I've been trying to find that really long thread that compared HP vs. torque - does anyone remember it? If I recall there were some really intelligent posts from one of our members that talked about how the 2 are inter-related, there was an RPM where they both met in the hp/torque band, it was something like 4545 or 5454 or something like that...

Anybody remember it? I have been searching but for the life of me can't find it...

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91 W124 300E
86 W126 560SEL
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79 W123 250
78 W123 280E
75 W114 280

This post has a formula like you mentioned.

Torque/HP

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The rpm is 5252.

The only thing that matters in an engine is power. Power has 2 components, torque and rpm. These combined make up the power number known as horse power.

For example, if you have an engine making 200 ft/lbs of torque at 2000 rpm, the power is 200x(2000/5252) = 76hp

If you have an engine making 100 ft/lbs of torque at 4,000 rpm, the power is 100x(4000/5252) = 76hp

Thus both engines in this scenario are at those moments in rpm are delivering exactly the same power and would deliever exactly the same acceleration results.

Think of riding a bicycle and torque being the tension that you are exerting on the chain. RPM (cadence) is how fast you are turning the pedals. If you are exerting 50 lbs of tension on the chain and suddenly change that to 100 lbs without changing your rpm, you have doubled the power you are delivering. Likewise, if you keep exerting 50 lbs of tension on the chain but double the rpm you turning the pedals, you have also doubled you power.

To see the power of an engine, you must look at the hp numbers, which account for both torque and rpm. If an engine delivers 1,000 ft lbs of torque at 100 rpm, it is making 19 hp. If an engine delivers 50 ft lbs of torque at 4000 rpm, it would be delivering 38 hp and be making twice as much power.

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Ali Al-Chalabi

2001 CLK55
1999 Dodge Ram 2500 Cummins Diesel
2002 Harley-Davidson Fatboy
Merlin Extralight w/ Campy Record

Thanks for the excellent explanation - that 5252 was the magic number and helped me find it. The thread mentioned above was great, but this is the one I recall being really impressed by:

Inline vs. V6

__________________
08 W251 R350
97 W210 E320
91 W124 300E
86 W126 560SEL
85 W126 380SE Silver
85 W126 380SE Cranberry
79 W123 250
78 W123 280E
75 W114 280

The important issue to understand is that "power" is energy per unit time. Mechanical energy at the crankshaft is converted into vehicle kinetic energy via drive thrust at the wheels, so the more energy you apply per unit of time (which is power) the faster the car will gain kinetic energy(which means greater acceleration), and 150 HP is the same whether it is from a gasoline engine that makes 150 lb-ft torque at 5252 RPM or a turbo diesel that makes 300 lb-ft torque at 2626 RPM.

Duke

Probably an unnecessary reply I make here given the quality responses above, but my two cents anyway: As said, if you graph torque & horsepower simultaneously you will see a certain rpm where the curves cross. Torque, I believe, can be called "engine twisting power". For example, a 1967 Mopar 440 wedge motor with 375 hp, had very good torque at lower rpms (in most, if not all engines, maximum torque is seen to rise, then drop, sooner than horsepower. This is why the 440 could, if 440 is stock hi-performance, in the same chassis/transmission/gear ratios, etc, would beat a 426 hemi in the quarter mile. The hemi developed it's torque later, but above 3000 rpm the hemi is gaining on that 440. Couldn't beat a 440 in the quarter mile, generally, but if the race were a half mile, the hemi has come into it's own and devastates the 440. This difference in the quarter mile vs the half is because the hemi has more horsepower. Many may differ, perhaps with good reason, but it is a fair intuitive statement to make that "torque determines acceleration, horsepower determines top speed".

i bet with appropriate gearing the hemi would beat the 440 in the quarter.

tom w

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..I also have a 427 Cobra replica with an aluminum chassis.

No, as I explained previously, it's horsepower that accelerates the car. The shape of the power curve is important as is gearing. The area under the power curve in the rev range determined by gear spacing and shift points is the total energy input to the vehicle. The higher it is, the faster the car will achieve speed and distance.

An engine that produces peak torque and power high in the rev range needs shorter overall gearing and closer spaced ratios to have the same average power input through the gears compared to a high torque low revving engine of the same peak power such as the examples I listed previously.

