Relation between torque and effect. Why not linear?

[psalt]

What am I missing?

You are now on an other topic, gearing. This is a difficult issue and even the smartest people I know, aircraft engine designers and Phd astrophysicists among them, are willing to debate some things gearheads take as given. It think it may involve Zeno's paradox, so beware the simple explanation's.

There is usually an acceleration benefit to exceeding the hp power peak rpm before shifting, even though power is dropping. It has to do with the torque delivered after the shift at the higher rpm.

I think the Club Sport also had different valves and springs and fewer parts at a higher price, so a good business as well.

[DW SD]

Originally Posted by 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?

Livi,
You are missing the idea of leverage (in this case gearing). The ability to multiply an engine's torque by greater leverage (that is being able to remain in a lower gear) can increase your forward thrust and thus acceleration.

Most engines only hit peak torque at one spot in the rpm band, but that doesn't necessarily make the rest of the rpm band useless. Safely broadening the rpm range can increase forward thrust.

Doug

[livi]

OK. Thanks, everyone. I think I am hovering slightly closer to understanding the basics. I also understand that I am covering a very shallow area of this very complex story. Trying to simplify what is really much more comprehensive and difficult.

[Bill Verburg]

Originally Posted by livi

...
Anyway, as the peak power was reached significantly below the higher set rev limiter, why raise it at all? What am I missing?

Revs are the meat that feeds gearing

here is a comparison of the relatively minor change in tire height and how gearing magnifies and feeds on it

the y axis is the actual thrust pushing the car forward, it is the net result of the engines torque multiplied by gearing




here' another for my 993 w/ the powerband highlighted, you always shift because the engine runs out of revs, this one is comparing a street trans g50/20 and a pure race trans g50/30

[YTNUKLR]

These are not stupid questions!

Maybe some of these will be interesting. Flieger's explanation is pretty good though. I always like looking at equations in physics. Hopefully I don't add to the confusion.

Work = F*d*cos(theta)

Here force (F) acts on some object over a distance (d) and at some angle (theta), this angle between the displacement (an object's "trajectory"/"momentum direction") and the force vector(s) applied. If you are going north, then someone applies a force on your car going east, they have done NO work on you going north. The angle is 90 degrees. They only did work on you in the East direction! Now, if you ask how much work they did on you in the East direction, it is simply W = F*d because the angle between East and itself is 0 degrees, and cos(0)=1. [Please pardon me switching between radians and degrees here .]

Work is not energy, although the Work-Energy principle states that Work and Energy are exchangeable. Work is a change in Energy (E) in any chosen direction/reference frame. If you are driving along, your car has a certain amount of energy (kinetically). If you then press the brakes, the brakes are doing work on the car, reducing the amount of energy you have kinetically. The energy you removed from the car kinetically is changed into heat energy, and dissipated into the environment through the rotors of the brakes.

Power is a change in Energy over time. Watts for light bulbs is Joules (energy) per second. How much energy change over how much time. So, power is like Work/time.

Energy is defined in lots of ways, but kinetically,

K.E. (Kinetic Energy) = (1/2)*m*v^2

So, a car that weighs 1200kg going 50 m/s has .5*1200*50^2= 1,500,000 Joules of Energy

There is a rotational analogue to Kinetic Energy:

K.E.(rotation) = (1/2)*I*(omega)^2

Notice how the rotation equation looks almost exactly like the one above!

I is an inertial component, like mass is--its resistance to being moved--times the speed with which it rotates.

If you spin an engine very fast, you can see the energy of the assembly goes up very quickly, because it is being squared! One radian is 2pi. If you complete 2pi*18000revolutions in 60 seconds, the omega = d(theta)/dt = 1885 radians/sec. Square that number = 3,553,225 . You can see how spinning something faster greatly increases the energy of that thing!

Torque = F*d*sin(theta) [or r CROSS F sin(theta), which also tells you the direction of the torque vector ; I won't get into that here.]

Torque is a bit more complicated, but similar. You have to think of it as a rotational analogue of some other fundamental basis of classical mechanics. We already have the concept of momentum, P=m*v, or simply, momentum is just something's mass (m) times its velocity (v). Now, think of angular momentum, where some rotating thing has a certain component of weight (a force) and a certain component of velocity going in a circle. A special case of angular momentum is

L=I(omega).

I=.5MR^2 for a disk. Its moment of inertia in angular momentum is determined by 1/2 its mass times its radius squared. Omega is like velocity -- change in distance over change in time -- only now omega defines a change in angle around a circle per unit time. omega = d(Theta)/dt

If angular momentum is defined as L, then Torque is the change in L over a change in time: dL/dt -- the infinitesimal change of angular momentum related to an infinitesimal change in time.

