Yes, but the bit I'm grappling with is that at any instant, the CVT is a fixed gear. So, how does that work?

# Acceleration - Torque vs Power

### #301

Posted 03 November 2017 - 15:19

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### #302

Posted 03 November 2017 - 15:33

Hello RogerGraham.

You write:

"1. maximum acceleration in a given gear occurs at peak torque

2. if the gear ratio can be optimized (e.g. with a CVT) then maximum acceleration occurs at peak power

At face value, statement 1 implies that for statement 2, at any instant (i.e. when the CVT is at a "fixed" ratio at that instant), the maximum acceleration will occur at peak torque. But that's not the case."

A CVT being "fixed" at a transmission ratio is the same as a manual gearbox at a specific ratio (say 3rd).

Here is a CVT that can be "fixed" at various tranmsission ratios by locking the lever 7 at various angles:

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Suppose you are going with 30mph and 4,000rpm; you lock the lever 7 (i.e. you fix the transmission ratio in the CVT) and you open the throttle widely; the vehicle accelerates; the maximum acceleration will happen at the revs wherein the engine provides its peak torque (at the peak power revs the acceleration is lower).

Suppose now that you want to define the gear ratio giving the maximum acceleration at a specific vehicle speed, say at 50mph.

You "fix" a transmission ratio in the CVT (by locking the lever 7 at an angle) and you measure the acceleration when the vehicle speed passes 50mph.

You repeat for various "fixed" transmission ratios.

The maximum acceleration will happen with the "fixed" transmission ratio at which, at 50mph the engine runs at its peak power revs.

Thanks

Manolis Pattakos

### #303

Posted 03 November 2017 - 15:46

Yes, but the bit I'm grappling with is that at any instant, the CVT is a fixed gear. So, how does that work?

The CVT is not a fixed gear, it is continuously variable.

What this means is:

For a conventional gearbox, since Acceleration = Power / Velocity, the increase in speed *counteracts* the increase in power as rpms rise within a gear, therefore acceleration does not increase as power increases (necessarily).

Whereas for a CVT, power becomes independent of engine speed or road speed.

**Edited by V8 Fireworks, 03 November 2017 - 15:53.**

### #304

Posted 03 November 2017 - 15:59

The CVT is not a fixed gear, it is continuously variable.

Yes, I understand that, but my point was about the instantaneous nature of the CVT being a fixed gear.

I think Manolis answered what wasn't "clicking" for me. If I understand it correctly, those two points could be re-written as:

1. maximum acceleration in a given **gear** occurs at peak **torque**

2. maximum acceleration at a given **speed** occurs at peak **power**

If that's correct, then the light might have just switched on in here.

### #305

Posted 03 November 2017 - 16:05

1. maximum acceleration in a given

gearoccurs at peaktorque2. maximum acceleration at a given

speedoccurs at peakpower

If that's correct, then the light might have just switched on in here.

Yes, that's correct. Here is a paste of the "proof" I prepared earlier.

__Q: Does peak power or peak torque result in maximum acceleration?__

__A: Both!__

Analysing the relationship between torque and power and acceleration using physics leads to two seemingly contradictory, yet both completely correct, conclusions. I found this topic quite confusing before looking at it this way, hope this following clears it up for everybody. (Of course, this simplified analysis doesn’t include aerodynamic or frictional losses, deformation of the tyre, etc.)

Note, since Force = mass * acceleration and mass of vehicle is constant therefore maximum force is analogous to maximum acceleration for our purposes.

1) __Within a given gear, peak acceleration occurs for peak torque.__

Force = Power / Velocity

And, Power = Torque * Omega (omega = angular velocity of engine (i.e., rpm), and from geometry, Velocity = R * omega / total gear ratio, where R is radius of the tyre, so Omega = Velocity * total gear ratio / R)

Thus, Force = Torque * velocity * total gear ratio / R / Velocity

I.e., Force = Torque * total gear ratio / R

Since total gear ratio is constant (as is tyre radius, R), force (acceleration) is at a maximum when torque is at a maximum for a given gear ratio.

2) __However, for a given road speed, peak acceleration occurs for peak power__

Force = Power / Velocity

Velocity is constant for a given road speed, therefore, peak force (acceleration) occurs at peak power for a given road speed. (i.e., a CVT should choose the rpm of peak power to obtain maximum acceleration for a given road speed).

…….

TL;DR: Peak torque gives the maximum acceleration within a gear, peak power gives the maximum acceleration for a given road speed.

**Edited by V8 Fireworks, 03 November 2017 - 16:16.**

### #306

Posted 04 November 2017 - 03:11

With one rather theoretical addition. The curve of vehicle resistance to steady motion at a given speed MIGHT be such as to limit acceleration at the peak torque speed to less than that at some lower speed. For example, the banal example of a single fixed gear vehicle that is geared to reach top speed at max torque, might accelerate (slowly) up to top speed but won't go any faster. That's the wrong gearing for the vehicle, but it could happen,

### #307

Posted 13 November 2017 - 04:20

" you would have no sense of difference between an acceleration of 2m/s and 20m/s under sustained conditions." So those pictures of people with their faces pulled back and their eyeballs popping out on centrifuges are fakes?

Fake news!

Yeah, point taken. Hence my trepidation to shout too loudly.

I want to say the original basis of my incorrect statement is a misunderstanding of something you wrote, ages ago now, about not feeling acceleration, only rate of change. <heads off to search for incorrectly remembered vague statement>

### #309

Posted 13 November 2017 - 04:48

Aha!

From the spinning crankshaft thread of 2006. I have indeed read into your post things you didn't say.

Posted 19 October 2006 - 16:22

That's a good point. One of your more sensitive sensors is the tension in your neck muscles required to hold your head straight. Well, no it isn't. The thing you sense is the CHANGE in tension. That change in tension is proportional to the change in acceleration, which officially is known as 'jerk'. So, when your head feels like it is getting thrown about it is complaining about the change in acceleration, it tells you very little about the steady state acceleration.

Now, just to confuse things even more, your head has a certain resonant frequency in which it 'nods', on the stiffness of the muscles and tendons in your neck. So when you subjectively rate 'acceleration feel' a large part of your impression is due to the rate of change of acceleration of a single degree of freedom - which is a very long way indeed from what you are trying to measure.

That being said. the pressure in your back from the seat is a good indicator, but you have hardly any nerve endings there, and sigals from your back are desensitised to continual acceleration, otherwise you'd find lying on your back rather odd.