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 Horsepower, Torque, and all that...This page Copyright © 20032011, by Mark Lawrence.Email me, mark@calsci.com, with suggestions, additions, broken links. 
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Frequently we hear riders talk about how many horsepower their motorcycle makes. These claims are often not believed, and sometimes not believable. Also, we hear some riders state that they like torque more than horsepower. In this article, I'll explain exactly what torque and horsepower are, and why some motorcycles are dramatically faster than others.
Your motorcycle moves forward because the tire pushes against the road. This is the basic fact we'll use to understand everything else. Push is a nontechnical word, and engineers, like doctors and lawyers, love to use more complicated words. The engineering word for push is Force, and a force applied by something round like a wheel is called torque. So, torque is a fancy word for a push by a wheel. More torque equals more push, which equals more acceleration, which wins races.
In chart 1, there's a graph of torque vs. rpm for two HarleyDavidson big twins. Rpm is, of course, revolutions per minute  the number of times your engine crankshaft turns over each minute, and the number which is reported by your tachometer. One of the Harleys on the chart is a stock California model, and the other is modified "for offroad use only". A surprising fraction of all Harley big twins are apparently purchased for dirt riding and closed course competition. This particular modified bike has a Crane Fireball 310 cam, a Mikuni carburetor, and Cycle Shack exhaust pipes. As you can see, the modified engine produces about 25% to 50% more torque, and therefore 25% to 50% more acceleration. Since velocity is acceleration times time, we would expect the modified machine to take about 1/3 less time to go 0 to 60.
A popular performance test is a 50 mph, 200 yard rollon: full throttle for 200 yards, starting at 50 mph. Let's see what our modified Harley will do in these circumstances. At 50 mph in 5th gear, a big twin is doing about 2200 rpm. At 70 mph, it's doing about 3000 rpm. Over the range of 2000 to 3000 rpm, the modified engine is only producing about 510 more foot pounds of torque than the stock engine; a gain of about 10%. The final speed in a 200 yard rollon improves from about 72 to about 73. This is not so impressive as the 30% reduction in 0 to 60 times. The calculations used to figure this out are in the "mathematics" sidebar.
The problem is that the modified engine is producing a lot more power, but at a higher rpm. In 0 to 60 tests, we run the engine up to the red line, but in the rollon, we never get much beyond 3000 rpm. If we did the same roll on test in 3rd gear, we would expect the stock engine to get to about 74, and the modified engine to get to about 80.
Now, we get our complication: the torque is applied at the rear wheel, but it is not produced by the wheel, it's produced by the engine. If the wheel and the engine were directly connected, as they are in a speedway bike, we'd be done. But, on almost all bikes, there's a transmission. The gear ratios in the transmission divide the engine rpm and the torque, with higher gears producing less rpm and less rear wheel torque at a given speed.
The best way to understand this is to make a picture. We'll graph the torque available at the rear wheel at various road speeds. Of course, this graph is going to look a little complicated, because, for example, at 30 mph you could be in any of the five gears, which means you can choose between five available rearwheel torques and five engine rpm's.
To make this graph, first we need to know how fast the bike goes in its various gears. Harley Davidson supplies the overall gear ratios in their product literature, so all we need is one calibration point. A motorcycle magazine recently reported than in 5th gear at 60 mph a '94 Harley is doing 2570 rpm. Since all '94 Harley big twins use the same rear tire, transmission, and belt pulleys, they all share the same overall gear ratios. Using this information, I filled in the numbers in table 1. For example, at 4000 rpm in 5th gear, the Harley is going 93 mph (60 mph * 4000 / 2570). At 3000 rpm in 3rd gear, the Harley is going 44 mph (60 mph * 3000 / 2570 * 3.15 for fifth gear / 5.05 for third gear).
If you own an earlier evolution big twin, then here are the rules: in '94 all big twins use 29 tooth and 70 tooth pulleys. In earlier years, some used 27 tooth and 70 tooth pulleys, and some used 27 tooth and 61 tooth pulleys. If you have a 2770 (FXR's and glides), multiply all speeds in this article by 27/29, about .93. If you have a 2760 (most softtails), multiply all speeds in this article by 70/61*27/29, about 1.07.
