Gear ratio confusion

[Seth]

the question about a "long" 4th gear brought me back to a spreadsheet I had developed to calculate rpm to speed for my R1150RS.
All the numbers seemed to make sense.
I thought I'd do the same calculation for my R100RS, but the numbers don't make sense.
My calculation is:
RPM / gear.ratio / final.drive.ratio * 60(minutes per hour) * tire.circumference.in.inches / 12(inches per foot) / 5280 (feet per mile)
1000 / 2.05 / 2.91 * 60 * 53.604 / 12 /5280 = 9

The R1150RS has transmission gear ratios of giving speed per 1000 rpm of:
1st - 2.05 9 mph
2nd- 1.6 11 mph
3rd - 1.27 14 mph
4th - 1.03 17 mph
5th - 0.9 19 mph
6th - 0.7 25 mph
These speeds seem to make sense

On the other hand, the 5 speed gearbox in my R100RS has gear ratios of
1st 4.4
2nd 2.86
3rd 2.07
4th 1.67
5th 1.5
and has the same final drive ratio. The tire is slightly taller, but not enough to make a substantial difference.
These gearbox ratios are much lower (higher numerically) than the oilhead and there is not any other factors I know of.
Given the same above calculation, at 6000 in 5th gear, my R100RS would only be doing 74 mph.
6000 / 1.5 / 2.91 * 60 * 56.7437 / 12 / 5280 = 74

The Airhead gear ratios don't seem to make sense. Most transmissions that I'm familiar with tend to have top gear (5th, in this case) to be 1:1 or an overdrive, similar to the Oilhead.

Can someone let me know where I'm confused?
Thx

[Kurt in S.A.]

My equations are designed to compute RPM given a certain speed. But if I put in speeds and try to get to 6000 RPM for the same 2.91 rear end, I get around 100-105 mph in 5th gear. I'd have to devolve my equation into what you're using to see where the differences are.

Could I get you to put parantheses around as required in your equation? For instance, the 5280 factor...what all is that divided into? It matters in what order you do the calculations.

Kurt in S.A.

[barryh]

Your rolling circumference at 56.7 " seems too low. I think you must be using the wheel diameter 18" rather than the tyre diameter 26". On an airhead 18" wheel rolling circumference is more like 81"

This is what I get for a 2.91 final drive.

[Kurt in S.A.]

I get more or less the same thing as barryh when I substitute 26 inches...I had been using 25.6 inches for the diameter. Question...how do you get from 26 diameter to 81.10 rolling circumference? Straight math gives you 81.7 circumference. Are you accounting for tire flattening when sitting on the bike?

Kurt in S.A.

[barryh]

I get more or less the same thing at barryh when I substitute 26 inches...I had been using 25.6 inches for the diameter. Question...how do you get from 26 diameter to 81.10 rolling circumference? Straight math gives you 81.7 circumference. Are you accounting for tire flattening when sitting on the bike?

Kurt in S.A.

That spreadsheet is 10 years old but I recall attempting to measure it by rolling an unladen bike. Might not be very accurate. Then to counter that there is the effect of the tyre increasing in diameter at speed. I don't think the calculation can be done very precisely as there are other variables like a new 4.00 x 18 tyre can vary between 26" and 26.4" in diameter depending on make and then of course they wear.

[Kurt in S.A.]

Well at least were pretty close! I had come up with my calculations in order to help find an RPM for my tach-less R69S. I realized it wouldn't be exact, I just wanted to have a better sense of shift points and RPMs.

Kurt in S.A.

[melville]

I think there's a reduction gear on the input that is not part of the gear ratio calculation for the oilhead trans but that is part of the calculation for the airhead trans.

From this:

http://largiader.com/tech/oiltrans/sixspeed.html

See the input shaft at the bottom:



That looks like at least a 2:1 input ratio. So the Airhead ratios measure the difference between crank rpm and output rpm, while the published Oilhead ratios measure the difference between the two shafts with all the gears on them.

[Seth]

The parentheses don't matter, as it is all multiplication and division.
The order doesn't matter, other than rounding. It would if the formula included + and -.

In regard to circumference of the tire, I went to this web site:
https://www.bridgestone.com/products/mo ... 5D%5B4%5D=

and found the 120/90-18 has a diameter of which shows OD of the tire as 673mm. Converted to inches (divided by 25.4), which is 26.5" and reasonable for an 18" rim. Then multiply that times Pi (2πR or π*diameter).

So this is where I found my problem (thanks guys for being a sounding board to figure out).
As I said... I knew I was missing something.
I typo-d Pi as 2.14159 instead of 3.14159. Made a big difference in the circumference of the tire (83.24" vs 56.74").

Now I have to figure out what I did with my R1150RS spreadsheet because when I fix Pi there, the speeds are too fast!

Thanks again...

[Kurt in S.A.]

The parentheses don't matter, as it is all multiplication and division.

Probably right, but my old Mechanics 101 is showing! I like to see all of the multipliers in the numerator and the things that divide in the denominator. Helps me see how the equation is put together.

My equations don't deal with anything happening inside the transmission. I'm only concerned about the final drive 5th gear ratio, that value of 1.5.

Kurt in S.A.

[melville]

OK, some more info:

The primary ratio, the helical gears in the pic above, is 1.889.

See the second post for the source of the confusion:

https://forums.bmwmoa.org/showthread.ph ... and-1150RT