Acceleration of a car and jet plane problem

[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.

 

[vysqn]

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!

I admit, I was wrong, I didn't understand the basics.
That's why I came here to learn and understand more of basic physics.
I have read all posts and what I've learned (I think) is this:

Force causes the acceleration of a mass because F = m*a
Engine power generate a force which accelerate a car, engine changes rotation, into torque at the wheels thus causing forward movement. More power = more force pushing car forward.
Constant engine torque means constant acceleration because power increases proportional to speed, Constant engine power means decreasing proportional to speed - if there is no counter forces like air resistance etc in both cases.
If I in my car I want maximum acceleration throughout a given speed range I have to be at maximimum engine power which generate maximum wheel torque and as a consequences - fastest acceleration

The acceleration is NOT direct proportion to engine torque, is direct proportion to wheel torque.

If Jet engine produce constant trust that means constant acceleration (If mass doesn't change and there is no air resistance)
But there is a point when air resistance is so big that plane doesn't accelerate any more and that is top speed of the plane.
We can calculate power if we want from anything which produce force because P =F*vI have one more question:
If car or plane or any object stays in motion with the same speed and in the same direction it uses Newton 1st law of motion.
If car or plane or any object start to accelerate it uses Newton 2nd and 3rd law of motion.
Correct?

BTW - sorry for my english

 

[Dale]

I admit, I was wrong, I didn't understand the basics.
That's why I came here to learn and understand more of basic physics.
I have read all posts and what I've learned (I think) is this:

Force causes the acceleration of a mass because F = m*a
Engine power generate a force which accelerate a car, engine changes rotation, into torque at the wheels thus causing forward movement. More power = more force pushing car forward.
Constant engine torque means constant acceleration because power increases proportional to speed, Constant engine power means decreasing proportional to speed - if there is no counter forces like air resistance etc in both cases.
If I in my car I want maximum acceleration throughout a given speed range I have to be at maximimum engine power which generate maximum wheel torque and as a consequences - fastest acceleration

The acceleration is NOT direct proportion to engine torque, is direct proportion to wheel torque.

If Jet engine produce constant trust that means constant acceleration (If mass doesn't change and there is no air resistance)
But there is a point when air resistance is so big that plane doesn't accelerate any more and that is top speed of the plane.
We can calculate power if we want from anything which produce force because P =F*v

Awesome! I would say that your knowledge of physics now exceeds my knowledge of cars!

I have one more question:
If car or plane or any object stays in motion with the same speed and in the same direction it uses Newton 1st law of motion.
If car or plane or any object start to accelerate it uses Newton 2nd and 3rd law of motion.
Correct?

Yes, although Newton’s 3rd law applies any time there is a force regardless of whether there is acceleration or not.

 

[jim hardy]

The acceleration is NOT direct proportion to engine torque, is direct proportion to wheel torque.

Bear in mind that the gear train connecting engine and wheels makes those two torques proportional by the gear ratio. .
By "direct proportion " i did not mean a one-to-one proportion.
My mistake, i mixed four thoughts in one sentence.
It started out okay but i appended a 'run-on sentence fragment' in parentheses. .
Here it is:

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 )

That's the danger of run-on sentences, they mix thoughts which leads to thoughts getting overlooked.

Excruciating attention to detail, both technical and grammatical, is the price of clear communication.
I consciously strive to write one thought per sentence and one sentence per line.
Sometimes i forget to do that.
Mea Culpa.

Torque converters add a level of complexity.
They're not quite a CVT but are a step toward one.
They transmit torque according to the difference between input and output RPM's and can actually increase torque .
That's why you'll find a car with an automatic transmission almost always has a different drive axle ratio than the same model equipped with a manual transmission.
(And it's why i put that small print caveat at the end of my run-on sentence fragment.)

Sorry for any confusion i caused.

old jim

 

[jim hardy]

My intent with this post is just to encourage simple stepwise thinking. I only want to address the real basic physics. I'm no race car expert.

