This went on a lot longer than I expected, so I cut it off at the physics side of the discussion and made a second article about how all this torque and horsepower stuff is related to engine mods and performance. If you're not into math and physics (I've tried to keep it simple, but there is a lot to explain) you can skip ahead to Horsepower in the Real World.
Lets start at the very beginning. Back in the 1700s, mines used teams of sturdy draft horses to haul coal and rock up from the bottom of mine shafts. Often several horses were hitched to a turnstile affair turning a hoist drum (known as a 'horse gin' or 'horse mill') that pulled a rope over a pulley at the top of the shaft to lift an elevator car (the elevator car itself would be counterweighted so the horses were only lifting the load in the car).
Horses meant stables and stable hands and deliveries of oats and hauling away manure - horses were a major expense. In 1782 a Scottish engineer named James Watt was in the steam engine business, and he had improved quite a bit on existing designs. Replacing all those horses with steam engines that burned coal seemed like a perfect fit for his new technology. What he needed was a way to compare the lifting ability of his engines to those teams of horses.
Legend has it Watt went into the mines and measured how fast the horses could lift various loads and found that an average horse could lift 100 pounds 220 feet every minute of an 8 hour shift. This is a pretty big oversimplification: a 2000 pound work horse can pull with a maximum force of nearly its own weight, a horse could easily lift several hundred pounds, but only for a short time. Even at lighter loads a horse would need multiple rest and water breaks throughout the day. What Watt did was find the total weight lifted up a 220 foot shaft over the course of a day and averaged that out over how many horses were used and the number of minutes it took, and came up with a per-horse average of 100 pounds per minute coming up the mine shaft, and he put those numbers together in the obvious way:
Legend has it Watt went into the mines and measured how fast the horses could lift various loads and found that an average horse could lift 100 pounds 220 feet every minute of an 8 hour shift. This is a pretty big oversimplification: a 2000 pound work horse can pull with a maximum force of nearly its own weight, a horse could easily lift several hundred pounds, but only for a short time. Even at lighter loads a horse would need multiple rest and water breaks throughout the day. What Watt did was find the total weight lifted up a 220 foot shaft over the course of a day and averaged that out over how many horses were used and the number of minutes it took, and came up with a per-horse average of 100 pounds per minute coming up the mine shaft, and he put those numbers together in the obvious way:
100 pounds x 220 feet / 1 minute = 22,000 foot-pounds/minute
If the mine-shaft was deeper, or the elevator bigger or smaller or slower or faster, you could plug those numbers in and figure out how many horses you needed or how big your steam engine had to be. Its not clear that Watt realized the physical significance of this number, but it was easily related to production numbers the mines were already tracking.
Watt knew there were losses due to friction in the hoist and elevator, so that the horses were actually doing more work than just lifting the weight, and he would have to account for that when sizing a steam engine that would drive the same elevator. He didn't have a handy way to measure the losses, so he used another engineering technique: the "simple wild ass guess". He just added 50% to the work he measured to get a conservative 33,000 foot-pounds/minute, or 550 foot-pounds/second, as a "standard horse power" - a number that is still with us today.
250 years ago - about the same time George Washington was fighting the British - scientists and mathematicians were still working out the basic physics that we teach high school students today. It would take another 30 years after Watt went into the mines to formalize the concepts of work and energy and power. The technical term work is a force applied over a distance. When a horse lifts a 100 pound weight at a steady speed, aside from the initial jerk to get the weight moving the hoist rope is applying a 100 pound force to balance the force of gravity pulling the weight down. Lifting that 100 pounds 220 feet does:
100 pounds x 220 feet = 22,000 foot-pounds of work
Scientists recognized that this definition of work is just the part of Watt's power definition that doesn't depend on time; that means power is just the "rate of doing work" - or how much work is done per second. It doesn't matter how fast the weight was lifted, the work is the same whether it took 1 minute or 1 hour to do the lifting - but if you want to lift the weight in less time you needed more power.
