Torque and Horsepower Theory
Posted: 31 Jan 2004 21:39
This is a bit heavy and not all my own words. I do not have a Physics or Mechanical Engineering Degree!
But here goes….
First of all you have to get to grips with the basics. Before talking about Torque lets understand the basic unit which is Work.
Imagine you have a one pound weight bolted to the floor and you try to lift it with one pound (or 10 or 50 or whatever) of force. Remember it is bolted to the floor so it will not actually lift.
In this case you have applied force and exerted energy but no work will have been done.
Now you un-bolt the weight and apply just enough force to lift the weight one foot.
You have now done one foot-pound of work.
If it took you one minute to lift the 1lb weight one foot then you were doing work at the rate of one foot-pound per minute. If it took you just one second to lift the weight then you were doing work at the rate of 60 foot-pounds per minute, and so on.
James Watt observed that the average horse at the time could lift a 550lb weight one foot in one second. So it was performing work at the rate of 550 foot pounds per second or 33,000 foot pounds per minute. So he made this rate of work ONE HORSEPOWER.
When you apply this to a running engine you find it is impossible to measure directly. What is measured on an engine dynometer is TORQUE so any calculations have to use this unit.
Torque is a twisting force. Imagine you had a steel rod in your hand held horizontal at arms length. The rod has a one pound weight hanging one foot along from your hand.
If you disregard the weight of the rod you will need to apply a foot-pound of torque (twisting force) from your arm to the rod to hold it horizontal.
OK?
So now say if we rotated that one pound force on its one foot rod in a circle a whole 360 degrees you have moved the end of the rod against a one pound force for a distance of 6.2832 feet (Pi x a two foot wide circle) so you have done 6.2832 foot pounds of work.
Now see if you can follow this.
Watt said 33,000 foot pounds of work per minute was ONE HORSEPOWER.
So if we divide the 6.2832 foot pounds of work into 33,000 foot pounds we get 5252.
SO!
One foot pound of torque at 5252 rpm is equal to 33,000 foot pounds per minute of work and so is equivalent to one horsepower.
So if we only move that one pound force at the rate of 2626rpm we are making ½ a horsepower.
So to calculate horsepower from torque you use this formula;
HP = (Torque x RPM) divided by 5252
You may be also able to see that at 5252rpm horsepower will always exactly match torque because 5252 divided by 5252 cancel each other out so at that exact rpm HP=Torque.
Look at any torque/horsepower dyno sheet for any engine and you can see the two lines always cross at 5252rpm.
You can also see that torque will always be higher than horsepower below 5252rpm.
So what is the real difference between torque and horsepower in the ‘real’ automotive world?
Well as a driver you can only ‘feel’ torque. It is that push in your back. You cannot feel horsepower.
Any car in any gear will accelerate at a rate that exactly matches its torque curve (disregarding air and rolling resistance etc). So a car will pull hardest at its torque peak in any gear.
Also a car making 300ft-lbs of torque will accelerate you just as hard at 2000rpm as a car that had the same torque at 4000rpm. However if you use the formula you can see that the horsepower is double at 4000rpm.
In contrast to a torque curve horsepower rises rapidly with RPM. More so when torque is also climbing. However horsepower will continue to climb until well past peak torque as long as the RPM keeps rising until a point where torque is falling faster than RPM is rising. It is after that point that HP drops off.
OK so lets get practical with this and see how this works in our field of interest.
To increase the power of our cars we normally fit a camshaft of a longer duration (the valves open longer). This has the effect of moving peak torque higher up the rpm range. We don’t have to go into how at this stage. Because I don't know! Just accept it does.
But why do we need to make torque at higher rpms? I just said that the car will pull just as hard no matter what rpm it makes peak torque at.
So lets look at something that makes a lot of torque at low RPM to see how it performs. How about a big steam engine?
Let us imagine a steam engine chugging away at 12rpm. Now a real big old steam engine like that could generate something like 2600 foot pounds of torque!
If you hooked that engine up to the drive wheels of a car with no gearing so it was driven directly it would go from 0-12rpm in a flash and the engine would hardly notice!
BUT 12rpm with normal car wheels is about 1mph. Not very fast is it? So why not just gear up the output speed of this steam engine to give a higher top speed?