Our brains don't do well in a thought experiment when we try to move multiple inter-related variables by ourself.
A fellow needs to boil the problem down to one variable that he controls, and see what Mother Nature does to the others.
We call the variable that's under our direct control the "Independent Variable" .
We vary it to stimulate the system under study and observe what the other, related variables do.
We call those related variables the "Dependent" variables.
I was taught to always plot independent variable on the horizontal axis and dependent ones vertically.

So, removing gear ratios and vehicle differences from the discussion,
in other words
boiling our thought experiment down to just one independent variable, RPM ,
and looking at a real speed-torque curve to see how torque and power and acceleration behave,
i posit:
neglecting rolling resistance, drivetrain friction, wind resistance,
and driving on level road that's neither uphill nor down
and staying in same gear !
physics tells us that

(red line is torque, blue is power..)
Acceleration will follow the red line.
because wheel torque is engine torque X the gear ratio which we're not changing for this thought experiment
and wheel tractive force pushing the car is wheel torque / wheel radius.At 2800 rpm, horsepower is 2π X 750 ft-lbs X 2800 rpm / 33,000 = 399.8 hp
At 1600 rpm, horsepower is 2π X 800 ft-lbs X 1600 rpm / 33,000 = 243.7 hp
which will be in the exact same ratio as the vehicle speeds at those RPM's (EDIT OOPS MIstake ! ) , as
make that line read ....
which will be in the exact same ratio as the power calculated by vehicle speed X wheel tractive force at those RPM's , as
@jack action pointed out earlier in his post number 42
where he pointed out OP's error of neglecting mechanical advantage.

========BORING ANECDOTE #√³∞
The fact is if you're going to drag race,
an accelerometer on the dashboard will do you more good than a tachometer.
Back in my high school days, early 60's, a good friend installed one in his hotrod.
He soon learned the "feel" of shifting after the torque peak,
and how far back along the torque curve each upshift would take him.
He optimized his acceleration over the thirteen or fourteen seconds it took him to go ¼ mile.

END BORING ANECDOTE============

now i'll try to blend basic physics with real world and my friend's experience
because i think the troubles in the thread stem partly from lack of clarity on relation between torque and power,
and partly from less than full awareness of the integral relations between acceleration speed and distance.

Acceleration is more important early in the race than late because
you need to build up speed early
so as to eat up distance quickly not waste seconds
after all you got to integrate acceleration to get speed and you got to integrate again to get distance;
and ∫(a big number) grows faster than ∫(a little number);
and you want that integral to reach ¼ mile ASAP. .

Next -- since Power is torque X (gear ratios et al) X speed
and since speed is less early in the run,
at maximum torque power is less there too. see the curve

Which takes us back to jack's conservation of energy.
Work done on the car during the race W is F X D (eq 0)
and neglecting friction&wind
it'll be all kinetic energy at the end of the track
so W = ½mv² (eq 1)
and if F = m X a
plugging that into (eq 0)
W = m X a X D (eq 2)
m and D are constant ::: mass of car, length of dragstip
to maximize W the only thing you can control is a and that's torque at the wheelsand for a sanity cross check,
going back to algebra
and equating eq's 1 and 2
W = ½mv² = m X a X D
v = √ (2a/D)
So, to maximize speed through the traps you maximize a and that's torque at the wheels..

...................

All that said,

@jack action quite beautifully explained the effect of adding multiple gear ratios to our thought experiment in that old thread he referenced.
It makes clear how and why you pick your shift points above the engine's peak torque rpm , and even above its power peak, to maximize torque at the wheels.
https://www.physicsforums.com/threa...from-engine-torque.870677/page-3#post-5482482
He plotted torque at the wheels which is engine torque X gear ratio, so his chart has a curve for each gear
worth reading...

shifting gears jumps you from one curve to the next.
i'd venture he doesn't upshift until wheel torque of the gear he's in falls below the maximum he can get from the next gear.
And an accelerometer on the dashboard will show him that.

Any help or just muddying ?old jim.

 

[Baluncore]

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

I am sorry I mentioned speed in post #52. I was under the impression that acceleration was the rate of change of speed.