So, "inertial torque" is a torque that is a product of the fact that a crankshaft has weight (mass x acceleration of gravity it experiences).

Now we see two distinctions:

-Torque is a change in angular momentum over time.

-Power is use of energy over time.

When you abruptly rev up the engine, the fuel applies a force at a distance from the crank, which is a torque. It adds angular momentum. Now, you could add a lot of angular momentum, just by applying a huge force. Imagine sticks of dynamite in the combustion chambers. They would apply a very quick, large force to the crankshaft (if they didn't blow the engine to pieces), and this would mean the dynamite exerted a large torque on the crank. But that doesn't mean the engine is spinning fast now; it means it is spinning "strongly" now.

A diesel is torquey because it applies large forces, using compressed fluid (air-fuel with turbocharger), dense fuel and high compression. Each explosion exerts a large force on the piston, but that doesn't mean it spins fast.

A torquey *AND* powerful diesel engine would be one that is volumetrically efficient at high engine speeds, meaning it can flow enough air to keep the engine running at a high speed, and still provide a forceful charge at that speed to generate a large torque.

Did that answer your questions?

Here I'll try to address it directly:
"Is it the volume of the engine?
No-it is about the volumetric efficiency of the engine. At its highest V.E. point, the engine will be able to make the best explosion--the highest force--the most torque. However, torque, as shown above, is a derivative of a linear function d/dt[L=I(omega)], while power is a derivative of a quadratic function, d/dt[KE=.5I(omega)^2]. Notice if you take d/dt[KE] you get L! d/dt[.5I(omega)^2 = I(omega) ]

Gear ratings?
Has nothing to do with measurements of power/torque.

Density/weight of different engine components?
Of course the weight definitely has a torque, because it exerts a force (mass*gravity) partially in the rotational mode. Heavy, lumbering engines are better at keeping trucks going when you let off the gas, compared to, say a superbike engine in a lorry.

Also, where in an engine is torque measured?"

Torque is measured like Flieger says. It's based on a calibrated friction disc ("torque plate"). If a dyno tester is rated to 1500 lb.-ft., it implies that there is a distance from the center where that is calculated. Torque= r X F , r is the distance from center and F is the force applied.

Now, I have to thank you for stimulating me to write this out ! I am so happy you forced me to recall Classical Mechanics and hopefully explain it ...

[RWebb]

this got neglected I think... momentum is a proper term in English, it is the product of the mass and velocity of an object; p = mv

things tend to keep moving once they are moving & they tend to sit still until acted on by an outside force

livi, I think you would enjoy reading a book that is some sort of introduction to how IC engines work - I don't know of one, but maybe somebody can post a title...

There is also a nice book by, IIRC, Phillip Smith "The Design And Tuning Of Competition Engines." It is early post WWII and out of print. You could buy a used copy or get it from your library via ILL. a bit more advanced but not an engineering text by any means.

Ytnuklr points out why I always think of power as being the time derivative of energy...

Now, you can think about an engine as an air pump - if you pump more air, you get more oompah. So, how can you do that?

- bigger cylinders
- more cylinders
- spin everything faster
- supercharger
- turbocharger
- design the motor for better airflow - aerodynamics apply inside the engine, right?

No one mentioned the frictional forces inside the engine yet, but they can be troublesome. For any given displacement, there is a certain # cylinders that is a sweet spot (optimum) - very tiny V-8 motors have been built (most recently by a Japanese co.), and gigantic 1 cyl. engines have been built ("thumper") but they are more design exercises usually. Also, as technology advances, you can reduce the frictional losses inside an engine, so more cylinders could be used at smaller displ.s

Then there are pumping losses - one reason to use a dry sump...

Design criteria for motors also include ease/cost of manf. (and one would hope, of repair), fuel consumption, emissions, and packaging constraints. Porsche has generally lowered the profile of the 911 motors and the ht. of the rear shelf in a 996 is substantially lower than in the air cooled cars. Same thing for VW Buses/Vanagons.

So, I hope that helps. If not, I hope it at least obfuscates everything sufficiently that you have all forgotten the original question.

[Bill Verburg]

Originally Posted by YTNUKLR

.....
Gear ratings?
Has nothing to do with measurements of power/torque.

...

