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A rant on torque and horsepower.

3.9K views 36 replies 19 participants last post by  Pyrgnome  
#1 ·
For years I have felt like I didn't fully understand the relationship of torque and horsepower.
I mean you look up the technical description and it seems so simple.

http://en.wikipedia.org/wiki/Horsepower#Relationship_with_torque

For a given torque and speed, the power may be calculated. The standard equation relating torque in foot-pounds, rotational speed in RPM and horsepower is:

P [ {\rm hp}] = {(\Tau [{\rm ft \cdot lbf}]) (\omega [{\rm RPM}]) \over 5252}

Where P is power, Τ is torque, and ω is rotations per minute. The constant 5252 comes from (33,000 ft?lbf/min)/(2π rad./rev.).
It seems so simple. Horsepower is basically just a matter of torque and RPM.
It's also how much work can actually be done by a motor.
So where I had been confused for so long is listening to all the arguments you hear all the time.
Low end torque is better then high end hp, Hp is good on the straights but coming out of the corner you want good low end torque, The blacktop makes good high end Hp but the 2 GR makes better low end torque, ect.
I thought there must be something I am missing. People make it sound like this complicated relationship, I must not understand how it applies or something.

Finally I realized it really is that simple.
Comparing torqe to hp is like comparing apples to lemonade. Sure they might be related but you are just overcomplicating a very simple situation.

Ok so torque is easy, twisting force is all it boils down to. We americans tend to use inch pounds and foot pounds. If you don't get it read this
http://en.wikipedia.org/wiki/Torque#Relationship_between_torque_and_power

Horsepower is how much work that torque can accomplish over time.

So since for ICEs we need to worry about torque curves and such let's simplify this to two single speed electric motors.
Given optimal gearing which would acelerate your car faster, a motor that makes 400 ft/lbs of torqe at 1000 rpm or a motor that makes 75 ft/lbs of torque at 14000 RPM?

Even though the latter motor makes substantially less torque it makes considerably more hp. This means it is able to do much more work faster than the other motor.

Heres the other thing to think about.
I say given the right gearing because one will need a much greater reduction.
What does a gear reduction do? It increases torque.
So at the wheels the 14000 RPM motor will be able to deliver more torque than the 1000 rpm motor.
Remember when you dyno your car HP is measured the same (Minus drivetrain loss) at the motor as at the wheels. Torque however is much different at the motor than it is at the wheels.
Let's say you have a .5:1 gear reduction. The hp will be the same at both points, the motor would be able to move half as much twice as fast as the output after the gear reduction.
Hp is the same, torque is doubled by the gearbox.

So lets say we have a motor that makes 100 ft/lbs of torqe at 5252 rpm and we have a motor that makes 5252 ft/lbs torque at 100 rpm we have two 100 hp motors.
If we gear them so both output shafts are spinning the same rpm you will get the same amount of hp and torque out of both motors. Again of course plus or minus drivetrain loss.

So what's better apples or lemonade?

Here's a cool converter I found to find hp from torque and RPM.
http://www.ajdesigner.com/phphorsepower/horsepower_equation_rotating_horsepower.php
 
#2 ·
So what does this mean to a tuner.
Really if you want maximum acceleration your primary concern should be HP and gearing.

If you want to alter your HP curve you want to look at torque.
If you want more power at 4k rpm then one part of the equation is already fixed so now you need to understand how to make more torque at that RPM.
If you make more torque at that RPM you will make more HP at that RPM.
It may not effect your peak hp or it may even lower your peak hp.
Really understanding the relationship of the two is the only way to understand the effects it will have.
 
#3 ·
Finally someone else who understands!


Ive noticed that with most NA graphs (I dont look at boosted graphs much) that the HP line and the torque line look identical. Just tilt your graph 45* roughly so the hp curve is flat and its very close to the torque curve. Another interesting bit is the AFR graph tends to mirror the HP/TQ curve.