A vehicle is not designed to be a flywheel. Torque is only being used to transmit energy from the engine to the driving wheels, where the rubber meets the road and torque is converted from a rotational to a linear force by the wheel radius. That is where the mass of the vehicle and F = m*a can finally come into play. The gearbox and differential ratios simply adjust the torque to RPM matching ratio in the drive-line. Torque * RPM will always be the rate of energy transmission = power.

A real vehicle is not a virtual mass sliding in a vacuum across a friction-free plane surface. Neither torque nor power implies acceleration of a real vehicle. Energy can flow to change the kinetic or the potential energy, or to losses. Climbing a hill requires both RPM and torque to transfer the energy needed to increase the potential energy of the vehicle as it climbs to a greater height. Aerodynamic drag, or a headwind also require torque just to maintain velocity without acceleration.

It is better with laymen, in almost every case, to consider “energy flow” in joules/sec = watts, than it is to involve the often misunderstood term torque. “Energy flow” may often be a better term than power as it is less ambiguous and more meaningful to a layman. The management and transmission of energy is fundamental to all engineering.

 

[Dale]

I was under the impression that acceleration was the rate of change of speed.

Precisely. It is the rate of change of speed, not speed. The two quantities are orthogonal.

A real vehicle is not a virtual mass sliding in a vacuum across a friction-free plane surface. Neither torque nor power implies acceleration of a real vehicle.

Good point. But in all cases the wheel torque is the mechanical quantity most directly related to the net force and therefore to acceleration.

 

[Baluncore]

But in all cases the wheel torque is the mechanical quantity most directly related to the net force and therefore to acceleration.

Only for you.

 

[jim hardy]

It is better with laymen, in almost every case, to consider “energy flow” in joules/sec = watts, than it is to involve the often misunderstood term torque. “Energy flow” may often be a better term than power as it is less ambiguous and more meaningful to a layman. The management and transmission of energy is fundamental to all engineering.

Now we're talking about how to teach.? That's subjective.

Everybody has his own life experiences that affected his thought processes.
My own concepts of force momentum and torque were formed at about age 10 to 12, pushing boats around at a marina.
That really nailed the sensory 'feelings'
and when i took high school physics, learning the names ascribed to those already familiar concepts was immediate and pleasurable.
My feel for momentum got a name mv, and that energy was ½mv² was easy enough to remember -- we didnt integrate in my high school.

so for this old layman the torque approach works just fine and is intuitive.

i think were i teaching gearheads, which is an affectionate not a derogatory term for laymen,
i'd use the torque approach and relate it to their childhood bicycling experience.
We can feel a force and estimate its magnitude
but it's a bigger mental step to sense energy with our muscles.

you notice i used your energy method as my sanity check. I'm so mistake-prone i have to cross check myself all the time.and i mistrust my math until I've cross checked two or three calculations.

Teachers should encourage students to apply physics to their everyday experiences, and vice versa. Getting one's intuition aligned with his math saves a lot of rote memorization.

just my two cents

old jim.

 

[Adam Talman]

I suppose it depends on what language and framework you are working under. At the atomic level you need the energy and collisions from atoms in order to generate a force. Therefore, if you have energy from the atoms bumping you have power producing the force. In the case of engines it may be considered the other way around. Engines produce power that accelerates the vehicle. However, I agree with Dale, I am pretty sure it is the force that you feel. My intuition tells me that is the case.

 

[Mandy D]

I realize that I am late to the party, but my thoughts on this are that I would rather consider tractive effort (force) than torque. It more directly relates to what is happening to the vehicle as a whole. However, I agree that torque is more relevant to the calculations related to acceleration than is power. I frequently have this argument with lads driving sports cars who think power is more important. My proof is to pitch my Land Rover against their sports car, select low first and floor the accelerator. It almost does not matter how much power they have (except perhaps in the extreme) against my miserable 101 kW (136 BHP) they cannot match my initial acceleration. Girls 1, Boys nil. OK, so they catch up and pass me - eventually.

