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

Copyright, 2014, R. Fleischer
ringgears.htm
Article #48

 

Almost all of the rest of this article is concerned with all the above EXCEPT repairing your speedometer/odometer.
Go to the following website for how to open-up and do some repairs in your instrument pod:

http://www.airheads.org



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 a small amount by manufacturer and model, sometimes considerably though, and this is usually with off-road 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; those are usually small effects.       Larger effect:  SLIPPAGE of tire rubber at the road surface. You do NOT have to feel the slippage, it is always occurring, except when the motorcycle is not moving.

The unloaded to loaded measured diameter of a 4.00-18 rear tire versus a 120-90x18 (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 are THEORETICALLY fairly 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 paragraph 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 5-8% 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 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 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 side-stand nor center-stand), 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 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. ..........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.  

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.

Ring Gear
Ratio

Teeth

RPM,
55 mph

RPM,
70 mph

MPH,
7200      rpm

speedo
 ratio,

 Mph

speedo
 ratio,
 Kph

Notes:
 on rear drive ratio; speedometer ratio, colors of numerals on the speedometer face

2.615           

34/13  

         

Racing ratio used on /5 and later

2.91

32/11

3050

3881

130

1.078

0.67

White numerals 1974-1977; R100RS, R100S.   1981+ all had green numerals.  Some old books have 2.91 on some R75/5 and R75/6, & show Kph ratio as .665 & mph ratio as 1.0625.   One book shows that as 1.155.

UNconfirmed:
R75/5 with 200kph speedometer:  W=660
          with 120mph                      W=1050

3.00

 33/11

3147

4005  

126

1.112

0.691  

White numerals 1974-1977; R90S, R100/7. 1978-1980, green numerals on some R100/7.   1981+ all had green numerals.

3.09

34/11

3241

4125

122  

1.144

0.711

White numerals 1974-1977; R90/6.   For 1978-1980, was green numerals, used on some R100/7.   3.09 was also used on R100R and R100GS

3.20

32/10

 3357

4273

 118 

1.186

0.737

White numerals 1974-1977; R75/6, R75/7.  For 1978-1980, was green numerals, used on R80/7.   3.20 was also used on R80R, some R80GS

UNconfirmed:

R75/5 with 200kph speedometer:  W=715
          with 120mph                      W=1155

3.36

 37/11

3525

4486

112

1.244

0.773

White numerals 1974-1977; 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.

UNconfirmed:
R60/5 with 200kph speedometer:  W=760
          with 120mph                      W=1215

3.44

31/9

3608

4592

110

1.259
1.267?

0.793 ?

R65.   Some had 3.56.
Some manuals say the speedometer ratio is 1.267 for the 3.44 gearset for miles (.793 for Kph)

3.56

32/9

3734

4752

106

1.318

0.819

White numerals 1974-1977.   R65 models had 3.56 & 3.44.  R50/5 had 3.56. Books  may show Kph ratio as 0.811, and the miles ratio as 1.297.
 

UNCONFIRMED:
NOTE:  R50/5 models with 3.56:1 rear drive ratio were available with 200kph speedometers, for which W=800.  Similarly, the R50/5 with the 120mph speedometer will have W=1300.

3.89

35/9

     

1.441

0.895

R45, 35 hp model (at 7250 rpm)

4.25

 34/8

     

1.575

0.978

R45, sometimes called R45N, 26 or 27 hp (both at 6500 rpm), manuals vary on hp.

               

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.
There is also a 33/12; 2.75:1 ratio, and while the books and on-line fiche show it as being used on numerous models, I have never seen it.

 


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 1960-1969

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 on-line 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 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
07/12/2012:  updated R65/R45 information very slightly
10/13/2012:  Add QR code; add language button, update Google Ad-Sense 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

 


Copyright, 2014, R. Fleischer
 

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