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Thread: Horsepower explained perfectly.

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    Wrench Monkey Not Verified Feedback Score 1 (100%) TwIzTeD_3kGt's Avatar
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    Horsepower explained perfectly.

    Think of this as a PSA. I DID NOT WRITE THIS SO DON'T CREDIT ME. I just think more people should fully understand torque and horsepower, and I know I wondered for a long time before I finally understood it. The original source I couldn't find, but I got this here: Auto Talk for Dummies - What is Torque? - GotApex? Forums Enjoy


    Torque is the power the engine generates. HP reflects the amount of work that the engine is doing based on the gearing and rpm.

    If you have lots of time, read this:

    Force, Work and Time

    If you have a one pound weight bolted to the floor, and try to lift it with one pound of force (or 10, or 50 pounds), you will have applied force and exerted energy, but no work will have been done. If you unbolt the weight, and apply a force sufficient to lift the weight one foot, then one foot pound of work will have been done. If that event takes a minute to accomplish, then you will be doing work at the rate of one foot pound per minute. If it takes one second to accomplish the task, then work will be done at the rate of 60 foot pounds per minute, and so on.

    In order to apply these measurements to automobiles and their performance (whether you're speaking of torque, horsepower, newton meters, watts, or any other terms), you need to address the three variables of force, work and time.

    Awhile back, a gentleman by the name of Watt (the same gent who did all that neat stuff with steam engines) made some observations, and concluded that the average horse of the time could lift a 550 pound weight one foot in one second, thereby performing work at the rate of 550 foot pounds per second, or 33,000 foot pounds per minute, for an eight hour shift, more or less. He then published those observations, and stated that 33,000 foot pounds per minute of work was equivalent to the power of one horse, or, one horsepower.

    Everybody else said OK.

    For purposes of this discussion, we need to measure units of force from rotating objects such as crankshafts, so we'll use terms which define a *twisting* force, such as foot pounds of torque. A foot pound of torque is the twisting force necessary to support a one pound weight on a weightless horizontal bar, one foot from the fulcrum.

    Now, it's important to understand that nobody on the planet ever actually measures horsepower from a running engine. What we actually measure (on a dynomometer) is torque, expressed in foot pounds (in the U.S.), and then we *calculate* actual horsepower by converting the twisting force of torque into the work units of horsepower.

    Visualize that one pound weight we mentioned, one foot from the fulcrum on its weightless bar. If we rotate that weight for one full revolution against a one pound resistance, we have moved it a total of 6.2832 feet (Pi * a two foot circle), and, incidently, we have done 6.2832 foot pounds of work.

    OK. Remember Watt? He said that 33,000 foot pounds of work per minute was equivalent to one horsepower. If we divide the 6.2832 foot pounds of work we've done per revolution of that weight into 33,000 foot pounds, we come up with the fact that one foot pound of torque at 5252 rpm is equal to 33,000 foot pounds per minute of work, and is the equivalent of one horsepower. If we only move that weight at the rate of 2626 rpm, it's the equivalent of 1/2 horsepower (16,500 foot pounds per minute), and so on. Therefore, the following formula applies for calculating horsepower from a torque measurement:

    HP = (Torque x RPM)/5252

    This is not a debatable item. It's the way it's done. Period.

    The Case For Torque

    Now, what does all this mean in carland?
    First of all, from a driver's perspective, torque, to use the vernacular, RULES :-). Any given car, in any given gear, will accelerate at a rate that *exactly* matches its torque curve (allowing for increased air and rolling resistance as speeds climb). Another way of saying this is that a car will accelerate hardest at its torque peak in any given gear, and will not accelerate as hard below that peak, or above it. Torque is the only thing that a driver feels, and horsepower is just sort of an esoteric measurement in that context. 300 foot pounds of torque will accelerate you just as hard at 2000 rpm as it would if you were making that torque at 4000 rpm in the same gear, yet, per the formula, the horsepower would be *double* at 4000 rpm. Therefore, horsepower isn't particularly meaningful from a driver's perspective, and the two numbers only get friendly at 5252 rpm, where horsepower and torque always come out the same.

    In contrast to a torque curve (and the matching pushback into your seat), horsepower rises rapidly with rpm, especially when torque values are also climbing. Horsepower will continue to climb, however, until well past the torque peak, and will continue to rise as engine speed climbs, until the torque curve really begins to plummet, faster than engine rpm is rising. However, as I said, horsepower has nothing to do with what a driver *feels*.