RPM  1st gear (10.212)  2nd gear (6.96)  3rd gear (5.05)  4th gear (3.86)  5th gear (3.15) 
2000  14 mph  21 mph  29 mph  38 mph  47 mph 
3000  22 mph  32 mph  44 mph  57 mph  70 mph 
4000  29 mph  42 mph  58 mph  75 mph  93 mph 
5000  36 mph  52 mph  72 mph  94 mph  117 mph 
6000  43 mph  63 mph  87 mph  113 mph  140 mph 
Now, this is not to say a Harley will necessarily go 140. This just says that if a '94 big twin were ever in 5th gear doing 6000 rpm, it would be doing 140 mph. In fact, the stock Harley rev limiter kicks in at 5200 rpm, and a California big twin will actually only do about 95105. Also, different model years of Harleys have different gear ratios.
Now, using this table, we can construct our realwheel torque vs. road speed graph. To do this, we look at the torque curve in chart 1, and at the road speeds in table 1. At 2000 rpm in 1st gear, the bike is going 14 mph. At 2000 rpm, the engine is making 65 footpounds of torque. At the rear wheel, this is 65*10.212 = 664 footpounds of torque. So, at 14 mph, we make a dot at 664 footpounds for 1st gear. At 4000 rpm in 3rd gear, the bike is going 58 mph and the engine is making 55 footpounds, which is 55*5.05 = 278 footpounds at the rear wheel, so we make a dot at 58 mph and 278 footpounds for 3rd gear. I'm sure you see how this goes now, so, here's the resulting graph:
In chart 2, we see a graph of the rear wheel torque at various road speeds in each gear. If you look at 50 mph, you see that there is 200 footpounds of torque available in 5th gear, about 240 ftlbs in 4th gear, about 270 ftlbs in 3rd gear, and 320 ftlbs in 2nd gear. Thus, downshifting this engine from 5th to 3rd gear at 50 mph only gets us about 35% more torque; similarly, upshifting from 3rd gear to 5th gear at 50 mph only costs us about 28% of our torque. Thus we see that stock Harleys don't change their performance very much when you shift gears. In fact, at 80 mph, 5th and 3rd are almost identical in performance, and 4th is only about 10% better.
The arrows in the graph point at the places where the rear wheel torque curves cross going from one gear to the next. These are the optimum shift points: at about 40, 56, 73, and 95 mph. However, we also see that with this engine, there is very little difference if we shift directly from 2nd to 4th at about 55, or from 3rd to 5th at about 70. We must remember that these shift points are for a '94 Harley; different years have different gearing and different shift points. Since we put in the dots at 2000, 3000, 4000, 5000, and 6000 rpm, we can estimate the optimum shifting rpm: about 5500, 5500, 5000, and 5000 rpm on a 94 Harley. Actually, these rpm estimates are not too bad for nearly any nearly stock Harley big twin.
In chart 3, we see overlaid on the stock torque curves the torque curves for the modified engine. I've left off the dots for the stock CA Harley torque curves to make the chart more readable. From chart 1, we see that the modified engine torque peak is at 4000 rpm. Thus, if we have the modified engine, and we are willing to run it at 3500 to 5500 rpm, we can see from chart 3 that the performance will be much better  there's more available torque, and therefore more available push and acceleration. On the other hand, if we shift at 3000 rpm, as many Harley riders do, there will be very little improvement. For example, at 3000 rpm in first gear, the bike is doing about 22. At 22, there is very little difference between the stock and modified engines in first gear, and there is also very little difference between them in second gear at 22 mph. So, our modified engine will pull much harder, and go a lot faster, but only at a much higher rpm.
In chart 3, the shift points are indicated for both the stock and the modified engines. We see that they are not very different: 42, 57, 78, and 102 compared to 40, 56, 73, and 95 mph. However, we see that shifting gears in the modified engine produces a large effect, while shifting gears in the stock motor produces relatively little effect. At 50, when we downshifted the stock motor from 5th to 3rd, the torque increased from 200 to 270  about 30%. With the modified motor, the torque increases from about 220 to 400  almost double. However, as long as we stay in 5th gear, there's not much difference between the two motors. Again, these numbers are all for a '94 Harley; different years with different gearing will have different shift points in mph.
The modified engine has shift points we can estimate at 5700, 5500, 5400, and 5300 rpm. These numbers are consistently a bit higher than for the stock engine, and above the stock 5200 rpm rev limiter, but within reasonable limits for the engine. Evolution engines are pretty well engineered and can take a reasonable amount of abuse.