F = ma
P = Tw
T2 = TR
F = T2/r

F = accelerating force
m = mass of car
a = acceleration of car
T = torque at flywheel
T2 = torque at wheels
R = gear ratio (total, main box x transfer box x axle ratios)
r = rolling radius of wheel

Calculate F from T2/r, plug back into F = ma, et voila we have an acceleration. I hope I have made no mistakes, here. :)

 

[cjl]

And this is why those of us familiar with the argument get frustrated.

Your land rover has no hope against a sports car off the line if the sports car launches well (either with a high stall torque converter, launch control, or just a careful modulation of the clutch). In addition, at all other speeds, the sports car will still accelerate harder because it has more horsepower. Horsepower is the relevant factor when figuring out how fast you can add kinetic energy to the vehicle, and a higher horsepower will always be able to accelerate faster.

 

[russ_watters]

I suppose it depends on what language and framework you are working under. At the atomic level you need the energy and collisions from atoms in order to generate a force. Therefore, if you have energy from the atoms bumping you have power producing the force.

I'm sorry, but this really isn't generally true. Only glasses have collisions between molecules and even then what you say suggests energy expenditure, which doesn't happen.

 

[cjl]

Good point. But in all cases the wheel torque is the mechanical quantity most directly related to the net force and therefore to acceleration.

Not really though, since you still have to account for tire size to convert from wheel torque to tractive force. This is why power is the easier way to approach it - you can bypass all the details of gear ratios, wheel sizes, etc, and you can directly figure out acceleration based only on knowing vehicle speed and current power production.

 

[russ_watters]

Not really though, since you still have to account for tire size to convert from wheel torque to tractive force. This is why power is the easier way to approach it - you can bypass all the details of gear ratios, wheel sizes, etc, and you can directly figure out acceleration based only on knowing vehicle speed and current power production.

I like this approach. Torque is a component of power, but not the only component. And wheel torque at any instant (along with mass and a fixed wheel size) tells you acceleration, but when people say "acceleration" for a car they are usually talking about average acceleration presented as a time to a speed (0-60, 50-70, etc), not instantaneous acceleration.

By knowing what people want, including seeing through lack of specificity and how "car guy" terminology differs from the standard physics terminology you can bridge the gap and make sure we're answering the question that was intended to be asked.

 

[vysqn]

I never ever thought, that this discussion will develop so much I asked super stupid question showing that my knowledge of physics is misunderstood by myself. But I analized all post and I drew conclusions which i wrote at post #61

 

[Dale]

Not really though, since you still have to account for tire size to convert from wheel torque to tractive force. This is why power is the easier way to approach it - you can bypass all the details of gear ratios, wheel sizes, etc, and you can directly figure out acceleration based only on knowing vehicle speed and current power production.

As you accelerate wheel size remains constant while speed does not. So the relationship with power is certainly not more direct.

When wheel torque peaks acceleration peaks. When power peaks acceleration does not peak. Acceleration can be non zero while power is zero, and at that time it has the same fixed relationship with torque as always. Acceleration will decrease if power is constant, and at that same time it has the same fixed relationship with torque as always.

Sorry, but your argument does not seem consistent with the facts to me. I maintain that in all cases the wheel torque is the mechanical quantity most directly related to the net force and therefore to acceleration.

 

[jim hardy]

Your land rover has no hope against a sports car off the line if the sports car launches well (either with a high stall torque converter, launch control, or just a careful modulation of the clutch). In addition,...
... Horsepower is the relevant factor when figuring out how fast you can add kinetic energy to the vehicle, and a higher horsepower will always be able to accelerate faster.

i don't think that's quite so.

Her point is that with higher ratio gearing
her 136 horsepower off road truck can
at low vehicle speed
deliver more torque to the drive wheels than a sports car equipped with more horsepower and lower ratio(nearer 1::1) gearing .
That's how mechanical advantage works.
Selecting "Low Range" in a 4wd increases mechanical advantage typically between two and four fold.

A 'modulated' clutch transmits torque without loss, ie torque in equals torque out
but it does NOT transmit power without loss
because the clutch disk itself in that modulated clutch,
sandwiched as it is between the flywheel and pressure plate metal surfaces,
rotates at lower RPM than those two surfaces (and the engine that's driving them.)
There's slip between those metal driving surfaces and the composite clutch disk's driven surface.
So a goodly chunk of the engine's power is dissipated as heat at those sliding surfaces so never reaches the driving wheels..
Power lost in the clutch is equal to product torque X (engine rpm - clutch disk rpm) and goes to heat not kinetic energy .

