The idiot's guide to power & torque
As a car nut, with a gun at your head, can you explain power and torque? Do you know what these things are, or have you been faking it?
Spoiler alert: there is actual science in this report. You know - the magic voodoo that makes the world work, which the facile think is boring, but which is really the only thing stopping us from still living in caves and dying in our 20s.
THE ACID TEST
So: Do you know what power and torque really are? Here's how you tell: Explain it in three concise sentences. Right now.
If you failed the test, keep reading, or watch the video (below).
SCIENCE IN THE BEER GARDEN
Beer - because science would be too hard to learn any other way
There is actually a whole calculus explanation. We'll skip that. (It's only relevant if you are truly scientifically literate.) So here’s a more useful ‘science in the beer garden’ explanation:
Simplest way to look at it. Engine power makes shit happen, and by ‘shit’ I mean ‘acceleration’, and torque is one of power’s two fundamental building blocks. It’s power that throws a car into motion when the lights go green. Fuel and air goes into an engine - lots of stored energy. Magic happens inside. A lot of sucking, squeezing, banging and blowing - pornography on amphetamines - and much less energy comes out the tailpipe. The difference (minus friction and other losses) comes out the crankshaft, as power. Torque and revs. Good shit.
Power causes acceleration. Twice the power, twice the acceleration - as long as a bunch of other things are equal, and you’ve still got grip. You literally do power out of a corner.
So, this is like cooking. Jamie Oliver-style, only in a lab. If you cook a roast dinner, you need the ingredients, right? Dead chook, potatoes - whatever. If you want to cook power the ingredients are torque and revs. Simple.
Power = Torque x Revs
1 Rev = 6.283 Radians
1000 rpm = 104.7 rad/sec
EASIEST EQUATION ON EARTH
Power equals torque times revs. But there’s a catch for the mathematically illiterate: You need to convert revs (commonly expressed in revs per minute) to a maths thing called radians per second.
Ooooohhh - scary. (But stay with me: it’s not quite Stephen Hawking o’clock just yet.)
Radians are very cool, mathematically, because they’re dimensionless. Just accept it, and move on. Mathematically, in the physics beer garden, you need to take very good care of the units. Otherwise you break your equation.
(Then it betrays you. And you might end up being a journalist. And nobody who was ever an engineer would want that.)
Imperial takes itself very seriously, but operates just the same as metric, albeit with different units
METRIC V IMPERIAL
Same equation, different units.
If you’re in Australia you’re working metric - watts (or kilowatts) for power and Newton-metres for torque. So, kilowatts equals Newton-metres x rpm x pi, divided by 30,000. That’s just how this works. Trust me.
If you’re in North America (or anywhere else imperial) power in horsepower equals torque in foot-pounds times revs times pi divided by 16,500. It just is.
All you really need to know is that pi is a big, long number representing the ratio of the circumference of a circle to its diameter - it goes on for ever, but 3.1 is good enough
PUTTING PI ON ITS FACE
If you’re really illiterate mathematically (please don’t breed; the next generation does not need your genes - put the condom on now, pre-emptively).
Just know that pi is a big, long irrational number - but 3.1 will do for most jobs. Probably not a moonshot, but many other jobs. Three is almost good enough sometimes.
Just to put pie on the face of those two conversions: Kilowatts equals Newton-metres times revs divided by 9549. Horsepower = foot-pounds times revs divided by 5252. Every dynamometer on earth knows this.
Dynos (that's engine and chassis dynos) measure torque and revs, and they calculate power from those measurements
WHAT DYNOS DO
Dynamometers don’t actually measure power. They measure torque and revs, and they calculate power from those measurements.
Because that’s just how this works.
Because: Science rocks, and being a dumb shit doesn’t.
PEAK PERFORMANCE
Let’s talk about the numbers presented by carmakers. Power and torque. The keyword here is ‘peak’. Peak power. Peak torque. They’re the numbers that are commonly quoted. They’re useful, but many people consider them without the critical context. Or at least, without enough context.
Almost identical peak power, but achieving it at lower revs, makes Mazda's 2.5i petrol a better real-world performer than Honda's antique 2.4 VTEC
Here’s an example:
Honda CR-V with its crappy old antique 2.4i V-TEC petrol engine. 140kW at a hugely impractical 7000rpm. Mazda CX-5 2.5i petrol engine: makes 138kW at a more accessible 5700rpm. Unfortunately, a lot of scientifically illiterate car buyers go: ‘The Honda is slightly better. It makes a bit more power. I had a Honda in the 1990s. They’ve always been in front of Mazda. Looks like they still are.’ [PAUSE] This is, of course, mentally retarded.