But what does all this mine-shaft stuff have to do with automobiles?
The whole "force over a distance" applies everywhere. If you've ever pushed a manual shift car with a dead battery across a parking lot to start it, you are applying a force with your hands on the back of the car over whatever distance you need to get the car up to speed; you are doing work, putting kinetic energy (energy of motion) into the car and it's that energy that will turn the engine over when the driver pops the clutch. You may notice as the car picks up speed it gets harder to push - because it takes more and more power to apply the same force at a higher speed than when it first started to roll.
But what does all this mine-shaft stuff have to do with automobiles?
The whole "force over a distance" applies everywhere. If you've ever pushed a manual shift car with a dead battery across a parking lot to start it, you are applying a force with your hands on the back of the car over whatever distance you need to get the car up to speed; you are doing work, putting kinetic energy (energy of motion) into the car and it's that energy that will turn the engine over when the driver pops the clutch. You may notice as the car picks up speed it gets harder to push - because it takes more and more power to apply the same force at a higher speed than when it first started to roll.
The same is true when it's the engine pushing the car down the road: the faster the car goes the more power is needed to maintain the same force at the drive wheels. If we go back to Watt's definition of horsepower:
power = force x distance / time
we see there is a (distance / time) term in there, which sounds a lot like velocity (speed). We can rearrange that relationship to be:
power = force x velocity
If we look at the force the driving wheels are applying to a car and multiply by the car's speed (in the right units), we'll find the power being delivered to the car by the wheels. The applied force has to both balance the force of aerodynamic drag pushing against the car and provide the force needed to accelerate the car. At low speed aerodynamic drag is fairly small, and most of the power applied goes to acceleration. We know from the 2nd law of motion that:
force = mass x acceleration
and combining these two,
power = mass x acceleration x velocity
We can put numbers in this formula to find out how much horsepower a car needs to accelerate at a certain rate at a particular speed. The units are kind of messy: use mass in kilograms, speed in meters/second, acceleration in meters/second-squared, and you get power in Watts (using English units is even more painful).
- A 2600 pound Z-car masses 1200Kg.
- 0-60mph in 6 seconds is an acceleration of 4.5 meters/second/second.
- 60mph is 26.8 meters/second
Power = 1200 x 4.5 x 26.8 = 147,936 Watts
Divide by 745.7 Watts per horsepower to get 198 (wheel) horsepower.
That's the power required at the wheels at 60mph to maintain 0.45G acceleration (less power is required at lower speeds on the way up to 60mph). Of course if the car is going 60mph and still accelerating, it will soon be going faster than 60mph and require still greater power to maintain that acceleration. If the engine can't make more power, then the acceleration will decrease.
Lets Circle Back to Torque
Applying a force to an object - pushing or pulling in a straight line - in a way that makes it want to rotate is said to generate a torque. Force and torque are closely intertwined: in a mechanical system forces generate torques and torques create forces. A mine horse applies a force to a turnstile, that generates a torque on the hoist shaft, that turns a hoist drum that generates a force on the hoist rope connected to the bucket of coal being lifted.
Most of us have a natural understanding of torque from removing bolts with a wrench: you apply force on the wrench (push one end) and the bolt turns. If a bolt is really tight you can get a longer wrench - or slide a pipe over the wrench you have - which seems to magically let you apply more torque and loosen the bolt (or just rip the head off the bolt if you're having a bad day). For the simple case of a wrench on a bolt, the torque is just the force you apply times the length of the wrench (a distance known as the "lever arm"). If I'm loosening lug nuts to change a tire, and I push down on an 18 inch (1.5 foot) breaker bar with all of my 250 pounds, I'm applying a monstrous 250 x 1.5 = 375 foot-pounds of torque!