Duke

...by that answer your research does not include Wankel, turbine or any propeller driven airplane? I ask to be sure we are all on the same page IE: ONLY piston/direct (no electric) drive, as there are VERY few constants accross the board. But, as always, F=MA, E=IR, PV=nRT etc. the rest are only 'favorite flavors' BTW here's a little aside to muddy up the mix. In Gemrnay, and most EU, car engine max output is listed in kW (you mean they went back to the original derivation) - power defined in watts?

You're right Tom. I was just making the point with the same gearing/tranny, etc. Now, if both the wedge & the hemi are set up tougher, the hemi wins even in the quarter. Part of the problem, a large part, is that if the owner fooled with the linkage between the two Carter 4 barrels on the Hemi, they generally messed it up by thinking they need to be put exactly in sync as regards when the primarie's opened. That is not the case. The rear carb primarie's, if I remember correctly, provide more of the fuel at idle due to their location relative to the cylinder banks. Just comparing the 440 wedge with the 426 Hemi as regards potential, well, the 440 was a tough engine to beat compared to any stock Detroit Iron, but the Hemi with a more appropriate camshaft, properly configured tube headers, is a Monster.

...doesn't make any difference. If you have power at a shaft, HP= TxN/5252. You can get the same horsepower with high torque and low revs or low torque and high revs. Aircraft engines are rated by "shaft horsepower", which is the power at the output shaft that drives the propellor, so it includes the reduction gearbox, which is required for turbines and big recips.

To drive a ship or aircraft the power is applied to a propellor that delivers a propulsive force. In a car the propulsive force is generated at the tire/pavement interface.

At steady vehicle speed on level ground (or level flight) the required horsepower is equal to force times velocity in feet per second divided by 550. If you know the total drag force, that times velocity times propellor efficiency (in the case of aircraft and ships) times the proper conversions for dimensional homogeneity is delivered shaft horsepower. If more power is delivered the vehicle accelerates, if less it deccelerates.

Duke

Back in the "BC era" - before computers - engine lab dynos were usually electric - essentially a big DC generator with a large resistance grid that you used to control the load. Water brake dynos were also in use, but the old DC generator type was easier to control for lab work, especially if you wanted to control speed at various constant values over a wide range of loads.

The dynamometer frames were mounted on bearings that allowed them to rotate freely, but they were constrained by a lever arm that rested on a scale.

To do a WOT power run, you set the load high then opened the throttle fully and adjusted the load to achieve a steady speed. Then the operator read the scale and RPM. He then reduced load to allow the engine to accelerate and then added more load to stabilize at the next test speed, read the scale and RPM, and so on and so forth at more test speeds up to the maximum speed planned for the test.

So what you ended up with was a data set of RPM and scale load reading in pounds, and knowing the lever arm length allowed you to compute the torque at each RPM point. Then, using torque and the famous HP = T X N/5252 formula you computed horsepower and could then plot both the torque and power curves versus RPM.

So where did this formula come from?

Answer: Basic physics.

"Work" (which is the same as energy) is a force acting through a distance or a torque acting through an angle. If I use one "unit" of force, say pounds, to push a brick across a table one unit of length, say feet, I have expended one unit of work or one foot-pound, which was dissipated as one foot-pound of friction energy.

Similarly, if I use a one foot lever and one pound of force to rotate a shaft that has some friction resistance through one unit of arc length (which is that same distance as the radius) I have expended one foot-pound of energy that was also dissipated as one foot-pound of friction energy. Recall that pi is the ratio of the circumference of a circle to its diameter, which can also be expressed as circumference is equal to 2Pi times radius. One radian is defined as the length of arc along the circle equal to the radius, so there are 2pi radians in a complete circle.

I other words, if I apply a force on a one foot lever arm through a complete revolution, the distance is two pi feet so the work is 2pi time the force. If I apply the force on the lever arm for ten revolutions the total work is ten times the work for one revolution.

Since torque and work/energy have the same fundamental units the current convention is to use "force-length" or pound-feet for torque, and "length-force" or foot-pounts for work/energy to avoid confusion in what we are dealing with.

Recall that power is work or energy over a period of time, so a torque, T, in pound-feet, from a shaft that rotates a complete revolution, which is 2pi radians, over a time period, t, produces power as follows

Power = torque(2pi)/t

If our old fashioned dyno shows 50 lbs at a scale with a two foot lever arm, which is 100 lb-ft at 6000 RPM ( time period of .01 second for one revolution) the power produced is

100(6.28)/.01 = 62,800 ft-lb/sec

Or we can convert to ft-lb/minute by multiplying by 60 and the result is 3,768,000 lb-ft/minute.