One thing I think is interesting is how many people seem to thing that by increasing the displacement of a 4agze (7agze) you will gain upwards of 20whp. But when you think about how the SC is a fixed positive displacement air pump and take into account the extra air consumed by the 7ag vs 4ag in the end peak power wont change since the amount of air still hasnt changed. Instead everything under the curve would increase.



Its an interesting thing that you brought up here. Alot of old gear heads stick to the idea that torque wins races and hp sells cars (not saying its false) but when we look at the old muscle cars that were making 400hp/tq and only ran a 15-16s 1/4 time factory.


Gearing is part of the reason that Hondas are so damn quick. Our ratios blow in comparison.
 
#5 ·
jimmer411 said:
Its an interesting thing that you brought up here. Alot of old gear heads stick to the idea that torque wins races and hp sells cars (not saying its false) but when we look at the old muscle cars that were making 400hp/tq and only ran a 15-16s 1/4 time factory.
And that is why some of us geriatric petrol heads like our MR2's modified.
SC Aw11 can really deflate the neighbour, with his new V8 club sport, ego.
Good HP/Torque + gearing + low weight + handling = fun.
 
#6 ·
Gearing is something WAY too overlooked, I guarantee you it doesn't escape the V8 ********. When you fit a set of cams, the dynamic compression ratio drops on the bottom end due to the increased overlap. This is also why bigger cams take more timing, assuming you don't change the static comression ratio. This is why big cams want higher static compression ratios. Anyway, the torque builds later and lasts longer without dropping off thus giving you the high peak hp numbers (since hp is a a factor of torque and RPM), but it's not necessarily more torque, rather the torque band has shifted higher and doesn't drop off as quickly. Now your shift speeds blow, 1st gets an extra 5mph 2nd an extra 10mph and so on. The car should feel overgeared and a little more sluggish especially around a corner. Without dropping the gear ratio you won't realize the full potential of what you've done to your engine, you need to multiply that torque since there might be a little less of it (but still more hp). Now that you've changed the gearing, you effectively put the same or more peak torque to the wheels and since it no longer drops off like stock did and the car hauls ass and your shift speeds have come back down where they need to be.
 
#7 · (Edited)
dx/dt said:
interesting read. :) i always had this in mind. wondering which would be better?
Here we go comparing them again.
You need both, they are a symbiosis.
Of course straight forward answer is it doesn't matter how much torque a motor makes as long as it makes your hp goal.
The one problem with that is that less torque means you will rely on more RPMs.
The higher the RPMs the harder it is on the motor. Parts will wear out and fail much faster, there is more loss from friction, you need heavier valve springs which robs more power, etc.
Rods and pistons see insane forces at high RPM and can only take so much. If you want to go higher you will either need much beefier internals or much more advanced and expensive materials to keep the weight down.

F1 cars can afford to do this. Like supercharged111 said they are just tuned to maintain that torque curve to sky high RPMs and that makes a lot of HP.
They also need to be rebuilt all the time.
Same thing for sport bikes and one of the reasons people say 1000 miles on a sportbike motor is something like 100000 on a car motor.
Reving too high on an ICE (internal combustion engine) is just impractical so you need to make enough torque within the scope of a practical rev range to meet your hp goals.
Beond that you would want to start moving away from the ICE.
Gas turbine engines rely almost completely on RPM.
A 750 hp gas turbine engine at 40000 rpms would only be making 100 ft/lbs torque.
 
#8 ·
The ******* definitions of horsepower and torque:
Horsepower is how fast you're going when you hit the wall
Torque is how far you drag the wall with you

As far as winning races... I'll take the horsepower.
For my street car? I'd rather have the torque down low vs. the hp in the powerband. BSFC's are based on horsepower, which is based on RPM. If I can get the same "pull" away from the stoplights at lower RPM, I'm using less fuel (ignore the fuzzy math) putting less wear on my clutch and my wallet is happier
 
#11 ·
Each cylinder fires once during two revolutions of the crankshaft. The combustion force transmitted through the pistons during those two revolutions is the basis for engine power (force*distance=energy, energy/time=power).

Power can be increased by producing more combustion cycles per unit time (increase RPM), or by producing more force (torque) in the individual combustion cycles (greater displacement, better breathing, forced induction).

