Acceleration of a car and jet plane problem

[vysqn]

Newton is right. Sorry, none of these videos is teaching you correct physics.

if it is true, it is ruining my worldview. I start to learn some physics just for fun some time ago because I was curious how torque and power works. And those guys looking trustable for me...
And now I feel crushed...

 

[Dale]

How is that possible that those 2 enginers are wrong?

Note, the requirements of PF, as I have already mentioned above, are that all posts on PF must be consistent with the professional scientific literature. That means textbooks and peer-reviewed papers. Youtube videos are not peer-reviewed and they are not vetted. They are often of low quality scientifically, as here.

I am sure that if those engineers were preparing a scientific publication then they would have been more correct in their statements. But it is not our goal to correct all youtube errors so it is pointless to send lots of videos containing such errors. We recognize that they exist and that is precisely why the acceptable standards here are higher.

 

[vysqn]

Note, the requirements of PF

What is PF ?

And what proffesional scientific literature You suggest me to learn about power, torque force etc?

 

[jack action]

@vysqn :

I'll try to demonstrate the problem from another perspective. You start with the engine and try to figure out where the power/torque goes. It is in my opinion that it is best to look at what needs to be achieved to reach the desired objectives.

There is a vehicle (car or plane or whatever) of mass $m$, it has a velocity $v$, an acceleration $a$ and some resistance $R$ (drag, rolling resistance, etc.).

To maintain this set up, you must also have a force $F$. The force $F$ can be found with the following relationship:
$$F = R + ma$$
But, there is also the notion of power $P$ that is important. The following relationship must also be respected:
$$P=Fv$$
What does this means?

Whatever power source you have (combustion engine, jet engine, electric motor, horses or humans pulling the vehicle; anything), it must be able to produce the force $F$ and the power $P$.

Usually, the force $F$ is easy to achieve (with a gearbox for example), no matter what the power is; no matter whether this power is composed (at the source) of 'force' or 'velocity'. But power is maintained through any change (not considering minor losses) due to the principle of conservation of energy.

What happens if $a=0$? Then $F=R$ and $P=Fv$. If this is the maximum power you can produce, then $v$ is your maximum velocity.

If you can increase the power by $\Delta P$, then - at this velocity $v$ - the force $F$ will increase ($F+\Delta F=\frac{P+\Delta P}{v}$), thus the acceleration $a$ will increase ($0+\Delta a=\frac{F+\Delta F -R}{m}$ or $\Delta a=\frac{\Delta F }{m}$), which in turn will increase $v$, setting you to a new equilibrium. Note that you might need to do some transformations along the way to make sure $P=Fv$ for the vehicle (like changing the gear ratio for example).

What happen if $v=0$? Then $F=R+ma$ and $P=0$. This means that as long as the power source can produce the force $F$, you are OK. How much power does it [keyword]needs[/keyword] to produce? None.

So a 5 hp lawnmower engine can theoretically produce the necessary force to reach the same acceleration that a 10 000 hp dragster engine can produce ... at $v=0$ and only at $v=0$. Note that in reality, there might be so much losses in the transmission that the force $F$ will not be reached (In fact, either $R$ or $m$ will be greater in some way).

But if the engine produces, say, 300 hp at $v=0$, where does it all go? It goes into wasted heat (the tires spin, clutches slip, etc.), mechanical energy (stored in rotating parts because of inertia) or elastic energy (parts will deform).

What I'm saying is that instead of starting with the engine and trying to figure out what you can do with it, try to analyze what is required by the vehicle.

 

[Baluncore]

What is PF ?

You are there. PF is www.physicsforums.com

There is a different language out there where the identical words have completely different meanings.

When I pointed to the two faded blue marks on the tachometer and asked if they were the equal power points I was told; “No, those are the equal torque points”, and that “it is not power until it gets to the back wheels”. I chose NOT to argue, so the inspector granted my license upgrade.
I do know that you should change gear at equal power points, which happen to be equal torque points at the back wheels, but they are not equal engine torque points. The engine RPM and gear ratio steps have a lot to do with that.

