Torque and RPM relation

[TurboLag]

xpensive is correct here, you other guys are overcomplicating this big time!

Mechanical path of force moving the car is:
1: cylinder pressure (lbs/square inch), acting on a
2: piston (square inches), giving force (lbs) to the
3: crankshaft with a radius (ft), makin torque (lb.ft) through a
4: gearbox which multiplies the torque by reducing the speed at different ratios to suit the engine and make better use of the energy available, which a
5: final drive can fine tune for different wheel/gearbox setups. At this point we're still talking about a rotational torque at the hubs. The
6: Wheels give a radius between the "torqued" hub and the contact patch. This gives force to accelerate the car.

Higher gearing ratios, giving a higher force acting on the contact patch, is the reason why you accelerate faster in 1st gear than in 3rd gear.

This mumbo jumbo about "internal friction forces overpowering available force" can be thrown away, your conrods, wrist pins, block or valvetrain have given up way before this is even close to reality.

The reason why power (kW) is the relevant factor every time is this: When you increase the torque at the hubs by reducing the speed, the torque increase and speed decrease factors are the same. This means that, if you disregard drivetrain losses, your power at the wheels stay the same whatever gear you have. This is why, as someone said earlier, you want horsepower. You got a gearbox for the rest.

Bottom line, you can have 10.000 Nm of torque and not move at all. It's just the available torque. A bolt can have torqe, but your part doesn't move. Power indicates speed. 0 Nm and 10000 rpm is no acceleration force. 10.000 Nm and 0 rpm is still standstill. You need both, but given enough speed 1 Nm is all you need.

[xxChrisxx]

My word we've gone in a circle to post 3.

[xpensive]

My word we've gone in a circle to post 3.

We have?

To most of us Power is still Force times Speed.

[xxChrisxx]

Figured out the answer yet?
Yes or no?

[xxChrisxx]

At a very fundamental level, ignoring all the constraints of reality (i.e. In maths world).

If we want to know the ultimate performance we only need to know power.
More power = faster delivery of energy = the more work you can do.

Is the same as.

The reason why power (kW) is the relevant factor every time is this: When you increase the torque at the hubs by reducing the speed, the torque increase and speed decrease factors are the same. This means that, if you disregard drivetrain losses, your power at the wheels stay the same whatever gear you have. This is why, as someone said earlier, you want horsepower.

Bottom line, you can have 10.000 Nm of torque and not move at all. It's just the available torque. A bolt can have torqe, but your part doesn't move. Power indicates speed. 0 Nm and 10000 rpm is no acceleration force. 10.000 Nm and 0 rpm is still standstill. You need both, but given enough speed 1 Nm is all you need.

The only difference is that I went on to at least pay attention to the fact that real machines have constraints.

The real world we are constrained by the machines we can produce, and limitations of usability. Which is where torque and transmissions become important. We can deal with this in another post (or this one will becomes a monster).

[Tim.Wright]

The force has a relation to the engine's torque, but then you need to know the gearbox ratio, final drive and wheel radius,
why just using Force, Power and Speed is so much simpler.

I'm going to set out a scenario and ask you a question:

We want to work out the in gear acceleration for a vehicle with 5 gears (already pre-set, but we don't know what the ratios are). Giving it's actual acceleration profile throughout it's speed range. Assuming no slip, or traction limit.

Are you sure you don't need the overall ratio between engine speed and road speed, for you to use power force and speed.


Think about your answer carefully.

Unless you have an engine delivering constant power over its complete rev range, then you need to know the gear ratios in addition to power curve to calculate the tractive force. For example, a car with a CdA of 0.8 and 300kW should theoretically be able to hit 300km/h. Realisticallly though, unless you setup the gearing so that at 300km/h the engine RPM is that which coincides with its peak power of 300kW, then you won't hit 300km/h.

Regarding the use of the term torque incorrectly, its not something worth getting so bent out of shape about. The only inaccuracy is that the man in the pub attributes 100% of a car's acceleration capability solely to how much engine torque exists, forgetting that the torque is modified by the gearbox. But in the end the car's acceleration is proportional to engine torque and if you modify the engine without changing the gearbox (as is the case in 99% of all engine mods) then any difference in acceleration you feel will be due to a different torque curve.

Horses for courses... depending on the subject at the time, sometimes its more meaningful to speak of power, sometimes its more meaningful to speak of torque.

[xxChrisxx]

Unless you have an engine delivering constant power over its complete rev range, then you need to know the gear ratios in addition to power curve to calculate the tractive force.

By the way expensive ^_^ that's the correct answer.

[machin]

. But in the end the car's acceleration is proportional to engine torque and if you modify the engine without changing the gearbox (as is the case in 99% of all engine mods) then any difference in acceleration you feel will be due to a different torque curve.

Except that if you have two cars, one with diesel engine reving to say 4000rpm, and a petrol engine reving to 8000 rpm even with the same gearbox, final drive and wheel sizes, if the two cars are coming out of a 60mph corner, the diesel engine may have to be in 3rd or 4th gear, whilst the petrol may be in 2nd gear (by virtue of the longer rev range). This means that it is still torque x rpm (i.e. power) that is the determinant of acceleration, not just the torque alone.

(FYI My experience backs up the science: In the Westfield Speed Series (see my avatar) it was quite a common upgrade to change the engine (strengthened internals and big valve heads, longer duration cams, etc) to increase the rev range, whilst torque remained the same (engine displacement was limited by the class rules), and maintaining the same gearbox: performance was much improved, it just meant you were changing gear at different points).