You get more "pull" by increasing torque- the question is, where in the RPM range do you want it? (Everywhere? Get a bigger engine.)

A car with more torque down low may not produce that much more HP, but will accelerate better at low RPMs and can be driven with less drama. A car with more torque up top makes more HP and is ultimately faster, but requires skill -and perhaps gearing changes- to keep the RPMs in the necessary range.

I like my AW11, but I wouldn't mind not having to wind it out just to merge onto the freeway. More displacement would be nice.
 
#12 ·
The rules of thumb about power and torque come about because they are rough indicators of engine tuning. Peak power is essentially useless unless it is available over a wide enough band so that you can access it during actual driving conditions. You can generally tune an engine for more peak power by pushing the power peak upward with cam timing and induction tuning. This results in a narrower power peak, and it reaches diminishing returns quickly. More gears are not necessarily the answer, because your torque is zero while you are shifting. An engine with a high power to torque ratio has probably been sharply tuned, and it may be a real dog off the power peak. If the ratio is low, the engine should have a broad power peak that is easy to find and will launch you out of a corner without having to play hopscotch with the gears.
 
#13 ·
Both Torque and HP are mathematical measurments of the power produced by your engine. They are tied directly together by RPM. That is the reason all TQ/HP graphs cross at exactly 5252 RPM.

(Torque X RPM) / 5252 = HP
and
(HP X 5252) / RPM = Torque

At 5252 RPM Torque = HP always. You couldn't change it if you wanted to.

You can't even measure Torque and HP separately they are flip sides of the same coin.

However they are very useful ways to describe the quality of power that a particular engine produces.

I have always liked the description published on the Yaw Power web page. Unfortunately it looks like that site is gone but someone posted the page here:
http://www.jacobmcdonald.com/weblinks/hptq2.html
 
#14 ·
My favorite way of explaining HP and Torque is
Horsepower is how fast you can hit the wall, Torque is how far you can take the wall with you, after you hit it.
and the other confusing to most is:
Understeer is when you hit the wall with the front of the car, Oversteer is when you hit the wall with the rear of the car.
 
#15 ·
jimmer411 said:
One thing I think is interesting is how many people seem to thing that by increasing the displacement of a 4agze (7agze) you will gain upwards of 20whp. But when you think about how the SC is a fixed positive displacement air pump and take into account the extra air consumed by the 7ag vs 4ag in the end peak power wont change since the amount of air still hasnt changed. Instead everything under the curve would increase.
Correct. In that example, the supercharger is regulating mass air flow through the engine. When you compare a naturally aspirated 4AG to an equivalent 7AG, you don't have that regulating factor, and the horsepower differences are proportionate to the difference in displacement between the two engines.


jimmer411 said:
...when we look at the old muscle cars that were making 400hp/tq and only ran a 15-16s 1/4 time factory.
There are all sorts of other issues at play there. You had manufacturers blatantly underestimating and overestimating their power output. Cars were built with much less consistency and a much greater set of variables, and a lot more things could be out of tune than on modern cars. And you also had tires made out of chalk with a contact patch the size of a postage stamp. It's really interesting to pick up car mags from the 60s and read their road tests. Sometimes they'd take a box-stock muscle car and get a couple seconds of ET improvement just by correcting all the errors and setup problems (incorrect ignition timing and jetting, for example), uncorking the exhaust and putting on some decent tires. Like anything else, numbers and statistics only tell part of the story.

Now, not to get too off track, the relationship between torque and horsepower really is a simple one. Torque is effectively how much work an engine can do, and horsepower is effectively how fast it can do that work. To move a car, you need both. To make it fast and/or fun, you need both in reasonable quantities and in the correct proportion to each other.
 
#17 ·
I'd much rather have the low end torque necessary to throw you back in the seat. I loved the kick my diesel Jetta got. With 275 Ft/Lbs at 2100RPM the only problem was keeping the tires on the ground. I'd much rather have a torquey engine than a high-horsepower only engine any day.