...you can directly figure out acceleration based only on knowing vehicle speed and current power production.

add to that knowing what fraction of current power production goes to acceleration.

Either approach can be made to work and anyone's preference is just that - a preference.

old jim

 

[Randy Beikmann]

To simplify this discussion, I would assert that Newton's laws and the laws of thermodynamics/energy are equally important. There's no reason to argue about which is more so here. To accelerate a car, there must be a force F at the tire patch to cause it, so that F=ma (neglecting drag). But, except for the trivial case where v=0, creating this force requires the power P=Fv, where v is the vehicle speed. Using the two equations, you see that P=mav. So as speed increases, it takes more power to produce the same acceleration.

So accelerating the car requires a force, and creating that force requires power, except for the infinitesimal time period when v=0. Why make this complicated?

Note that traction force and engine power each have limits, and either can be the limiting factor to your acceleration. At low speeds the power (P=mav) required to accelerate is small, so acceleration is limited by the maximum available traction force Fmax: then a=Fmax/m. Beyond a certain speed (v>Pmax/Fmax, where Pmax is the maximum power), the engine can't produce enough power to fully utilize the tire traction, so a=Pmax/(mv). (I've neglected drag and driveline friction here, which don't change the main conclusions.)

 

[cjl]

i don't think that's quite so.

Her point is that with higher ratio gearing
her 136 horsepower off road truck can
at low vehicle speed
deliver more torque to the drive wheels than a sports car equipped with more horsepower and lower ratio(nearer 1::1) gearing .
That's how mechanical advantage works.

Selecting "Low Range" in a 4wd increases mechanical advantage typically between two and four fold.

But in reality, that's very unlikely, for a number of reasons. First of all, in low range, a truck or SUV cannot deliver anywhere close to full horsepower to the wheels. The reason for this is that trucks and SUVs tend to have relatively heavy flywheels, and in extremely low gears (such as a low range provides), most of the horsepower will actually be spent just accelerating the engine. The inertia of the engine and driveline prevents you from efficiently delivering that power to the wheels. Also, sports cars are generally geared to provide high acceleration based on their engine properties and the design of the car, so their first gear is generally more than low enough to get the car off the line effectively.

A 'modulated' clutch transmits torque without loss, ie torque in equals torque out
but it does NOT transmit power without loss
because the clutch disk itself in that modulated clutch,
sandwiched as it is between the flywheel and pressure plate metal surfaces,
rotates at lower RPM than those two surfaces (and the engine that's driving them.)
There's slip between those metal driving surfaces and the composite clutch disk's driven surface.
So a goodly chunk of the engine's power is dissipated as heat at those sliding surfaces so never reaches the driving wheels..
Power lost in the clutch is equal to product torque X (engine rpm - clutch disk rpm) and goes to heat not kinetic energy .

True, but a clutch eliminates that drivetrain inertia problem mentioned above because the engine is already at speed, so the torque transmitted to the wheels is quite a bit better. In addition, you can actually get well above the engine's rated torque during a launch in a manual car since you can take advantage of the engine's inertia to help accelerate the car. Using a proper launch, I'd bet on nearly any sports car to beat an older, 136hp Land Rover from 0-20 every time.

add to that knowing what fraction of current power production goes to acceleration.

In most gears, at most speeds, you can reasonably assume that fraction to be about 85%

Either approach can be made to work and anyone's preference is just that - a preference.

old jim

Except that a lot of people use the "torque" arguments to draw erroneous conclusions, which is the source of this whole discussion in the first place.

 

[Dale]

Except that a lot of people use the "torque" arguments to draw erroneous conclusions, which is the source of this whole discussion in the first place.

And some people (such as the OP) use the “power” arguments to draw erroneous conclusions.