Here's the tricky part: this kind of torque that you measure with a torque wrench, where nothing is moving, is not exactly the same as what we call the torque generated by an engine. You may be straining your muscles with all you've got pushing on the wrench, but if the bolt doesn't turn no energy is transferred and no work is done. Now imagine this is a really rusty old bolt and you break it loose and have to apply a constant 100 pounds of force on the wrench to turn the bolt one turn. Now that there is motion, the applied torque does work (and in this case that work, or mechanical energy, is turned into heat due to friction in the threads - the bolt gets hot).
Let's say the wrench is 1 foot long, so that your 100 pounds of force is applied over the distance the wrench handle travels - in a big circle with radius 1 foot. High-school geometry tells us the distance around the circle is just:
Here's the tricky part: this kind of torque that you measure with a torque wrench, where nothing is moving, is not exactly the same as what we call the torque generated by an engine. You may be straining your muscles with all you've got pushing on the wrench, but if the bolt doesn't turn no energy is transferred and no work is done. Now imagine this is a really rusty old bolt and you break it loose and have to apply a constant 100 pounds of force on the wrench to turn the bolt one turn. Now that there is motion, the applied torque does work (and in this case that work, or mechanical energy, is turned into heat due to friction in the threads - the bolt gets hot).
Let's say the wrench is 1 foot long, so that your 100 pounds of force is applied over the distance the wrench handle travels - in a big circle with radius 1 foot. High-school geometry tells us the distance around the circle is just:
pi x 2 x radius = 3.14 x 2 x 1 foot = 6.28 feet
And the applied torque is just:
force x lever-arm = 100 pounds x 1 foot = 100 pounds-feet of torque
Since we're pushing on the wrench with 100 pounds of force, every turn of the wrench requires:
force x distance = 100 pounds x 6.28 feet = 628 foot-pounds of work
If we made the wrench longer then we wouldn't have to push as hard to apply the same torque, but we'd have to push the wrench through a bigger circle, and the amount of work done for each rotation would stay the same. This relationship:
Work/rotation = 2 x pi x Torque
holds for any rotating shaft, including the crankshaft of a Datsun engine.
If we attach a gear reduction (transmission) to the crankshaft, we can get more torque at the axle, but the wheel will turn at a lower RPM, and the same amount of work will come out of the gear reduction as the work that went in (minus a bit lost to friction between the gears). What all this means - and it is pretty subtle - is that what we call the torque of an engine - or shaft torque - is really the amount of work it can do per radian of crankshaft rotation, where a radian is a mathematical unit of measure for an angle. There are 2 pi radians in a full rotation (360 degrees), so a radian is 57.29 degrees. In physics equations radians are unitless (or more accurately, they have units of length/length). If that's confusing don't worry - we mostly won't talk about radians again.
If we attach a gear reduction (transmission) to the crankshaft, we can get more torque at the axle, but the wheel will turn at a lower RPM, and the same amount of work will come out of the gear reduction as the work that went in (minus a bit lost to friction between the gears). What all this means - and it is pretty subtle - is that what we call the torque of an engine - or shaft torque - is really the amount of work it can do per radian of crankshaft rotation, where a radian is a mathematical unit of measure for an angle. There are 2 pi radians in a full rotation (360 degrees), so a radian is 57.29 degrees. In physics equations radians are unitless (or more accurately, they have units of length/length). If that's confusing don't worry - we mostly won't talk about radians again.
Since the units of shaft torque and work look the same, engineers often use the unit pounds-feet when talking about torque, and foot-pounds when dealing with work to distinguish between the two. Just remember when you see "foot-pound" in a car magazine it's almost certainly the shaft torque of the engine they're talking about.