It drives me crazy that I have to wind this car out to get power out of it. Someday it'll have a v6 instead of the blacktop
 
#20 ·
te51levin said:
To make it fast and/or fun, you need both in reasonable quantities and in the correct proportion to each other.

this is probably one of the better statements on here.

You can do the math equations on paper and keep all other factors constant and make one engine look better than another based on HP. The problem in doing so is that even if you look at the gearing of the transmission you aren't necessarily taking into account the gearing of the rear end/diff, the weight of the car, the aerodynamics of the car etc.

If an engine's ability to just run and make power at a given RPM then we would all be running around in self-propelling sterling motors. The problem with a sterling motor is tht it can make horsepower but little to no torque. When you factor in the weight and aerodynamics of a car the engine simply won't work.

I also don't think that I would agree with the statement of:
"So what does this mean to a tuner.
Really if you want maximum acceleration your primary concern should be HP and gearing."

Yes, gearing is important but there's not a large quantity of tuners who are going to be swapping gears out. You might be able to find a transmission here or there that has different gear sets that are easily transferrable, but typically that isn't the case and/or to change the gearing can be quite expensive. Ultimately this means that this modification overall can have a lower impact per dollar spent when compared to other modifications.

A comparison of a 4age against a 4agze is a very good one. Even if you compare a US 4agze against a blacktop 20V. The blacktop makes more top end power, can rev higher, has the VVT to add power across the band, but in a straight line race given the same cars and transmissions (and keeping all other factors constant and considering that the gearing is not biased to either engine) the 4agze which makes less overall HP will actually win. This is because of the powerband itself and the broadness of the curve. If you compare a 4agze dyno graph to a 4age blacktop graph you will see vast differences, and in the 4agze you will see that there is more overall power much earlier on.

Similarly you can throw (and I use this everynow and then) a supra CT26 onto a 4age and make lots of horsepower up top. The problem is that when you look at the whole picture there are pieces of the puzzle missing and you'll actually see that the car will struggle to be "very fast" because you've essentially thrown a large restriction into the airpath to the intake and boost won't be made until a much higher RPM -- you've lost lowend power. Yes, you can then make the car much faster by regearing it but the question still becomes how much is it going to cost and if a more efficient system overal that didn't concentrate purely on high end horsepower would have been a better decision.


The 4agze vs. 7agze debate I'm not 100% sure I'm on board. Yes, the sc12 would have problems supplying a constant 10psi of pressure at a higher rpm because that is the ineffeciency of the supercharger. However, if you compare a 4age to a 7age and you factor the volume each cylinder can hold you actually are changing the amount of air being "forced" into each cylinder. The SC12 is built to supply a given amount of air for a given amount of rpm's and a given amount of pressure. At 3,000 rpm's all of the air the SC12 could produce is not entering into the cylinders which is why there aren't any issues with the sc12 down low. Meaning it's able to supply the needed amount of air to the cylinder at that given PSI for the amount of time that the valve is open. With a 7agze the story is the same -- the amount of air the SC12 is ABLE to supply at that given RPM is a higher volume of air given the higer volume of displacement. the problem with a 7agze and an SC12 is if you're running at 7,500 rpm's at 10psi the supercharger might have difficulties supplying the required amount of air that the engine demands to keep the pressure in the intake manifold at a constant 10psi.
 
#21 ·
toyotaspeed90 said:
The 4agze vs. 7agze debate I'm not 100% sure I'm on board. <SNIP> The SC12 is built to supply a given amount of air for a given amount of rpm's and a given amount of pressure. <SNIP> the problem with a 7agze and an SC12 is if you're running at 7,500 rpm's at 10psi the supercharger might have difficulties supplying the required amount of air that the engine demands to keep the pressure in the intake manifold at a constant 10psi.
You're right, mostly, but maybe saying it differently than I would. To clarify:

That supercharger is a positive displacement pump. It works in volume, and (within reason, and assuming constant intake air density) it simply does not care about pressure. Barring any internal leakage, it pumps 1200cc of air per rotation, and could not care less where it goes after it has pumped it.

