Torque vs. Horsepower

by Rod Heilfron


 
  I've been reading car and motorcycle magazines for more than 36 of my 52 years and I've always seen articles about Torque vs. Horsepower but I've never seen one that does the subject justice. So I'm going to try to tell you just what is Torque and what is Horsepower. As a note, I’m not going to go into heavy math and rocket science, like how you magnetize a spider in a super magnetic field and suspend it in the air. I’m am going to discuss things just like any backyard mechanic would, with simple math and a good understanding of the laws of physics. I will be simplifying things a bit and I’m not going to go into detail explanations for everything I say. You’ll just have to trust me, honest.

 
  Engine Torque is a measure of the LOAD on a rotating part. As far as motorcycles are concerned it is the load imposed on the primary drive's drive gear, the one attached to the crankshaft. If you over-torque the head of a bolt, you’ll break the head off. If you built an engine with too much torque you’d break the crankshaft or sheer the teeth off of the primary’s drive gear (or some weaker part farther down in the drive train). When you increase the torque of an engine on a pre-made bike you increase all the loads on the clutch, transmission gears, drive chain or belt or shaft and, of course, the rear tire. But when you're designing an engine from scratch all the gear ratios are undetermined and you can't even calculate the load on the clutch from Engine Torque alone because the load on the clutch is equal to Engine Torque times Primary Gear Ratio. As an example, lets make a test bike, with a 1.5:1 primary ratio, a 3.0:1 first gear and a 3.0:1 final drive ratio. If the test engine produced 80 ft lbs of torque the clutch has to handle 120 ft lbs of torque (80 ft lbs times 1.5 primary drive ratio). The output from the transmission in first gear is 120 x 3.0 or 360 ft lbs. The torque is further multiplied by the 3.0 final drive ratio to 1080 ft lbs. Let's say that we loose 20% of our torque do to "transmission losses", we end up with 864 ft lbs of torque at the rear wheel. This is the maximum amount of torque at the rear wheel of our test bike in first gear and will only be available at one rpm, peak torque’s rpm. At all other rpms the torque will be less. Actually, if you rev the engine with the clutch in, then let the clutch out, you’ll have much more torque available for a drag racing launch because the energy stored in the rotating crank, flywheel, clutch, etc. is released as they slow down. The heavier these parts are, the more load you put on the clutch, transmission, drive chain or belt or shaft, the rear wheel spokes, and rear tire. It feels like you have more power but what you’ve done is store a lot of energy in rotating masses and then applied it to the bike all at once. Once the engine and rear tire are running in sync only the engine torque will accelerate you and the extra mass of the flywheel will actually slow you down. It’s impossible to tell the difference between low end torque and heavy flywheel effect when you rev the engine and release the clutch from a stop. Now, to make rear wheel torque useful for calculating acceleration we must convert it into lbs of force at the rear tire’s contact patch by dividing the rear wheel torque by the rear tire radius. So 864 ft lbs divided by 1.0425ft (12.5" radius for a 25" diameter tire) is 829 lbs of forward thrust at the rear tire. If our bike weights in at 500 lbs plus a 200 lb load for fuel and rider, that's 700 lbs of weight. From one of Newton's laws of motion: f = ma or more useful for us: a = f/m. a = 829/700 = 1.18 g's. Now, this means that if the rear tire can handle it at one point during the acceleration in first gear the bike will reach a little over 1g acceleration, kind of like taking a step of off a building's roof, very scary. If we have a 1:1 gear ratio in 5th gear our maximum acceleration will be 80 x 1.5 x 1 x 3.0 / 1.042  x 80% / 700  = .39g's. That's: Engine Torque x Primary Gear Ratio x Transmission Ratio x Final Gear Ratio / Tire Radius x (100% - Transmission Loose) / Weight . And all the gears 2 though 4 will be somewhere in between. Now, in the real world, the maximum acceleration will be much less because we've got to fight the wind. In reality, we’ll get about .8g's in first and .15 to .20g's in high gear, depending on what rpm (and therefore what wind speed) the engine produces that maximum torque figure. Actually, the maximum acceleration will occur at a speed just below maximum torque since lowering the rpms reduces the torque just a little but the reduction in speed reduces the wind resistance by a lot.

