of throttle position and injector pulse rates), I decided I wasn't going to take the trouble if I could illustrate the point graphically so it made sense even if it wasn't quite correct.

I do feel bad though because the slide did compromise the integrity of the physics of the rest of the document. Maybe I should have explained what I was trying to illustrate instead of trying to pass it off as good science. I apologize for that.

If I find the time after Diwali, I'll try to do that slide right. but most probably not. I really don't want to get into modeling 3 dimensional data arrays to create that slide correctly.

Probably the best thing to do is just delete the slide, as you suggest. Attached is the v3 PDF

But thanks very much for the appreciation and for keeping me honest.

[gkrishk]

Wonderful, Harbir!
A very detailed,lucid explanation of the science behind power, torque and acceleration. Knowing this will help make me a better driver even though I've been driving for decades. Many thanks for this thread and the accompanying PDF.

[R2D2]

Thanks very much Harbir.

This has got to be one of the best, if not THE best thread I've read on TBHP in a long time. As a technology freak and former technician (worked in a workshop soon after graduation repairing & tuning bikes/cars) your lucid explanations worked like a charm in dispelling some oft repeated myths.

Look forward to more insights from you.

[Sutripta]

Hi guys,
Part of this thread deals with the torque produced by diesels. There is a thread exclusively dealing with that, and the OP has posted on that thread.
http://www.team-bhp.com/forum/techni...ml#post2973598
If the OP doesn't mind, suggest all discussions regarding diesel/ torque be taken to that thread.

Regards
Sutripta