Torque - Why it doesn't matter, but it does

[zeussy]

It has been a busy last week (27th June - 3 July) and have not got as much work done as one would like.

I have started to work on calculating the final statistics for a car. Such as 0-100 km/h times (0-62 mph). In fact the acceleration times is first thing I have set myself to work out (and are still in the midst of writing the calculations for). So first question first, What actually makes the car accelerate? The force of the tyres pushing against the ground and using Newton's second law F=ma and a bit of jiggery pokery we can work out how fast a car would accelerate with a given force and known mass (a=f/m). That's all great, but how do you get the force at the edge of the wheels?

Well, we need to calculate the wheel torque, which is why torque matters. Torque is measured as force at a distance from a pivot, in Newtons Meters (Nm) or Foot-pounds (ft-lb). Once we have the wheel torque we can divide it by the wheel's radius and calculate the force at the edge of the tyre.

Example:

Torque / Radius = Force

4000 Nm / 0.3 m = 13333.3 N

Force / Mass = Acceleration

13333.3 N / 1000 kg = 13.3 m/s^2 (1.35g)

So torque does matter! But only at the wheels. The job of the gearbox and differential is to multiply the crank torque. If the gearing reduces crank RPM to wheel RPM by 9x you also get 9x the torque at the wheels. If we have 2 engines, a low revving but 'torquey' V8, and a high revving 'torqueless' L4 that both produce peak power of 200kW at differing RPM.

V8: 2000 RPM - 200kW - 954.88 Nm

L4: 8000 RPM - 200kW - 238.72 Nm

We can work out the torque from these figures, as power is just a function of torque by RPM.

Lets work out how fast our wheels would be turning at 100 km/h. It takes the wheel above with radius 0.3m, 530 revolutions to cover a km. At 100 km/h we would be covering 1.66 km a minute. Then calculate a gear ratio to allow us to have peak power at 100 km/h:

WheelRPM = 1.66 * 530 = 883.3 or call it 900

So what gearing would we need:

V8: 2000/900 = 2.22 (Reduce Crank rpm by 2.22)

L4: 8000/900 = 8.88 (Reduce Crank rpm by 8.88)

Which would give us wheel torque of:

V8: 954.88 Nm * 2.22 = 2119 Nm

L4: 238.72 Nm * 8.88 = 2119 Nm

So there we have it it, torque doesn't matter. If both engines produce the same power, and have correct gearing they will produce the same torque at the wheels. Of course the consistency of the torque curve through the rev range matters. The other thing I like about this is how and why higher speeds take longer to accelerate. I never really thought about it before, it is not just the build up for air resistance upon the car, but also as the gears get longer the engine torque is being multiplied by a smaller amount (longer gearing) and so the output force is smaller, and as acceleration is force/mass a small force gives a smaller acceleration. A quick bit maths shows this:

Again calculate what the perfect ratio would be for peak power at 200Km/h:

200 km/h = 3.33 km per minute

WheelRPM = 3.33 * 530 = 1766.6 again all it 1800

V8: 2000/1800 = 1.11

V8: 954.88 Nm * 1.11 = 1061 Nm

Wheel Force at 100 Km/h:

Torque / Radius = Force

2119 Nm / 0.3 = 7063 N

Wheel Force at 200 Km/h:

Torque / Radius = Force

1061 Nm / 0.3 = 3536 N

Acceleration:

100Km/h: 7063 N / 1000 kg = 7 m/s^2 (0.713g)

200Km/h: 3536 N / 1000 kg = 3.5 m/s^2 (0.356g)

So without even taking into account air resistance, the car is now accelerating at half the pace.

So now you can see how fun my general days are, and this doesn't get into weight transfer, tyre friction coefficients and all of that fun stuff. Back to work I go!

Read

[robt100]

Sounds like you've been doing your homework! I'm just going to go and sit in a darkened room after reading all that

[machalel]

I like!

[Killrob]

Not only did he do is homework, it's correct too
Now I can sleep at night knowing there are no crimes to physics committed in Automation
Well done Zeussy!