How wrong you are. Notice the differences in the curves above, that same difference would be plotted if the graphs were wheel torque instead of thrust


again it is worth repeating

100ft-lb of torque at 1000 is not the same as 100ft-lb @4000 because gearing can change the latter into acceleration very easily. You would need 400ft-lb @1000rpm to match it. It is far easier, lighter and economical to generate the 100ft-lb @4000rpm and the drive train to go w/ it than to generate 400ft-lb @1000rpm and the drive train to go w/ it


you can get bogged down all day w/ the underlying math, but that doesn't get to the heart of what was asked.

torque is just the twisting force which the crankshaft delivers to the clutch, from there gears/tires do the rest

also to repeat torque can be measured in several ways
1) engine torque is measured on an engine dynomometer, this gives what is called brake torque because the engine is run against a load that brakes the engine, the load is usually hydraulic but it can also be electromagnetic
2) wheel torque is measured at the wheels on big rollers again the rollers are hydraulically or electromagnetically braked to load the engine sometimes the rollers are not braked in that case there known mass is used to determine how long it takes to spin them to a specified rpm this is called an inertial dynomometer and is the least useful tho most common type found. It is least useful because you can't hold the engine at a given steady state rpm as w/ other types
3) hub torque is measured by attaching the dynomometer brake to the wheel hubs, I like this best for us amateurs because it eliminates the tire friction w/ the dyno roller as a variable and is far easier to use as you don't need to pull the engine to do a test run(and incidentally you can see the measured difference in torque in each gear)

[911st]

Originally Posted by livi

...
As far as I remember from school there is a linear and direct relation between work/torque and effect.

This is correct.

Forgetting how a motor actually operates and using a typical (rpm) x (HP&TQ) graph, the following would hold true.

If you piloted TQ in a straight line by rpm (say fixed at 100 ft lbs from zero to red line), HP would be a straight line increasing by rpm.

Then, if you piloted HP at a straight line (say fixed at 100hp form zero rpm to red line), TQ would be in a straight decreasing line. It would be highest at zero rpm and lowest at red line.


Now, if you plot TQ on a curve like with a typical motor, as long as TQ is increasing HP is increasing

Also, as long as TQ is decreasing but at at a 'rate' that is less than rpm's are increasing, HP will climb. Example, if TQ is decreasing at 10% and rpms are increasing at 15%, HP will be climbing.

At the point where TQ falls off at a rate equal to the rate RPM's are increasing, that is typically where HP flatens and peaks. Example, if rpms are increasing at 15% and TQ is decreasing at 15%, the HP line will be flat.

When RPM increase at a rate faster than the rate TQ is falling off, the HP curve will start to fall. Example, if rpm are increasing at 15% and TQ is decreasing at less than 15%, HP will be falling off.

----

The point where a motor is at its most efficient point of operation and making the most power with each stroke, is where TQ peaks.

The point where a motor is at its most total power is at its HP peak. This is where increases in RPM can no longer make up for the rate TQ or efficiency is falling off.

Also, as long as the rate RPM's are increasing is more than the rate TQ is falling off, the motor's HP curve will continue to climb.

----

Further:

It takes twice the TQ at half the RPM to make the same HP.

It takes half the TQ at twice the RPM to make the same HP.

Move the TQ curve to the right 10% and HP will increase 10%.

[YTNUKLR]

Obviously, gear ratios affect the thrust you feel in a car. Duh. Gear ratios and tires are range multipliers/reducers, sure, for the operating range of the engine. But we're talking about engines by themselves. I'm not wrong on that. If this were the case you would say things like, "my engine has 1000 hp...as long as you use X and Y gear ratios." I think you are talking about acceleration, which has other considerations like tires, gear ratios, etc.

I think the gold mine in this thread is this, slightly reworded but expressed by 911st:

The point where a motor is at its most [volumetrically] efficient point of operation and exerting the largest force upon the pistons, is where TQ peaks.

The HP peak is where increases in RPM can no longer make up for the rate TQ or efficiency decreasing.

That's as simple as it gets, and no simpler, I think. Einstein would be proud.

[911st]

Well said Scott. I can get wordy. Thanks.

Acceleration is at its highest at HP peak.

Increase your averagee HP and you have a faster car.

You can do this by increasing your total HP.

Or, you can also do this by having closer gears so you spend more time at a higher power levels.

For example, say you shift into second at 50mph near red line and that puts you at say 4500rpm where you are making 200hp. If you put in a shorter second gear that lets you come in at say 5200rpm where you are making say 230hp, your average HP will be higher and you will be faster.

Please forget the handed down sayings about gears, they will only get in the way.

What gears do is have a direct effect on what point on the HP curve you operate and thus your averagee HP'.

The car that operates at the highest averagee HP is going to get there the fastest.

[jcge]

One more way to measure torque.....strain (twist) in a shaft can be measured without contact with the shaft...(magneto elasitcally)

ABB's Torductor S is used in F1 and engine / transmission development by OEM's to measure torque (and in F1 tune EFI) in real time.

