Calculating wheel torque from engine torque

[russ_watters]

I said, "Power must increase at the same rate as velocity to maintain constant acceleration."

And that's true! That's the linear relationship you are claiming doesn't exist!

Let's start with power and assume we want to find acceleration.

What you are or should be doing is relating acceleration to power. That's the relationship you are saying doesn't exist. Mathematical handwaving that doesn't connect acceleration to power - when you easily could - doesn't say anything useful.

Power = (mass X acceleration X distance / time).

To find acceleration from power

This is just basic algebra:
P=MAD/T
A=PT/(MD) = P/(VM) -- Just like I said.

...we have to multiply power by the inverse of [mass X (distance / time)]. So we need a factor whose dimensions are [1 / (mass X velocity)]. Once again power is converted to force and you wind up with force / mass.

If you want to find if power is related to acceleration, you shouldn't cancel-out the power, you should leave it there and just re-arrange the equation around it. I feel like either you don't understand basic algebra here. All you do to re-arrange an equation is multiply both sides by the factor you want to move from one side to the other. For example:
Y=5X
Y*1/5=5X*1/5
Y/5=X

What about the issue of an infinite number of values for power for any value of acceleration? If you've got an infinite number of answers for the same question then there is no relation.

As you can see from the equation that you don't want to admit exists, there is only one value of acceleration per value of power.

 

[OldYat47]

This is my second to last post on this subject. I'm going all the way back to define what I'm saying, because it seems I'm speaking in a different language.
I say that power and acceleration are not related. I say that because there is no formula that will give a result in acceleration knowing the power and the mass. So far all the formulas in all the replies that claim to do that use velocity to convert power to force. Compare: acceleration = (force / mass) and acceleration = [power / (mass X velocity)]. Note that the second equation does not relate power to acceleration because (power / velocity) = force. So the second equation is identical to the first equation.

I think (I hope) that we can all agree that, given a constant mass and a constant force, acceleration is constant. I think we can all agree that if acceleration is constant power will increase directly proportional to speed. I think we can all agree that, given a constant mass and a constant power, acceleration will decrease directly proportional to velocity. These last two statements say that power and acceleration are not related. Why? Because in the second statement acceleration is constant, power is increasing, and in the third statement power is constant and acceleration is decreasing.

I said this was my second to last post. If anyone posts a formula that directly relates power to acceleration without using velocity to convert power to force I will post "Good job!". So you need a formula that will solve this question:

Some mass is moving. The power involved at some instant is known. Velocity at that instant is unknown. What is the acceleration of the mass at that point in time?

P. S.
For any given mass and any given acceleration there exists an infinite number of values for power.
(acceleration = (power / velocity) / mass. Insert any acceleration and any mass. There exists an infinite number of combinations of (power / velocity) that will make the equation correct. Once you divide power by velocity you get a single value for force.

 

[jack action]

I don't understand why you assume the mass is constant in $a = \frac{F}{M}$, but you can't assume the mass and the velocity are constant in $a = \frac{P}{Mv}$. You know the mass can change while the vehicle is moving, right? You can consider the mass of fuel that is burned along the journey, or even the case where a tanker is emptying its load while moving.

Let's look at the statements you feed us but assuming mass is not constant when using the force equation:

I say that because there is no formula that will give a result in acceleration knowing the power and the mass.

«I say that because there is no formula that will give a result in acceleration knowing only the force.»

I think we can all agree that if acceleration is constant power will increase directly proportional to speed.

«I think we can all agree that if acceleration is constant force will increase directly proportional to mass.»

I think we can all agree that, given a constant mass and a constant power, acceleration will decrease directly proportional to velocity.

«I think we can all agree that, given a constant force, acceleration will decrease directly proportional to mass.»

If anyone posts a formula that directly relates power to acceleration without using velocity to convert power to force I will post "Good job!".

«If anyone posts a formula that directly relates force to acceleration without using mass to convert force to acceleration I will post "Good job!".»

Some mass is moving. The power involved at some instant is known. Velocity at that instant is unknown. What is the acceleration of the mass at that point in time?

«Some mass is moving. The force involved at some instant is known. Mass at that instant is unknown. What is the acceleration of the mass at that point in time?»

For any given mass and any given acceleration there exists an infinite number of values for power.

«For any given acceleration there exists an infinite number of values for force.»