 

[Dale]

Please don't tell me that average 100Nm between 2000-4000RPM (from 50-70km\h) will accelerate car faster than average 50Nm between 8000-10000RPM (from 50-70km\h)

Why not. That is exactly right. A higher average torque directly means a higher average acceleration. Note, I am talking about torque at the wheels, not torque at the engine.

Edit: and I am assuming the RPM is the engine RPM and the mass and wheel size is identical. If you intended something different then my answer would be different

 

[jim hardy]

You started this thread a few days ago
https://www.physicsforums.com/threads/is-engine-torque-a-static-force.959297/#post-6083015
and were shown the error of your ways

But you are trying to hold to to your old mistaken preconceived word salad ideas. Forget them they're only confusing you. And a lot of other car enthusiasts too.
Here's what Abbe de Condillac said about such thinking about 250 years ago:

"Instead of applying observation to the things we wished to know, we have chosen rather to imagine them. Advancing from one ill founded supposition to another, we have at last bewildered ourselves amidst a multitude of errors. These errors becoming prejudices, are, of course, adopted as principles, and we thus bewilder ourselves more and more. The method, too, by which we conduct our reasonings is as absurd; we abuse words which we do not understand, and call this the art of reasoning. When matters have been brought this length, when errors have been thus accumulated, there is but one remedy by which order can be restored to the faculty of thinking; this is, to forget all that we have learned, to trace back our ideas to their source, to follow the train in which they rise, and, as my Lord Bacon says, to frame the human understanding anew.

In an automobile you feel acceleration which is in direct proportion to engine torque, (of course multiplied by gear ratios and wheel radius, and both of those are constant so long as you stay in any particular gear...and don't have a torque converter ahead of the gearbox )

Power is NOT in proportion to torque , it's in proportion to PRODUCT of Torque and RPM.
Horsepower = 2π X Torque_ft-lbs X RPM / 33,000

PS
That Condillac quote comes from a good introduction to straight thinking by Lavoisier. It's at https://web.lemoyne.edu/giunta/lavpref.html , and is worth digesting.old jim

 

[jim hardy]

Power is a RATE of doing work. So it inherently includes a unit of time. Something per second or minute, see horsepower equation above.
Torque is not a rate it's just a force albeit a force of rotation not straight line pull. No time necessary .

 

[jim hardy]

And what proffesional scientific literature You suggest me to learn about power, torque force etc?

start here ?
http://hyperphysics.phy-astr.gsu.edu/hbase/force.html
Search on words you do not understand, and even those you think you do.

 

[jack action]

In an automobile you feel acceleration which is in direct proportion to engine torque

This is wrong. The acceleration is in direct proportion to wheel torque. The difference is rather important in this case.

Please don't tell me that average 100Nm between 2000-4000RPM (from 50-70km\h) will accelerate car faster than average 50Nm between 8000-10000RPM (from 50-70km\h)

Why not. That is exactly right. A higher average torque directly means a higher average acceleration. Note, I am talking about torque at the wheels, not torque at the engine.

Why not? Because the vehicle goes at the same speed in both cases (The OP did take the time to mention it). This means that the wheel torque will be 1.5 times higher [= (50 * 9000) / (100 * 3000)] in the first case compare to the other, which is exactly comparing power outputs. This shows that a vehicle's wheel torque is proportional to power when compared at the same car velocity (as long as there is a velocity, i.e. $v \neq 0$). Your first 2 sentences are in direct contradiction with your last sentence.

For any advisors who would like to continue debating on this thread, I'm suggesting reading this https://www.physicsforums.com/threads/answering-simple-questions.953955/. At this point, the answers given are not helpful at all. They bring up confusion and frustration. Also, here is a little reminder of what can be found on PF home page (my emphasis in green text):

The Physics Forums Way
We Value Quality
• Topics based on mainstream science
• Proper English grammar and correct spelling
We Value Civility
• Positive and compassionate attitudes
• Patience and diplomacy while debating
We Value Productivity
• Disciplined to remain on-topic
• Honest recognition of own weaknesses
• Solo and cooperative problem solving

 

[Dale]

This is wrong. The acceleration is in direct proportion to wheel torque. The difference is rather important in this case.