    You don't believe all this?

    Fine. Take your non turbo car (turbo lag muddles the results) to its torque peak in first gear, and punch it. Notice the belt in the back? Now take it to the power peak, and punch it. Notice that the belt in the back is a bit weaker? Fine. Can we go on, now? :-)


    The Case For Horsepower

    OK. If torque is so all-fired important, why do we care about horsepower?

    Because (to quote a friend), "It is better to make torque at high rpm than at low rpm, because you can take advantage of *gearing*.

    For an extreme example of this, I'll leave carland for a moment, and describe a waterwheel I got to watch awhile ago. This was a pretty massive wheel (built a couple of hundred years ago), rotating lazily on a shaft which was connected to the works inside a flour mill. Working some things out from what the people in the mill said, I was able to determine that the wheel typically generated about 2600(!) foot pounds of torque. I had clocked its speed, and determined that it was rotating at about 12 rpm. If we hooked that wheel to, say, the drivewheels of a car, that car would go from zero to twelve rpm in a flash, and the waterwheel would hardly notice :-).

    On the other hand, twelve rpm of the drivewheels is around one mph for the average car, and, in order to go faster, we'd need to gear it up. To get to 60 mph would require gearing the wheel up enough so that it would be effectively making a little over 43 foot pounds of torque at the output, which is not only a relatively small amount, it's less than what the average car would need in order to actually get to 60. Applying the conversion formula gives us the facts on this. Twelve times twenty six hundred, over five thousand two hundred fifty two gives us:

    6 HP.

    Oops. Now we see the rest of the story. While it's clearly true that the water wheel can exert a *bunch* of force, its *power* (ability to do work over time) is severely limited.


    At The Dragstrip

    OK. Back to carland, and some examples of how horsepower makes a major difference in how fast a car can accelerate, in spite of what torque on your backside tells you :-).

    A very good example would be to compare the current LT1 Corvette with the last of the L98 Vettes, built in 1991. Figures as follows:

    Engine Peak HP @ RPM Peak Torque @ RPM
    ------ ------------- -----------------

    L98 250 @ 4000 340 @ 3200
    LT1 300 @ 5000 340 @ 3600

    The cars are geared identically, and car weights are within a few pounds, so it's a good comparison.
    First, each car will push you back in the seat (the fun factor) with the same authority - at least at or near peak torque in each gear. One will tend to *feel* about as fast as the other to the driver, but the LT1 will actually be significantly faster than the L98, even though it won't pull any harder. If we mess about with the formula, we can begin to discover exactly *why* the LT1 is faster. Here's another slice at that formula:

    HP = (Torque x RPM)/5252

    If we plug some numbers in, we can see that the L98 is making 328 foot pounds of torque at its power peak (250 hp @ 4000), and we can infer that it cannot be making any more than 263 pound feet of torque at 5000 rpm, or it would be making more than 250 hp at that engine speed, and would be so rated. In actuality, the L98 is probably making no more than around 210 pound feet or so at 5000 rpm, and anybody who owns one would shift it at around 46-4700 rpm, because more torque is available at the drive wheels in the next gear at that point.

    On the other hand, the LT1 is fairly happy making 315 pound feet at 5000 rpm, and is happy right up to its mid 5s redline.

    So, in a drag race, the cars would launch more or less together. The L98 might have a slight advantage due to its peak torque occuring a little earlier in the rev range, but that is debatable, since the LT1 has a wider, flatter curve (again pretty much by definition, looking at the figures). From somewhere in the mid range and up, however, the LT1 would begin to pull away. Where the L98 has to shift to second (and throw away torque multiplication for speed), the LT1 still has around another 1000 rpm to go in first, and thus begins to widen its lead, more and more as the speeds climb. As long as the revs are high, the LT1, by definition, has an advantage.

    Another example would be the LT1 against the ZR-1. Same deal, only in reverse. The ZR-1 actually pulls a little harder than the LT1, although its torque advantage is softened somewhat by its extra weight. The real advantage, however, is that the ZR-1 has another 1500 rpm in hand at the point where the LT1 has to shift.