Why are you allowed to assume that mass is constant and we are not allowed to assume that velocity is constant too?

Again, I challenge you to show us a mathematical equation (or real life example) where two vehicles are accelerated from $v=0$ to $v= v_f$, one reaching $v_f$ faster than the other, and that the fastest one is not using more power than the other one. Even more precise, try to show me an example where the increase in instantaneous power is not directly proportional to the increase in instantaneous acceleration when comparing both vehicles.

I showed you my math, but you never comment on it. Do you understand what I do? Ask questions if you don't understand some of it. Again, you are not wrong, it is just that you are setting arbitrary limits without justification (mass is constant, velocity cannot be constant) .

We cannot be all wrong and you being the only one who's right.

 

[jack action]

@OldYat47 :

OK, I got another image for you, to help you show where you err.

The area $A$ of a rectangle is the length $l$ times the width $w$, or $A = lw$.

The volume $V$ of a box is the area $A$ times the height $h$, or $V = Ah$.

But we can also say that $V = lwh$, right?

Is the volume $V$ related to width $w$? If I increase $w$, does that translate into more volume? I think everyone agree with the fact that it does.

Of course, one can say: «but if you decrease $h$ at the same time, the volume will stay the same.» That is true, still, everyone say that there is a direct relationship with the width of a box and the volume of the box. It is not because the volume of the box is also related to another dimension (which can increase or decrease independently of $w$), that the relationship between $w$ and $V$ disappears.

Assume now that $V$ is the power, $A$ is the force, $l$ is the mass, $w$ is the acceleration and $h$ is the velocity:
$$V=lwh$$
$$P=Mav$$
Can we not say the same thing?

Is the power $P$ related to acceleration $a$? If I increase $a$, does that translate into more power? I think everyone should also agree that it will.

Of course, one can say: «but if you decrease $v$ at the same time, the power will stay the same.» That is true, still, everyone say that there is a direct relationship with the acceleration and the power. It is not because the power is also related to another dimension (which can increase or decrease independently of $a$), that the relationship between $a$ and $P$ disappears.

Conclusion: If you have an increase in acceleration, you must have an increase in power too.

It is simple algebra.

 

[russ_watters]

This is my second to last post on this subject. I'm going all the way back to define what I'm saying, because it seems I'm speaking in a different language.
I say that power and acceleration are not related. I say that because there is no formula that will give a result in acceleration knowing the power and the mass.

[Moderator hat]
It does feel like we are speaking different languages and the language problem is with math: you seem genuinely unable to perform basic algebraic manipulation of an equation. This is a knowledge gap and one we can fix, but only if you make an effort to learn.

This discussion feels like a debate, but it cannot be: this is easy/settled physics and is not debatable. So if you do choose to continue posting in this thread, you will need to change your approach from trying to debate to trying to learn. PF rules prohibit arguments against established science. [/Modhat]

 

[OldYat47]

OK, now I have to respond. I'm not debating, I'm pointing out the simple physics and algebra. I'll run through some of it again.
My basic claim is that power and acceleration are not related, that there is no algebraic function that allows calculation of acceleration directly from power. To calculate acceleration using power you must also know velocity and use velocity to convert power to force. The result is rate of acceleration at one velocity only.
I also stated that
[power / (mass X velocity)]
is not that equation since
(power / velocity) = force,
so the equation is identical to [acceleration = (force / mass)].
I also pointed out that using
acceleration = [power / (mass X velocity)]
for any given rate of acceleration and mass there is an infinite number of values for power and make the equation true. This is mathematically true, just select the velocity that makes it all work out.
I could expand and rephrase that statement: Any value of power can accelerate any mass at any rate of acceleration.
Example question: Can 0.1 (watt) accelerate a 100 (kilogram) mass at a rate of 100 (meters / second^2)?
Answer: Yes, when the velocity is 0.00001 (meters / second).

So my premise remains that power and acceleration are not mathematically related. You can't calculate acceleration directly from power, you must convert power to force first. If you can calculate acceleration directly from power please reply with the equation.

 

[jack action]

I'll try again before they close this thread (I fought for you @OldYat47 ).

You stated that $a = \frac{F}{M}$ and that $M$ is constant, so $a$ is related to $F$. True.