Yes! I agree. Torque is not a conserved quantity, and gearing ratios can dramatically change the torque from the engine to the wheel. Power on the other hand is conserved (energy rather) so gearing ratios only change power indirectly through making the engine more or less efficient (neglecting small mechanical losses).

Your first 2 sentences are in direct contradiction with your last sentence

It isn't a contradiction. I specified wheel torque. He was unclear.

 

[jack action]

It isn't a contradiction. I specified wheel torque. He was unclear.

Even if he was specifying wheel torque & rpm, the fact that both cases have the same linear velocity means that the wheel radii are different, thus the forces at the wheel contact patch are still in proportion to the power:
$$P_{out} = P_{in}$$
$$Fv = T \omega$$
$$F = \frac{T\omega}{v}$$
Case 1:
$$F_1 = \frac{T\omega}{v} = \frac{50\ N.m \times 9000\ rpm}{60\ km/h} = 7500 \frac{N.m.rpm}{km/h}$$
Case 2:
$$F_2 = \frac{T\omega}{v} = \frac{100\ N.m \times 3000\ rpm}{60\ km/h} = 5000 \frac{N.m.rpm}{km/h}$$
[Too lazy to do unit conversions ]

Still in such case, the propulsive force is 1.5 times larger.

I'm specifying that because conservation of energy plays a major role here. In the debate «power vs torque», it is the great forgotten on the «torque» side. They understand Newton's 2nd law but refuse to acknowledge the principle of conservation of energy. I don't want to give them more ammunition when they'll read this thread and say: "Scientists on PF say only torque matters in acceleration, power is meaningless".

It must be clear that this is not up for debate and that it is based on fundamental scientific principles.

 

[Dale]

Even if he was specifying wheel torque & rpm, the fact that both cases have the same linear velocity means that the wheel radii are different

Oops, you are right, good point here. I was also not clear. I was assuming identical vehicle mass and wheel size, hence the specifications would be wheel torque and engine RPM.

I believe that most of the problems in the discussion come from lack of clarity. Engine vs wheel. Average vs peak vs max. Comparison criteria, etc.

They understand Newton's 2nd law but refuse to acknowledge the principle of conservation of energy

Energy is conserved, certainly. But that is not the question here. The question is about acceleration, and at all times for a given vehicle acceleration is directly proportional to wheel torque, not power. Conservation of energy is a great principle, but not the relevant one for the specific question of acceleration.

I have already explained the clear contradiction at rest, but even at high speed there is another clear contradiction. At high speeds (but neglecting dissipation) assuming a continuously variable transmission you could accelerate at constant power. In doing so your acceleration would decrease. Your power would be constant but your wheel torque would decrease, in exact proportion to the decreasing acceleration.

My assertion that torque (wheel) causes acceleration is correct, and in no way should be misconstrued to indicate that energy is not conserved. Power is important for acceleration, but only indirectly as when the maximum available power is what limits instantaneous wheel torque.

 

[cjl]

It's important to note though that at all times at a given vehicle speed, acceleration is directly proportional to horsepower. Wheel torque is almost never directly measured or referenced when discussing cars, and discussions like this lead to misconceptions like the very common believe that engine torque matters more than horsepower.

 

[Dale]

It's important to note though that at all times at a given vehicle speed, acceleration is directly proportional to horsepower.

Not at rest. From a stand-still power is 0 regardless of acceleration.

Wheel torque is almost never directly measured

Yes, that is a problem. Also, there is often a confusion about instantaneous torque vs max torque.

discussions like this lead to misconceptions like the very common believe that engine torque matters more than horsepower.

But the alternative leads to misconceptions on the physics as demonstrated by the OP. Here I am concerned about fostering correct physics much more than fostering correct purchasing decisions.

