The Wonders of Science, estimating engine power Options

[lapuwali]

A few years ago, when I still raced motorcycles, there were a number of jokers who ran a team called The Army of Darkness. Not Satanists, just troublemakers. They wrote up a series of great technical articles referring esp. to a now dead engine designer named Phil Irving. Irving divulged the following simple formula:

cyl size / (valve_size * lift * pi * valve_count) * ((rpm/2))/60

This gives the mean gas speed through the intake tract, which, when crunched against the stats for a wide variety of bikes they available, turned up the fact that the maximum gas speed for a normally-aspirated engine was about 12.5m/s. Above that gas speed, power always falls off, presumably because at that point, more airflow simply doesn't happen (sonic wall). This means that the formula above can show what the max USEFUL revs will be for given valve sizes and lift. This worked on every bike engine they tried (and a few they didn't, which I did later).

Today, with some time to kill, I tried the Type 4. I have a 1.7, so that's what I used. 1679cc, so 419.75cc per cylinder. Valve sizes are 39.33mm, and there's one intake per cylinder. Lift I didn't know for the stock cam, but a troll through some other references suggested it was somewhere between 10-11mm (at the valve, not the cam). I tried the above for 10mm, and BING! max gas speed at 4500rpm is 12.7m/s. 4500rpm is the power peak for a stock 1.7. Looks like this formula works for the Type 4, too.

What else can we find out? Well, hp = torque * rpm / 5252. Increase engine speed w/o altering torque and power rises. Problem is, if the engine doesn't breathe at the elevated engine speed, torque drops off, so power drops off. If you can raise the engine speed w/o harming breathing, you'll get more power.

Well, with 42mm valves (stock for the 2.0) and the 10mm lift, the power peak only rises to 4700rpm. This suggests only a mild power increase (about 4%). With a cam/rocker combo giving 12mm of lift, however, the power peak rises to 5700rpm (26%). With the cam alone and stock 1.7 valve sizes, the power peak rises to 5300rpm (18%). This suggests that with 2.0 heads and a 12mm lift cam, you can get 100hp out of a 1.7. With just the cam, you can't do better 95.

All of this ignores a whole host of other factors, but it's interesting that first order approximations seem to work. It's esp. interesting that Irving wrote this work in 1948, and it still works today.

[lapuwali]

Another amusing estimation formula is to look at Brake Mean Effective Pressure (BMEP), which is the average combustion pressure during the entire combustion cycle. This is related to power roughly this way: (engine size (in cu. in.) * rpm * BMEP)/793,000 = hp. A really good race engine will have a BMEP approaching 200psi. An average road car will have a BMEP around 125psi.

BMEP peaks at the torque peak. With a torque peak of 4900rpm, and a torque figure of 120ft/lb, and the relationship of torque, hp, and rpm given earlier, we have 111hp at 4900rpm, for a BMEP of about 165psi, which is pretty decent for a streetable engine. With a power peak of 6000rpm (and BMEP will fall past the torque peak), we can guesstimate that a BMEP there of 150psi would give a power figure of about 125hp. If it managed to hold the 165psi all the way to 6000, it would be 135hp.

Funny, I was dreadful in math at school, and these days I spend a lot of time fooling around with formulae like this.