 
Now lets explore the acceleration due to Engine Torque a little more in depth. Lets say we've got 2 identical cruisers with two riders that weigh the same. At 60 mph both bikes make 75 ft lbs of torque and both accelerate around an 18 wheeler at the same time. Now one of the riders believes that acceleration is caused by torque and the more you have the better and he notes that his engine will produce more torque as he accelerates from 2500 rpm if he keeps his bike in 5th gear. The other rider (me) believes that horsepower, not torque, accelerates the bike and he down shifts into 3rd gear, revving to 3900 rpms knowing that all the time he's accelerating, his torque will be decreasing. The first bike accelerates at a pretty constant .2g's  to .16g's while the second bike accelerates at first at .3g's slowing to .2 g's as it reaches the top speed available in 3rd gear. This second bike accelerates at a much higher rate even though it’s torque is going down while the torque of the first bike is going up! What's going on? Well, the people that say that Engine Torque is what accelerates a bike forgot about the gear ratios. Rear Tire Force, not Engine Torque, is what accelerates the bike and Rear Tire Force is Engine Torque times all the gear ratios and then modified for the rear tire diameter. Engine Torque only determines the load on the Primary Drive's drive gear, that's all. It's the most misused property of an engine ever. Knowing the torque that an engine produces only tells you it's displacement and nothing about the bike's acceleration unless you know the gear ratios and rear tire diameter. Oh, by the way, in the truck passing example the second bike was able to pass the truck and pull in front of it about 100 feet before it's competition on the first bike, who, unfortunately didn't have an extra 100 feet to spare and became a splat on the front of the 18 wheeler that was coming the other way.

 
  Magazine articles that you've read that say they measured the torque at the rear wheel and got 45 to 120 ft lbs are not telling you the truth. Rear Wheel Torque is 200 ft lbs to well over 1,000 ft lbs depending on what gear the bike was tested in and can not even be measured on a rear wheel dyno. Rear wheel dynos measure Horsepower not Torque, the Engine Torque is calculated from the equation: Horsepower = Torque x RPM / 5252 or Torque = Horsepower x 5252 / RPM. People that claim that horsepower is just the result of a calculation are wrong, the equation just relates different aspects of the engine: Torque, RPM and Horsepower. If you know any 2 of the aspect you can calculate the 3rd. For example if you know the Horsepower and the Torque you can calculate the RPMs, that doesn't make the RPMs just some calculated item. The math is just used to calculate what ever you don't know, with an inertia dyno (rear wheel dyno)  you know the RPMs and the Horsepower and you calculate the Engine Torque, NOT the REAR WHEEL Torque.

 
  Engine Torque is about as useless an attribute of a bike as can be. Two equal weight bikes, both make a maximum of 70 ft lbs of torque, which one accelerates faster? Why, the one with the most Horsepower! 70 ft lbs of torque at 5,000 rpms can't beat 70 ft lbs of torque at 10,000 rpms! Why? Because torque times rpms equals horsepower and it is horsepower that moves your bike down the road. You can gear a 10,000 rpm engine twice as low as a 5,000 rpm engine thus doubling the Rear Wheel Torque and therefor the force at the tire contact patch.

 
  The torque required to go a certain speed increases as the square of the speed, so it would take 4 times as much torque to go 100mph as it does to go 50mph but it would also require the engine to rev twice as high. And 4 times as much torque revving twice as high is 8 times as much horsepower. Therefore the horsepower required to go 100mph is 8 times as much as that required to go 50mph. So to figure how much horsepower is required to overcome the wind resistance of a Harley sized bike at speed you multiply the cube root of the horsepower by 30.2. This constant is approximate and changes do to the size of the bike.