When we talk about an engine making a certain amount of torque, it's always at a certain RPM (automobile engines only do work or produce power when the crankshaft is turning). 1 RPM is a rotation every 60 seconds. If we know the torque and the RPM and the definition of a standard horsepower, we can convert torque at some RPM to horsepower at the same RPM:
Torque x 6.28 x RPM x 1 rotation/60seconds x 1horsepower/550 foot-pounds-per-second = Horsepower
or if you multiply out all the constants, we get the familiar relationship:
When we talk about an engine making a certain amount of torque, it's always at a certain RPM (automobile engines only do work or produce power when the crankshaft is turning). 1 RPM is a rotation every 60 seconds. If we know the torque and the RPM and the definition of a standard horsepower, we can convert torque at some RPM to horsepower at the same RPM:
Torque x 6.28 x RPM x 1 rotation/60seconds x 1horsepower/550 foot-pounds-per-second = Horsepower
or if you multiply out all the constants, we get the familiar relationship:
Torque-in-pounds-feet x RPM / 5252 = Horsepower
This tells us we can convert from torque-at-RPM to horsepower-at-RPM, or vice-versa, with no extra information. Both measures carry exactly the same information. If we look at a real engine, we see that for much of the RPM range, torque stays fairly constant as RPM increases, which means that horsepower increases with RPM. This has convinced a lot of shade-tree "experts" that somehow horsepower is only important at high RPM and torque at low RPM, but they are really just different ways of talking about the same thing.
So why the fascination with max torque?
There is an old joke about the difference between Americans and Europeans: Americans think 200 years is a long time and Europeans think 200 miles is a long distance. The United States is a big place, and many of its cities were built in the age of the automobile; it's not unusual for Americans to have a 30+ mile commute from home to work every day. If you live in the country, a weekend trip to the nearest city to catch a ball game or go shopping at a big-name store can be 100+ miles each way. To cover all that distance American cars of the 1950s and 60s were built with big engines that didn't have to work very hard and were as unbreakable as an iron ball, even when hauling a 3-ton family car down the interstate a quart low on oil.
In everyday driving, there was no reason for those big displacement V8s to rev much past 3000RPM, and when they did the sounds they made did not inspire confidence. Even as horsepower ratings and factory red-lines inched up, that 3000RPM limit became ingrained in American drivers, passed on from generations of parents to countless teenage drivers. Detroit responded by building ever bigger V8s, not because anyone really needed a 300 horsepower station wagon, but because that was the only way to provide the 100 horsepower drivers did need to merge onto a highway with the gas pedal only halfway to the floor and the engine barely ticking over.
And at low RPMs torque does matter. As you pull away from a red light and the engine revs just past idle, more torque means more horsepower right now, and a bigger kick in the seat of the pants, in the one place that everyday drivers will notice the greater acceleration. A smaller engine with less torque but the same horsepower can accelerate the car just as hard by using lower gears and a looser torque converter (or slipping the clutch) and revving the engine higher, but at the unofficial 3000 RPM red line the smaller displacement, lower-torque engine will always have less power available than the bigger one.
Semi real world example: Let's say we have two different engines rated at 240 crank horsepower: a 2.0 liter 4-cylinder and a 3.0 liter 6-cylinder. In high-performance street tune, we would expect the 2.0 liter to generate (about) 150 pounds-feet of torque, which means it will hit 240hp at a lofty 8400RPM. And for the 3.0 liter engine, we'd expect 225 pounds-feet, and 240hp at roughly 5600RPM. Both engines have the same horsepower, but the bigger engine has 50% more torque.
These are roughly the specs of the actual 2001 model year Honda S2000 and BMW Z3, two otherwise similar front-engine RWD 2-seaters, both weighing about 2900 pounds. If torque is what creates acceleration, the Z3 should be a lot quicker than the S2000 - but the car magazines that flogged them both got the same low 6 second 0-60 times (a few magazines managed high 5 second times).