 

[cjl]

Not at rest. From a stand-still power is 0 regardless of acceleration.

Yes, but acceleration from a standstill is a very small subset of the "how fast will my car accelerate" case, and is complicated by a number of other factors.

But the alternative leads to misconceptions on the physics as demonstrated by the OP. Here I am concerned about fostering correct physics much more than fostering correct purchasing decisions.

I feel like the constant "no, power doesn't determine acceleration" in this thread is leading to far more misconceptions about physics than my statement above. In addition, knowing that it's proportional to power is fundamentally more useful, since a car's power is easily determined from its specifications and is independent of things such as driveline configuration and gear ratio. It's much simpler for a driver to know that to maximize acceleration, they must simply select whatever gear puts the engine closest to max power rather than suggesting that they must calculate wheel torque based on varying gear ratios and engine RPM.

For an example of how this can be misleading, you very confidently stated that the statement in the video in post #8 was wrong. You are wrong about this. The video is absolutely correct. At best, your statement is extremely misleading, since the video was quite clear about its statement that horsepower determines rate of acceleration (correct), and acceleration determines the reaction force between you and the seat of the car (also correct).

Fact: At all nonzero speeds, acceleration is directly proportional to power to weight ratio, and inversely proportional to speed

 

[Dale]

knowing that it's proportional to power is fundamentally more useful

Except that it is not proportional to power, it is proportional to power divided by speed (ie torque) and speed changes during acceleration. So stating that acceleration is proportional to power is kind of dodgy since the constant of proportionality is not constant. That isn’t the usual relationship meant by “proportional”.

At all nonzero speeds, acceleration is directly proportional to power to weight ratio, and inversely proportional to speed

Sure, because power divided by speed is directly proportional to wheel torque.

Look, I am not familiar with this apparently heated debate. I have no stake in it and I am just teaching physics. The power people have apparently convinced the OP of some incorrect physics as you can see from the OP. So overemphasizing power is not the be-all end-all solution.

Instead of having a power vs torque argument, wouldn't it be better to actually teach the physics of how power and wheel torque are not independent concepts but are closely related? Then you can show them how to calculate torque from power and thus figure out the acceleration.

 

[jim hardy]

For any advisors who would like to continue debating on this thread, I'm suggesting reading this https://www.physicsforums.com/threads/answering-simple-questions.953955/. At this point, the answers given are not helpful at all. They bring up confusion and frustration. Also, here is a little reminder of what can be found on PF home page (my emphasis in green text):

If i was uncivil i hereby extend my apology
was trying to be a bit forceful to break down what i perceived as a mental barrier , that's all

old jim

 

[jack action]

At high speeds (but neglecting dissipation) assuming a continuously variable transmission you could accelerate at constant power. In doing so your acceleration would decrease. Your power would be constant but your wheel torque would decrease, in exact proportion to the decreasing acceleration.

Yes, but if you double that constant power, you will double the acceleration at any speed. And this is the only way you can achieve that.

Look, I am not familiar with this apparently heated debate. I have no stake in it and I am just teaching physics. The power people have apparently convinced the OP of some incorrect physics as you can see from the OP. So overemphasizing power is not the be-all end-all solution.

Instead of having a power vs torque argument, wouldn't it be better to actually teach the physics of how power and wheel torque are not independent concepts but are closely related? Then you can show them how to calculate torque from power and thus figure out the acceleration.

I see the problem now from your perspective. So you are unfamiliar with the problem and don't see how it is to "teach" a «torque» person about the importance of power in vehicle acceleration? Let me get you up to speed with this thread. The fun starts with post #15 with OldYat47 (and, yes, it goes all the way to post #100). This type of discussion has been going on forever in the automotive community and the web forums are filled with those. You might appreciate more why you must be careful about the wording you choose when entering this debate.

 

[Dale]

Yes, but if you double that constant power, you will double the acceleration at any speed. And this is the only way you can achieve that.

Agreed, because doubling the power will double the torque. There is no power vs torque objection there.