 
  The formula is:    Top Speed = Constant x (Horsepower ^ 1/3)

 
Where Constant = 30.2      for a large cruiser
                              31.79    for a medium sport bike
                              32.99    for a small sport bike
  Examples:

 
          Horsepower     Harley Top Speed     VFR750 Top Speed
------------------------------------------------------------------------------------------
                 20 hp                      82mph                          86mph
                 60                         118                               124
               100                         140                               148
               150                         160                               169
               200                         177                               186

 
  Now you'll notice that I don't need to know what rpms the horsepower is at nor the gearing of the bike in order to calculate it's top speed potential using horsepower. When you build the bike, you have to put it on a dyno to find out what rpm it reaches maximum horsepower at, then gear the bike accordingly. If I used the engine's torque I'd have to use the amount of torque the engine produced at maximum horsepower and the rpms at maximum horsepower to make the calculation for top speed.

 
  Engine Horsepower is a measure of the engines ability to do work per unit time and work per time is the moving of a weight some distance in a given amount of time. The units of horsepower is Foot Pounds per Second. 1320 feet times 815 lbs divided by 13.6 seconds is equal to power. If you increase either the weight or the distance while keeping the elapsed time the same you are making more horsepower. If you can keep the distance and the weight the same and decrease the time you are also making more horsepower. Of course, all of this has to take into consideration wind resistance which increases as your speed increases. So, 60 Hp in a 815 lb cruiser bike (stock Harley 88") gets you down the 1/4 mile in 13.6 seconds at 98 mph but 83 Hp (from the same engine) gets the same bike down the 1/4 mile in 12.9 seconds at 108.8 mph. Both bikes make the same amount of Engine Torque but the faster bike makes more horsepower. Horsepower is not related to engine displacement, Engine Torque is related to engine displacement. Horsepower is related to the engine's piston area, or the bore squared times the number of cylinders. This is easily seen from the equation Horsepower = Torque x RPM  (I'll be leaving out the constants from now on since constants are only used to convert units of measurement) where Displacement can be substituted for Torque. I'm not going to explain why, you'll just have to take my word for it that if you double the displacement of an engine you will double it's torque. Now, 1/Stroke can be substituted for RPM because we want to keep the average piston speed the same in our engines. Piston speed is the limiting factor in an engine's ability to rev and for our purposes 4,000 ft/min will be used. This means that a 4" stroke Harley 88" engine would have a redline of 6,000 rpm and a 1.9" Honda VFR750 would redline at 12,500 rpms. Both can make about the same amount of horsepower, somewhere in the low 90's, but the Harley makes about double the torque and revs about 1/2 as much. Now, making the substitutions in the formula we have:

 
     Horsepower = Displacement x 1/Stroke
but
     Displacement = Bore squared times number of cylinders times the Stroke,
therefor:
     Horsepower = Bore squared times number of cylinders

 
which is the piston area of the engine. The engine’s stroke has no affect on horsepower, it simply determines the redline of the engine. If you doubled the stroke of an engine, you’d double the torque but you must limit the redline to 1/2 of what it was to prevent the engine’s piston speed from exceeding what it was with the stock stroke. Double the Torque and 1/2 the RPMs is the same amount of Horsepower. If Displacement (and therefor Torque) ruled acceleration then big twin motorcycles would be the fastest bikes on Earth but they are about the slowest. The new big twin cruiser drag racing record set recently is 9.8 seconds at 133 mph on a highly modified twin cylinder Yamaha Road Warrior, yet 20 years ago that was matched by a stock 4 cylinder engine Yamaha VMax. Why? Because the piston area of the twin is about the same as the 4 cylinder VMax and therefor the Horsepower is about the same yet the twin makes much, much more torque than the 4 cylinder engine but isn't any faster. Piston Area, not Displacement, determines how fast your bike is!

 
  If you’d like to guess what your bike will do in the 1/4 mile, the formula is:

 
                    1/4 mile Speed = Constant * (Horsepower ^ 1/3) / Weight

 
Where the Constant = 20350 for a large cruiser
                                    20800 for a small sport bike
This constant is for the wind resistance of the bike, it gets smaller the bigger the bike is.

 
The ET will depend on how well you launch but the formula will be approximately:

 
                     1/4 mile ET = Constant / 1/4 mile Speed

 
Where the Constant = 1340 if you launch well
                                    1440 if you launch poorly
And any number in between for a launch between well and poor.