This will find its way to production cars in the next few years (driven by the need to minimise emissions)

ABB Torductor PDF

How it works...for the technically minded US Patent 6532832

[911st]

Here is one for you.

The more TQ you can make, and at a higher RPM, the more HP you make. (Lets call this TQ-1)

The more HP you make and the gear ratio you operate at determine your rear wheel TQ. (say TQ-2)


TQ-1 and TQ-2 are both Torque. But they are not the same Torque.

For example, a diesel car could have twice the TQ-1 as a gas car (but at about half the rpm) and they could be operating at the same torque level measured at the rear wheels (TQ-2). Thus, different motor torque values can equal the same wheel TQ.

Please try to forget all the hand me down sayings about Torque you have heard. Things like a transmission is a Torque multiplier, we want to come in at TQ peak when we shift, and it is TQ that accelerates a car.

All these are based in truth if applied correctly and to a different degree, however they will only get in the way for most when trying to understand if TQ or HP or Power is what makes us fast.

The highest average HP a car can maintain at the lowest car weight will make for the fastest car acceleration.

Just my two cents.

[Zeke]

911st, you just made a case that TQ is useless; only a by-product. Or, am I missing something?

And, yes, I'm the bunny with a pancake on its head when is comes to the theories presented in this thread.

[Bill Verburg]

Originally Posted by 911st

Here is one for you.

The more TQ you can make, and at a higher RPM, the more HP you make. (Lets call this TQ-1)

The more HP you make and the gear ratio you operate at determine your rear wheel TQ. (say TQ-2)


TQ-1 and TQ-2 are both Torque. But they are not the same Torque.

For example, a diesel car could have twice the TQ-1 as a gas car (but at about half the rpm) and they could be operating at the same torque level measured at the rear wheels (TQ-2). Thus, different motor torque values can equal the same wheel TQ.

you got off to a good start, but just a restatement of what was previously stated

Originally Posted by 911st

try to forget all the hand me down sayings about Torque you have heard. Things like a transmission is a Torque multiplier, we want to come in at TQ peak when we shift, and it is TQ that accelerates a car.
....

wrong wrong wrong

torque & rpm are the only things that are important, torque at high rpm makes for high hp and faster acceleration

again going back to my previous comparison
400ft-lb @ 1000 rpm is the same hp as 100 ft-lb @ 4000rm but the first will make a great truck engine and the second a better car engine

hp is derived from the product of torque & rpm and is sort of useful in describing the nature of an engine, but make no mistake about it torque is what pushes a car down the road

current transmissions are torque multipliers, it is just a matter of how much the torque is multiplied, each gear is different

yes, there is a difference between flywheel torque and wheel torque, the difference is simply the amount of multiplication done by the gear sets, cwp & tires

[911st]

Torque is the starting point and with out it there is nothing.

However, it needs its multiplier, RPM, to make HP so it can reach its potential.

The more TQ and the more RPM, the more power.

Big Torque dose not necessarily mean big power or acceleration.


For example we could take three power plants.

A gas V8 that makes 500 lbs at 5200rpm TQ and 500hp.

A Diesel truck motor that makes 700 lbs at 1600 rpm and 400hp.

A steam engine that makes 2000 lbs of torque at 100rpm or 38hp.

Put each in a truck weighing 5500lbs with the perfect 6 speed transmission for the motor and it will most likely be the motor with the most HP that is the fastest and the one with the most TQ that is the slowest.

However, make big TQ at big RPM and you have really big HP.

[Bill Verburg]

Originally Posted by milt

911st, you just made a case that TQ is useless; only a by-product. Or, am I missing something?

And, yes, I'm the bunny with a pancake on its head when is comes to the theories presented in this thread.

No, torque and rpm are what is important for performance, hp is derived

hp = (torque x rpm) x constant
torque is in lb-ft
rpm is self explanatory
constant is 2pi/33000

[911st]

Bill,

You left out or missed my statement that followed my suggestiong that people try to forget the hand me down sayings so that they do not get hung up on TQ.

Originally Posted by 911st

All these are based in truth if applied correctly and to a different degree, however they will only get in the way for most when trying to understand if TQ or HP or Power is what makes us fast.

Yes, TQ and RPM make power.

I did restate the same thing many different ways hoping someone might hear somthing in a way that sticks.

I think we are saying the same thing, but that my wrighting sucks.

[911st]

I think maybe HP is 'the result'.

[911st]

I am thinking the 'constent' is nothing really except agreeing on the size of the horse.

[Zeke]

Let's try one more for the uneducated: What is the definition of the "power band?"
IIRC, when setting up a trans for a particular track, you want to keep the revs within the PB as you make your way thru the gears and around the track. So, if not going below max TQ when upshifting, what is the goal?

And why?