Ring &
Pinion Gears & their Ratios.
RPM and Road Speeds versus
ratios.
Speedometers/Odometers.
Instrument numeral colors, calibration, etc.
Airheads and slash 2
© Copyright, 2014, R. Fleischer
ringgears.htm
Article #48
Website for how to openup and do some repairs in your instrument:
http://www.airheads.org
Find the article, under Technical tips.
for the /5, see:
http://velobanjogent.blogspot.ca/2011/04/bmwmotometerinstrumentstwin.html
Variables:
Your actual ontheroad tire diameter varies
from that which is in manufacturer's books, or that which is
calculated. The tire is NOT round where it hits the pavement. There is also modest
effect when the tire is new to when well worn. Even in same size, tires vary a small amount by
manufacturer and model, sometimes considerably though, and this is usually with offroad tires, like enduro tires, which can be widely variable in the same size as a road tire. Tire pressures/temperature
have an effect, so does the rim width; but those are usually small effects.
Larger
effect: SLIPPAGE of tire rubber at the road surface. You do NOT have to,
and usually do not, feel the slippage, it is always occurring, except when the motorcycle is not moving.
The unloaded to loaded measured diameter of a roadtype 4.0018 rear tire versus a 12090x18 (or other similar) rear tire is only about 15 mm in the WORST case I know of. The actual rolling circumference USUALLY differs by only about 2%. Hence the values shown below in the text and charts are THEORETICALLY reasonably accurate, and many are taken from a BMW chart dated 1978, others are calculated, and some are actual test data. Keep in mind the variables in the paragraphs above!
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 exactly the
same results for rpm (and speed) as in the table, due to
accumulated errors, tolerances, etc.
Probably the rpm it takes
for the table speeds will be about 58% more. Interestingly, this
is about the amount many stock BMW speedometers are in error...ON PURPOSE!
see NOTE 3.
Example:
If you have a 3.20 rear gearset, 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 085 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
10211996. The bulletin states that the
MAXIMUM amount the speedometer will read fast is: 10% of
true speed, PLUS 2.4 mph.
Note 4: deleted
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
sidestand nor centerstand), 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 rear axle to the floor. If you have no square or level
to use, have your buddy measure the center of the rear axle at both its ends, and
YOU adjust the lean of the bike until both measurements are
identical. Take that measured true distance from center of axle
to floor; ....
multiply it by 2; then multiply that by pi (or by
22/7)....and that will give the working circumference close
enough to the actual inuse 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 12090 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. ..........AND, the tire slips.
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 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 likely find only the 3.20 and the 3.09.
Regarding the speedometer
"ratio" (the tiny numbers located on the speedometer face, except most /5 models), 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. NOTE
that it might be expressed as W=1.112 or W=1112.
The following table is for the Airheads, which means /5 and later, through the end of airhead production in 1995. Another table, below this one, covers earlier models.
NOTE that instrument ratios are shown in the Notes section where W= is a different format and calculation. You can just add the decimal point......but, note the difference in values. I do NOT have a definitive explanation
for you here.
WARNING: The below figures are the PUBLISHED figures and are NOT correct with regards to MPH/KPH if you convert yourself.
The problem is that BMW wrongly converted Kph to MPH in its bulletin. BMW's original chart used 101 Kph to be 55 mph.
The correct speed is 62.6 mph for that conversion.
NOTE: Speedometer gear ratios can be shown in literature in two ways.
An example would be W=760. The other way to show that is W= 0.760.
SOME instruments may not conform to precisely the W figures shown. In motorcycle shipments to some countries, requirements for more precise accuracy (read that as less optimism on speed) means that a slightly different W figure is used on the instrument.
Ring Gear 
Teeth 
RPM, 
RPM, 
MPH, 
speedo 
speedo 
Notes: 
2.615 
34/13 
Racing ratio used on /5 and later. See last note in this right side column for others. 