Now we see a general rule about making power. In order to make more power, mostly you have to spin the engine faster. Also, each time you shift gears, the torque gets divided by the same ratio that the rpm gets divided. So, to go fast, you want a motor where you don't have to shift gears as often. In fact, if two bikes make the same peak torque  say, 80 foot pounds  the motor which makes the torque at a higher rpm can stay in lower gears longer and therefore go faster. This makes us think it would be useful to have a single number which reported both the peak torque and the peak rpm.
In fact, there is just such as number: horsepower. Horsepower equals torque times rpm; thus an engine which makes 80 foot pounds of torque at 8000 rpm makes twice as many horsepower as another engine which makes the same 80 foot pounds at 4000 rpm. Although the two engines deliver the same amount of torque, and therefore the same amount of push, the first engine can go twice as fast in each gear. While I'm doing 60 topped out in second gear on my 80 footpound Harley, some other guy can be doing 60 not quite topped out in first gear on his 80 footpound Kawasaki ZX11. Of course, he's winning the race.
It's about time we considered some different bikes. In chart 4, we see the torque curves for several different engines overlaid. The bikes are all about the same in terms of engine size  a bit over one liter. Interestingly, with the exception of the California Harley and the BMW, we see that they all produce about the same amount of peak torque  about 80 foot pounds. We all know that Harley engines can make significantly more power than what the factory supplies. Based on these curves, we suspect the same is true for the BMW.
In chart 5, we see the horsepower curves for the same five bikes. In spite of the similarity of the peak torque, the horsepower curves are very different.
Notice that the modified Harley, which makes the most torque up to almost 5000 rpm, also makes the most horsepower up to 5000 rpm. The Honda ST1100 makes the most torque and horsepower from 5000 to 6500 rpm, and the Kawasaki makes the most from there up.
Let's see how to calculate horsepower. There's no big trick at all. From chart 1, we see that a stock California Harley is making 65 footpounds at 2000 rpm, 64 ftlbs at 3000, 55 at 4000, and about 45 at 5000. Horsepower is torque times rpm divided by 5252; so this Harley is making 25 horsepower at 2000 rpm, 37 hp at 3000 rpm, 42 at 4000, and 43 at 5000. (Yes, it's true: stock California big twins make about 43 horsepower. 49 state big twins make about 50 horsepower.)
Here's something interesting: the torque peaks at about 2000 rpm, but the horsepower peaks at about 5000 rpm. Even though the torque is going down, the rpm is going up faster than the torque is going down, and therefore the horsepower is increasing.
Also, we see from the formula that at 5252 rpm, horsepower is equal to torque. This is always true. If your dyno tells you that the horsepower and torque curves cross anywhere other than 5252 rpm, your dyno is broken.
Finally, we see that at any given rpm, the engine which makes the most torque at that rpm also makes the most horsepower at that rpm. To make more horsepower, an engine has to either make more torque or run at higher rpm. The ZX11 makes the same 80 footpounds of torque as the modified Harley, but it makes this torque at 8000 rpm  exactly twice the 4000 rpm peak of the modified Harley. Because of this, the ZX11 makes twice the horsepower  120 hp  at 8000 rpm that the modified Harley makes at 4000 rpm  60 hp  even though both are making 80 footpounds of torque.
Since the Harley torque curve drops off a bit gradually from 4000 to 5000 rpm, and the ZX11 torque curve drops more quickly from 8000 to 10000 rpm, the ZX11 doesn't quite make twice as much horsepower as the modified Harley  "only" 130 hp compared to 71 hp. Kawasaki riders need not totally despair  the ZX11 ram air system is not active on a dyno. It is believed that at 150 mph, the Kawasaki is making about 145 hp due to the ram air effect.
We see that if all you care about is engine peak torque, you would be equally happy with the Harley and the ZX11. If all you care about is Horsepower, you definitely want the ZX11. If what you're really interested in is power at low rpm, now you definitely want the Harley. So, those riders who claim to prefer torque over horsepower really mean they prefer engines with power at low rpm.
Let's see how this horsepower advantage translates into a torque advantage. We'll make the same picture for the ZX11 rear wheel torque that we made for the Harleys. In table 2 below, there are the gear ratios and road speed worked out for the ZX11 (the gear ratio data was supplied by U.S.Kawasaki). The ZX11 has a six speed transmission. I've worked out the road speed in 2,000 rpm increments from 2,000 rpm to 10,000 rpm. The ZX11 actually has a red line of 11,000 rpm, so each gear actually goes a little faster than the table shows.