The trouble is that as you increase the output speed you decrease the output torque proportionally. So if you double the output speed you half the torque at the output.
To make this car go 60mph you would have to multiply the wheel speed with gears x60. That will reduce the torque at the output x60 to about 43 foot pounds! That is less torque than a car would need to get pushed along at 60mph.
So what horsepower would this steam engine have?
12 x 2600 divided by 5252 = 6HP
So you can see that despite having an enormous amount of torque this steam engine is limited in the amount of Work it can do over Time. Or to put it another way it has no Power.
What happens if you make torque at a higher rpm?
Let us take a performance 426 hemi making, say, 600lbs/ft of torque at 5,500 rpm.
Again lets us drive the wheels directly with no gears at all so that the wheels rotate at 5,500rpm. That rpm at the wheels of a typical car is 426mph! But again the amount of torque we have would not actually push a car along at that speed. Air resistance alone would limit its speed.
What is its horsepower?
600 x 5,500 divided by 5252 = 628HP!
What if we fitted an axle with 4.10:1 gears to reduce the speed of the wheels and the mph?
Now we are only doing 103mph but the amount of torque at the wheels has gone up by the same proportion to 2460lbs/ft of torque! That is easily enough force to push even a very heavy car or truck along at 103mph.
So gearing the speed up makes less torque and you cannot go fast. Gearing the speed down makes more torque but you need to make the torque at high rpms to be able to do that and still go fast.
So you see if you want to go fast it is better to make torque at higher rpms than lower. Because you can take advantage of gearing to multiply torque.
If you then take this 426 hemi engine and fit a gearbox between it and the axle to reduce the gearing even more you can see that with a typical 2.45:1 first gear ratio as well as the 4.1 axle gear you will make 3930lbs/ft of torque at the rear wheels. That is enough to lift the average muscle car! But that is launching at 5,500rpm mind.
This is also why we use lower gearing in the axle on drag cars. I went from a 3.23:1 ratio to a 3.91:1 ratio a while ago. That is about a 17.5% reduction in rear wheel speed. But that meant a 17.5% increase in rear wheel torque so the car accelerates faster! Since then I have fitted a 4.3:1 gear to make the car leave even harder.
Some racers even fit a lower 1st gear in the trans.
What about top speed or a land speed record car?
Well here is where HP is even more important because you need to be at peak torque to overcome all the forces trying to slow you down. So if you want a high top speed you need that torque at as high an rpm as possible so you can use less gearing.
OK
So it is easy to make an engine perform on a drag strip or at the speed trials isn’t it? You just make a huge amount of torque at a high rpm and away you go!
Ah but nothing in life is that easy. There are many forces at work to stop you doing that.
Have you noticed when you look at engine torque curves that torque seems to drop off very quickly at high rpms? Want to know why?
Well one of the reasons is Volumetric Efficiency (VE). The higher the rpm the less time the cylinders have to draw in air/fuel. The amount of air/fuel you burn is what makes the torque. If the cylinder only fills 75% of its total capacity (VE is 75%) that is the same as reducing the displacement of the engine by 25%. Which means a proportional loss in torque.
Let me explain that another way. Airflow into the engine usually increases with rpm (or more accurately – piston speed) until it reaches the maximum flow capacity of the carb, or intake runners, or ports, or valves (whichever is smallest) and then it levels off and becomes constant despite increases in rpm. The engine is then flow limited and VE (and therefore torque) drops off.
Another rpm limiting factor is mechanical losses. This is made up of stuff like piston ring friction. Bearings and seal friction, valvetrain and spring pressure, accessory drag, pumping losses (dragging the air in and compressing it) etc. The losses induced by these things increase with engine speed. But they increase with the square of engine speed. That is to say that you double engine speed and you quadruple the mechanical losses.
Also included in these losses is the inertia of the moving parts. Any part that has to change direction robs power. Things like the pistons/rods, even the lifters, rockers and valves. The heavier the part the more power it robs. Again – these losses go up as the square of engine speed. 4 x the engine speed and you get 16 x the losses.
This is the reason that engines are not made by the factory to be high rpm screamers. Engines are simply a lot more efficient at low rpms. So the manufacturer has to balance the need for power against the need for efficiency.
