Torque vs Horsepower

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People are always asking "do you want torque or horsepower in your engine?"
That is an invalid question. The two represent different physical quantities.
Torque is twisting force.
Power is the rate at which work is done.
You can't have one without the other.
An engine can't make any power unless it makes torque.
 
RayCJ and Garak are correct.

The equation HP = (TQ x RPM)/5252 (approximately!) is really a lazy person's shortcut to obtain power in units of horsepower when using torque in foot-pounds and rotational speed in RPM. That shortcut won't work, in other words, if you're using metric units, or if torque is in inch-pounds, for example.

In purer terms, IF you're using any mathematically consistent units, power=angular velocity×torque.

For a metric example, 500[radians]/second ×200 newton-meters = 100,000 newton-meters/second = 100,000 watts = 100kw (= about 134 Hp)
 
Not sure where I read it - 'Horsepower is how fast you hit the wall, torque is how far you take the wall with you'.
 
Originally Posted by RayCJ
Originally Posted by DGXR
I understand what each means but I don't understand the mathematical equation that all the engineers use:

HP = (TQ x RPM)/5252

How could this equation be true for every engine? There are SO MANY different engine designs: different bore x stroke, different compression ratios, 2 large valves vs 4 small valves per cylinder, different camshaft profiles... all these factors will affect the output of torque vs HP at different RPMs and different throttle settings. Specifically I am thinking of the long-stroke Harley-Davidson motorcycle engines that produce loads of torque off-idle vs an equivalent displacement Honda 4-cylinder motorcycle engine that produces comparatively little torque off idle but way more peak HP than the Harley. In this scenario the Harley has high TQ at low RPM, which would generally equal a high HP number. And the Honda has a low TQ at a low RPM, which would generally equal a low HP number but the Honda ultimately produces more peak HP. So again it does not make sense to me.
What am I missing here? Someone please explain, preferably in the simplest terms possible.
Thank you!


In the simplest terms without using much math...

A long time ago, folks settled on the idea that a horse could pull a rope connected to a pulley and lift a 550 lb weight at constant rate of 1 foot per second. Since there's 60 seconds per minute, that converts to an equivalent of 33,000 pounds per minute because 550 x 60 = 33,000. This calculation is for things moving in a straight line. Engines have shafts that rotate so, conversions must be done to convert linear speed to rotational speed. The circumference of a round shaft is 2 x Pi x radius (Pi = 3.1416).

When all is said and done, the 5252 comes from 2 x Pi / 33,000 (because 2 x 3.1416 / 33,000 is roughly equal to 5252). Think of it as a conversion factor from linear motion per second to rotational motion per minute.

Thus: Horsepower ends-up equaling (Torque x RPM) / 5252.


Taking it a little further, Torque = Force x Distance. ( Example: Think of a 1 foot long wrench with 5 lbs of weight at the end. The torque will be 5 ft lbs).

Horsepower is the rate at which you can apply torque and is: (Force x Distance) / Time.

In other words, Horsepower = Torque / Time.



Your train of logic goes off the rails when you get here. You are equating torque to work done, and that is incorrect. To convert torque to work done, multiply torque by 2*pi. For example, if an engine is producing 100 lb*ft torque, and rotates through 2 revolutions, then it has done 100 lb*ft x 2 revolutions x (2*pi) radians/revolution = 1256 lb*ft of work

The definition of Horsepower was originated by James Watt when he was developing steam engines to pump water out of coal mines in England. He put a scale on a horse pushing a capstan on a pump and measured 181 pounds of force while covering 180 feet per minute. Multiplying, the work done per unit time was 32,580 lb*ft/min, which Watt rounded up to 33000, and called a Horsepower. The creators of the Metric system honored James Watt by naming its unit of power the Watt, which is a Newton*meter / second.
 
Originally Posted by DukeOfFrontenac
Not sure where I read it - 'Horsepower is how fast you hit the wall, torque is how far you take the wall with you'.

That would be momentum
 
Originally Posted by Anduril
Originally Posted by DukeOfFrontenac
Not sure where I read it - 'Horsepower is how fast you hit the wall, torque is how far you take the wall with you'.