So you are unfamiliar with the problem and don't see how it is to "teach" a «torque» person about the importance of power in vehicle acceleration?

Having “torque” people and “power” people is silly. They are not independent quantities.

 

[cjl]

I see the problem now from your perspective. So you are unfamiliar with the problem and don't see how it is to "teach" a «torque» person about the importance of power in vehicle acceleration? Let me get you up to speed with this thread. The fun starts with post #15 with OldYat47 (and, yes, it goes all the way to post #100). This type of discussion has been going on forever in the automotive community and the web forums are filled with those. You might appreciate more why you must be careful about the wording you choose when entering this debate.

Huh. I'd forgotten about that thread. I was expecting this one

 

[Baluncore]

The flow of energy is what it is all about. That is where the money is.
Energy is conserved and must be accounted and paid for.
Power is the rate of flow of energy.

Given a long enough lever and a fulcrum to rest it on, you can apply as much force as you want to a mass, only you will be limited by the distance you can move that mass.
Given the right gearbox, you can have as much torque as you want, but your speed will be limited because power (= energy flow), is determined by the engine's capacity to transform electrical or chemical energy into mechanical energy.
Whenever torque is mentioned there must be an RPM specified before energy or power can be considered, or fairly accounted for.

If engine torque is flat across a wide engine speed range then power increases with the engine RPM because power = torque * angular velocity.
If a mass is not free to move there will be no energy transferred to that mass by a force acting on it. If a shaft is not free to rotate there will be no energy transferred along that shaft by a torque acting on it. A static torque is sometimes called a moment, physicists and engineers differ in terminology there.

 

[Dale]

you can have as much torque as you want, but your speed will be limited because power

The question wasn’t about speed, it was about acceleration.

 

[jim hardy]

To return to the vernacular of car-guy circles,
(where we all like short explanations)
...
do these two statements paint a more concise yet still accurate word picture?

TORQUE determines acceleration.
POWER determines to what speed that acceleration can be sustained.

keep in mind that
in car-speak, torque and power are both functions of RPM that are nonlinear.
while
In physics-speak we like to hold one of them constant and focus on the other two as a simple ratio..

Perhaps that's been the origin of some discord in the thread?

Please correct or improve my word-picture...

old jim

 

[Dale]

Let me get you up to speed with this thread.

I really like this plot you posted in that thread:

View attachment 187751

Note that there is one unique point of peak wheel torque corresponding to the one unique peak acceleration. There are four points of peak power, none of which are the peak acceleration.

Any justification you can give as to why power should be considered as being proportional to acceleration are just torque expressed in terms of power. In any way that wheel torque differs from power, acceleration follows torque not power.

 

[russ_watters]

I didn't read all the recent discussion, but the bottom line for me is this: The videos led the OP to or reinforced in the OP a very, very wrong understanding of physics. He actually said force doesn't cause acceleration! (and in a PM to me said this even while citing f=ma). How can we endorse any explanation that leads to such a fundamental/basic wrong?

I really don't think it should be difficult to teach this correctly. The problem with the videos is they skip steps. One even had a long equation for calculating power with all the necessary elements, but without really explaining them, particular the starting point. So here's how I'd work through the explanation of power and torque in cars:

1. Linear force between the ground and wheels causes a car to accelerate. (I watched two videos and neither stated this, though one had it embedded in an equation.)
2. Linear force between the ground and wheels is generated by torque at the wheels. (Not stated or confused between wheel and engine torque.)
3. Power is torque times speed (linear or rotational), so:
a. As a car accelerates at constant torque, power increases proportional to speed.
b. As a car accelerates at constant power, torque decreases proportional to speed.

That's it. Now, this real-world torque vs power thing is based on a bunch of sloppily defined scenarios and other obfuscations. Peak vs operating points, "all else being equal" except that oops we didn't mention gearing, acceleration measured as time to a certain speed, etc. In terms of the physics, torque and power go hand-in-hand, so there is nothing to debate! The only way for torque to be different given the same power is for an accidental or purposeful deception regarding other variables.

