Relation between torque and effect. Why not linear?

[livi]

Morning, guys!

Doc Fluffer here. Not posting much these days, but here is a question for you technically inclined.

As far as I remember from school there is a linear and direct relation between work/torque and effect. The former measured in Nm or J and the latter measured in W or horsepower. Time (s) being the third denominator. I hope I remembered that correctly.

That would imply a direct and linear relationship between torque and horsepower in a car engine.

Now, what are the factors in an engine the affect the disruption of this linear relationship? Typically a big diesel truck engine makes a huge torque with a relatively moderate bhp output, while a small race engine develops a lot of horsepower but, conversely, a modest torque.

Is it the volume of the engine? Gear ratings? Density/weight of different engine components? Other things?

Also, where in an engine is torque measured?

I have tried to grasp this particular questions since I was a teenager. Alas, so far, no cigar. Anyone able to explain this so I understand it will get a wild card for free fluffing a whole year.

Thanks!

[Flieger]

Torque causes movement over a distance which is work. Power is the time derivative of Work. Torque is like a force (here it is a force x distance so Newton-Meters or Pound-Feet). Work is that Torque being applied to a load, integrated over the whole distance (degrees or revolutions) that load travels. Think of pushing a rock up a hill.

Power is how fast the Work is done. It is dW/dt (time derivative). dW/ds (distance derivative) is Torque.

Basically, what you want to know is that:

Torque x engine speed (rpm) = Power

Torque x # of revolutions total = Work

Torque is measured on a dynomometer by putting a load on the engine (usually a water brake) and seeing how hard it can turn. Since they cannot stall the engine without stressing it too much, they apply a moderate load and measure how fast that work is done to get power.

When you multiply torque by the rpm it is achieved at, the graphs look like they do.

As with basic calculus, the derivative of x^2 is 2x and the derivative of 2x is 2 so a constant torque would yield a linear power slope...

basic calculus and physics.

By the way, in the USA, Horsepower = (lb-ft x rpm)/5252

[livi]

Brilliant! Thanks a lot, Flieger!

I will have to read your post a few times and see if I really grasp the essentials. Being a tech ignorant its very frustrating trying to comprehend interesting matters when it just won´t compute upstairs.

[psalt]

Typically a big diesel truck engine makes a huge torque with a relatively moderate bhp output, while a small race engine develops a lot of horsepower but, conversely, a modest torque.

Is it the volume of the engine? Gear ratings? Density/weight of different engine components? Other things?




Yes, torque is proportional to displacement, about 80 ft/lbs per liter N/A tops. Horsepower is just an abstraction, it is not measured, it is calculated by multiplying by rpm. That is how a 2.4 ltr F1 engine can have 800 hp. When you multiply by 18,000, things happen. Peak torque in an engine occurs at the VE peak, when the engine inhales the highest percentage of its displacement. Raise the VE, the peak torque rpm goes up, the calculated horsepower goes up

[livi]

Thanks!

Given that torque x rpm = power, why does the latter tend to drop off in a graph at the end of the curve? It would seem an engine has a peak power (and torque) at a certain rpm and higher revolutions per minute will not gain any more, rather the opposite. Why is that?

[psalt]

Because the torque is dropping faster past the peak. Try looking at some hp and torque charts. Hp=torqueX rpm/constant(5250). Hp almost always peaks above the peak torque rpm and the lines cross at 5250. The torque curve is a proxy for VE, it starts out low and climbs to the peak (say 90%), then drops off, sometime dramatically, after the peak torque rpm. If you can keep the slope of the torque drop low, you will make more power. Engines with fixed valve timing must balance low speed performance with high rpm breathing. Engines with ideal valve timing for high rpm breathing are lousy performers at low speed. Variable valve timing was invented to improve the compromise. You can pretty much tell an engine's power band by focusing on when the intake valve closes.

[livi]

Thanks, Paul. That is very informative and interesting reading. I wish I could learn more about the basics of engine "physiology". Can´t seem to find any appropriate literature however. Its either too basic or far too comprehensive.

[Bill Verburg]

Originally Posted by livi

......
That would imply a direct and linear relationship between torque and horsepower in a car engine.

Now, what are the factors in an engine the affect the disruption of this linear relationship? Typically a big diesel truck engine makes a huge torque with a relatively moderate bhp output, while a small race engine develops a lot of horsepower but, conversely, a modest torque.