Rotating at a given speed, it might feed into a 1587cc engine that induces 10psi of backpressure (boost) in the intake manifold, because the engine is a restriction to the supercharger. Or, rotating at the same speed, it might feed into a 1762cc engine that induces only 7psi of backpressure (boost) because the engine is capable of pumping more air per revolution than the smaller engine can.

Changing the shape of the torque curve, the gearing, and many other factors have a huge impact on both the feel of the car and the performance. You can go equally fast with a 455ci Olds V8 or a 301 Chevy (look it up), but they will do it in very different ways.
 
#22 ·
edmcguirk said:
Both Torque and HP are mathematical measurments of the power produced by your engine. They are tied directly together by RPM. That is the reason all TQ/HP graphs cross at exactly 5252 RPM.

(Torque X RPM) / 5252 = HP
and
(HP X 5252) / RPM = Torque

At 5252 RPM Torque = HP always. You couldn't change it if you wanted to.

You can't even measure Torque and HP separately they are flip sides of the same coin.
Actually you can measure torque without hp.
Torque is simply twisting force.
You can't measure HP without torque. Well you can't make hp without torque though you can find torque if you know how much work is being done over a fixed period of time.


To move a car, you need both. To make it fast and/or fun, you need both in reasonable quantities and in the correct proportion to each other
See I disagree with this.
Who cares if your motor makes 200 ft lbs or 100 ft lbs if they had the same hp and a big enough power curve to utilize proper gearing then the amount of torque put to the wheels would be the same and amount of work potential (How much can be done over time) will be the same.

Now from the real world perspective there are concerns like RPMs kill motors and other things but my point is I see no reason to compare the two.
Ok so on a particular track it might be advantageous to make more power down low. Perhaps up high on another track. As mentioned it could be easier to change the location/characteristics of your tq/power curve than the gears in your trans. It still doesn't mean we need to compare the two.

Look at a gas turbine engine on a helicopter. I can't imagine how much torque it takes to spin those blades at that RPM but I'm sure it's a lot.
Gas turbine engines though don't make great torque. However if it puts out 40 ft lbs at 50000 RPM and you geared it down to spin a rotor at 5k rpm that rotor is seeing 400 ft lbs torque. If the rotor spins 2500 RPM it would see 800 ft lbs torque.

Torque is drastically different but the total amount of work that can be done is the same.
You could put a diesel engine in that helicopter that made 800 ft lbs at 2500 rpm and it would be just as effective assuming they both had suitable power curves.


Yes, gearing is important but there's not a large quantity of tuners who are going to be swapping gears out. You might be able to find a transmission here or there that has different gear sets that are easily transferrable, but typically that isn't the case and/or to change the gearing can be quite expensive. Ultimately this means that this modification overall can have a lower impact per dollar spent when compared to other modifications
True you can move your curve easier than change your gearing and that is done quite often in racing. However you don't necessarily need to be swapping out your gears. Maybe you are going to be doing a lot of driving where you want maximum performance from 5k to 7k rpm in third you just need to try and fudge your torque peak into that range.
If you have a much higher speed track you don't need to change your gears you just find that you will be driving more at 4k to 6k in fourth so you move your curve down a little bit.
I'm not saying all you need to care about is peak hp I'm saying the real factor is how much work can be done over time. If you will be driving at 4k RPM that's a fixed part of the equation now all you can do is modify torque at that RPM to effect how much work you can do. If at 4k you can slip it into third and be making more hp you will be able to accelerate faster even though you are making much less torque than you were at 4k in fourth.
 
#23 ·
yoshimitsuspeed said:
Look at a gas turbine engine on a helicopter. I can't imagine how much torque it takes to spin those blades at that RPM but I'm sure it's a lot.
Gas turbine engines though don't make great torque. However if it puts out 40 ft lbs at 50000 RPM and you geared it down to spin a rotor at 5k rpm that rotor is seeing 400 ft lbs torque. If the rotor spins 2500 RPM it would see 800 ft lbs torque.

