What is the relationship between engine power, force, and speed?

[jonnybmac]

Homework Statement

I am having difficulty understanding the conversion between power and rotation at the engine and at the wheel. Can you please state which parts are right and wrong, and why please as I think I've spent that long on researching I've confused myself with too much information.

Homework Equations

P = FV
P = mav
P = Γω
Γ = Fr

The Attempt at a Solution

(1) I know that the piston moving up and down causes a torque and angular speed of the engine shaft. increasing the times of the explosion, and therefore the faster up and down motion of the piston increases the speed of the rotations.
My understanding would be that the torque is constant at the engine, since r is constant and the force applied from the explosion will also be constant. That leaves RPM to increase power directly at the engine - but from every video I've watched and read, it states that power at the engine is almost always constant which conflicts this analogy.

(2) If an engine is in the same gear constantly. At max RPM, the power of the engine will be at max, so what happens at low RPM in the same gear? Is the power kept the same and torque increased as it is inversely proportional to RPM so will increase as the RPM decreases? Or does the power at the engine decrease with RPM and torque kept constant at the engine?

(3) Moving then to the wheels. at max RPM, and max power at the engine in a low gear the wheels get delivered maximum torque for low rpm. As the wheels move faster and therefore the RPM increases, the torque will decrease inversely proportionally.
But to keep up a constant acceleration, the car will have to change gear and therefore start from low RPM to high RPM. what is happening in this stage? as the car is at low RPM, what is the torque and power doing at the engine?

(4) I understand gears change the ratio of torque and speed, but is that changing the engine speed to the torque of the wheels?Many thanks for reading

 

[Al_]

RPM to increase power directly at the engine

In some engines, yes, power increases proportional to RPM within a certain rev range, as torque remains constant. But there are limits where gas flow and other things limit the power.
This is the "Power Curve" graph.
To make an engine more easy to use, often an engine's gas flow & electronic control is altered so the torque drops off as the revs rise.

 

[Al_]

power kept the same and torque increased

Often deliberately, for drivability, the engine gives more torque at lower rpm. To discourage over-revving and allow the engine to be more durable.

 

[Al_]

But to keep up a constant acceleration, the car will have to change gear and therefore start from low RPM to high RPM. what is happening in this stage? as the car is at low RPM, what is the torque and power doing at the engine?

Changing gears does not give constant acceleration if the engine has constant torque. (In the rev range)
Constant acceleration requires ever increasing power, when pushing against ever speedier tarmac. (Force times velocity)
If the engine has constant torque, when you change up, the acceleration steps down according to the change in gear ratio.
But most cars have torque that drops off as revs rise, in a gear. in fact it's often made just right so that changing up puts the engine back into higher torque and the acceleration starts off the same!

 

[jonnybmac]

Changing gears does not give constant acceleration if the engine has constant torque. (In the rev range)
Constant acceleration requires ever increasing power, when pushing against ever speedier tarmac. (Force times velocity)
If the engine has constant torque, when you change up, the acceleration steps down according to the change in gear ratio.
But most cars have torque that drops off as revs rise, in a gear. in fact it's often made just right so that changing up puts the engine back into higher torque and the acceleration starts off the same!

So if
P = mav
P = Γω

mav = Γ(rpm)So as rpm increases, it needs to reduce either Γ or mav.
But as rpm increases, v increases,
Since m is constant, it means then
v(rpm) = Γma
so an increase to the v(rpm) means a reduction of Γ and/or a

Sorry if this is what's already been stated. My head feels like it is going to explode so I'm going to take a rest and come back tomorrow

 

[CWatters]

(1) I know that the piston moving up and down causes a torque and angular speed of the engine shaft. increasing the times of the explosion, and therefore the faster up and down motion of the piston increases the speed of the rotations.
My understanding would be that the torque is constant at the engine, since r is constant and the force applied from the explosion will also be constant. That leaves RPM to increase power directly at the engine - but from every video I've watched and read, it states that power at the engine is almost always constant which conflicts this analogy.

If you are going to mention sources such as "videos" you should provide a link to them.

The piston force isn't constant and even if it was the torque applied to the crank shaft varies as the shaft rotates. So the torque at the engine isn't constant. It's probably better to think of the engine as providing pulses of energy to the flywheel which smooths out these pulses to provide more or less smooth power to the gearbox... but I'm sure there are better descriptions.

Clearly the power produced by a car engine isn't constant. Press the accelerator and the engine consumes more fuel converting it to more mechanical power. Release the accelerator and less fuel is consumed and less mechanical power is produced.

(2) If an engine is in the same gear constantly. At max RPM, the power of the engine will be at max...

No that's not correct. Car engines are not "ideal" engines. The power they produce isn't linear. They have a power curve as Al_ has stated. Here is an example...

Source: http://www.fordscorpio.co.uk/images/powertdi.jpg

Note how the power curve in blue has a peak at 4000rpm for this engine.

so what happens at low RPM in the same gear? Is the power kept the same and torque increased as it is inversely proportional to RPM so will increase as the RPM decreases? Or does the power at the engine decrease with RPM and torque kept constant at the engine?