[xxChrisxx]

This is all could, woulda, shoulda.
Lets get a proper worked example going.

[machin]

Gearbox ratios (from Ford Focus):

1st : 3.67:1
2nd : 2.14:1
3rd : 1.45:1
4th : 1.03:1
5th : 0.83:1

Final drive: 3.82:1

Diesel engine: 200bhp @ 4000 rpm = 262lbft of torque
Petrol engine: 200bhp @ 8000 rpm = 131lbft of torque

Lets say travelling at 60mph (26.9m/s) with 670mm diameter driven tyres (2.1m circumference). Meaning that wheel rpm is 768rpm.

The diesel engine has to use 4th gear (for an engine speed of 3021, as 3rd gear would've resulted in an engine speed of 4254rpm.

The petrol engine can use 2nd gear (for an engine speed of 6278 rpm ( 1st gear would've been 10766rpm).

So the petrol engine's torque is multiplied by 2.14 x 3.82 = 8.178
and the diesel engine's torque is multiplied by 1.03 x 3.82 = 3.935

If we assume that both engines have a flat-ish torque curve, then the petrol engine has 1071lbft available at the driven wheels, and the diesel engine has 1031 lbft. i.e. very very similar (as you would predict from the identical power outputs), despite the hugely different flywheel torque outputs from each engine.

[strad]

assume all you want this is getting so old.

[machin]

Don't like maths?

Well, below is a chart showing the results of 27 road tests conducted by Autocar magazine. The graph shows flywheel torque/ton on the x-axis and 30-70mph acceleration on the y-axis. You can see that there is almost no correlation between flywheel torque and acceleration:-



If we now take the result of those exact same cars, but display the relationship between flywheel power/ton and 30-70mph acceleration, we can see that there is a very strong correlation. In fact, if we only know the power/ton figure we will be able to fairly accurately predict a car's 30-70mph acceleration time:-



Of course this second chart could just as easily say "lbft x RPM / ton" on the X-axis, showing that whilst flywheel torque alone is a useless figure, torque x rpm is very useful. but in that case you may as well just use power (which is torque x rpm).

[xxChrisxx]

I have come up with a spreadsheet to work through finding tractive force from power and torque based on different levels of information available. Once I've gone through the problems, I thought that we could work through Machin's example. Looking at comparing two different engines and optmising gear ratios.


To prevent the posts from getting too big, I will split them up into 3 posts, then maybe a comparison post at the end depending on the questions and comments.

Post 1 will be: Estimating tractive effort based on a power curve without, and with tacho (engine RPM) references.
Post 2 will be: Calculating tractive effort based on Power curve with the overall gearing ratio
Post 3 will be: Calculating tractive effort based on the torque curve and gearing

DISCLAIMER:
I will generally try to work in SI units to find the traction. Maybe convert to more common units afterwards, to cut down on conversion errors. I've also bashed this out fairly quickly, so is not gaurantteed to be error, free. It all seems to add up, but more pairs of eyes tend to expose blunders!


The Goal
To find the tractive effort curves for a car with a 5 speed transmission, with fixed but currently unknown gear ratios and wheel size.


1. Power Curve with No Tacho Reference
A power curve has been measured. Though we had no tacho reference.


As we have no engine tacho, we don't know what road speed corresponds to what engine speed. The best we can do is assume that we can use peak power at all times. This then allows us to use:

Power = Force * Speed
(be happy xpensive )

This generates the following curve. It's the maximum possible performance given that power
N.B. Power was in Watts, Speed in m/s to give Force in Newtons.


Force is inversely proportional to speed for constant power

However, we know that the assumption of constant power is not strictly valid. As we have a power curve, and discrete gearing. So we can't be at constant power at all times.

1b. Power Curve with a Tacho Reference
A power curve has been measured with a tacho reference. In terms of calculating the tractive effort we are still in the same position as above. We know the engine speed, but we don't know what engine speed corresponds to what road speed.

We can however, now find the engine torque curve from:
Power = Torque * Angular Velocity

Angular velocty is in radians/s. So we will have to convert some units.

Torque (Nm) = 9458*(Power (kW) / Speed (RPM))


Conversely:
If we know the engine torque output, and the power output, we can find the RPM.
If we know the torque output and the tacho referece, we can calculate the power.
This is because there are three variables in the expression that are all intrinsic. If we know two variables, we know the third.

Unfortunately we can't gain any more insight into the performance without referencing engine speed to a road speed.

On to post 2... having a reference between road speed and engine speed.

[gruntguru]

So what?

All you are proving is that a knowledge of power band (the rpms at which the engine makes close to peak power) is required to be able to select optimum transmission ratios. With correctly selected ratios, the tractive effort curves for each gear will touch the "constant power" tractive effort curve you have already drawn. The closer the ratios the smaller the gaps between "touches".

A knowledge of torque band (the rpms at which the engine makes close to peak torque) is pretty much irrelevant because the optimum shift points are dictated by the power band.

Yawn!!!!!

[Just_a_fan]

This whole discussion is getting boring. It's like the arguments between Catholics and Protestants - you're all arguing about the same thing, you're just arguing about what name to call next Tuesday.

Torque and Power are intrinsically linked. You can't have one without the other any more than you can have good without evil. They define each other. Take one away and you have nothing.

Sometimes discussions in here are like trying to talk to the Taliban. "Agree with me or die".