Torque vs Power - some clarity...
Posted: Mon Jun 03, 2019 9:58 am
A recent off forum discussion refers....
yes Manuel - I'm talking about you,
A lot of people seem to really not understand the relationship between torque and Power - although they bandy around 'facts' and opinions based on these numbers quite freely.
most of it is misinformation - statements like 'horsepower is how fast you hit the wall, Torque is how far you move it' illustrate the total misunderstanding between the concepts. thee statement is quite correct in a way, and very wrong in another way, but people don't really understand why and tend towards the incorrect understanding.
One of the BIGGEST problems is that , from school, kids from metricated countries start off with being taught completely incorrectly.
We are taught weight is measured in kg, and that you can convert kg to lbs in the imperial system.
Total total screw up and completely wrong.
kg is a measurement of MASS, the imperial equivalent measurement of mass is a 'slug'. you CANNOT convert kg to lbs.
Pounds (lbs) is a measurement of FORCE. the equivalent unit in metric system in the Newton. (N)
so, 100 000lbs of thrust is the correct way to measure the output of a rocket or jet engine. it is NOT 45000kg of thrust. it's impossible. it equates to 445 000N of thrust.
it is entirely correct to ask for 4 pounds of (whatever) , and to check it by weight, because weight is a Force - the force an object places upon a surface.
there is nothing wrong with asking for 5kg of (whatever) because you are asking for a mass of (whatever) which is 5kg. but it's not weight. if you weigh it, your scale is performing a conversion for you - it weighs the object by reading the force it exerts on the plate in Newtons, then divides that figure by +/- 9,81 on the scale to give you a mass in kg. the scale works on earth, but it wouldn't work on the moon because the the moon's gravity is around 25% of earths. BUT 5kg of (whatever) is still 5kg of (whatever) even if the scale only shows 1,25kg on the moon (or indeed zero in orbit)
There is a' new measurement' that people use now called kgforce. lets be clear here - It's Bullshit. it's done so that whiny millennial snowflakes that get a gold star for spelling their name right, get a medal for starting a race can believe they understand while making coffee and thinking 'Barista' is a real job . Which is BS because (a) it actually makes things more complicated and (b) whiny millennial snowflakes drive Polos and are really really annoying and we hate them.
So.
Newtons is a metric measurement of force and 1 Newton is equal to the imperial 4,45 lbs
Kg is the metric measurement of mass and 14,5kg is equal to 1 imperial slug.
important.
note - for the sake of simplicity we'll call g on earth 10m/s/s for now - i.e. a 10kg mass will weigh 100N on earth for our purposes.
Now onto further misconceptions
Force is .. force. when you push something you exert a force on it. this is measured (metrically) in Newtons. If you place a 1kg weight on a surface on earth a force of +/- 9,81 N is exerted onto that surface. If you push something you exert a force on it, whether it moves or not.
So - here is a misconception problem in terminology - If we see a person who is strong - lets say he can raise a mass of 200kg (2000N) above his head (on earth) easily. We would call him powerful. THIS IS NOT POWER. this is FORCE.
We might compare him to a gym bunny who bounces around all day. she can only lift 20kg (200N) (on earth) but she does is a lot (which we'll get to later)
she can still exert a force of 200N on the Weight lifters 2000N bar - but it won't move. HOWEVER - it now 'weighs' 200N less - it's exerting only 1800N on the floor because of her 200N lift.
When it comes to PUSHING the Muscle head can still apply a force of 2000N to an object, and the gym bunny can still only apply a force of 200N to it.
so, as Force equals mass x acceleration, the Muscle head can accelerate the object away from him far faster than the gym bunny can.
It is important to note that FORCE is the only thing that can accelerate a mass - Power and Torque are merely ways to quantify the force that can be applied to an object.
Make sense so far?
Now - this is where the confusion sets in. Torque is a measurement of rotational FORCE. it's a rotational force on an axle and it's measured in N.m.
This is a fairly easy concept for most to understand.
you lock your shaft/axle in place, attach a 1m long lever to it so it's horizontal to the ground and stand on the end of the lever. The Force must be at right angles to the lever - The twisting action on the axle/shaft is now (lets say it's Manny with an approximate mass of 150kg) so - 1500N x 1m - 1500N.m
If you make the lever 2m long, and Manny stands on the end it's 1500Nx2m = 3000N.m
etc.