Is it the volume of the engine? Gear ratings? Density/weight of different engine components? Other things?
...........

hp = torque * rpm * constant

because rpm and torque are multiplied the net effect depends on the relative slope of the 2 curves.

rpm always has a + slope(ie goes up from left to right), torque slopes vary depending on whats going on inside the engine, they will be very + at points where the engine is working harmoniously inside, less + as things get out of sync and also go - when inertia catches up to gas flow volumes

what's happening in side all the cylinders collectively determines torque #s. The most torque comes from having the most massive fuel/air charge compress and burn most efficiently/completely in the right time window, this generally is easiest to accomplish at lower rpm. The diesel runs at low rpm and has minimal intake restriction and high compression ratio compared to a gas engine hence it's high torque.

when there is a wide rpm range it is harder to optimize torque at all points so w/o using variable geometry engines(to keep it simple) torque is optimized at a single point in the rpm range. If the point is down low you have a torquey engine, think truck or family sedan, if the point is up high you have a sportier engine used in a sports car, higher yet and you have a race car

w/i an individual cylinder there are many factors that determine the mass of the fuel/air mixture to be burned. The biggest is the available time during which the intake valve is open, the pressure differential between the intake manifold and the cylinder and the resonances/flow patterns that are occurring. At high rpm there is simply less time for the cyl. to fill so the torque curve tends to flatten then drop as rpm increases but the resonances in the intake and exhaust can be used to increase the mass of fuel/air charge at very specific and limited rpm points. If a variable geometry is used(vari ram & vari cam) the mass of fual/air charge ingested(volumetric efficiency) can be raised over a much wider rpm band

When both slopes are + hp goes up fastest, when one is positive and the other less so, hp increases at a slower rate, when one is more positive then the other( even if the other is -) hp can still go up but more slowly, when one is more - than the other is + hp goes down

small torques are amplified by gearing, gearing includes the transmission gear sets, cwp and tire dynamic loaded radius

Originally Posted by livi

Also, where in an engine is torque measured?

depends on the measuring tool
a chassis dyno measures at the rear wheels or hubs in some cases
an engine dyno measures at the flywheel

[livi]

Wow, thanks, Bill!

Just found your post above. I think I will put my Norman Mailer book aside tonight. This is all good reading.

Thanks a lot, everyone!

[RWebb]

BTW - Power is the time derivative of Energy, not Work...

[RWebb]

also Marcus, it is easy to get an intuitive understanding of torque

- find a shaft that is spinning and grab it - how hard it is to stop the shaft (or slow it down) relates to the torque

[Flieger]

Originally Posted by RWebb

BTW - Power is the time derivative of Energy, not Work...

I must disagree. Power is how fast work is being done.

However, the change in an object's kinetic energy is equal to the total work done on it (assuming no frictional losses), so work and energy are very close.

[Bill Verburg]

Originally Posted by Flieger

I must disagree. Power is how fast work is being done.

However, the change in an object's kinetic energy is equal to the total work done on it (assuming no frictional losses), so work and energy are very close.

work and energy have exactly the same units, and are closely related concepts
power is the rate at which work is done and includes an additional time element in the denominator which is not found in the other 2 quantities.

dimensional analysis shows what are equivalents and what are not
dimensionally
work - ML^2T^-2
energy - ML^2T^-2
power - ML^2T^-3

[livi]

Thanks again, everyone. I have read all your posts repeatedly. I grasp the general laws of physics applied here but I am still curious as to what are the specifications in an engine that tends to give it relatively higher torque vs effect given a certain rpm.

As Randy mentioned, torque is what makes it difficult to stop a cylinder from rotating - is momentum a proper term in English? If so, what characterizes an engine with relatively higher degree om momentum? I instinctively suppose the general size of the engine, but specifically what parts? Or is that a mute line of questions?

Still confused but on a higher level. Thanks!

[Flieger]

What do you mean torque vs. effect? By effect do you mean power?

An engine with little torque can make loads of power if it spins fast- like a sportbike or an F1 car.

Torque comes about by two means. Inertia torque and gas torque. Gas torque is the actual force due to the combustion pressure. Inertia torque is the torque that remains after the combustion has stopped and is due to the momentum of the system. A heavy or large diameter flywheel has a lot of inertia and therefore lots of angular momentum. The reciprocating pistons and the rods travelling in general plane motion also have momentum and cause a force on the crankshaft because impulse = change in momentum. Impulse is force times time. The force varies with the orientation of the crankshaft throw and the changing leverage.

At high rpm, the inertia torque dominates the gas torque and this is where a properly balanced crankshaft really shines in smoother running. At low rpms, gas torque dominates and the firing order is more important.