That would be momentum


Mass x velocity = Force. Once at speed I could cut the engine off before hitting the wall …

More like torque x RPM / constant
 
Originally Posted by A_Harman
Originally Posted by RayCJ
Originally Posted by DGXR
I understand what each means but I don't understand the mathematical equation that all the engineers use:

HP = (TQ x RPM)/5252

How could this equation be true for every engine? There are SO MANY different engine designs: different bore x stroke, different compression ratios, 2 large valves vs 4 small valves per cylinder, different camshaft profiles... all these factors will affect the output of torque vs HP at different RPMs and different throttle settings. Specifically I am thinking of the long-stroke Harley-Davidson motorcycle engines that produce loads of torque off-idle vs an equivalent displacement Honda 4-cylinder motorcycle engine that produces comparatively little torque off idle but way more peak HP than the Harley. In this scenario the Harley has high TQ at low RPM, which would generally equal a high HP number. And the Honda has a low TQ at a low RPM, which would generally equal a low HP number but the Honda ultimately produces more peak HP. So again it does not make sense to me.
What am I missing here? Someone please explain, preferably in the simplest terms possible.
Thank you!


In the simplest terms without using much math...

A long time ago, folks settled on the idea that a horse could pull a rope connected to a pulley and lift a 550 lb weight at constant rate of 1 foot per second. Since there's 60 seconds per minute, that converts to an equivalent of 33,000 pounds per minute because 550 x 60 = 33,000. This calculation is for things moving in a straight line. Engines have shafts that rotate so, conversions must be done to convert linear speed to rotational speed. The circumference of a round shaft is 2 x Pi x radius (Pi = 3.1416).

When all is said and done, the 5252 comes from 2 x Pi / 33,000 (because 2 x 3.1416 / 33,000 is roughly equal to 5252). Think of it as a conversion factor from linear motion per second to rotational motion per minute.

Thus: Horsepower ends-up equaling (Torque x RPM) / 5252.


Taking it a little further, Torque = Force x Distance. ( Example: Think of a 1 foot long wrench with 5 lbs of weight at the end. The torque will be 5 ft lbs).

Horsepower is the rate at which you can apply torque and is: (Force x Distance) / Time.

In other words, Horsepower = Torque / Time.



Your train of logic goes off the rails when you get here. You are equating torque to work done, and that is incorrect. To convert torque to work done, multiply torque by 2*pi. For example, if an engine is producing 100 lb*ft torque, and rotates through 2 revolutions, then it has done 100 lb*ft x 2 revolutions x (2*pi) radians/revolution = 1256 lb*ft of work

The definition of Horsepower was originated by James Watt when he was developing steam engines to pump water out of coal mines in England. He put a scale on a horse pushing a capstan on a pump and measured 181 pounds of force while covering 180 feet per minute. Multiplying, the work done per unit time was 32,580 lb*ft/min, which Watt rounded up to 33000, and called a Horsepower. The creators of the Metric system honored James Watt by naming its unit of power the Watt, which is a Newton*meter / second.



I guess it depends on which history book you want to believe. Watt had a very hard time selling the notion of horsepower and it's quite possible there are different explanations of why it came about. In your example, you've gone from arbitrary revolutions to radians. In my example I'm showing that the constant 5252 is the rounded value of (33,000 ftâ‹…lbf/min)/(2Ï€ rad/rev) but I'm not showing the details of conversion because most folks have a hard time understanding radians (as evidenced by the countless freshmen and sophomore college kids I taught this class to).

https://en.wikipedia.org/wiki/Horsepower

Horsepower (hp) is a unit of measurement of power, or the rate at which work is done. There are many different standards and types of horsepower. Two common definitions being used today are the mechanical horsepower (or imperial horsepower), which is about 745.7 watts, and the metric horsepower, which is approximately 735.5 watts.

The term was adopted in the late 18th century by Scottish engineer James Watt to compare the output of steam engines with the power of draft horses. It was later expanded to include the output power of other types of piston engines, as well as turbines, electric motors and other machinery.[1][2] The definition of the unit varied among geographical regions. Most countries now use the SI unit watt for measurement of power. With the implementation of the EU Directive 80/181/EEC on January 1, 2010, the use of horsepower in the EU is permitted only as a supplementary unit.[3]
 
Originally Posted by DGXR
I understand what each means but I don't understand the mathematical equation that all the engineers use:

HP = (TQ x RPM)/5252

How could this equation be true for every engine? There are SO MANY different engine designs: different bore x stroke, different compression ratios, 2 large valves vs 4 small valves per cylinder, different camshaft profiles... all these factors will affect the output of torque vs HP at different RPMs and different throttle settings. Specifically I am thinking of the long-stroke Harley-Davidson motorcycle engines that produce loads of torque off-idle vs an equivalent displacement Honda 4-cylinder motorcycle engine that produces comparatively little torque off idle but way more peak HP than the Harley. In this scenario the Harley has high TQ at low RPM, which would generally equal a high HP number. And the Honda has a low TQ at a low RPM, which would generally equal a low HP number but the Honda ultimately produces more peak HP. So again it does not make sense to me.
What am I missing here? Someone please explain, preferably in the simplest terms possible.
Thank you!