The converse is also true.
if we twist the axle/shaft with a FORCE of 3000N.m we exert a FORCE of 3000Newtons to the end of a 1m lever or 1500Newtons at the end of a 2m lever.
your tyre on your vehicle is the lever - where it touches the ground it translates the rotational force into a linear force. So, we take our torque on the shaft and divide by the tyre radius to give us the Force available to push the vehicle forward - this will either accelerate the vehicle or overcome opposite forces on the vehicle.
so, if we have 500N.m acting on the axle on a 700mm Diameter tyre the vehicle is 'pushed' forward with a force of 500/0,35 = 1428 Newtons
If we fit a new tyre with a diameter of 800mm the torque remains the same - 500N.m - but it's now acting on a lever of ,4m - so 500/0,4 = 1250 Newtons is applied. so bigger tyres do not affect torque (or power) but the FORCE that can be applied because of the gearing - in this case 178N less FORCE is available.
Like our gym bunny trying to pick up the weightlifters bar - if the force required to overcome the opposing forces is more than can be exerted - it's going nowhere. so, gym bunny can't get the vehicle to move up a slight incline but Musclehead can come along and push it up the pass....
but now....
the Gym Bunny could run off and get a lever and a fulcrum. by using the lever and the fulcrum she could lift the 2000N weight or move the car up the hill.
she could, indeed, if she found a big enough lever and a suitable fulcrum, move the earth out of it's orbit.
Gears are simply rotating levers on a fulcrum (the axle or shaft) that multiply Torque in exactly the same fashion that a lever and fulcrum multiplies Force. Double the Ratio - you double the Force(torque) and half the travel (rpm)
so even the smallest motor can, theoretically, be geared up to move entire planets - but the more force you can exert at the source the smaller your lever sets need to be, which translates to less losses through drag in the real world.
and note again - TORQUE is ROTATIONAL FORCE. the confusion steps in because it's measured in N.m and so is Energy - Energy is measured in Joules and 1Joule = 1N.m and these 2 concepts are not related despite using the same unit of measurement, In an equation you cannot use them interchangeably despite the similar unit of measurement. The 'metre' (or inch or foot in imperial terms) is simply a convenience because the radius of the Wheel/Sprocket on which the torque will act (thus creating linear Force) is unknown.
to calculate the usable information - the force - you need to divide the Torque number by the effective radii of the various wheels/sprockets on which the torque acts.
Now onto Energy.
Pretty simple in physics - Energy is the capacity to do work. It's measured in N.m
So, a mass of 1kg suspended 5m above a surface (on earth) has a (POTENTIAL) Energy of 10Nx5m = 50Nm or 50Joules. - the energy is stored - energy was expended to lift it into place, and now it awaits being expended. if the string is cut it will accelerate until it hits the ground and expend its 50J of energy. that energy could be expended by (say) lifting another weight through a series of pulleys, or simply through a loud bang as it hits the ground .
If it's mobile, Energy is calculated by the formula E=0,5.mv^2 - so a 1000kg car, travelling at 10m/s is carrying 0,5x1000x10x10 = 50 000 Nm = 50 000Joules and again DO NOT CONFUSE THESE Nm with TORQUE Nm.
so, to stop the vecicle we need to expend the 50kJ - which is usually done by converting the energy to heat through the brakes - but can also be done by generating electrical current and stored in a battery for later use, or in a hydraulic pressure accumulator to be released later to accelerate the vehicle
this is extremely simplistic and is simply to understand the difference between Torque and Energy.
Now the next step is Power.
Power is the release of Energy or work. it's measured in Joules/ second or Nm/s
AGAIN - that Nm in the Nm/s has nothing at all to do with torque. it's a measurement of energy.
so , from the above Power is measured in Watts and 1 Watt is defined as the Work done by exerting a Force of 1N on an object for a distance of 1m in 1 second.
so, to go back to Muscle head and gym bunny.
As noted Muscle head can lift 2000N the 2m above his head - but it takes him 5 seconds to struggle it up there before dropping it.