For those of you who aren't familiar with ZX11's, this bike has been clocked by radar guns at 172 mph, stock. It does 135 mph in the quarter mile in about 10.3 seconds. These days, the ZX11 pretty much defines fast.
The ZX11 engine torque curve is illustrated in chart 4 above. We do the same crossreference look up exercise as before, and we get the rear wheel torque curves. Interestingly, these curves seem to indicate that, for racing purposes, fourth gear could be eliminated with no effects, and fifth gear is only useful from 120 mph to 135 mph. It looks like removing fourth and fifth gear and replacing them with one gear with the ratio 5.372 (31/25 internally) would be an improvement.
In chart 6, we see a direct comparison of the rear wheel torque of a modified Harley, and a Kawasaki ZX11. As you can see, the ZX11 has a much larger advantage over the modified Harley than the modified Harley has over the stock Harley. Not only does the ZX11 make more rear wheel torque, it can also go faster in first gear than the Harley can go in second gear, and it can go about as fast in third gear as the Harley can go in fifth. And, in fact, it is now well established that a ZX11 can pretty much beat any Harley, any where, any time, in any race. So, how come Harleys outsell ZX11's about a hundred to one?
RPM  1st gear (12.133)  2nd gear (8.905)  3rd gear (6.890)  4th gear (4.996)  5th gear (3.15)  6th gear (4.485) 
2000  12 mph  17 mph  22 mph  26 mph  30 mph  33 mph 
4000  25 mph  34 mph  44 mph  52 mph  60 mph  67 mph 
6000  37 mph  50 mph  65 mph  78 mph  90 mph  100 mph 
8000  49 mph  67 mph  87 mph  104 mph  120 mph  134 mph 
10000  62 mph  84 mph  109 mph  130 mph  150 mph  167 mph 
In the Fall 1994 issue of American Rider, Joe Minton presents a graph of horsepower for a Harley 1340. His article did not specify the modifications made, but in the context of his article, we can safely assume they include substantial head work. His engine's torque curve can be easily deduced from the horsepower curve: at each rpm, we multiply the horsepower by 5252 and divide by the rpm. The result indicates an engine making between 87 and 93 footpounds of torque from 2500 to 6250 rpm. This is an engine with the same torque per cubic inch as a ZX11, and a power band which is 25% wider. If true, this is quite an accomplishment.
In chart 7, I have graphed the rear wheel torque curves for Mr. Minton's bike. As you can see, the performance would be substantially better than either the stock or the lightly modified Harley. Also, we see that this engine is poorly mated to its gear box: optimum shifting points would occur at 7,500 to 6,500 rpm. This level of rpm severely over stresses an evolution big twin. It appears that a change of camshafts to move the torque curve down 500 to 1000 rpm would give this bike performance better suited to its gear box and engine design parameters.
With Mr. Minton's bike, we would expect the 0 to 60 times to be cut roughly in half compared to a stock CA Harley, and the 50 mph rollon speed to be about 75 mph in fifth, and 86 mph in third. We would also expect that when shifting from first gear to second at 6000 rpm, the bike's acceleration would drop dramatically.
Mark Lawrence has a degree in Engineering. He has been riding motorcycles since 1969. In this time he has owned 21 bikes, ridden 305,000 miles through 28 states, accumulated 27 traffic tickets, and set a California state record for traffic school attendance. He currently rides a Road King with a modified "closed course competition use only" motor. He has not yet raced his Road King in a Grand Prix, but expects to do well if he ever does.
Sidebar 1:
The Mathematics
For those who are interested, here's a brief summary of the physics and mathematics used in this article.
To calculate the rollon performance, here's what I did:
published final speed = 72 mph.
Modified bike has 10% greater torque, average, over 5080 mph.
By equation 5, velocity = K * square root( force )
new velocity / old velocity = square root( new force / old force ) = square root( 1.1 ) = 1.05
old velocity = 72  50 = 22 mph. 5% of 22 mph = 1 mph. new velocity = 50 + 22 + 1 = 73 mph.
For third gear modified bike, I noted that the modified bike is making about 370 footpounds of rearwheel torque in third gear from 50 to about 80, and it's making about 220 footpounds from 50 to 80 in fifth gear, so the math is the same up to:
new velocity / old velocity = square root( new force / old force ) = square root( 380 / 220 ) = square root( 1.7 ) = 1.3
30% of 23 is 7, so the modified bike hits about 50 + 23 + 7 = 80 mph in third gear.
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