But $F = \frac{P}{v}$ and we can assume that $v$ is constant (you can do it with $M$, why not with $v$?), so $F$ is related to $P$. Also true.

If $a$ is related to $F$ and $F$ is related to $P$, therefore $a$ has to be related to $P$. Otherwise it doesn't make sense.

Sorry, but the equation you are looking for is $a = P$ and that doesn't exist, just like $a = F$ doesn't exist either. But $a \propto F$, $F \propto P$ and $a \propto P$ all exist, and that is what we are trying to explain to you.

 

[jack action]

If you can calculate acceleration directly from power please reply with the equation.

On my website, I have an acceleration simulator where I explain how I find the acceleration, which is found with equation 1b, which is basically $a = \frac{F}{M}$, where $F = \frac{P}{v}$, when there is enough traction. I can calculate the acceleration of any vehicle from power only and it is pretty accurate. You cannot have a better proof than this.

 

[OldYat47]

Please re-read the last paragraph of my last comment. My challenge is for someone to demonstrate going from power to acceleration without first converting power to force by dividing force by velocity. Please review the algebra.
Let's assume we have some constant mass.
Acceleration is proportional to force because with any force there is a single unique value for acceleration. Values for acceleration change directly with changes in values of force.
Force is not proportional to power. We know this because you can have many different values for force at any given power. (velocity dependent)
Acceleration is not proportional to power. We know this because you can have many different values for acceleration at any given power. (velocity dependent)
Dividing power by velocity = force, which we agree on. But that takes power out of the equations and puts force into them.

 

[jack action]

Please re-read the last paragraph of my last comment.

I wish I could, but it seems you are the one who is not reading our comments.

You are simply repeating the same thing over and over again without challenging what is told to you. If you did, you would see where you err.

 

[berkeman]

Thread closed for Moderation...

 

[berkeman]

Thread re-opened.

 

[thichiuem]

To Jack_action and OldYat47
It looks like you are in 2 different frames of reference:
Acceleration increases, torque increases, that's ok, but if you know the torque of 2 motors, is it true that every motors with greater torque will have a greater acceleration? that's not yet.
Wish you will have good Ideals to us.

 

[jack action]

but if you know the torque of 2 motors, is it true that every motors with greater torque will have a greater acceleration?

The vehicle with the greatest torque will produce the greatest acceleration.

At zero velocity, any motor can produce any level of torque with the proper gearing.

At any other speed, the maximum vehicle torque only depends on the vehicle power output, which is the same as the motor power output (less some drivetrain inefficacies). So gearing the maximum motor power output to the desired vehicle speed will give the maximum vehicle torque and thus its maximum acceleration at that speed.

@OldYat47 is long gone.

 

[thichiuem]

@jack action : Between an elephant and a horse, which acceleration is greater?

 

[cjl]

Probably the horse, even though the elephant has a much higher power output. Acceleration is based on power to weight though, and in the case of horses vs elephants, a lot of other biomechanical factors that really aren't relevant to the discussion at hand.

 

[jack action]

@jack action : Between an elephant and a horse, which acceleration is greater?

I read that a horse can produce a peak of 15 horsepower. I cannot find a similar value for an elephant, but when comparing with horses, they seem to be able to pull a similar weight ratio compared to their mass, maybe even larger. This would suggest that their acceleration would be similar from a standstill start, maybe even larger.

But horses will be able to reach a higher maximum speed, meaning they accelerate faster at higher speeds (while the elephant's acceleration goes to zero). But this may be like comparing two identical vehicles with different transmissions: One accelerates fast at low speeds but reaches quickly a top speed, and the other accelerates slower, but over a much wider speed range. With the horse and the elephant, that would be comparing their biomechanics.

As an aside, on a 40-yard dash, this is what a professor of applied physiology and biomechanics had to say:

Squirrel: The nutty rodents can hightail it at up to 14 mph—on a good day

Elephant: Although much more massive, they can sprint at roughly the same speed as a squirrel

 

[thichiuem]

That is to say, you must have the same frame of reference.
To compare two equivalent cars (in terms of mass, gear ratio, wheel radius, ...) it can be said that the vehicle with the greater torque has the greater acceleration.
As for comparing 2 cars (assuming there is no loss), because P=ma*v, the car with larger P/m will have a greater acceleration.
Thank you for your reply and would like to learn more.