If you managed to read this far you are either a very sad person or very intelligent. Unfortunatly I am more the former.
My brain hurts. Can I stop now?
But here goes….
First of all you have to get to grips with the basics. Before talking about Torque lets understand the basic unit which is Work.
Imagine you have a one pound weight bolted to the floor and you try to lift it with one pound (or 10 or 50 or whatever) of force. Remember it is bolted to the floor so it will not actually lift.
In this case you have applied force and exerted energy but no work will have been done.
Now you un-bolt the weight and apply just enough force to lift the weight one foot.
You have now done one foot-pound of work.
If it took you one minute to lift the 1lb weight one foot then you were doing work at the rate of one foot-pound per minute. If it took you just one second to lift the weight then you were doing work at the rate of 60 foot-pounds per minute, and so on.
James Watt observed that the average horse at the time could lift a 550lb weight one foot in one second. So it was performing work at the rate of 550 foot pounds per second or 33,000 foot pounds per minute. So he made this rate of work ONE HORSEPOWER.
When you apply this to a running engine you find it is impossible to measure directly. What is measured on an engine dynometer is TORQUE so any calculations have to use this unit.
Torque is a twisting force. Imagine you had a steel rod in your hand held horizontal at arms length. The rod has a one pound weight hanging one foot along from your hand.
If you disregard the weight of the rod you will need to apply a foot-pound of torque (twisting force) from your arm to the rod to hold it horizontal.
OK?
So now say if we rotated that one pound force on its one foot rod in a circle a whole 360 degrees you have moved the end of the rod against a one pound force for a distance of 6.2832 feet (Pi x a two foot wide circle) so you have done 6.2832 foot pounds of work.
Now see if you can follow this.
Watt said 33,000 foot pounds of work per minute was ONE HORSEPOWER.
So if we divide the 6.2832 foot pounds of work into 33,000 foot pounds we get 5252.
SO!
One foot pound of torque at 5252 rpm is equal to 33,000 foot pounds per minute of work and so is equivalent to one horsepower.
So if we only move that one pound force at the rate of 2626rpm we are making ½ a horsepower.
So to calculate horsepower from torque you use this formula;
HP = (Torque x RPM) divided by 5252
You may be also able to see that at 5252rpm horsepower will always exactly match torque because 5252 divided by 5252 cancel each other out so at that exact rpm HP=Torque.
Look at any torque/horsepower dyno sheet for any engine and you can see the two lines always cross at 5252rpm.
You can also see that torque will always be higher than horsepower below 5252rpm.
So what is the real difference between torque and horsepower in the ‘real’ automotive world?
Well as a driver you can only ‘feel’ torque. It is that push in your back. You cannot feel horsepower.
Any car in any gear will accelerate at a rate that exactly matches its torque curve (disregarding air and rolling resistance etc). So a car will pull hardest at its torque peak in any gear.
Also a car making 300ft-lbs of torque will accelerate you just as hard at 2000rpm as a car that had the same torque at 4000rpm. However if you use the formula you can see that the horsepower is double at 4000rpm.
In contrast to a torque curve horsepower rises rapidly with RPM. More so when torque is also climbing. However horsepower will continue to climb until well past peak torque as long as the RPM keeps rising until a point where torque is falling faster than RPM is rising. It is after that point that HP drops off.
OK so lets get practical with this and see how this works in our field of interest.
To increase the power of our cars we normally fit a camshaft of a longer duration (the valves open longer). This has the effect of moving peak torque higher up the rpm range. We don’t have to go into how at this stage. Because I don't know! Just accept it does.
But why do we need to make torque at higher rpms? I just said that the car will pull just as hard no matter what rpm it makes peak torque at.
So lets look at something that makes a lot of torque at low RPM to see how it performs. How about a big steam engine?
Let us imagine a steam engine chugging away at 12rpm. Now a real big old steam engine like that could generate something like 2600 foot pounds of torque!
If you hooked that engine up to the drive wheels of a car with no gearing so it was driven directly it would go from 0-12rpm in a flash and the engine would hardly notice!
BUT 12rpm with normal car wheels is about 1mph. Not very fast is it? So why not just gear up the output speed of this steam engine to give a higher top speed?
The trouble is that as you increase the output speed you decrease the output torque proportionally. So if you double the output speed you half the torque at the output.