    There are numerous examples of this phenomenon. The Integra GS-R, for instance, is faster than the garden variety Integra, not because it pulls particularly harder (it doesn't), but because it pulls *longer*. It doesn't feel particularly faster, but it is.

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    There will be Blood! verified Feedback Score 4 (100%) CoopKill's Avatar
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    Nice examples to explain things. Good find...

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    Now with more poop-smear Not Verified Feedback Score 8 (100%) IPD's Avatar
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    as i once heard:

    columbus sailed the ocean blue in 1492
    if you divide the number of the year by two,
    you get the number of watts in a horsepower


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    Member Not Verified Feedback Score 2 (100%) DK77's Avatar
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    Very good find. I've been wondering that myself. So basically, the torque curve is what's really important, and if you torque is still high at higher RPMs, your car will be faster.

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    Quote Originally Posted by DK77 View Post
    Very good find. I've been wondering that myself. So basically, the torque curve is what's really important, and if you torque is still high at higher RPMs, your car will be faster.
    it's simpler than that. you just want a flat torque curve.

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    No, you want a flat **horsepower** curve through the rev range you are operating in.

    The article is correct in that torque and horsepower are two different ways of looking at the same thing. One is a mathematical expression of the other. If you know the torque curve, you know the horsepower curve, and vice versa.

    However, if you want to understand what accelerates the car, you look at the horsepower curve, because HP is an expression of potential work.

    Think of it this way - the torque figure tells you how hard the car pushes with each impulse. The HP figure incorporates how hard the car pushes per impulse, but also accounts for how many impluses you get per unit of time.

    Assuming that the impulse is large enough to overcome inertia and drag, the car will accelerate faster with two impulses of 500 lbs in a minute than with one impulse of 1000 lbs in a minute, and so on.

    The number of impulses per minute is directly tied to how fast the engine is spinning, which is why the HP calculation includes engine RPM.

    Now it is a function of fluid dynamics that the strength of the impulse coming out of the engine is also dependant on engine RPM. Any given engine has an optimum speed for cylinder filling; any slower or any faster than that RPM and the cylinders don't fill completely, so the strength of the impulse is reduced. On top of that, it takes a finite amount of time for the mixture to burn, but as RPM increases the amount of time available to burn drops, which reduces the amount of time to extract work from the expanding burn, which further drops the strength of each individual impulse. So cars naturally produce a curve of force-per-impulse (torque) which varies with time - rising to a peak, and then falling off.

    You can change the location of the peak by playing with things that affect cylinder filling (camshaft timing, manifold runner dimentions, etc) and the height of the curve by how much mixture comprises a "fill" (displacement, boost, etc).

    There's more, but those are the biggest influences.

    So torque (strength per impulse) rises, then drops with RPM. But the number of impulses rises with RPM, so the amount of WORK (which is what accelerates the car) also rises, then falls, but it lags the torque curve. The power peak always occurs later in the rev range than the torque peak.

    How fast the power curve drops depends on how fast the torque curve drops. A torque curve that drops very quickly after the peak may result in a power curve that drops off to a lower value on the far side of the power peak than the power value the same distance away on the near side of the peak, before it reaches the rev limit.

    A torque curve that drops less quickly results in a power curve that drops less abruptly, and a gentle enough torque dropoff (or a very late in the rev range torque peak) can result in a power curve that doesn't drop at all; instead always rising with increasing RPM.

    OK, so now we have a power curve. It is a principle of calculus that maximum acceleration occurs when the area under the power curve between the shift points is maximized. This, typically, means straddling the power peak - exactly if the curve is symmetrical between the shift points, biased to one side if the power curve is flatter on one side of the peak than the other.

    On a real race car, you can change the gear ratios and the number of ratios to exactly maximize the area under the power curve in each gear. You can put up with a tall but peaky power curve by narrowing the shift range and adding more gears. For a street or OEM-based trans car, those ratios are fixed, so you cannot compensate for a tall and peaky horspower curve. All else being equal, a flatter power curve across your rev range will acellerate the car faster, because you never are in a "low spot" on the power curve - and because the rev range on a street car is so wide.

    For a drag car, you can afford a narrow rev range, so you can go for peak power (which normally implies a late peaking torque curve) and high revs.

    DG
    Last edited by DG; 03-01-2011 at 10:48 AM. Reason: Fixed some clunky wording

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