Step back from the problem and think about it in general terms.
Power and torque are output quantities from an engine.
All the possible engine design variations you listed are just inputs to the system. Adjusting them only changes torque output at different crankshaft speeds.
As a consumer of power, you are only concerned with the output.
Peak power occurs where torque x rpm is maximum.
 
Good discussion so far.

What I would add is that the term "torque vs horsepower" really only applies in terms of putting the two on a graph. This way one can see their relationship with each other and how it changes thruought the RPM tange. That's what engeers use to design the engines, transmissions and final gearing of a vehicle that is matched to a specific role it needs to perform.

But to a lot of people that term "torque vs horsepower" is interpreted as two competing units for some reason.
 
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Simplest way to look at it...

HP is torque at a specific RPM.

150HP diesel has the same capacity for work as a 150HP motorcycle engine.

They will have very different HP ratings at low RPM which would reflect the large torque difference.

If we were conditioned to look at a HP/RPM graph, rather than HP and TQ at peak ratings, TQ numbers by themselves wouldn't be important.
 
Don`t know if this will help but torque is twist, a diesel makes a lot of twist/torque at low rpm a gas engine makes less torque at low rpm but more horsepower at higher rpm given the same cubic capacity. Turbo chargers increase capacity.
 
Originally Posted by RedOakRanch
A flat torque curves yields better HP at low RPM's. That's why the new 2.0t gas engines in sedans pull as good as the larger V6 engines with more peak HP.


So, do you see a correlation between having more torque across available RPM range and the rate of acceleration or HP?

If you do, I find your earlier post that torque by itself is not important quite puzzling.
 
I prefer my torque traction motors 100% torque ALL RPMs

total output is 472ft at 4100 rpm.

but will have at lest a minimum of 300-350 in the whole power band thanks to the electrical motors
 
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Boy, what a lot of confusion about basics in this thread, starting with the confused title!

With all due respect Mr. Watt and his invention of the Horsepower unit, it's archaic. We might be less confused if we switched to measuring mechanical power in watts and kilowatts, as the rest of the world does, and even the US does in the context of other forms of power.
 
We once dyno'd a Veloster that made exactly 100.00 hp. Now occasionally we refer to it like an engine making 658 hp as making 6.58 Velosters. Maybe we could catch it on as a new trend.
 
Originally Posted by DGXR
I understand what each means but I don't understand the mathematical equation that all the engineers use:

HP = (TQ x RPM)/5252

How could this equation be true for every engine? There are SO MANY different engine designs: different bore x stroke, different compression ratios, 2 large valves vs 4 small valves per cylinder, different camshaft profiles... all these factors will affect the output of torque vs HP at different RPMs and different throttle settings. Specifically I am thinking of the long-stroke Harley-Davidson motorcycle engines that produce loads of torque off-idle vs an equivalent displacement Honda 4-cylinder motorcycle engine that produces comparatively little torque off idle but way more peak HP than the Harley. In this scenario the Harley has high TQ at low RPM, which would generally equal a high HP number. And the Honda has a low TQ at a low RPM, which would generally equal a low HP number but the Honda ultimately produces more peak HP. So again it does not make sense to me.
What am I missing here? Someone please explain, preferably in the simplest terms possible.
Thank you!


Anduril has the best answer to this and most other people answering seem to be augmenting their opinions or preconceived notions with anecdotal "rules of thumb" which really just add to the confusion when Anduril came in the the facts of the matter. I am going to post a dyno graph of a car I tuned several years back and will try to elaborate just a little on a few things.

[Linked Image]



First, notice that that HP and TQ cross at 5250 rpms on the "before" and the "after" tuning. ("Before tuning" was actually another tuner that didn't know what he was doing)
It will always cross there. HP is just a function of TQ and rpm. I can post other dyno charts of different engines and they will all cross there. You can also do the math at any point HP =(TQ x rpm)/5252 or even run it backwards on the HP line.