The graph shows how much torque and power an engine can produce an any given engine rpm. Remember the actual torque and power depend on the throttle setting which controls how much fuel/energy is available. So the engine could be operating anywhere below the curve.

But to keep up a constant acceleration...

Cars almost never maintain constant acceleration. The usually accelerate faster at low speeds than at high speeds.

.. the car will have to change gear and therefore start from low RPM to high RPM. what is happening in this stage? as the car is at low RPM, what is the torque and power doing at the engine?

Long answer sorry..

There are two main forces acting on a car. Let's call them...

F_D which is the sum of all drag forces (air resistance, rolling resistance, friction in bearings etc). This force increases with speed and
F_I which is the inertial force required to accelerate the car (eg F_I=ma). This force increases with acceleration.

At any given velocity and acceleration the power the engine has to produce is the net (sum) of these forces times velocity eg..

P = (F_D + F_I) * velocity

If you want max acceleration that implies F_I will be large. To maximise the right hand side you need to maximise the left hand side. So to maximise acceleration you need to operate the engine as close as possible to maximum power. Ideally that would mean keeping the rpm constant at 4000 (for the above engine) regardless of road speed. Obviously this can't be done with a fixed gear ratio so all cars have a number of gears. For maximum acceleration the driver would choose when to change gear so that the engine rpm stays as close to the max power point as possible.

Typically as the car goes faster there comes a point where the rpm goes over the top of the peak in the power curve and power output falls. Changing up reduces engine rpm bringing the engine rpm back to nearer the peak increasing power.

As the car goes faster there is more air resistance so F_D increases and there is less power available for F_I, meaning that the acceleration reduces. eg most cars accelerate fastest at slow speeds when air resistance is lowest.

 

[jonnybmac]

If you are going to mention sources such as "videos" you should provide a link to them.

The piston force isn't constant and even if it was the torque applied to the crank shaft varies as the shaft rotates. So the torque at the engine isn't constant. It's probably better to think of the engine as providing pulses of energy to the flywheel which smooths out these pulses to provide more or less smooth power to the gearbox... but I'm sure there are better descriptions.

Clearly the power produced by a car engine isn't constant. Press the accelerator and the engine consumes more fuel converting it to more mechanical power. Release the accelerator and less fuel is consumed and less mechanical power is produced.
No that's not correct. Car engines are not "ideal" engines. The power they produce isn't linear. They have a power curve as Al_ has stated. Here is an example...

View attachment 217898
Source: http://www.fordscorpio.co.uk/images/powertdi.jpg

Note how the power curve in blue has a peak at 4000rpm for this engine.
The graph shows how much torque and power an engine can produce an any given engine rpm. Remember the actual torque and power depend on the throttle setting which controls how much fuel/energy is available. So the engine could be operating anywhere below the curve.
Cars almost never maintain constant acceleration. The usually accelerate faster at low speeds than at high speeds.
Long answer sorry..

There are two main forces acting on a car. Let's call them...

F_D which is the sum of all drag forces (air resistance, rolling resistance, friction in bearings etc). This force increases with speed and
F_I which is the inertial force required to accelerate the car (eg F_I=ma). This force increases with acceleration.

At any given velocity and acceleration the power the engine has to produce is the net (sum) of these forces times velocity eg..

P = (F_D + F_I) * velocity

If you want max acceleration that implies F_I will be large. To maximise the right hand side you need to maximise the left hand side. So to maximise acceleration you need to operate the engine as close as possible to maximum power. Ideally that would mean keeping the rpm constant at 4000 (for the above engine) regardless of road speed. Obviously this can't be done with a fixed gear ratio so all cars have a number of gears. For maximum acceleration the driver would choose when to change gear so that the engine rpm stays as close to the max power point as possible.

Typically as the car goes faster there comes a point where the rpm goes over the top of the peak in the power curve and power output falls. Changing up reduces engine rpm bringing the engine rpm back to nearer the peak increasing power.

As the car goes faster there is more air resistance so F_D increases and there is less power available for F_I, meaning that the acceleration reduces. eg most cars accelerate fastest at slow speeds when air resistance is lowest.

Wow, I really appreciate the time you have put into such an informative reply with picture and mathematical models (Not discrediting Al_'s input and thank you also).

I actually jumped the gun in terms of trying to learn something before I was actually ready. Since I am distance learning, the next book was all about how an engine produces power and transfers it through gears - so my understanding has become somewhat better over the last 2 days of reading.

I've just read all of these posts and they have made things a lot more clearer; so thank you for the assistance and patience in explaining I appreciate it

 

[haruspex]

the power curve in blue has a peak at 4000rpm

Does this result mainly from the inertia of the piston? ... a sort of forced-damped oscillation.

 

[CWatters]

Does this result mainly from the inertia of the piston? ... a sort of forced-damped oscillation.

I believe the drop in power after the peak is mainly due to issues with the way engines breath. Can't get the fuel/air in and out fast enough. Something like that.