But if you know about the magic equation, the strict mathematical relationship between power, torque and revs, it’s easy to figure out that the CX-5 actually accelerates better at all normal driving revs, and you actually have to rev the Honda’s tits off - to 7000rpm, where both the Honda’s double-D cups are bouncing off the limiter - to get to the point where it accelerates about the same as the Mazda does at 5700 revs, and frankly that makes the Honda a undignified SUV drive. Power of pipedreams. See my Mazda CX-5 guide >> and also close competitors Hyundai Tucson >> and Kia Sportage >>
Petrol wins on peak power, buy is murdered by diesel earlier in the rev range
DIESEL V PETROL
Diesel and petrol: Kinda the same thing. People always say, of diesels, they can feel the low-end torque. Which is bullshit - you cannot feel engine torque from the driver’s seat. You can feel the low-end power, which makes shit happen. Diesels make a lot of low-rpm power.
Compared with the two-litre petrol engine you can buy, the average modern diesel engine is making almost three times the power (and consequently you get three times the acceleration) at low-ish revs. Hyundai-Kia two-litre diesel makes 84kW at 2000rpm. The same company’s comparable petrol engine is making 29 at 2000. Which one do you think feels stronger? Full report on petrol versus diesel >>
BOOSTING ENGINE PERFORMANCE
Boosting engine performance: there's a cheap and useless approach or a pricey, effective way to do it
Let’s say you’re a proper propeller-head, sitting in a car company’s secure R&D facility. You’re a serious braniac, and your job is to up the ante on power delivery for the next iteration of some engine. How do you do it?
If the budget is limited - you just spin the engine faster. More revs equals more power - provided you can maintain the torque. That’s the easiest way to do it. Unfortunately it’s also of the least benefit to owners. Because, below those extra revs, the engine’s going to feel - and perform - exactly the same as before. Maybe even slightly worse. So, this is like how to develop a ‘marketing department’ power increase.
You could also increase the capacity - but that usually requires a major redesign. There’s not a lot of extra space in there, generally. Or you could turbo- or supercharge it (because that effectively increases the capacity). Or you could increase the combustion efficiency. All of these options are, unfortunately, expensive, requiring advanced technology like direct injection and/or forced induction. But it’s those kinds of advances that are of the most benefit to drivers.
People put a lot of stock in peak power - but we generally never use it
USING PEAK POWER: IT'S GENERALLY TOO HARD
It’s worth remembering that peak power is notoriously irrelevant to most people. To exploit peak power you have to be a) at those sky-high revs, b) at wide-open throttle, and c) working hard against a balancing load - like the world’s longest, steepest hill, or aerodynamic drag at 250km/h, or strapped to a dynamometer.
Not that practical. For most drivers. What really matters in the real world is low- and mid-rpm performance. These figures are generally not quoted by carmakers, unfortunately. And there are really big differences in that kind of performance in close competitors in every segment at low and mid revs. But they’re encoded in plain sight. All you have to be is be scientifically literate, and you can crack this kooky code, which is the whole point of this video.
The 'fat man 500Nm application test' is easy to pass - but doing it while spinning at 2000rpm isn't
TORQUE IN PERSPECTIVE
Three complete brain-benders before I let you go: First one is torque. Holden Colorado. 500 Newton-metres (370 foot-pounds). Awesome. But, you know, 500 Newton-metres is actually not that impressive. You take your basic 90-kilo middle-aged bald fat man (if we could find one of those) and you march him about two feet out along a plank above shark infested waters.
So this experiment requires a short plank and a short 200-pound fat guy. And a ship. And some sharks, and some salty water to put them in. At the end of the two-foot plank, just before the Jaws gets his hors d’oeuvre, fat-man is applying 500Nm of torque to the ship. So is not that hard to apply big torque in the real world.
Seems like fun in the moment - but usually a bad idea
WARP SPEED
The real magic of engines is not the torque - it’s being able to apply that torque while spinning at 2000rpm. A middle-aged fat man cannot do this. Or so I’ve heard. 2000rpm is fast - 33 revs a second. Blink your eyes - that’s three-and-a-half revs. At 2000rpm we’re talking 67 combustion events every second in a four-cylinder engine.