Back in the early eighteeth century, James Watt, inventor of the steam engine, spent a considerable amount of time studying horse drawn pumps that pumped water out of coal mines. The horses were harnessed to a capstan and walked around in a circle.

Watt determined that a typical draught horse could deliver 33,000 ft-lb/minute of power continuously over a long period of time and DEFINED this amount of power as ONE HORSEPOWER.

So the above relationship can be rearranged as follows where N is engine speed in revolutions per minute.

HP = T(2pi)N/33000 = TxN/5252

There are many units for power. We are still stuck with Watt's definition from the archane English system of units. Nations that have adopted the SI (Metric) standard use kilowatts and 1KW = 1.34 HP, or 1HP = 0.746 KW.

In the above example our 100 lb-ft of torque at 6000 RPM is delivering 3,768,000/33,000 = 114 horsepower, which is the same as 100 x 6000/5252. In other words 100 pounds of force is being applied with a one foot lever arm over 6000 revolutions in one minute - force over a distance, in this case using a one foot lever arm a total of 6000 times in a circle in one minute.

The power would be the same if it was 400 lb-ft at 1500 from a truck engine.

The common inertia chassis dyno of today continuously records instantaneous angular acceleration and rotational speed of the drum, and this data combined with the known drum rotational inertia is input into a simple software formula that computes instantaneous power. The famous formula, rearranged to HP(5252)/RPM is then used to compute torque from the power data. The basic output data is HP and Torque versus MPH, but most shops have an inductive pickup that they can attach to a plug wire so HP and torque versus engine RPM can be displayed and printed.

So the old fashioned electric dyno "output" is load on the scale that we use to compute torque and then with the RPM data compute power. An inertia dyno continuously records instantaeous roller acceleration and RPM, and uses this data to compute instantaneous power and then torque and plots out a continuous curve of both. Same end, different means.

Modern water brake lab dynos can be programmed to allow the engine to accelerate and measure power in the same way. The usual acceleration value is 300 RPM/sec. It's a lot easier to get a torque/power chart using the inertia technique than the way I did BC - a lot easier on both the operator and the engine!

Duke

Duke,
I very much appreciate the valid information you've given & it is not lost on me that you have a deep academic background in the fundamentals of what we are discussing. I raise an argument with you, not so much to say you are wrong, but for you to show me I am wrong. This is my honest thinking & if I'm incorrect I would like to know that; especially since this topic is of fundamental academic & practical importance.
So, as you say, we start with Watt's equation, replacing N with rpm:
HP=horsepower
T=torque
rmp=revs per minute
HP=(T*rpm)/5252
So, correct me if I'm wrong, though this isn't the point I wish to eventually make: So, when we graph both HP & T as a function of rpm, the curves intersect at 5252 rpm. Now, I realize that if one knows the value of HP, then the value of T can be directly derived, which seems to me important that the two phenomena (even being metrics, it still seems phenomenology to a large extent). And vice versa. Yet, we want to distinguish the two, and we can, though they are equal at 5252rpm, the two curves can have very different trajectorie's.
Now, this is where I believe we differ. I made the statement that it is Torque that determines Acceleration. In the graph of T&HP as a function of rpm, if we add Acceleration as a function of rpm (speaking of a car here where we ignore air density, road friction, etc) to our graph, my understanding is that the Acceleration curve exactly falls atop the Torque curve. Gearing has no effect on this.
For example, 100 foot pounds of torque will yield precisely the same acceleration (ignoring air density & all the rest) whether that 100ft/lb torque is produced at 2000rpm or 4000rpm; yet, per the formula, HP has doubled at 4000rpm as we arbitrarily hold Torque at 100. The doubling in HP, holding Torque the same, yields no further gain in Acceleration. So, this is just a restatement of my original "it is torque that determines acceleration".
HP, as you related in using shaft HP in an engine driving a propellor; in our car, this would relate, to my thinking, to the top speed of our car.
To beat the dead horse a bit further, though I certainly allow for my being incorrect, graphing acceleration, horsepower & torque as a function of rpm, the torque curve and acceleration curve fall upon one another across the measured rpm range. (edit) If I am incorrect that the acceleration curve of an object in free space (which is our hypothetical car that is not affected by air density, frictional power losses, etc) precisely overlaps the torque curve, but not the hp curve, I still argue this view is correct to at least a first approximation. I think the better way to state it, as you used Areas Under the Curve, one sees that the torque AUC more closely predicts acceleration than the HP AUC. As a last thought, when we go back to HP= (T*rpm)/5252 it is obvious that if we know either one of HP or T we can directly derive the other. I'm not oblivious to the fact of forum members describing relationships to speed, gear ratios, etc, that become of prime importance if one were to build a car with certain desired characteristics. But, it is not without some truth, be it great or small, that if one builds an Indy car, one wants a car with high HP capable of running at high rpm, maximizing the HP AUC; if one builds a drag car one wants to maximize the Torque AUC, though this is not to say that rpm is meaningless. It seems to me that both T&HP are brother's or cousins of Force, and I do apologize for not refreshing myself on Newtonian Mechanics, other than the particular case argued here. So, if at any given rpm, and knowing either of the other two degrees of freedom, we know the last, this, I believe, tells us that we shouldn't go hog-wild in our belief that T & HP are two metrics which should enjoy some special status, that is, one over the other.
So, where is my error in fact or logic to say, "Torque determines acceleration."?
(edit) In re-reading all the posts I see it said that Torque in combination with the rest of Watts equation determines HP, or even vice versa. How can we say that either T or HP is dominant as neither has any independent status; one metric yields the other metric. So, to give one or the other, again (I'm sorry), special status as regards the contribution to acceleration, one need to measure both over time as well as (rpm), then calculate the AUC's of both HP & T. It is building an engine where T has the greater AUC that yields maximal acceleration. This is always the case in the purest sense, leaving gearing & the rest out of it. Both HP & T AUC's need be considered when building our car optimized for certain tasks.