 

[jim hardy]

In most gears, at most speeds, you can reasonably assume that fraction to be about 85%

not when you're riding the clutch.

and i reject the 'heavy flywheel' hypothesis as straw-grasping to defend a position.

As i said a preference is only a preference.

When you can make both approaches agree you nave mastered the subject.

old jim

 

[cjl]

Of course not when you're riding the clutch, but the clutch is only a factor in the first portion of the acceleration. As for the "heavy flywheel" argument, you'd be surprised how much of the engine's power is sucked up just accelerating the drivetrain (mainly the flywheel) in low gears. It makes a very significant difference.

 

[Dale]

my thoughts on this are that I would rather consider tractive effort (force) than torque. It more directly relates to what is happening to the vehicle as a whole.

I think this is a good suggestion. It avoids the entrenched positions in this weird debate and is accurate.

 

[jack action]

I realize that I am late to the party, but my thoughts on this are that I would rather consider tractive effort (force) than torque. It more directly relates to what is happening to the vehicle as a whole.

Of course it is better to use the tractive effort. It further proves how much futile torque is. Imagine the force is the result of a jet engine: Where is the torque in that vehicle? Only power matters.

My proof is to pitch my Land Rover against their sports car, select low first and floor the accelerator. It almost does not matter how much power they have (except perhaps in the extreme) against my miserable 101 kW (136 BHP) they cannot match my initial acceleration.

Assuming both vehicles have a transmission designed to extract the most from their engines (which they probably have), a Land Rover gets more acceleration at low RPM because it has more power at low RPM than a sports car has at low RPM. That is the only way.

The «extreme» ones that do beat the Land Rover - guess what? - they have more low RPM power than the Land Rover can produce. That is the only way.

OK, so they catch up and pass me - eventually.

How can a vehicle «catch up» without producing more acceleration than the vehicle it overtakes? The reason the sports car produces more acceleration at one point is because it enters its RPM range where it produces more power than the Land Rover (which also enters its most powerful RPM range); and they both stay there by shifting gears.

Yes, the source of acceleration is the torque. But the source of the torque is the power produced.

At $v=0^+$, the amount of torque is dependent on the amount of energy released by the engine $dE$ during a displacement $d\theta$: $T = \frac{dE}{d\theta} = \frac{Pdt}{d\theta} = \frac{P}{\omega}$. Theoretically, for the nanosecond that $v=0$ while power is applied, the wheel torque is infinite and the tire friction force reaches its maximum, leading to slipping. A mere nanosecond. After that, traction force can be derived directly from power (as long as it is not limited by the tire maximum friction force).

 

[Dale]

Only power matters.

Again, no

By the way, you did not respond to my questions to you above.

Assuming both vehicles have a transmission designed to extract the most from their engines (which they probably have), a Land Rover gets more acceleration at low RPM because it has more power at low RPM than a sports car has at low RPM. That is the only way.

The «extreme» ones that do beat the Land Rover - guess what? - they have more low RPM power than the Land Rover can produce. That is the only way.

In all of these arguments you could simply replace the word “power” with “wheel torque” and have an equally valid argument. Your arguments are neutral evidence in scientific terms, they do nothing to distinguish between the two hypothesis.

If you wish to have some actual evidence then you need to consider ways in which wheel torque and power differ. In all those ways acceleration follows torque, not power. But it seems that you are so blinded by the overarching argument that you are more interested in chanting “power” than in actually looking at sound science.

 

[jim hardy]

Of course it is better to use the tractive effort.

which is wheel torque divided by wheel radius.

 

[jack action]

I guess you are talking about these questions:

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?

Configuration can be changed: they are different gear ratios. With a CVT, you have an infinite number of gear ratios. For any given speed, the peak acceleration will occur at peak power. Maximum acceleration is a function speed.

If it is at peak power then which of the four peak power points has the highest acceleration and why?

They all are. Maximum acceleration is a function of speed. Maximum available power is usually constant with respect to speed.

Do you believe that in all engines the peak power occurs at the same point as the peak wheel torque?

Yes. At any given speed that is.

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.