Gym Bunny can lift her 200N 10 times from floor to above her head and drop it in 10 seconds.
so - they have both done the same work / expended the same energy, Musclehead has expended 2000Nx2m = 4000Joules and gym bunny 200Nx2mx10 = 4000Joules.
but because Musclehead does the work in 5 seconds - 4000Joules/5sec = 800 J/sec = 800 Watts and Gym bunny does the work in 10 seconds - 4000J/10sec=400J/s = 400Watts we can now call Musclehead really more powerful.
However, lets say Gym Bunny has a couple of Redbulls with Vodka before the contest, and she is able to do the 10 lifts in 4 seconds.
that means she is now performing work at 4000J/4sec = 1000Watts and is actually now more powerful than Musclehead despite being unable to apply anything like the same force to an object.
So, to work out Power from Force we need to know distance and time as well. Power = Force(N) x distance(m) / Time (s) to give us Nm/s or Watts.
to work out Power from Torque is the same - we need to know distance and time. the distance in the torque figure has to be altered to give us a linear distance to work in the Power equation.
so to translate it from a rotational to a linear is pretty easy - the circumference of a wheel is 2 x pi x radius
In effect - by multiplying it out, you've now translated the figure to Energy. 2pi Nm(torque) = 1 Nm (Energy) = 1J
So, we now know Force x distance (for 1 revolution) and just need to add time to get to Watts.
We measure speed of work in a motor in rpm (generally)
so, to add that into the equation we must divide the rpm by 60 to get to seconds AND we must multiply by the number of revolutions in one second as our figure is only for 1 revolution.
we'd also like the figure to be in kW (not Watts) so we divide by 1000
so, the final equation to get from Torque to Power (metric) is:
Power = Torque x 2pi x rpm/60/1000
As Pi is constant as well as the 60 and 1000 we can shorten it to:
Power = Torque x rpm /9549
as can be deduced - High Torque at low rpm (e.g. A big Diesel making 500Nm at 1500rpm is making only78kW) can make the same power as a motor making low torque at high rpm e.g. a proper F1 motor that revs to 19000rpm but makes only 300Nm is making 597kW
Basically... for Manny ... This means... that for any rpm less than 9549 the Torque figure will be higher than the power figure
at 9549 rpm power figure and torque figure will be equal
and over 9549rpm the Power figure will be higher than the Torque figure.
now hopefully I never have to see anyone declaring that you convert torque to power by using the stroke of the engine ever again!
yes Manuel - I'm talking about you,
A lot of people seem to really not understand the relationship between torque and Power - although they bandy around 'facts' and opinions based on these numbers quite freely.
most of it is misinformation - statements like 'horsepower is how fast you hit the wall, Torque is how far you move it' illustrate the total misunderstanding between the concepts. thee statement is quite correct in a way, and very wrong in another way, but people don't really understand why and tend towards the incorrect understanding.
One of the BIGGEST problems is that , from school, kids from metricated countries start off with being taught completely incorrectly.
We are taught weight is measured in kg, and that you can convert kg to lbs in the imperial system.
Total total screw up and completely wrong.
kg is a measurement of MASS, the imperial equivalent measurement of mass is a 'slug'. you CANNOT convert kg to lbs.
Pounds (lbs) is a measurement of FORCE. the equivalent unit in metric system in the Newton. (N)
so, 100 000lbs of thrust is the correct way to measure the output of a rocket or jet engine. it is NOT 45000kg of thrust. it's impossible. it equates to 445 000N of thrust.
it is entirely correct to ask for 4 pounds of (whatever) , and to check it by weight, because weight is a Force - the force an object places upon a surface.
there is nothing wrong with asking for 5kg of (whatever) because you are asking for a mass of (whatever) which is 5kg. but it's not weight. if you weigh it, your scale is performing a conversion for you - it weighs the object by reading the force it exerts on the plate in Newtons, then divides that figure by +/- 9,81 on the scale to give you a mass in kg. the scale works on earth, but it wouldn't work on the moon because the the moon's gravity is around 25% of earths. BUT 5kg of (whatever) is still 5kg of (whatever) even if the scale only shows 1,25kg on the moon (or indeed zero in orbit)
There is a' new measurement' that people use now called kgforce. lets be clear here - It's Bullshit. it's done so that whiny millennial snowflakes that get a gold star for spelling their name right, get a medal for starting a race can believe they understand while making coffee and thinking 'Barista' is a real job . Which is BS because (a) it actually makes things more complicated and (b) whiny millennial snowflakes drive Polos and are really really annoying and we hate them.
