I'm snowed in today, couldn't get to work, figured I'd take a crack at doing this mathematically.
I welcome others to critique and modify this. I'm not a physics expert by any means, I'm a 48 year old electrical engineer who hasn't sat through a physics class in about 28 years. But it doesn't seem very complex to me (maybe that's a bad sign!).
Looking at the formulas around this stuff, you see not just variables like velocity and drag and power, but also air density, Cd, Area, rolling resistance, etc. I don't think we want to get into the business of guessing differences in rolling resistance between bikes, I really don't think that matters. Likewise we don't want minimums that change depending on the air density that day. Nor do we want to worry about how to reconcile the thousand ways to measure horsepower, i.e. crank, net, gross, corrected, etc, or worry about how every dyno seems to give a different number.
The only way around that mess, that I can see, is to distill the formulas down to the couple basic relationships between power, speed, and CdA, and apply those relationships to a reference point, i.e. a class and minimum we all agree is reasonable. Having a reference point like that, and knowing the mathematical relationships between power, speed, and CdA, we should be able to calculate a reasonable minimum for any other class.
The two basic relationships are that horsepower required goes up as the cube of the speed increase, and drag goes up as the square of the speed increase, or conversely, speed goes down as the square root of the drag increase, which is what we really care about. Check me on that, but the formula is V = sqrt(F/.5CdA). Since drag and CdA are proportional, we can just use CdA. Drag has got air density as a component and we don't want to go there.
Both of these relationships assume that air density and rolling resistance and the like stay constant. They also let us ignore things like how the horsepower is measured. We're just talking about the relationship between power levels assuming an identical measurement.
So anyway, if we have a reference class and minimum, and we want to know a different class minimum, all we have to know is:
- the difference in horsepower
- the difference in CdA, if the class you're calculating has no fairing and the reference number does, or vice-versa
The first one, horsepower, is the more complex, but I don't think it's that bad. What have we got for variables?
- displacement
- OHC or pushrod
- Boosted or NA
- gas or fuel
- current or vintage
- production or not
others?
Displacement is pretty easy to deal with, power capability roughly scales with displacement.
That leaves 5 other variables, each with 2 possibilities. 5 bits is 32 possibile combinations, less several non-allowed combos like Production-Fuel, Vintage doesn't have pushrod/OHC, etc. Write'em all down and come up with a horsepower factor for each of those. Your chosen reference bike will be a factor of 1.00, and you'll scale the power based on whichever configuration you're trying to calculate. You'll also, of course, scale the result based on the percentage difference in the displacement. Presto, you've got horsepower.
The difference in CdA we'd have to figure out empirically. Ideally you'd have two bikes, with the same horsepower, one with a good representative fairing and another naked but optimized within the rules. Square the ratio of their speeds and you've got the difference in CdA. But those numbers are probably a fairly difficult thing to come up with, at least accurately.
The main thing is to reduce this to one single number, i.e. an unfaired bike as "X" percent the CdA of a faired bike. Or maybe you have two faired numbers, one for APS and one for MPS, since I believe the APS rules are a little more lenient, no? If nothing else, the longer wheelbase gives the opportunity for slightly better aerodynamics. You
could also scale this number slightly based on the motor size, since smaller bikes have the opportunity for somewhat smaller CdA. In any event, the point is to reduce it to a small number of factors. That gives less numbers to argue about
OK, let me give an example of what I'm talking about. I'll throw some numbers out for all of our factors, and then show how the calculation works. I haven't put a lot of thought into these factors so don't take them seriously, it's just an example:
Reference class: MPS-PG 2000, minimum is 200mph (I think this one is pretty reasonable, based on my calculations)
Fairing factors:
MPS: 1.00 (our reference bike)
APS: .98 (i.e. you've got 2% less CdA in an APS class)
unfaired: 1.15 (i.e. you've got 15% more CdA in an unfaired class)
Engine factor:
PG: 1.00 (our reference bike)
PF: 1.5 (fuel ought to make 1.5 times the power of the reference bike)
PBG: 1.5 (boosted ought to make 1.5 times the power of the reference bike)
PBF: 2.1 (boosted with fuel ought to make 2.1 times the power of the reference bike)
G: 1.4 (OHC ought to make 1.4 times the power of the reference bike)
F: 2.0 (OHC on fuel ought to make 2 times the power of the reference bike)
BG: 2.5 (Boosted OHC ought to make 2.5 times the power of the reference bike)
BF: 3.0 (Boosted OHC on fuel ought to make 3 times the power of the reference bike)
(I'm leaving out vintage and production to make this simpler. But what are there? 20 engine variations total? BFD)
OK, so now let's say we want to calculate the minimum for M-F 1350cc. How is it done?
First, scale the engine by displacement. 1350 divided by 2000 = .675, or 67.5%.
Now multiply by the factor above, to compensate for the fact that it's OHC on fuel. .675 times 2.0 = 1.35. There, you've decided that this bike ought to make 35% more power than the reference bike.
Apply this to the 200 minimum for the reference class. The cube root of 1.35 is 1.105. So 35% more power means the bike can go 10.5% faster, all else equal. 200 times 1.105 = 221 mph. That's what the minimum would be if this was 1350cc MPS-F.
But wait, this bike has no fairing, so it's got 15% more CdA than the reference bike. CdA is proportional to drag, and as we said, speed goes down as the square root of the CdA increase. The square root of 1.15 is 1.072, 221 / 1.072 = 206 mph. There's your 1350cc M-F minimum.
So anyway, this is just food for thought. Personally I think it would be very straightforward to come up with a spreadsheet to calculate any class. You'd still have a set of numbers for people to argue over (the motor and aero factors), but it'd be a whole lot smaller set of numbers than we have now.
