At v=0 the second statement is completely false for any vehicle, and it is a very poor approximation for low speeds for automobiles. And the third is never correct, there are always other factors involved.At any given velocity:
The force applied to the vehicle dictates the acceleration it gets;
The power applied to the vehicle dictates the force it gets;
Therefore, the maximum possible acceleration of the vehicle depends solely on the maximum power available for the vehicle.
I agree with this statement, and if the statement were specified that way then it would be correct.The question here is, given a set of parameters for your vehicle, which one do you care about for maximizing acceleration. Nobody, *nobody*, specifies a vehicle by tractive effort
Acceleration is not the rate of addition of kinetic energy. That is not merely reframing the question; it is a different question with a different answer.you could easily reframe acceleration as being the rate of addition of kinetic energy.
I would not say “all you need” because power and wheel torque are closely related and saying “all you need” is an oversimplification that misses a lot of important physics.You are saying that all you need to create an acceleration at velocity v is wheel torque
And this is clearly wrong. It is not “all you need”. As @Randy Beikmann clearly and correctly pointed out it is not even the limiting factor at low speeds.I'm saying that you all you need to create an acceleration at velocity v is wheel power
I disagree, neither is true. The truth is that either “all you need” statement is myopic and misses the interplay between the various factors involved. The truth is that wheel power and wheel torque are closely related.Both of these statements are true.
For that problem I would unambiguously choose the power equation also. This is a different question and hence has a different answer. In that case power is clearly the more appropriate quantity to use and so I would use it.But let's take a look at the same vehicle with a slightly different problem: Finding the maximum velocity.
What I am saying is: teach physics!I guess what I´m saying is: Don´t feed the trolls.
That energy is conserved is indisputable, but where it goes depends on the situation. At low vehicle speeds (say 5 mph), your engine will not be able to run at maximum power Pmax, because if you put your right foot to the floor, the driving tires will spin until your engine goes to redline. At no engine speed would you be able to reach Pmax=T_Engine*omega, because the traction will limit the torque that can be developed. Plus, some of the energy the engine creates will go into the vehicle's kinetic energy, but some will be converted to heat at the tread as the tires slide against the pavement. There simply isn't enough traction to handle the force you would calculate at the tire/road interface in assuming Pmax there.
What if there is no traction limit? Well the passengers inside the vehicle will die if the acceleration is too great. That is another limit.because the traction will limit the torque that can be developed
If the question is whether power or torque is "a better indicator of acceleration", then I'm afraid there is no general answer. It depends on the full question/problem definition - there are always "if's" that will determine the answer. It's like when someone asks you, "What's the best car to buy?" The answer must be qualified by your purposes, budget, etc.The problem right now is that the question is not about what are all the possible limits of acceleration, it is about a single one: Is power or torque a better indicator of acceleration? Google will send all the users typing this question to the insight I wrote and other similar threads because they have the terms ¨power¨, ¨torque¨ and ¨acceleration¨ in it.
Sure the acceleration depends on the power but it's not the maximum power available, it's the power available at that velocity.
We are talking about an acceleration at a given velocity (other than zero). More precisely, over a speed range.Are we talking about instantaneous acceleration at a particular engine's torque peak, or are we talking about accumulated (integrated) acceleration, like trap speed at a drag strip?
Pmax might not be important, but power still is. If the maximum friction force (or any other limiting factor you can think of) allows for, say, 10 000 N at a speed of 1 m/s, knowing the torque produced by the engine alone won´t be enough information, no matter the gearing or tire radius. You have to make sure the engine produces enough power, i.e. the exact same amount needed at the wheel. It doesn´t even matter how much torque it produces and at what rpm. It doesn´t even matter if it is a combustion engine or not. All that matters is how much power it produces.Now, if the question stipulates low vehicle speeds, all that matters is that the engine can produce enough power to produce the force at the tread that fully utilizes the tires' traction, and the maximum amount of power available (Pmax) is not important.
I think this is getting to the heart of the matter. As soon as you specify a particular speed, then torque and power are essentially two sides of the same coin, speed being the conversion factor. This whole discussion is similar to arguing whether a pressure differential in a pipeline causes a flow, or whether a flow causes a pressure differential. I would say neither, or both, if you like. They just happen together. In the same way, 10 000 N at 1 m/sec IS 10 000 W, and it's a matter of convenience (or personal opinion) which is considered the primary quantity and which is the derived quantity. Again, only because the speed is specified.The acceleration needed at the wheel from my example will be 10 000 N divided by the mass of the vehicle (ignoring rotational inertia to keep it simple). What do I need from the engine? 10 000 W (= 10 000 N X 1 m/s).
Funny that you mention pressure differential and a flow. If you had a hydraulic motor powering my vehicle, I don´t know what would be the its pressure differential or volumetric flow rate, but the combination of both would have to produce 10 000 W. This is the only characteristic required to be sure I can produce the desired force (or acceleration) at the given velocity. It would be a mistake to think that only the pressure is relevant because that is what will cause the wheel torque. Any pressure can produce that torque, as long as it has the appropriate volumetric flow rate.This whole discussion is similar to arguing whether a pressure differential in a pipeline causes a flow, or whether a flow causes a pressure differential.
I am certainly not excluding zero velocity. You would certainly like to exclude it since it makes your claim obviously wrong, but I do not consent to the limitation.We are talking about an acceleration at a given velocity (other than zero).
Let’s examine it for the simple lossless case:Is power or torque a better indicator of acceleration?