 
You might note some discrepancies between my figures and ones you calculate. That’s because I use a computer program for my numbers which is a little more accurate than these simple calculations.

 
  It may sound like I'm putting down torque and I'm all for rpms and horsepower but the truth is I like having a low rpm, therefor high torque, engine to get the horsepower needed, because rpms affect power bandwidth. I define an engine's power bandwidth as the rpm range from below and above the peak torque where the torque is 80% of the peak divided by the redline. So if your engine, an 88" Harley, makes 80 ft lbs of torque at 3100 rpms and it makes 64 ft lbs of torque at 1000 and at 5000 rpms with a redline of 6000 you'd have "(5000 - 1000) / 6000", or a 67% power bandwidth. If on the other hand you have a Honda VFR750 with 50 ft lbs of peak torque and 40 ft lbs at 5,600 and 11,700 with a redline of 12,000 rpms you'd have a 51% power bandwidth. You'd have just as much power at the top end but less at the low end (and top end and low end are measured in mph not rpm when comparing bikes with different engine redlines and different gearing). It's power bandwidth that makes a bike easy to drive, keeps it from stalling when taking off in first gear and makes it unnecessary to down shift in order to accelerate well. We rarely drive our bikes at peak torque rpms, usually we are well below that. The lower the redline, the broader the power bandwidth and the better the bike is to drive on the street. So I hope that Yamaha builds the new VMax with a 2 litter engine and a 7500 rpm redline. It would make more than 150 rear wheel horsepower and have a very broad power bandwidth. Then I'd have something to replace my current VMax with. Think they will, well, probably not.

 
  Now I'd like to discuss horsepower and torque graphs and just how useless they are. Have you ever tried to compare power graphs between two engines that have different redlines? It's impossible to get anything useful out of the comparison. Which bike accelerates best from 50 mph or from 80 mph? Which is quicker in the 1/4 mile? You can't tell. Which bike accelerates best in 3rd gear when passing an 18 wheeler? Again, you can't tell. Horsepower and torque graphs are fine for tuning an engine but useless for comparing two different types of engines. The only graph motorcycle magazines need to display is an acceleration vs. speed, in each gear. Measuring performance vs. rpms is useless, if I get my VMax going 7,000 rpms you can't even get a Harley to go that fast, so we can't even have a roll-on test from a given rpm. So instead we both start our roll-on acceleration test from 50 mph regardless of the rpms the engines are turning. All acceleration test should be relative to mph, it's meaningless to care about what rpms the engines are turning, just as meaningless as horsepower vs. rpms is. Horsepower vs. mph is much more meaningful but even that doesn't allow for different bike weights and different wind resistances. So knowing the horsepower of a bike is useless, only the actual acceleration, measured in g's, vs. mph is meaningful. I have seen such a graph only in one British motorcycle magazine and I wish the American magazines would change to it. It would really be nice if they were printed on a transparent sheet and all were the same size with the same maximums in both the X and Y directions, then you could cut them out and lay them on top of each other to compare different bike's accelerations. Or make them Online, like the stock market does with companies’ stock prices vs. time, so you can compare any number of bikes on one graph. But I'm just dreaming, aren't I? Will it happen in my lifetime, it would be nice, but who knows.

 
  Well that's it for now. Maybe next time I'll discuss the truth about how counter steering works or why gyroscopic progression of the front  wheel is meaningless as far as motorcycle steering is concerned. Or perhaps why low centers of gravity aren't the way to go for best handling. Or maybe how gear ratios should be chosen for a street bike. Or why I don't like chain drives (unless fully enclosed) for the street. Or what engine/transmission oil to use and how often to change it. Or what effects changing the fork oil level has on your bikes front end’s ride. Oh, there are so many things to talk about, I can't wait till my next article!
 
Thanks for listening,
 
Rod (over 384,000 miles of bike riding)
1981 Yamaha XV920RH (65,000 miles) enclosed chain drive
2000 Yamaha VMax  (30,000 miles) shaft drive