So.
Newtons is a metric measurement of force and 1 Newton is equal to the imperial 4,45 lbs
Kg is the metric measurement of mass and 14,5kg is equal to 1 imperial slug.
important.
note - for the sake of simplicity we'll call g on earth 10m/s/s for now - i.e. a 10kg mass will weigh 100N on earth for our purposes.
Now onto further misconceptions
Force is .. force. when you push something you exert a force on it. this is measured (metrically) in Newtons. If you place a 1kg weight on a surface on earth a force of +/- 9,81 N is exerted onto that surface. If you push something you exert a force on it, whether it moves or not.
So - here is a misconception problem in terminology - If we see a person who is strong - lets say he can raise a mass of 200kg (2000N) above his head (on earth) easily. We would call him powerful. THIS IS NOT POWER. this is FORCE.
We might compare him to a gym bunny who bounces around all day. she can only lift 20kg (200N) (on earth) but she does is a lot (which we'll get to later)
she can still exert a force of 200N on the Weight lifters 2000N bar - but it won't move. HOWEVER - it now 'weighs' 200N less - it's exerting only 1800N on the floor because of her 200N lift.
When it comes to PUSHING the Muscle head can still apply a force of 2000N to an object, and the gym bunny can still only apply a force of 200N to it.
so, as Force equals mass x acceleration, the Muscle head can accelerate the object away from him far faster than the gym bunny can.
It is important to note that FORCE is the only thing that can accelerate a mass - Power and Torque are merely ways to quantify the force that can be applied to an object.
Make sense so far?
Now - this is where the confusion sets in. Torque is a measurement of rotational FORCE. it's a rotational force on an axle and it's measured in N.m.
This is a fairly easy concept for most to understand.
you lock your shaft/axle in place, attach a 1m long lever to it so it's horizontal to the ground and stand on the end of the lever. The Force must be at right angles to the lever - The twisting action on the axle/shaft is now (lets say it's Manny with an approximate mass of 150kg) so - 1500N x 1m - 1500N.m
If you make the lever 2m long, and Manny stands on the end it's 1500Nx2m = 3000N.m
etc.
The converse is also true.
if we twist the axle/shaft with a FORCE of 3000N.m we exert a FORCE of 3000Newtons to the end of a 1m lever or 1500Newtons at the end of a 2m lever.
your tyre on your vehicle is the lever - where it touches the ground it translates the rotational force into a linear force. So, we take our torque on the shaft and divide by the tyre radius to give us the Force available to push the vehicle forward - this will either accelerate the vehicle or overcome opposite forces on the vehicle.
so, if we have 500N.m acting on the axle on a 700mm Diameter tyre the vehicle is 'pushed' forward with a force of 500/0,35 = 1428 Newtons
If we fit a new tyre with a diameter of 800mm the torque remains the same - 500N.m - but it's now acting on a lever of ,4m - so 500/0,4 = 1250 Newtons is applied. so bigger tyres do not affect torque (or power) but the FORCE that can be applied because of the gearing - in this case 178N less FORCE is available.
Like our gym bunny trying to pick up the weightlifters bar - if the force required to overcome the opposing forces is more than can be exerted - it's going nowhere. so, gym bunny can't get the vehicle to move up a slight incline but Musclehead can come along and push it up the pass....
but now....
the Gym Bunny could run off and get a lever and a fulcrum. by using the lever and the fulcrum she could lift the 2000N weight or move the car up the hill.
she could, indeed, if she found a big enough lever and a suitable fulcrum, move the earth out of it's orbit.
Gears are simply rotating levers on a fulcrum (the axle or shaft) that multiply Torque in exactly the same fashion that a lever and fulcrum multiplies Force. Double the Ratio - you double the Force(torque) and half the travel (rpm)
so even the smallest motor can, theoretically, be geared up to move entire planets - but the more force you can exert at the source the smaller your lever sets need to be, which translates to less losses through drag in the real world.
and note again - TORQUE is ROTATIONAL FORCE. the confusion steps in because it's measured in N.m and so is Energy - Energy is measured in Joules and 1Joule = 1N.m and these 2 concepts are not related despite using the same unit of measurement, In an equation you cannot use them interchangeably despite the similar unit of measurement. The 'metre' (or inch or foot in imperial terms) is simply a convenience because the radius of the Wheel/Sprocket on which the torque will act (thus creating linear Force) is unknown.
to calculate the usable information - the force - you need to divide the Torque number by the effective radii of the various wheels/sprockets on which the torque acts.
