A listener discussion about HP & torque

We got this email from listener Bryan Skinner, and thought the emails back and forth would make a good blog post. From Bryan: I stumbled upon your Podcast in search of finding an enjoyable conversation on motorcycling and I've really been enjoying listening to you both. Question: The issue I'm confused about is how can a Yamaha FJ-09 which is 847cc have so much more horsepower than my Honda VTX1300 cc ? My 1300cc has 57HP and 75 torque verse the FJ-09 847cc and 115HP and 65 torque. Doesn't cubic inches relate to Horsepower. Is it because the Yamaha is more modern than my 2005yr Honda VTX 1300 ? James: Bryan,
Thanks for writing. I think we’ll queue this up for an up coming show but I’ll respond here as well.
Displacement is only part of the equation. It’s really about squeezing quantities of gas and air and making it explode. I don’t know the numbers off the top of my head but I’d guess that the VTX tops out at around 6000 RPM. The FZ-09 probably doubles that number. It has less displacement but it can produce power more often. There are many other factors that can contribute such as compression ratio, power loss to friction in the motor, restrictions in the air box, other design decisions made by the engineers to produce the “feel” that they want out of the engine. RPM and compression are probably the biggest contributors.
On the upside, you’re probably getting better gas mileage AND buying cheaper gas than FZ-09 owners.
Chris: And if I may expand with some technical details to flesh that out...
Horsepower, while useful for bench racing and marketing, is a mathematically contrived measurement that's got a lot of factors going into it. In its basest form, calculating HP is simply a matter of taking the torque at an RPM, multiplying it by that RPM, then dividing that number by a fixed value of 5252. 
In the case of your VTX 1800, the I've seen docs suggesting that the torque maxes out at 120 foot pounds. To make the math easy, let's assume a good, flat torque all the way to redline. Your redline is 5750. So the resulting formula is:
T x R / 5252 = hp
120 * 5750 / 5252 = 131.4 , theoretical maximum horsepower.
In the real world, the VTX 1800 gets closer to about 105 hp with around 100 ft lbs of torque. This is because the overall breathing inefficiencies, the torque falling off at higher RPM, and mechanical drag in the engine, etc. 
According to this chart ( http://images.motorcycle-usa.com/PhotoGallerys/05PCTorque.jpg ), the VTX 1800 is good for 98 ft lbs maxed at 3700 RPM, and it starts falling off after that. So, 3700 RPM is where the engine makes its PEAK EFFICIENT POWER (which is different than maximum power) - the formula would then be:
98 * 3700 / 5252 = 69 max EFFICIENT horsepower. 
Using that chart, at max rpm of around 5500, the engine is putting out around 80 ft lbs.
80 * 5500 / 5252 = 83.8 horsepower.
No slouch by any means, especially in the "feel my arms stretch" department. 
So, as you can see, real-world numbers and theoretical, marketing numbers can vary GREATLY. 
You can modify those real world numbers a bit with better exhaust and airbox flow, tuning, etc.
But horsepower, as a thing, is fully contrived and 99.9% completely made up theoretical BS. 🙂
Me...? I'll take a nice big torque number a lower or mid-level RPM range over theoretical horsepower all day long. It's why I like twins and triples so much more than I4s. They develop their torque in lower RPM ranges, typically, and feel more spry around town.
The triple in question revs much, much higher and has a very different feel, and can produce higher contrived, theoretical (and very real) horsepower, but your VTX 1800 is going to FEEL so, so much more powerful in real-life RPM and driving speeds. Because.... it is. The Triple will have to rev much higher and feel more frenetic to develop its higher overall power.
Hope this helps. 🙂