Second thing, the hp and tq curve are much more important than the arbitrary number that is usually "advertised" to us. That is so 1 dimensional to boil an engines performance down to 1 or 2 numbers. Look at the dyno graph I posted again. The "before" run was just shy of 200hp at 4700 rpms while the "after" tuning hits the 200 hp mark by 3900rpms and stays over 200hp for the entire rpm band. If you are only looking at the before and after peak rpm the car made 32hp more but I can promise that the car felt more than 32hp faster. As a matter of fact there are a few places that the old vs new gained much more than 32hp, but peak power vs peak power is all most people process. But see, that is what hp and tq numbers are for is boiling an engine down to a number, and it works kinda. It gives us a decent idea of what to expect out of an engine but those numbers are not absolutes. Having a dyno graph available and knowing how to actually read it can give you all the information you need, especially when you can overlay the competing engine's dyno chart or at least compare them side by side.

A third thing to note: Anduril made mention of a s2000 and an f150s engines and their factory power ratings. I thought it was worth noting how this engine on the graph I posted is a 2.4L turbo charged engine and how it for sure bridged the gap between the s2000 and the f150. It really sounds like it would be suitable in either vehicle especially when you consider the factory rated power levels are sae hp at the flywheel and this is actual rear wheel hp on the dyno chart. I have thought for years and years that strong built 4cyl engines with turbos running either on e85 or using water injection would be suitable v8 replacements for people that need to be able to tow in their half tons but only do that 5% of the time. I love seeing now that direct injection is taking off and is making the need for premium fuel (or better) to be used no longer an issue with turbocharged engines. Direct injection was not something I foreseen taking place of premium fuel 10 years ago. Ford has had a couple v6 eco boosts for a few years and is really putting them in everything and gm has their large inline 4 they are going to be putting in the trucks. I like v8s, I like big diesels, but I also like high strung smaller engines. I really hope that these small turbo truck engines end up being reliable because I have seen time and time again that the 4 cyl and 6 cyl turbo engines can have a very desirable power and tq curve that would make any truck owner salivate.

and...
Another thing, just because we are talking about dynos, DynoJet dynos, most Mustang dynos and all inertia based dynos are terrible for tuning. Even if they have eddy current brakes, if they are a weighted roller they are inertia based and are not to be tuned on. If you are ever about to get a car tuned and the tuning shop is not using a eddy brake type dyno (dyno dynamics, dyno tech, dynapac) then drive away. They do not know enough about tuning to be altering your computer in any way.
Why is this? I am going to pick on dynojet but MOST dynos are the same way and are to be avoided. They ESTIMATE HP by seeing how fast you spin up the roller. They have your rpm by either getting into your obd2, or clamping a plug wire, or gearing you in ect. So they then run the math backwards and figure your TQ based on the ESTIMATED HP. Dyno Dynamics knows your tq because it has tq sensor connected to the eddybrake and knows your rpms the same way a dynojet does.
Because of the weight of the roller is so high, usually around 3000lbs there tends to be some harmonics that happen between the car and the dyno. This has to be fixed with smoothing or the graph looks very erratic. Smoothing will usually be present on the graph and on the screen of the dyno. 5 is a typical value and the higher, the more the tuner is trying to look "smooth" but is also telling on himself. This can hide actual high hp/tq spots, but more often than not it hides low hp/tq "bad spots" and "dips" that need addressed. Can be rich or lean cells, or spots with too little or too much timing. Too much of any negative condition can lead to engine failure even if everywhere else is perfectly tuned, no engine can handle detonation for long and each time it hits that "dip" a little damage is done and the dice were rolled in cracking a piston.
Dynos like Dyno Dynamics do not even have a smoothing option or need for one. They are very sensitive and if you see a dip you can program the dyno to hold that rpm. It will not let the car past it, but will let it get there very easy. Like driving on ice and then to climbing the steepest grade with the largest trailer as soon as you hit that rpm. No matter how much more gas petal you give, you stay at that rpm and can explore with the fuel and timing maps. You can see if you are doing good or bad with your changes by looking at the tractive effort or how much effort the dyno is having to put out to hold your engine back. This is actually how I liked to tune back when I tuned. I usually was not looking at a hp or tq number at all but would dial in an rpm to the dyno and have it hold me there and I would tune the fuel and timing for all pedal positions and all boost levels and then go to the next set of rpms. I usually only did a full pull at the beginning (if safe) and end. On a dyno jet your only option is to do full throttle full pulls every time. Nothing you do on one of them should be considered tuning. Tuning means adjusting everything perfectly and you just do not have that option with a dynojet. They are however great for racing series with hp limits, making sure everyone is at the same arbitrary limit. As long as the smoothing is the same level for everyone there is very little that the operator could do to offer an advantage to one person over another.
 
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