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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
http://bmwmotorcycletech.info/ringgears.htm
Article #48


Website for how to open-up 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/bmw-motometer-instruments-twin.html

 


Speedometer & Tachometer parts and service work:   

Instrument housings, NEW: http://www.bmwbayer.de/

Terry Vrla; 776 SE 3rd Ave; Hillsboro, OR 97123; 503 421 5782   Airhead instrument pod overhauls, repairs, parts, etc. Speedometers, Tachometers, can even fix the threaded insert areas.  Highly recommended!
 
For ODOMETER gears, all models:
http://www.odometergears.com/products/BMW/R+&+K+Motorcycles/42

http://www.speedometer.com/bmw_cycles.html  Repairs and calibration of speedometers, odometers, mechanical & including the electronics type on the K bikes. I think they can do actual circuitry repairs.  Rick Borth

North Hollywood Speedometer www.nhspeedometer.com

Palo Alto Speedo www.paspeedo.com in California.

West L.A. Automotive www.speedometerplus.com  877-900-9009   310-838-7350   In Los Angeles

Southern Electronics, Inc, in Richmond, Virginia do speedo/tach repairs....and can do things quite in-depth. They can do mechanical and electronics units, even BMW radios. 800-446-2880; 800-572-2880 www.instrumentclusters.com  Their radio site is http://www.CarRadio.com


One specific item!....whilst well known for his driveshaft repairing, he carries the small rubbery button that fits over the button on your odometer on later models...a hard to find goody. Guy Hendersen (209) 962-7500  guy@hendersenprecision.com http://www.hendersenprecision.com/index.html  Sales@hendersenprecision.com Hendersen Precision; 22105 Feretti Road,
Groveland, California 95321


NOTE 1.    Variables:
Your actual on-the-road tire diameter varies from that which is in manufacturer's books, or that which is calculated. Most ROAD type tires have a rather close tolerance as to diameter...BUT, the tire is NOT round where it contacts the pavement.  There is also 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 (this is usually with off-road tires, like enduro tires, which can be widely variable in the same size as a road tire...especially width, but sometimes diameter too).   Tire pressures/temperature have an effect, so does the rim width; but those are usually very small effects.    There is a considerably larger effect, the 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.  Because it is the rear tire that drives the motorcycle, if the speedometer and odometer are driven by either wheel, the result varies with WHICH wheel.  Manufacturer's compensate for that, of course....but, it almost always results in the speedometer reading higher than actual speed due to company policy on never having the speedometer read slow.  The ODOMETER almost always is very accurate, or reads very slightly higher, due to slippage from takeoffs.   ALL these various variables are not large.

The unloaded to loaded measured diameter of a road-type 4.00-18 rear tire versus a 120-90x18, typically the largest rear tire on early Airheads that was ever used as standard, 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!  Be sure to read the various notes in this article, regarding such as BMW's WRONG conversion of Kph to Mph, regarding the ratios that the speedometer/odometer use.

The values in the chart, below, are THEORETICAL rpm & speeds for original stock size tires at recommended original inflation pressures, loads, ETC.  While Mph figures are shown, I suggest you use the Kph speeds, and YOU convert from Kph to Mph, & disregard BMW's Mph figures, as those are shown here with BMW's own original errors.

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.  It is MY BELIEF that BMW did NOT chart these things for ON THE ROAD; but under some factory controlled setup or calculations, and it is MY BELIEF that you will, assuming accurate instruments in and of themselves, ALWAYS have a higher rpm ON THE ROAD, for a given speed.  Probably the rpm it takes for the charted 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.  Do not forget what I said about YOU converting Kph to Mph (and NOT vice-versa!!!).

NOTE 2. 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, in general, 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 3.The most accurate methods of calibrating a speedometer are, in NO specific order of accuracy are Mile posts and stopwatch; Radar gun; GPS 

NOTE 4. If you are really anal; 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 100% 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:
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 5:  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.