I think you missed the fundamental relationship that Power = force x velocity. Torque does not take time into account. Power does, and any calculation involving a dynamic variable, such as vehicle acceleration or velocity, must include time. Force and torque are not a dynamic quantities unless they act over a distance in some time period, which is power.

It's a difficult concept to comprehend, and not at all easy to explain.

Sitting down with a basic physics tests and reviewing the concepts of work, energy, and power might help you out.


Duke

Neither torque nor horsepower explicitly takes time into account in the discussion. The torque or horsepower is calculated instantaneously for rpm X, then for rpm x+1, etc, until we generate the discussed curvilinears. Yet, in practice, such as in the acceleration of an automobile from idle rpm to it's maximum rpm, we now have taken time into account and can calculate the torque across that entire time period; this is no different than Power(horsepower) as regards the temporal element.
Yes, it is true to say that one can calculate velocity by measuring the distance travelled over a defined time. But, it is not a necessary condition that time be considered. Any variable can be described as to it's value as a function of time, or it can be described in an instantaneous fashion.
If one is to say that velocity is unequivocallyknown by measuring the distance a body travels over a known non-zero period of time, that is false, in principle. A Body A, at t=0 resides at Point A. One hour later that same body is at Point B, which is 100 miles from Point A. Does one then say the velocity of Body A is 100mph? I can envision Body A travelling that 100 miles over a time period of one hour, but sometimes having an instantaneous velocity of 200mph, sometimes 0mph. So, 100mph is only assured to be an average velocity. In principle, the true velocity of that body, if it be 100mph over the distance of 100 miles, can only be stated if all (which is impossible, in practice & principle) instantaneous velocitie's are known (instantaneous velocities have no time nor distance components, just a relationship with some arbitrary reference frame, even if it be a reference frame fixed nicely for our little measurement exercises). So, what is an instantaneous velocity? It is a velocity that has no finite time component. It has a time component, but since the time component is always zero, no time vector exists for each and all velocity measurements. Power is no different. Any fondness to name this or that variable as "dynamic" and another not to be so is not good thinking and is rife with arbitrariness and assumptiveness. It is the instantaneous values we have, and that is all we have. We can graph the instantaneous values as a function of time surely, but you are not correct to say that you have taken time into account when measuring power or velocity or torque or acceleration, or anything else for that matter. As soon as we take non-zero time into account we only have the average value of whatever we are measuring as expressed over an arbitrary interval of time and have buried the instantaneous values, which alone have any physical meaning. As soon as we throw time in the mix we lose the true velocity (or power or torque, etc) and are left with an average.