 

[russ_watters]

do these two statements paint a more concise yet still accurate word picture?

TORQUE determines acceleration.
POWER determines to what speed that acceleration can be sustained.

More or less. But per my previous, I would prefer hammering on the fact that they really aren't separate things, but are merely two components of the same state. E.G., a car at X speed and Y acceleration has A horsepower and B torque being delivered to the wheels.

For real-world car performance, the only real caveat I'd add (probably should have in my last post) is that at the engine, if you have higher rpm and lower torque to generate the same horsepower, theoretically they are identical in performance, but in real life the lower rpm and higher torque is probably better because it should have lower losses, less rotational inertia, etc.

 

[Dale]

The videos led the OP to or reinforced in the OP a very, very wrong understanding of physics. He actually said force doesn't cause acceleration!

Exactly!

If you want to teach the importance of power, that is fine. But it must not lead to a result like this.

 

[jack action]

Note that there is one unique point of peak wheel torque corresponding to the one unique peak acceleration.

Sadly, it is not the "peak" wheel torque. It is in that gear ratio. You could have a lower gear ratio and get a higher peak wheel torque. Even at that same exact velocity, you can reach a higher wheel torque - the highest possible - which, guess what, correspond to the peak wheel power! (more details in this post)

This particular example has different gear ratios. But what if you want to compare an electric motor with a combustion engine? Or even if you want to verify a claim from someone presenting a new kind of motor? Which one has more potential to give the largest acceleration over a given speed range? It's the maximum power output you can maintain in that speed range that really tells everything you need to know. The only way it wouldn't matter is if you power a vehicle with something like gravity, where the force is constant and not limited power-wise. Although, note-worthy, it is a very unusual case that doesn't relate to most machines we know, especially cars. When someone ask about cars, I don't think assuming a power-limited machine is too big of an assumption.

The real "torque vs power" problem is «Should you maintain your engine at peak torque or at peak power to get the maximum acceleration throughout a given speed range?» The answer to that question should be unequivocally "peak power". For some unknown reasons, there are still people claiming "peak torque", mostly because $F = ma$ and there is no power in that equation.

If you want to teach the importance of power, that is fine. But it must not lead to a result like this.

Agreed. It must be corrected. Correcting is not only saying «You are wrong», but also explaining the proper way, given the sought information. I'm sure you mean well but the posts you have written that I dislike were posts #28 and #32. These posts are elitists, add nothing to the discussion and just throw every other insights out the window. They obviously left the OP confused and frustrated (Except for obvious crackpot theories, that is usually a sign that the posts are not answering the question, even though they are technically correct). This is not good for bringing people to the scientific ways. There is a context here (subject, education level, language barrier) since post #1 and the answers must be in line with this context.

but in real life the lower rpm and higher torque is probably better because it should have lower losses, less rotational inertia, etc.

In real life, the low-rpm engine will be much bigger than a high-rpm engine; there is no way around it. So the gain on the inertia point of view might not be as good as one might think. FWIW, for the last hundred years, it seems that all engine designs tends to evolve while favoring low torque and high rpm features, i.e. smaller engines.

 

[Dale]

Sadly, it is not the "peak" wheel torque. It is in that gear ratio. You could have a lower gear ratio and get a higher peak wheel torque

But that vehicle does not have a lower gear. For that vehicle that is the peak torque and the peak acceleration occurs at the peak torque not at peak power.

This is your own example, surely you don’t think it is a bad or unrealistic example. So then, without changing the configuration, just looking at that plot as is, where does the peak acceleration occur? Is it at the peak torque or the peak power? If it is at peak power then which of the four peak power points has the highest acceleration and why?

Do you believe that in all engines the peak power occurs at the same point as the peak wheel torque? If not, then for those engines does peak acceleration occur at peak torque or at peak power?

Which one has more potential to give the largest acceleration over a given speed range? It's the maximum power output

Yes, that is the one with the largest potential acceleration. And which one has the largest actual acceleration? It is the one with the largest wheel torque.