Torque is drastically different but the total amount of work that can be done is the same.
You could put a diesel engine in that helicopter that made 800 ft lbs at 2500 rpm and it would be just as effective assuming they both had suitable power curves.
Of course in a helicopter that's assuming they both weighed the same and I'd love to see a 200 lb diesel that puts out 400 hp haha.
 
#24 ·
yoshimitsuspeed said:
See I disagree with this.
Who cares if your motor makes 200 ft lbs or 100 ft lbs if they had the same hp and a big enough power curve to utilize proper gearing then the amount of torque put to the wheels would be the same and amount of work potential (How much can be done over time) will be the same.
There are other factors involved. Taking your example of two engines making identical horsepower (say 150 bhp), the engine that makes 200 ft/lb of torque will probably be making that 150 bhp at roughly half the RPM that the 100 ft/lb engine makes it. They'll both have similar idle speeds, but the grunter will have a lot more power (torque) available right off idle, and will be better suited to lugging a bid sedan around town, but it won't have a lot of personality, and won't make great noises or be much fun on the track.

On the other hand, the little 100 ft/lb engine might make its peak horsepower at twice the RPM of the bigger engine. It will not be capable of making any real torque (nor of doing any real work) until it is spinning much faster than its idle speed. That means there are a few thousand RPM that simply aren't useable. It may be ideal on the track, and a lot of fun, but it will be a chore around town. You can gear it down, sure, but after a point, that is equivalent to pulling a plow with a thousand chickens rather than one strong horse.

Personally, in a sports car, I like an engine that has a wide, useable torque band, but one that gets stronger as the revs increase, with a nice high redline. This gives it more personality and makes it more playful than one that makes dump-truck torque, but won't rev or sing. Even if the big grunter goes faster, I prefer the personality of something a little spicier.

As with most things, there are many different ways to accomplish the same goal, and plenty of room for different tastes and preferences.
 
#25 ·
yoshimitsuspeed said:
Actually you can measure torque without hp.
Torque is simply twisting force.
You can't measure HP without torque. Well you can't make hp without torque though you can find torque if you know how much work is being done over a fixed period of time.
That may be true in the world of physics but engine Torque is not really the same thing as the world of physics.

The definition of torque in physics is simply force at a specific radius and it's true that motion is not actually necessary. However engines do not make any force when they are not moving. Once you say force at a specific rpm, you have introduced time into the equation and you are really talking about work not force.

What that means is the engine Torque is one kind of work while engine HP is another kind of work. They are really the same thing measured differently. Torque is really just a handy shorthand to help describe how broad the power band is. Once you know Torque at any specific RPM, you know the HP. You don't have to measure it, it's locked in.

That's why it is equally valid to talk about high end power is better or worse than low end power as it is to talk about Torque is better or worse than HP.

In general when I hear people talk as if an engine could have Torque and not HP as if one was not directly locked to the other, I know they really don't understand what they are talking about.

I am reading plenty of comments here where people are right for the wrong reasons and it's just not worth fighting them to prove that they are already right.
 
#26 ·
yoshimitsuspeed said:
See I disagree with this.
Who cares if your motor makes 200 ft lbs or 100 ft lbs if they had the same hp and a big enough power curve to utilize proper gearing then the amount of torque put to the wheels would be the same and amount of work potential (How much can be done over time) will be the same.
It seems like this, but its not true. To over come an opposing force, you need to have a greater force. Its like you have impact wrench and a bolt. Imagine the impacts per second as rpms, and the torque per (impacts per second) is horsepower, because it work over time.. The bolt needs 75 ftlbs to get lose, but your impact gun only produces 50ftlbs or torque, and goes at 20 impacts per second. On the other had you have another impact gun that produces 100ft lbs of torque and goes at 10 impacts per second. Both produce the same about of work (horse power), but the second one is the only one that will get it lose.

An easier way to look at the relationship of torque and horsepower, is horsepower is the integral of torque.

Imagine you had an engine that produced 10 ftlbs of torque at 20k rpms, and your try to move your car with the e-brake up. If you dump the clutch at 20k rpms, the clutch doesn't slip, and the engine components and flywheel are massless, Will you move?