To make this car go 60mph you would have to multiply the wheel speed with gears x60. That will reduce the torque at the output x60 to about 43 foot pounds! That is less torque than a car would need to get pushed along at 60mph.
So what horsepower would this steam engine have?
12 x 2600 divided by 5252 = 6HP
So you can see that despite having an enormous amount of torque this steam engine is limited in the amount of Work it can do over Time. Or to put it another way it has no Power.
What happens if you make torque at a higher rpm?
Let us take a performance 426 hemi making, say, 600lbs/ft of torque at 5,500 rpm.
Again lets us drive the wheels directly with no gears at all so that the wheels rotate at 5,500rpm. That rpm at the wheels of a typical car is 426mph! But again the amount of torque we have would not actually push a car along at that speed. Air resistance alone would limit its speed.
What is its horsepower?
600 x 5,500 divided by 5252 = 628HP!
What if we fitted an axle with 4.10:1 gears to reduce the speed of the wheels and the mph?
Now we are only doing 103mph but the amount of torque at the wheels has gone up by the same proportion to 2460lbs/ft of torque! That is easily enough force to push even a very heavy car or truck along at 103mph.
So gearing the speed up makes less torque and you cannot go fast. Gearing the speed down makes more torque but you need to make the torque at high rpms to be able to do that and still go fast.
So you see if you want to go fast it is better to make torque at higher rpms than lower. Because you can take advantage of gearing to multiply torque.
If you then take this 426 hemi engine and fit a gearbox between it and the axle to reduce the gearing even more you can see that with a typical 2.45:1 first gear ratio as well as the 4.1 axle gear you will make 3930lbs/ft of torque at the rear wheels. That is enough to lift the average muscle car! But that is launching at 5,500rpm mind.
This is also why we use lower gearing in the axle on drag cars. I went from a 3.23:1 ratio to a 3.91:1 ratio a while ago. That is about a 17.5% reduction in rear wheel speed. But that meant a 17.5% increase in rear wheel torque so the car accelerates faster! Since then I have fitted a 4.3:1 gear to make the car leave even harder.
Some racers even fit a lower 1st gear in the trans.
What about top speed or a land speed record car?
Well here is where HP is even more important because you need to be at peak torque to overcome all the forces trying to slow you down. So if you want a high top speed you need that torque at as high an rpm as possible so you can use less gearing.
OK
So it is easy to make an engine perform on a drag strip or at the speed trials isn’t it? You just make a huge amount of torque at a high rpm and away you go!
Ah but nothing in life is that easy. There are many forces at work to stop you doing that.
Have you noticed when you look at engine torque curves that torque seems to drop off very quickly at high rpms? Want to know why?
Well one of the reasons is Volumetric Efficiency (VE). The higher the rpm the less time the cylinders have to draw in air/fuel. The amount of air/fuel you burn is what makes the torque. If the cylinder only fills 75% of its total capacity (VE is 75%) that is the same as reducing the displacement of the engine by 25%. Which means a proportional loss in torque.
Let me explain that another way. Airflow into the engine usually increases with rpm (or more accurately – piston speed) until it reaches the maximum flow capacity of the carb, or intake runners, or ports, or valves (whichever is smallest) and then it levels off and becomes constant despite increases in rpm. The engine is then flow limited and VE (and therefore torque) drops off.
Another rpm limiting factor is mechanical losses. This is made up of stuff like piston ring friction. Bearings and seal friction, valvetrain and spring pressure, accessory drag, pumping losses (dragging the air in and compressing it) etc. The losses induced by these things increase with engine speed. But they increase with the square of engine speed. That is to say that you double engine speed and you quadruple the mechanical losses.
Also included in these losses is the inertia of the moving parts. Any part that has to change direction robs power. Things like the pistons/rods, even the lifters, rockers and valves. The heavier the part the more power it robs. Again – these losses go up as the square of engine speed. 4 x the engine speed and you get 16 x the losses.
This is the reason that engines are not made by the factory to be high rpm screamers. Engines are simply a lot more efficient at low rpms. So the manufacturer has to balance the need for power against the need for efficiency.
If you managed to read this far you are either a very sad person or very intelligent. Unfortunatly I am more the former.
My brain hurts. Can I stop now?