Ring & Pinion Gears & their Ratios.  RPM and Road Speeds versus ratios. 
Speedometers/Odometers ('and' repairing). 
Instrument numeral colors, calibration, etc.
Airheads and slash 2

© Copyright, 2011, R. Fleischer
ringgears.htm
Article #48

Almost all of the rest of this article is concerned with everything EXCEPT repairing your speedometer/odometer.
I have, thus, put that portion first.   Go to this website article for how to open-up and do some repairs in your instrument pod:

http://www.airheads.org/content/view/160/98/

What follows is a much expanded and updated version of the same article I posted to the http://www.airheads.org website.

Variables:
Your actual on-the-road tire diameter varies from that which is in manufacturer's books, or that which is calculated.  There is a modest effect when the tire is new to when well worn.  Even in same size, tires vary by manufacturer and model, sometimes considerably.   Tire pressures/temperature have an effect, so does the rim width; those are small effects.       Larger effect:  SLIPPAGE of tire rubber at the road surface. 

The unloaded to loaded measured diameter of a 4.00-18 rear tire versus a 120-90x18 (or other) rear tire is only about 15 mm in the WORST case I know of.   However, the actual rolling circumference USUALLY differs by only about 2%.  Hence the values shown below are THEORETICALLY fairly accurate, and many are taken from a BMW chart dated 1978, others are calculated, and some are actual test data.

NOTE 1. Values are THEORETICAL rpm and speeds for original stock size tires at recommended original inflation pressures, loads, ETC.  It is UNlikely that you will ACTUALLY have the same results for rpm nor speed as in the table, due to accumulated errors, tolerances, etc. Probably the rpm it takes for the table speeds will be about 5-8% more. Interestingly, this is about the amount many stock BMW speedometers are in error. 
                 Example:  If you have a 3.20 rear gear-set, expect closer to 62 mph at 4000; 3.44 expect 57 mph at 4000. Yes, I know the table does not list 4000 rpm.  You can interpolate, EH?

NOTE 2. If you have a standard 5 speed transmission, the following is in 4th gear:
2.91  32/11  4320 rpm for 70mph; 7200 rpm for 117mph
3.36  37/11  7200 rpm for 101.3mph

NOTE 3.  BMW speedometers are notorious for reading HIGH.  But the 0-85 mph speedometers are often very accurate. The ODOMETERS on ALL are usually quite accurate. When a rear drive RATIO is numerically LOWERED by ONE step, the speedometer error, if present, is OFTEN eliminated, without any need for speedometer internal work or a new speedometer.  The ODOMETER will be off, however. 
BMW purposely calibrates its speedometers to never read slower than the actual speed the motorcycle is traveling at; taking into account tire variations, temperature, instrument changes with conditions, and so on.  BMW has a bulletin on this, #2756, dated 10-21-1996.    The bulletin states that the MAXIMUM amount the speedometer will read fast is:  10% of true speed, PLUS 2.4 mph.

Note 5. The most accurate methods of calibrating a speedometer are, in NO specific order of accuracy:
a. Mile posts and stopwatch
b. Radar gun 
c. GPS 

NOTE 6. If you are really anal, here is the technical side of this:  
Have someone measure the radius of the tire, bike on tires (not stands), you and passenger seated on bike, bike pointed straight ahead, and balanced straight up.  The bike MUST be square to the surface!   Your buddy measures the CENTER of axle to the floor.  If you have no square or level to use, have your buddy measure the rear axle at both ends, and YOU adjust the lean of the bike until both measurements are identical.  YOU take that measured true distance from axle to floor; .... multiply it by 2, multiplied that by pi (or by 22/7)....and that will give the working circumference close enough to the actual in-use number. 

The formula for determining the relationships, suitably simplified is as follows:

Let T = the tach reading
Let M = miles per hour
Let C = circumference in INCHES
Let S = small number in the rear end ratio
Let L = large number in the rear end ratio

example: you have 37/11 gears (which is 3.36:1). 
S = 11; and L = 37
THEN, multiply the following: (T)(C)(S)
Divide that result by (1584)(L)
The result is M

Rearrange this formula to find any of the values, like you learned in jr. high school in beginning algebra. 

Practical example:
Most early BMW's came with a 4.00 x 18 rear tire. That tire is likely, even if you have an oversize 120-90 x 18, to measure about 80 inches in circumference.

The formula will show that for a 70 mph speed, the tach should be reading 4667 rpm.  Compare THAT to the chart (4486 rpm).  You can see that this goes right along with what you already know...your speedometer reads faster than you are going.

Suppose you want to know the engine rpm in any particular gear, for any particular tire and road speed.   Transmission ratios are in your owners book or on this website.  Rear end ratios are stamped into the rear drive.   You need to have a helper very accurately measure the radius of the tire with you and normal load, bike balanced on its tires as previously noted.     Select a mph speed, multiply that by the overall gear ratio which is the gear ratio of the rear drive and the transmission gear ratio (multiply them).  Multiply the result by 336 and divide by the tire DIAMETER in inches.   The result is the engine rpm.

Note 7:  The single sided (Monoshock) and the Paralever models have a very limited number of gear ratios available.    3.36 was popular on the ST and G/S (R80RT also) & late R65; and 3.00 was on the late R100RS and RT; and for the R80GS, R80R, R100GS, and R100R, you will find only the 3.20 and the 3.09.

Regarding the speedometer ratio (the small numbers located on the speedometer face), if you intend to use these numbers during testing, such as with a known rpm source driving the speedometer directly:
The applied rpm is multiplied by 1000, and is for Mph (or Kph as case may be).  Thus, a ratio of 1.112 really means 1112 turns of the speedometer cable PER MILE.  

The following table is for the /5 and later, through the end of airhead production.  Another table, below this one, covers earlier models.

 


The BMW /2 series had a very different set of rear drive gear ratios. Some were specifically for sidecar use. Available gearsets were (hopefully no errors here): 

revisions:

01/27/2008:  Incorporate all previous revisions.  Rename article to avoid problems with publishing its URL to E-mail messages.  Modify article so the data is presented in TABLE format, so that it is vastly easier to read, no matter what browser is selected, nor screen size.
06/14/2009:  slight cleanup
04/27/2010:  fix inadvertent typo that had 60 mph in the sentence on speedometer cable turns per mile.
04/18/2011:  add more data on 3.89 and 4.25 ratios
06/10/2011:  minor revisions. Add hyperlink to .org website article.
11/12/2011:  Checked a few areas for accuracy

© Copyright, 2011, R. Fleischer
 

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