Power Vs Torque
Auto, Aviation & Transportation / Science
Okay, time to take this to the Lazy Web. Most definitely, there are at least a few experts in my feed and/or within one handshake of my reach.
Prove me wrong. Please. Because if I’m right this would imply I am *really* bad at explaining myself. As the past few times I’ve been having this conversation offline I have failed miserably.
My claim: When talking about both acceleration and top speed, as well as when comparing the characteristics of various engines, as long as we can use all or most of the power of the engine, 𝗽𝗼𝘄𝗲𝗿 𝗶𝘀 𝗮𝗹𝗹 𝘁𝗵𝗮𝘁 𝗺𝗮𝘁𝘁𝗲𝗿𝘀, 𝗮𝗻𝗱 𝘁𝗼𝗿𝗾𝘂𝗲 𝗶𝘀 𝗷𝘂𝘀𝘁 𝗮 𝘀𝗲𝗰𝗼𝗻𝗱-𝗼𝗿𝗱𝗲𝗿 𝗻𝘂𝗺𝗯𝗲𝗿 𝘁𝗵𝗮𝘁 𝗽𝗹𝗮𝘆𝘀 𝗻𝗼 𝗿𝗼𝗹𝗲 𝘄𝗵𝗮𝘁𝘀𝗼𝗲𝘃𝗲𝗿.Several high-level arguments first.
One: Torque is pointless if we compare, say, an internal combustion engine to an electric one, or to a jet engine. Still, talking both about top speed and about acceleration, it is perfectly feasible to compare a car with various engine types.Two: The “RPM” is a bogus parameter. Not only because it doesn’t make sense for, say, a jet engine.
But also, because if I give you an “engine” as a black box, it doesn’t matter what RPM it is “best” at, ~1000, ~100, or ~10’000. Assuming I have a perfect gearbox and a perfect clutch, I can utilize the “sweet spot” of this engine RPM-wise with respect to its maximum power output, and this maximum power output is what would ultimately determine both acceleration and top speed.
Three: Simple physics. Top speed is simply the speed at which the engine’s [maximum] power is 100% balanced by external resistance; mostly air drag, the dreaded Cx, as far as I understand. And peak acceleration (the force that pushes you into the chair!) is simply about gaining velocity faster, where gaining velocity is about converting the power of the engine into the kinetic energy of the vehicle. For two cars of the same weight, the one whose engine outputs more power accelerates faster. It’s as simple as that.
(To be picky, the weight of the car, as well as of the very engine, will play a role. That’s why motorcycles have faster acceleration than cars. But this point is not that important if we are talking about cars of comparable weights, or, overall, about “civic” cars, not about sports cars. We’d have to get to some sub-2000-pounds territory, ex. Ferrari vs. Lamborghini vs. F1, in order for this factor to become important)
How I generally present my argument.
Part one. Let’s assume, without loss of generality, that our engine is a black box, and that its output is a single “spinning” axis. This will likely be the crankshaft, if we’re talking internal combustion engines, but, for the sake of the argument, let’s throw electric motors and jet engines into the same category.
My claim is that you can always pack this “black box” into a different “black box”, with any predetermined “gears ratio”. Can be 1:1, 10:1, 1:10, 1000:1, 1:1000, etc. And then, whatever number you decide on, I can still build the machinery around your “outer black box”, which would run this engine at its peak power (power! not torque!) and convert this peak power into peak acceleration and/or peak top speed.
Furthermore, applying the “gear ratio” by converting the “inner black box” into the “outer black box” does change torque proportionally. Power output stays constant, but the torque — it is possible to get to any number here, an arbitrary high number, if you wish — the torque will not play any role at extracting “the most” out of this “outer black box” engine when it comes to either peak acceleration or to top speed.
Part two: now, to a physically sound argument.(I am a physicist by education, after all. A pretty damn terrible physicist, compared to most people I’m fortunate enough to discuss physics with, but a first-principles physicist nonetheless.)
We are going to consider a car with the following properties:1) A perfect gearbox: can operate at a wide range of gear ratios, switching between them arbitrarily fast.2) A perfect clutch: while (1) above allows us to operate at very narrow bands of “input RPMs” from the engine, a perfect clutch will effectively enable extracting max. output for an arbitrarily precisely defined “output RPM”. From differences to calculus, we go!3) Perfect grip with the road surface. In fact, let’s assume I’ve got strings wrapped around my wheels a sufficient number of times. So, however much power I can transfer to my wheels, 100% of it gets into acceleration and/or speed.
Also, no one would argue that a car can accelerate ~2x faster or ~2x slower if we change the radii of its tires ~2x, right? It’s because it’s power, not torque, that matters!4) The “crankshaft”, whatever it is, is of negligible mass. If we don’t introduce this assumption, I could, in theory, given perfect (1), (2), and (3) above, accumulate enough energy in the rotational power of this crankshaft, to then “momentarily” release this energy, converting it into infinitely fast acceleration. If we don’t introduce this (4), we’ll end up in the “airplane on a conveyor belt” paradox territory, which I want to avoid for the purposes of this thought experiment.
Given the above assumptions, I claim that, given an engine of power P, the acceleration of a vehicle with this engine can be computed knowing that P * t = 0.5 * m * V^2, assuming we neglect air drag at low speeds.
(Computing the time it takes for this car to get from 0 to 60 MPH is left as an exercise for the reader. This equation would ignore air drag. Without it, the exercise is for some 5th year students; with it that’s probably 8th or 9th year, but I digress.)
And I claim that the top speed of a car with such an engine will be the function of P and the function that converts speed into the force of air drag; one would need to equate one to the other.
(Air drag, as I was taught in school, grows quadratically with velocity, at high velocities. So, this gives a good baseline to argue how much faster can a car go, if its top speed was, say, 150 MPH, and then we reduce its Cx by 10%, or make it 10% lighter, or give it a 10% more powerful engine. Mechanics 101.)
Nit-picking: of course, all resistance forces should be put into the equation, I just tend to think that, for the sake of this hypothetical thought experiment, air drag will be the major contributor. We can assume the engine itself has “pure” output, and we can assume that the bearings in the gearbox / the clutch / the wheels / etc. are good enough to be negligible at the top speed we plan to achieve on this reasonably powerful “civic” car.
Both top speed and acceleration depend entirely on the power of the engine, and they do not depend at all on the torque of the engine.I would really love to know if I am wrong in any part of the above argument. Thank you very much in advance.
Power Vs Torque