2.91 
32/11 
3050 
3881 
130 
1.078 
0.67 
White numerals 19741977; R100RS,
R100S. 1981+ all had green numerals.
Some R75/5 (to frame 2973204) had 2.91 and not 3.20. Some R75/6. Kph ratio is .665 & mph ratio in some literature as 1.0625. 
3.00 
33/11 
3147 
4005 
126 
1.112 
0.691 
White numerals 19741977; R90S, R100/7. 19781980, green numerals on some R100/7. 1981+ all had green numerals. The R100; R100T; R100RS; R100RT, some countries and years, had 3.00. 
3.09 
34/11 
3241 
4125 
122 
1.144 
0.711 
White numerals 19741977; R90/6. For 19781980, was green numerals, used on some R100/7. 3.09 was also used on R100R and R100GS and SOME R90S 
3.20 
32/10 
3357 
4273 
118 
1.186 
0.737 
White numerals 19741977; R75/5, R75/6, R75/7. For 19781980, was green numerals, used on R80/7. 3.20 was also used on R80R, some R80GS R75/5 with 200 kph
speedos 
3.36 
37/11 
3525 
4486 
112 
1.244 
0.773 
White numerals 19741977; R60/6, R60/7. Some
old books have R60/5 & R60/6 as 3.36:1 rear drive & 0.766 as Km ratio,
mph ratio as 1.266. 3.36 was also used on some R80G/S, R80RT,
R80ST, and R65 from 1986. 
3.44 
31/9 
3608 
4592 
110 
1.259 
0.793 ? 
R65. Some had 3.56. 
3.56 
32/9 
3734 
4752 
106 
1.318 
0.819 
White numerals 19741977. R65
models had 3.56 & 3.44. R50/5 and R60/7 had 3.56.
Books may show Kph ratio as 0.811, miles
ratio as 1.297. 
3.89 
35/9 
1.441 
0.888 
R45S, 35 hp model (at 7250 rpm) 

4.25 
34/8 
1.575 
0.970 
R45 

The 1978 models came to the USA with green numerals and lines. Earlier models had white numerals and lines. Note also that the 1978 had an electric tachometer; with some changes in the instrument pod terminal wiring. 


Not shown are some few ratios used by the factory and NEVER sold, even for racing; a FEW of some WERE used by the racing department. For the 2.812 (31/11 gears) and 2.75 (33/12) ratios: while the books and online fiche show the 31/11 being used on numerous models, I have never seen it; it was for racing anyway. The 2.615 (34/13) was available for the R75/5 racing, long ago. 
The
BMW /2 series had a very different set of rear drive gear ratios.
Some were specifically for sidecar use. HERE, /2 is used for all earlier
models, even though they may not be true /2.
25/8 3.13 
This was standard on the R69S. 
35/11 3.18 
This was standard on the R50/2. 
27/8 3.375 
Also used on the R50/2 
32/9 3.556 

25/7 3.58 
Used on the R50S in 1960 to 1962 
27/7 3.86 
Sidecar use, 1956 to 1967 
35/9 3.89 

25/6 4.17 
R27 
26/6 4.33 
Sidecar use 19601969 
35/8 4.38 

27/6 4.50  R25/2 
32/7 4.57 

36/7 
R25/2 with sidecar 
26/5 5.20 
Optional ratio for R27 
Here is an online calculator for various bike tires. You may find it useful:
http://www.tacomaworld.com/forum/tirecalc.php
revisions:
01/27/2008: Incorporate all previous revisions.
Rename article to avoid problems with publishing its URL to
Email 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
07/12/2012: updated R65/R45 information very slightly
10/13/2012: Add QR code; add language button, update Google AdSense code, minor other coding
08/20/2013: Add note about 1978 colors
10/06/2013: Add UNconfirmed values for /5 bikes
11/20/2013: Add tacomaworld hyperlink
02/05/2014: Add info on 2.75, 33/12
08/06/2014: Clear up some confusion on Euro speedometer ratios
12/18/2014: Explain why the confusion.
©
Copyright, 2014, R. Fleischer
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