Not surprisingly, both cars are geared to reach their peak horsepower right around 60mph in 2nd gear - just short of their redline so that you can safely buzz them all the way to 60mph before shifting into 3rd. However the two cars drive very differently; a 6 second 0-60 in the S2000 requires revving the engine and slipping the clutch to launch followed by winding 2nd to 8000RPM - much like a race car - to get the car moving and the engine into its powerband, while the Z3 can knock down a fast time with fewer theatrics by having more power available as soon as the clutch engages. Part of the difference is that the fastest Z3 ran wide 245mm rear tires compared to the S2000s 225s, allowing the Z3 to launch harder by just mashing the gas pedal. A few years into the S2000's run Honda would bump displacement a bit for greater low-RPM power and fit 245mm rear tires to make the car a little easier to drive fast and narrow the gap.
There is an old joke about the difference between Americans and Europeans: Americans think 200 years is a long time and Europeans think 200 miles is a long distance. The United States is a big place, and many of its cities were built in the age of the automobile; it's not unusual for Americans to have a 30+ mile commute from home to work every day. If you live in the country, a weekend trip to the nearest city to catch a ball game or go shopping at a big-name store can be 100+ miles each way. To cover all that distance American cars of the 1950s and 60s were built with big engines that didn't have to work very hard and were as unbreakable as an iron ball, even when hauling a 3-ton family car down the interstate a quart low on oil.
In everyday driving, there was no reason for those big displacement V8s to rev much past 3000RPM, and when they did the sounds they made did not inspire confidence. Even as horsepower ratings and factory red-lines inched up, that 3000RPM limit became ingrained in American drivers, passed on from generations of parents to countless teenage drivers. Detroit responded by building ever bigger V8s, not because anyone really needed a 300 horsepower station wagon, but because that was the only way to provide the 100 horsepower drivers did need to merge onto a highway with the gas pedal only halfway to the floor and the engine barely ticking over.
And at low RPMs torque does matter. As you pull away from a red light and the engine revs just past idle, more torque means more horsepower right now, and a bigger kick in the seat of the pants, in the one place that everyday drivers will notice the greater acceleration. A smaller engine with less torque but the same horsepower can accelerate the car just as hard by using lower gears and a looser torque converter (or slipping the clutch) and revving the engine higher, but at the unofficial 3000 RPM red line the smaller displacement, lower-torque engine will always have less power available than the bigger one.
Semi real world example: Let's say we have two different engines rated at 240 crank horsepower: a 2.0 liter 4-cylinder and a 3.0 liter 6-cylinder. In high-performance street tune, we would expect the 2.0 liter to generate (about) 150 pounds-feet of torque, which means it will hit 240hp at a lofty 8400RPM. And for the 3.0 liter engine, we'd expect 225 pounds-feet, and 240hp at roughly 5600RPM. Both engines have the same horsepower, but the bigger engine has 50% more torque.
These are roughly the specs of the actual 2001 model year Honda S2000 and BMW Z3, two otherwise similar front-engine RWD 2-seaters, both weighing about 2900 pounds. If torque is what creates acceleration, the Z3 should be a lot quicker than the S2000 - but the car magazines that flogged them both got the same low 6 second 0-60 times (a few magazines managed high 5 second times).
Not surprisingly, both cars are geared to reach their peak horsepower right around 60mph in 2nd gear - just short of their redline so that you can safely buzz them all the way to 60mph before shifting into 3rd. However the two cars drive very differently; a 6 second 0-60 in the S2000 requires revving the engine and slipping the clutch to launch followed by winding 2nd to 8000RPM - much like a race car - to get the car moving and the engine into its powerband, while the Z3 can knock down a fast time with fewer theatrics by having more power available as soon as the clutch engages. Part of the difference is that the fastest Z3 ran wide 245mm rear tires compared to the S2000s 225s, allowing the Z3 to launch harder by just mashing the gas pedal. A few years into the S2000's run Honda would bump displacement a bit for greater low-RPM power and fit 245mm rear tires to make the car a little easier to drive fast and narrow the gap.
Torque matters, but when it comes to acceleration and top-speed horsepower is king. There is still a lot more to say, but this seems like a good place to take a break. Tune in next time when I pull some real world numbers out of my hat.
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