At any given speed, the largest wheel torque is only dependent on the appropriate gear ratio selected. That appropriate gear ratio is the one that will give the highest power at that speed.

In all of these arguments you could simply replace the word “power” with “wheel torque” and have an equally valid argument.

I'm glad you agree that my argument is as valid as yours.

In all those ways acceleration follows torque, not power.

And wheel torque, as a function of speed, what does it follow?

If someone asks you: «How can I double my car's acceleration?» Are you going to answer: «All you need is a larger wheel torque. Double your gear ratio in your differential and you will double your acceleration. Better yet, just put wheels with half the radius, that will do the job.» You will be right, but be prepared to face a mad customer when he will find out his car goes at half the speed. Then you will probably say: «Oh! you wanted to keep the same speed range? You didn't mention that. If you want to do that, you have no other choices but to double your power if you want to double the acceleration.»

The problem you have right now is that you are trying to fit your definition of acceleration to the problem (i.e. instantaneous) and then say: «See, I'm right.» And, yes, you are. And, yes, it wasn't an error on your part to assume that definition at first.

But the acceleration that the OP talks about is the average acceleration over a given speed range. Again, it is OK you did not get that initially. There are no "right" definitions of acceleration. You went for the pure "physics" sense; car guys go for the more "practical" sense, with the words they know and without necessarily understanding that other definitions might be assumed.

But now that you understand what is at stake, you have enough knowledge to get what the problem is all about. Most car guys without university education don't have all the knowledge you have and cannot get what you are talking about. It is therefore your responsibility to reach to them as they don't get what you are talking about and they get confused and frustrated. They don't care about instantaneous acceleration. Stop talking about it. Stay on the subject at hand. Correct the language if you want, but stay on topic: Average acceleration over a given speed range.

I will cite again what @russ_watters said (emphasis mine):

but when people say "acceleration" for a car they are usually talking about average acceleration presented as a time to a speed (0-60, 50-70, etc), not instantaneous acceleration.

By knowing what people want, including seeing through lack of specificity and how "car guy" terminology differs from the standard physics terminology you can bridge the gap and make sure we're answering the question that was intended to be asked.

It is not about you being right, it about you answering the question asked, even if it requires some decoding on your part.

 

[russ_watters]

It is not about you being right, it about you answering the question asked, even if it requires some decoding on your part.

Agreed, and I will add the caveat that when one knows there is a miscommunication they should endeavor to correct it instead of arguing right/wrong. It is less confrontational to say a person is correctly answering a different question than just to say they are "wrong". Better yet, when in an emphatic argument, one should put effort into looking for the miscommunication.

So for this situation, I would say that the word "acceleration" is being misused, 0-60 time is what is intended and as such power is the critical factor. Further I would say that power and torque are not separate issues, so the entire debate is a misnomer: engine torque is not a relevant parameter on its own, and two otherwise identical cars with different rpm/torque ratios but generating the same horsepower at the same speed must by law of physics be delivering the same torque to the ground.

 

[Baluncore]

Imagine the force is the result of a jet engine: Where is the torque in that vehicle? Only power matters.

The OP referred to Force and Power, not to torque. We know his force is torque for wheeled vehicles, but we do not worry about drive wheel torque while driving because it is hidden from us by the engine-speed to road-speed matching device called a gearbox. For that reason we optimise power = energy conversion, so we can climb hills by increasing PE = m·g·h, or accelerate by increasing KE = ½·m·v².

Torque is unimportant unless the drive wheel radius and RPM is specified. Energy converted by the motor is transmitted as power = torque * RPM. Acceleration will reduce torque as the RPM increases. Vehicle acceleration will be a maximum when the vehicle first starts to move. Since engine torque and power are gear ratio independent, the drive wheel torque can be maximum only in low gear, at low road speed.

It is clear that for a fixed energy flow, torque must fall as speed increases. Since KE = ½·m·v², acceleration will reduce as road-speed increases, even with a perfect gearbox.

 

[Dale]

Maximum acceleration is a function speed

Since you are just outright lying now it is time to close this thread. There is only one speed at which the acceleration is a maximum as is clearly shown in your own figure.

Thread closed.