Sure, and it does so precisely by converting that engine power into greater wheel torque. As I said above, power is the primary criterion for selecting an engine. The wheel torque is not independent of the engine power, but the wheel torque remains the quantity that is more directly related to acceleration.Given those numbers, it must be very clear to anyone that the orange engine can produce way more acceleration than the blue one.
I like how you use the double negative. Instead of saying «is dependent of», you say «is not independent of». I prefer the positive version: Acceleration depends on wheel torque and wheel torque depends on wheel power, which is the same as engine power (not considering inefficiencies). And the reason why I can so easily jump to «acceleration depends on power» when considering a vehicle is because the speed range for any vehicle design is fixed. A passenger car has one, a tractor has another one, a race car another one. The speed range is a given, always.The wheel torque is not independent of the engine power, but the wheel torque remains the quantity that is more directly related to acceleration.
Underlying Assumptions and Limitations
Really there is only one assumption behind Ohm’s law; linearity. Not in the mathematical sense, but rather that a graph of voltage versus current shows an approximately straight line in a given range.
There are always limits to the range even though they may not be explicitly mentioned. For example, at high voltages breakdown and arcing can occur. At high currents, things tend to melt. In the old days, we said that real-world resistance can not be zero. But now we know that superconductors are an exception to that rule. ##R=0## is OK for superconductors.
Students often forget that limits exist. A frequent (and annoying) student question is, “So if ##I=V/R## , what happens when ##R=0##. Ha ha, LOL.” They think that disproves the “law” and thus diminishes the credibility of science in general. Their logic is false.
Even this one?
If so then state it clearly and if not then you need to address my specific justifications for that statement.So clearly, wheel torque is more directly related to acceleration than power
I am fine with that. Engine power is the start, wheel torque is the end. Why is it so hard for you to admit that the end is more directly related to the result than the beginning? That should be obvious.Acceleration depends on wheel torque and wheel torque depends on wheel power, which is the same as engine power (not considering inefficiencies).
In a pure sense, your statement will be true in any case (like when ##v=0##, for example). If you specified some context (like specifying acceleration over a speed range), then you cannot distinguish which of wheel torque or wheel power is more influential on acceleration. My text do specified the limits and context for my statement. Furthermore, I wanted to show that the statement is also true even if there is no wheel torque.Even this one?If so then state it clearly and if not then you need to address my specific justifications for that statement.
If so then state it clearly and if not then you need to address my specific justifications for that statement.So clearly, wheel torque is more directly related to acceleration than power.
Like I said above, in the specific case presented, they are equivalent and that is if wheel torque is present. So it ends up to be about which words you want to use to convey the message.I am fine with that. Engine power is the start, wheel torque is the end. Why is it so hard for you to admit that the end is more directly related to the result than the beginning? That should be obvious.
Excellent. I am glad you agree.In a pure sense, your statement will be true in any case
In the many cases where they are equivalent then it is indeed merely a choice of words. However, I carefully chose examples where they were not equivalent. Since they are not always equivalent, it is not always just a stylistic choice.in the specific case presented, they are equivalent and that is if wheel torque is present. So it ends up to be about which words you want to use to convey the message.
Agreed.However, I carefully chose examples where they were not equivalent. Since they are not always equivalent, it is not always just a stylistic choice.
This came with an Excel spreadsheet filled with the tables mentioned above, and more. He is obviously drowning in numbers. This was my answer:I would like to know what factors you take into account when selecting gear and diff ratios for performance applications.
I only have minimal manufacture specifications (weight, weight distribution, frontal area, rolling resistance) and a simple power curve to go off. I also have a speed trace of the track it would be going around.
The current list of factors I am using to derive and tune ratios are:
-Acceleration force per gear. (accounting for resistive forces I.e. drag)
-Tire grip *Wheel Spin* (accounting for vertical forces on the axel)
-RPM drop and where in the powerband it drops to
I was wondering if there were any major factors I am overlooking and should look into while selecting ratios.
I have attached my main tool if you have time to look at it. I appreciate that you’re probably quite busy and would completely understand if you didn’t have the time. But even a few pointers would be world of help.
The answer I got back was:The basic concept to remember is that, for any speed, the acceleration is proportional to wheel power.
Since power varies with RPM, you want to coincide the RPM where you get the maximum power with the speed where you spend the most time accelerating. Say you know you spend a lot of time accelerating between 150 and 200 km/h, then you should have one gear ratio that gives you peak power RPM when you are at 175 km/h. If you spend most of your time in that speed range, you may also want to set the lower and higher gear ratios closer to that ideal ratio. This will increase your average power in that speed range (closer to peak power).
This is what is shown in the next figures. It is actually based on the numbers from your attached file.
Wherever the lines crosses, these are your ideal shift points. You can see how the average power (between shift points) in the 150-200 km/h range is greater in the second figure, compared to the first figure. Of course, this is only an example, and the power lost at 130 and 200 km/h might be unacceptable. In such case, you either have to set a smaller overall speed range by bringing closer the 1st & 5th gear ratios (i.e. less power at low speed and a lower top speed possible) or you can add gear ratios to fill the voids (i.e. a 7-speed gearbox is required). Note that as you increase the number of gear ratios within a given speed range, you set the average power closer to the peak power (but shifting may cause some losses and/or get more complicated).
It is all about compromises.
Nobody thinks of it that way when they are new at this. Too many even refuse to do otherwise as they get experience. Why? Because they focus on «acceleration means torque».This is great, thank you so much! You gave me a lot of insight into the topic and I hadn't thought of it that way.