Because of these effects, Yamaha used a cross-plane crankshaft in its YZF-R1 sportbike with its inline 4. The firing order is crazy uneven so it fives up some top end horsepower. At mid-throttle openings, the power is smoother, though, because the gas and inertia torques are more balanced. This does not overwhelm the rear tire and allows smoother drives off corners and wears tires less. Ducatis with a big L2 have a big bang firing order which makes huge torque and then goes quiet for a revolution to allow the tire to catch up. Sort of like pumping the brake pedal to stop lock-up. They are notoriously hard to ride but have crazy top-end horsepower.

Some race riders can feel the Yamaha's lack of agility, however. It is due to the necessary heavier, stronger crankshaft which has more inertia, angular momentum, and therefore a greater gyroscopic stabilization effect on leaning the bike through a turn.

[livi]

Great post! Thanks!

Is it generally fair to claim then, that if two engines spinning at the same rpm with identical torque will have the same power output (bhp) and raising the rpm will continue to produce the same output.

You see, my original confusion is related to the fact that I read a whole lot of torque and power specifications about different cars and I always wonder why two cars with the same power output can have very different max torque numbers and vice versa. Is that all depending on at what rpm you measure the output?

I am really sorry to bother you guys with these stupid questions. I am a slow learner (and driver).

Thanks!

[Bill Verburg]

hp = torque * rpm * constant

to keep it simple lets ignore the constant and units, we will compare 2 engine w/ exactly the same maximum torque, say 100
but engine 1 makes max torque =100@2000rpm and engine 2 makes max torque =100@4000

engine 1: power = 100 x 2000 = 200,000
engine 2: power = 100 x 4000 = 400,000

remember we are ignoring all units and the constant so the #'s are for comparison only
also remember that each engine has a torque curve at rpm above & below the indicated ones.

what will the percieved difference to a hypothetical driver?

engine 1 will have a lot of low end grunt it will pull strongly, gearing will only add to the pull, it will have a relatively low top speed unless the gearing is highly overdriven, this sort of engine doesn't need lots of gears 4 or 5 is fine

engine 2 will have relatively poor pull down low but w/ proper gearing can be made to pull through out the rev range as gearing is a multiplier of torque, the more gear choices the better ie 6spd is better than 4

It is better to have torque high in the rev range because then you can take advantage of it w/ gearing

Now you can make a fast diesel as Audi has done by having lots of torque at relatively low rpm but then using lots of overdrive gears, but by far the more usual race engine strategy is to make torque at higher rpm then gear it to suit.

[livi]

Thanks Bill! I think I start to understand the concept.

This is not news to me, but worth repeating. The comprehensive knowledge and insight around here blows my mind. You guys are absolutely Impressive.

Dare I ask one more question. Along the line of Bills post above, what factors will decide at what rpm an engine develops max torque?

[psalt]

what factors will decide at what rpm an engine develops max torque?

Valve timing, intake length, valve curtin area/displacement, and port size. Experiments in the 1950's determined you could manipulate the torque peak (lower it) by increasing the length of the intake tract out to 33 inches, with the trade off of sharply lower high speed torque. Every intake length has an rpm (frequency) where a positive pulse returning to the intake valve will boost VE. This is the principle behind multiple length intakes.

If you want to understand torque, focus on the fact that torque is proportional to displacement. Regardless of the design or parts, torque output is limited to around 80 ft/lbs per liter. The only way to exceed this is to pressurize the intake.

Much of engine design history is distorted by artifical displacement limits and tax laws. We were racing 15 liter engines until the 3000 rpm limit was broken in 1912. Speeds rose so fast, displacement limits, first 5 liters, then 3 liters, then 2 liters, then 1.5 liters, all in the span of ten years to keep the drivers alive. The small displacement high reving engine for a road car is far from ideal. The ideal engine for a 4 person road car looks something like a 5 liter V-8 with variable cylinder deactivation, +35% EGR and a turbocharger. Two liter economy and 8 liter torque.

[livi]

Thanks, Paul. Good pieces of information. I start to think I am on my way to comprehend the basics.

The 3.2 Euro Carrera put out 231 bhp. The rev limiter was set at about 6250 rpm. Now, the Club Sport edition was blueprinted and the rev limiter was raised to around 6800 rpm if I remember correctly. PAG claimed no power gain but allegedly these engines had an output around 240-245 bhp.
Anyway, as the peak power was reached significantly below the higher set rev limiter, why raise it at all? What am I missing?