Now onto Energy.
Pretty simple in physics - Energy is the capacity to do work. It's measured in N.m
So, a mass of 1kg suspended 5m above a surface (on earth) has a (POTENTIAL) Energy of 10Nx5m = 50Nm or 50Joules. - the energy is stored - energy was expended to lift it into place, and now it awaits being expended. if the string is cut it will accelerate until it hits the ground and expend its 50J of energy. that energy could be expended by (say) lifting another weight through a series of pulleys, or simply through a loud bang as it hits the ground .
If it's mobile, Energy is calculated by the formula E=0,5.mv^2 - so a 1000kg car, travelling at 10m/s is carrying 0,5x1000x10x10 = 50 000 Nm = 50 000Joules and again DO NOT CONFUSE THESE Nm with TORQUE Nm.
so, to stop the vecicle we need to expend the 50kJ - which is usually done by converting the energy to heat through the brakes - but can also be done by generating electrical current and stored in a battery for later use, or in a hydraulic pressure accumulator to be released later to accelerate the vehicle
this is extremely simplistic and is simply to understand the difference between Torque and Energy.
Now the next step is Power.
Power is the release of Energy or work. it's measured in Joules/ second or Nm/s
AGAIN - that Nm in the Nm/s has nothing at all to do with torque. it's a measurement of energy.
so , from the above Power is measured in Watts and 1 Watt is defined as the Work done by exerting a Force of 1N on an object for a distance of 1m in 1 second.
so, to go back to Muscle head and gym bunny.
As noted Muscle head can lift 2000N the 2m above his head - but it takes him 5 seconds to struggle it up there before dropping it.
Gym Bunny can lift her 200N 10 times from floor to above her head and drop it in 10 seconds.
so - they have both done the same work / expended the same energy, Musclehead has expended 2000Nx2m = 4000Joules and gym bunny 200Nx2mx10 = 4000Joules.
but because Musclehead does the work in 5 seconds - 4000Joules/5sec = 800 J/sec = 800 Watts and Gym bunny does the work in 10 seconds - 4000J/10sec=400J/s = 400Watts we can now call Musclehead really more powerful.
However, lets say Gym Bunny has a couple of Redbulls with Vodka before the contest, and she is able to do the 10 lifts in 4 seconds.
that means she is now performing work at 4000J/4sec = 1000Watts and is actually now more powerful than Musclehead despite being unable to apply anything like the same force to an object.
So, to work out Power from Force we need to know distance and time as well. Power = Force(N) x distance(m) / Time (s) to give us Nm/s or Watts.
to work out Power from Torque is the same - we need to know distance and time. the distance in the torque figure has to be altered to give us a linear distance to work in the Power equation.
so to translate it from a rotational to a linear is pretty easy - the circumference of a wheel is 2 x pi x radius
In effect - by multiplying it out, you've now translated the figure to Energy. 2pi Nm(torque) = 1 Nm (Energy) = 1J
So, we now know Force x distance (for 1 revolution) and just need to add time to get to Watts.
We measure speed of work in a motor in rpm (generally)
so, to add that into the equation we must divide the rpm by 60 to get to seconds AND we must multiply by the number of revolutions in one second as our figure is only for 1 revolution.
we'd also like the figure to be in kW (not Watts) so we divide by 1000
so, the final equation to get from Torque to Power (metric) is:
Power = Torque x 2pi x rpm/60/1000
As Pi is constant as well as the 60 and 1000 we can shorten it to:
Power = Torque x rpm /9549
as can be deduced - High Torque at low rpm (e.g. A big Diesel making 500Nm at 1500rpm is making only78kW) can make the same power as a motor making low torque at high rpm e.g. a proper F1 motor that revs to 19000rpm but makes only 300Nm is making 597kW
Basically... for Manny ... This means... that for any rpm less than 9549 the Torque figure will be higher than the power figure
at 9549 rpm power figure and torque figure will be equal
and over 9549rpm the Power figure will be higher than the Torque figure.
now hopefully I never have to see anyone declaring that you convert torque to power by using the stroke of the engine ever again!
I am more stupid than I thought!