Suck-squeeze-bang-blow, times 67, every second. Amazing, when you think about it like that. It’s incredible in there, under the hood. Magically, pornographically incredible. All those intimate encounters. Even at mundane revs. Maybe you only think that if you’re a science geek.
Gearing changes rotational speed (ie revs) and torque, but essentially leaves power alone (unfortunately some is lost to friction)
HOW GEARING FITS IN
Brain-bender number two: gearboxes. Diff ratios. Gearing. You’ve got your power coming out of the crank, going into a gearbox, getting pumped through a diff and out to the wheels, finally, minus friction losses. So you’re at the lights, stopped, in first gear. Lights go green. Hit the loud pedal. How does first gear affect power?
It doesn’t. Gearing changes two things: Torque and revs at the wheels. First gear in your car has the biggest reduction in revs (at the wheels) and therefore the biggest increase in torque. Same power (minus friction). This is good - because you need a lot of torque to overcome the effect of inertia (and also gravity if you’re nose-up on a hill). All gearing does, on every machine on earth, is modify speed and torque in inverse proportion to each other. It leaves power alone.
Acceleration drops away as speed increases - even in a car like the BMW M6
GOING STRAIGHT
Number three: So far we’ve only been talking about power at the crankshaft, which is stuck up the engine’s bum, and rotates. But there’s power in the linear universe as well. The wheels push the car forward in a straight line. There’s power in them thar wheels. (Usually about a third less than at the crank, thanks to friction.
One last equation to cause you a mild intracranial bleed: Linear power equals MAD divided by time. Mass times acceleration times distance, over time. And MA is force (that equation brought to you today by Isaac Newton’s second law of motion) and distance over time is velocity, which you might think of as speed - but not the kind you suck into your sinuses through a rolled bank note.
So, in a straight line, the power at the wheels produces two things. Force, pushing you forward, making you accelerate, and speed, which you acquire along the way. These two things depend on each other, because the maximum amount of power that can be supplied at the wheels is fixed.
Top speed is always a balancing act between raw power, aerodynamic drag, and getting the gearing right
HOW SPEED AFFECTS ACCELERATION
This equation shows you something you’ve felt every time you take off at the lights. As you get faster, you can’t accelerate as hard. Every time you double your speed, the ability of the car to accelerate drops by half - because power is fixed. It’s easy to spin the wheels off the mark. It’s pretty hard to arc them up at 100 kays an hour.
TOP SPEED
So, as you accelerate through the gears, on the longest drag strip you can imagine, two things happen: acceleration reduces and aerodynamic drag increases. Ultimately your ability to accelerate hits an invisible brick wall. You’re at V-max - the car’s top speed. The engine is working very hard against aerodynamic drag, and increased speed has bent acceleration over in the prison shower, because power is finite and limited.
Ultimately, if the engineers did their modelling well, you get to this sweet spot where you’ve got the throttle mashed, the engine’s bang-on the right revs for peak power, and that power is being balanced by all of the resistances - but mainly aerodynamic drag, at high speeds.
In a decent - but not outrageous - performance car, that’s going to be about 250km/h, ballpark. About 160mph in the old money. Call it about 0.2 mach, at sea level. It’s incredible. Access to that much power.
If the gearing is too tall, aerodynamic drag will beat you before you achieve peak power. You won’t be able to get the engine to rev any higher. If the gearing is too short, you’ll bounce off the limiter before aerodynamic drag balances the engine power. Also an inelegant result for the engineers.
OK, so you'll never go this fast in a car - but in this test, 20% is definitely more than a pass
COME FLY WITH ME
But any way you look at it, being able to drive at 20 per cent of the speed of sound - however ill-advised, at times - is incredible. In all of human history this is an unprecedented access to power. It’s magic. Literally magic. We just call it physics. Engineering. Whatever. It’s magic. Then you crack the code. Then it’s just science.
Of course, in that magical V-max condition, if something goes wrong, there’s not generally an afterwards. That’s negative feedback. (Kinda like the comments area in YouTube.)
If physics were pornography - and it kinda is - admit it - if physics were porn, power, torque and revs is the threesome you’d download over and over. I know I do.