[AlfaDave]

explains why i never need to change gear up hills in my car i have 2.4l 212bhp/ 460Nm
Shame it runs the gm 6 speed gearbox f40 one its pants. thats why on the 159 they had their own gearbox in it. not like the 156's 6 speeds. the 5 speed is an alfa box tho and its a good one.
zeussy can you work out the best gearbox ratio's for my car and the proper top speed. max bhp is at 4000rpm and max Nm is at 1800. but i know it pulls really hard up until 4700 then it kinda die's off. i can climb most hills in 2nd on tick over its funny. tick over is 800rpm

[JeffreyCor]

That's quite an L4 to get 8000RPM and 200KW, Lotus maybe.
Anyway would have thought torgue (engine/flywheel) would be more useful for heavy pull than acceleration, hence the lower torque in high performance engines opposed to those in trucks and tractors. Make more sense seeing it worked out like that.

[Daffyflyer]

Ahh, there is somewhat of a reason for truck & tractor engines being torquey and low rpm.


You could make a Honda s2000 powered tractor, but to make the same torque at the wheels at would have to sit around plowing fields at 8000rpm...

this would probably not last very long, be very smooth, nor be effiecient (as friction rises as a square of engine speed)


Thus low rpm, but high torque rather than high rpm and low torque allows you to have a laid back, bulletproof tractor engine

[Killrob]

Recently in Automation:

Dave: "Hey Zeussy, can you work out the best gearbox ratio's for my car and the proper top speed."

Zeussy: "Of course, Dave! Your wish is my command."

... two weeks later ...

Daffy: "Ehh Zeussy, where is that car designer engine update you planned on finishing like 10 days ago!?"

Zeussy: "Sorry, I'm still calculating and simulating the proper gear settings for Dave."

Daffy: wtf!? o.O

Zeussy: -.-'

Community: *crucifies Dave*


Seriously dude... start using your brain, it has advantages. (Or stop posting while intoxicated.)
To add something constructive to your ramblings: optimal gear settings depend entirely on car usage.
Your normal cruise speed should probably be at the max torque, as the engine power curve is steepest there.
The rest depends on what highest speed you want to have and how sporty/economic the gearing needs to be.

[Kubboz]

Killrob, you've made me laugh. That was really funny.

[AlfaDave]

yes drunk lol. i was just wondering as you do. i know he is having a hard time getting things done by date i did not say can you do it urgently did i? i dont care if the answer comes in a year or not at all. just his post made me wonder.

[JeffreyCor]

LOL I can just picture a tractor going around the field sounding like an indy car

[T16]

at 1km/h

[Deus ex Machina]

what dave didnt say were 2 things:

1) its a L5 diesel
2) it has a turbo

[aknot]

It's been said, there is no optimal gearing, there is only optimized gearing, like most fuel efficient or highest power/acceleration.
One could take no matter what engine and layout the gearing either for fuel efficiency or max. acceleration. Since fuel consumption and power are very closely linked, you simply can't ever have both at the same time.
Since tracktors should be very fuel efficient, one makes gearing for low revs to minimize power and fuel consumption. Normal streetcars should be fuel efficient around cruise-speed (like on autoroutes), but should have enough power to run at high speeds (Highways). Therefore in low gears the gearbox is optimized around low revs and power, and the higher the gear the higher the optimal revs.

I'd like to say something else too though: torque doesn't matter at all, ever! It can be transformed into whatever you like by the gearbox. The only question is, can your engine make revs and torque or, mathematically: revs*torque=power ; therefore all that matters is power.
This can be understood also by looking at the physical definition of power: the speed of alteration of energy. Since more energy means higher speed, the integral of power equals gain in energy, which is: m/2*v^2, a square function of velocity. All this is completely independant of torque!

[Mil1983]

So, if my L4 produces 173 KW at 5500 RPM, what is my torque?
My registration document tells "max torque: 340 Nm"... Is it true, professor?
Numbers make me so confused I was almost forgetting I need a beer.