Manoah2u wrote:so go ahead, explain this.
So, where were we:-
(Torque at driven wheels) ∝ Acceleration
Hence
(Crankshaft torque) x (gear ratio) ∝ Acceleration
And
overall gear ratio = (Crank RPM)/(wheel RPM)
Therefore
(Crankshaft torque) x (Crank RPM)/(wheel RPM) ∝ Acceleration
So if we have an engine making 358lbft of crank shaft torque at 1800rpm (like the Diesel Merc in my example), travelling at a speed such that its road wheels turn at 800rpm, the overall gear ratio will be 2.25 (1800/800 = 2.25). So the torque at the driven wheels will be 358x 2.25= 805.5 lbft
If we have another engine making 250lbft of crank shaft torque at 2750rpm (like the pretrol Merc in my example), also travelling at the same speed with equal sized wheels/tyres, (i.e. driven wheels also turning at 800rpm), the overall gear ratio will be 3.44 (2750/800 = 3.44). So the torque at the driven wheels will be 250 x 3.44 = 860lbft.
If we just remind outselves that....
(Torque at driven wheels) ∝ Acceleration,
....we can see that with the two cars above they are both capable of very similar acceleration since they can generate similar torque at the wheels despite having vastly different crankshaft torque capabilities, because the wider rev range of the petrol engine allows a higher gear ratio to be used. In fact the petrol engine, despite having lower torque at the crank shaft, can actually achieve slightly higher torque at the wheels, and therefore we would expect it to have slightly higher acceleration.
So that is how you can have less crank shaft torque, but still have the same, or higher acceleration.
Now we could stop there... but I think we should go on:-
Now simple maths tells us that
Force x Moment Arm = Torque, which rearranges to
Torque/moment Arm = Force.
Now if we make the wording a bit more appropriate for our case this is:-
(Driven Wheel Torque)/(Driven Wheel radius) = Motive Force
Or, adding this to our earlier equation:-
((Crankshaft torque) x (Crank RPM)/(wheel RPM))/(Driven Wheel radius) = Motive Force
However, not all of this force is available to accelerate our car as some is used to overcome resistance (Rolling resistance, wind resistance, transmission resistance, gradient resistance), therefore we have:-
Force available for Acceleration = (((Crankshaft torque) x (Crank RPM)/(wheel RPM))/(Driven Wheel radius)) -(Resistance Forces)
Now we also know that
F=m.A thanks to our old friend Sir Isaac Newton, which rearranges to
Acceleration = Force / Mass
In our case the "Mass" term must also account for rotating inertia of wheels, tyres, brakes, drive shaft, gearing, engine crank shaft, flywheel, etc), but this means we can now substitute our "Force available for Acceleration" into our rearranged F=m.A equation:
Acceleration = ((((Crankshaft torque) x (Crank RPM)/(wheel RPM))/(Driven Wheel radius)) -(Resistance Forces)) / (Car Mass+allowance for Inertia).
So now, given sufficient data, we can actually calculate the acceleration of the vehicle. More than that we can calculate the top speed too, since at top speed the Motive Force = Resistance forces, and hence the acceleration is zero.
So there we go. Using Crankshaft torque, we can calculate the acceleration of our vehicle at any given road speed, and we can also calculate the top speed of our vehicle. But in order to do so,
we also need to know, and take account of the Crank RPM[/b] at which the engine is operating in order that we can calculate the gear ratio.
"Great", you might be thinking, "So torque is used to calculate acceleration
and top speed... where does
power come into all this?" No, its not about sustaining speed or any of that other stuff you may've read in a boy racer car magazine. Power is simply; (Crankshaft Torque) x (the Crankshaft RPM at which that torque is generated); it is just a really convenient figure..... I'll explain:-
Lets just remember:-
Acceleration = (((
(Crankshaft torque) x (Crank RPM)/(wheel RPM))/(Driven Wheel radius)) -(Resistance Forces)) / (Car Mass+allowance for Inertia).
And Top speed occurs when ((
(Crankshaft torque) x (Crank RPM)/(wheel RPM))/(Driven Wheel radius)) = (Resistance Forces)
Which means we can simplify the equations above by substituting Power =
Crank Torque x Crank RPM:-
Acceleration = (((
(Power)/(wheel RPM))/(Driven Wheel radius)) -(Resistance Forces)) / (Car Mass+allowance for Inertia).
And Top speed occurs when ((
(Power)/(wheel RPM))/(Driven Wheel radius)) = (Resistance Forces)
So Power can
also be used for calculating acceleration and top speed??!!! YES!!!!
So when we compare the accelerative or top-speed giving abilities of an engine we can either compare the values:-
(Crank Torque)x(Crank RPM)... which is a little complicated off the top of your head.... is 258lbft x 4000rpm higher or lower than 230lbft x 4500rpm???!
Or we simply compare
Power; is 196bhp higher or lower than 197bhp? -EASY!!!
The other point to bear in mind is that to determine the time taken to accelerate from one speed to another we also need to know the power (or indeed, the "crank torque x crank rpm") at all crank speeds used during the acceleration, not just the peak power or peak torque.
The sensible question you might now be asking is "Why do car magazines and brochures tell me the power at high rpm and the torque at low rpm, when really they should be telling me the power
or the "Crank Torque x Crank RPM" at high
and low rpm?" And the honest answer is "I don't know either -it is crazy, it is like saying
'This DVD is worth £4.00 and this other one is worth 3.65 x $2.4!!! You could wok out how they actually compare, but its not immediately obvious
Oh, and I just want to be clear; all those car performance figures on the link in my signature are independently tested by Autocar magazine.... not theoretical, not an analogy, not made up by me. Actual data.
one is a DIESEL engine, the other is a PETROL engine. so we can't compare!
A diesel engine is simply a metal box with a rotating output flange and clutch which attaches to a gearbox, as a petrol engine is also simply a metal box with a rotating output flange and clutch which attaches a to a gearbox, so the two can quite easily be directly compared to eachother if you use the correct methods to compare them.
You could also compare a gas turbine ("metal box with a rotating output flange")... or an electric motor ("metal box with a rotating output flange")... or a steam engine ("metal box with a rotating output flange")....
yes, but you claim the only difference to both cars is FINAL gear, not the rest of the gears.
"Final drive" does not mean top gear... it is the final gear ratio normally located in the differential (see below) which is, after, but in series with, the gearbox, and therefore changing that one "Final drive" gear ratio, actual changes the overall ratio in 1st gear all the way through to 7th gear, even though the gears in the gearbox themselves are physically the same.
Oh and by the way: the clutch on 99% of cars attaches to the flywheel... the flywheel attaches to the crank shaft. So "Flywheel torque" is the same as "Crank Torque" or "Torque at input to gearbox". here is a clutch attached to an engine flywheel:-
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