NOTE 6:  
BMW used different colored dials and pointers depending on model/year.  BMW used different plastic covers for the speedometer-tachometer and lights pods:
1973-1977 had the indicator lights at the bottom.
1978-1981 had the brake warning light at the bottom.  1978 was the transition year for the electronic tachometer; and BMW changed the numbers and text from white to green.
1981+ had a blue light plastic lens for the high beam indicator, and it was at the bottom.
Speedometers were 140 mph (with kph in smaller text); or, 220kph for metric countries.  There were 85 mph speedometers for the USA during the 55 mph speed limit years.


The following chart is for the Airheads, which means  /5 and later, through the end of Airhead production in 1995.  Another table, below this first one, covers earlier models.

Figures are the PUBLISHED figures & are NOT correct with regards to MPH/KPH if you do the conversion.  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.  If you convert backwards, from Kph, to Mph, you may do better.  As always, assume correct speedometer ratio shown (and in reality, actual), and correct rear drive ratio, you can do a comparison with a GPS on a flat straight road; and, you can use a precision tachometer to check your tachometer.  Various checks can be done in one's garage, using photo tach and photo pulse counting equipment, etc.

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.  W=0.737 means the cable turns 737 times PER KILOMETER....example of the use of that information, might be that if you rotated the cable at 737 rpm, the speedometer should indicate 60 km/hr (60 kph), or 1 per minute.
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.

Instruments may not conform to precisely the W figures shown.  In motorcycle shipments to some countries, requirements for more precise accuracy (read that as USUALLY less optimism on speed) means that a slightly different W figure is used on the instrument.   It is ALSO my belief that BMW made some speedometer ratio changes even for the same ring gear ratios now and then that were not necessarily for Country regulations reasons, and this may be ANOTHER reason why some books show different speedometer ratios.   I suspect BMW did this just to make minor corrections in instrument readings.

NOTE:  The ratio between speedometer ratios, Mph/Kph, is 0.621, always.
   1 Kph is 0.621 Mph
 

Ring
Gear
Ratio,
teeth

 

RPM,
55
mph

RPM,
70
mph

MPH,
7200      rpm

Speedo
 ratio,

 Mph

Speedo
 ratio,
 Kph

Notes:
 

2.615
34/13        

  

         

Racing ratio used on /5 & later.  See last note in this right side column for others.

2.91
32/11

 

3050

3881

130

1.078

0.67

White numerals 1974-1977; R100RS, R100S.   1978 began with green numerals. 1981+ all had green numerals.  Some R75/5 (to frame 2973204) had 2.91, not 3.20.  Some R75/6. Kph ratio is .665 & mph ratio in some literature as 1.0625.  

R75/5 with 200kph speedo: W=660.  With 120 mph speedo, 120mph W=1050

What can you REALLY EXPECT from a 32/11 rear drive ratio? Measurements taken on smooth road, 40# air pressure at 70F, medium worn tire, and all measurements at 4,000 rpm.  Speeds measured on straight road with GPS.   5th gear:  70 mph.  With standard 5 speed transmission, the following is in 4th gear:  4320 rpm for 70mph; 7200 rpm for 117mph

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.  White pointer.  The R100; R100T; R100RS; R100RT, some countries & years, had 3.00.  In general, from 1987, all USA/UK bikes had 3.00 ratio on the monoshock models RS/RT.

3.09
34/11

 

3241

4125

122  

1.144

0.711

White numerals 1974-1977; R90/6. 1978-1980, was green numerals, on some R100/7.   3.09 was used on R100R, R100GS & SOME R90S

3.20
32/10

 

3357

4273

 118 

1.186

0.737

White numerals 1974-1977; R75/5, R75/6, R75/7. 1978-1980, green numerals, used on R80/7; all R80/7 had electronic tachs.   3.20 was also used on R80R, some R80GS.  R75/5 with 200 kph speedos
W= .715.  With 120 mph speedos  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.

R60/5 with 200kph speedo W=760. With 120mph speedo, W=1215.

With standard 5 speed, the following is in 4th gear; 3.36  37/11  7200 rpm for 101.3mph

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 and R60/7 had 3.56. Books may show Kph ratio as 0.811, miles ratio as 1.297.
With 200kph speedos, W=800.  With 120mph speedos will have W=1300.

3.89
35/9

 

     

1.441

0.888

R45S, 35 hp model (at 7250 rpm)

4.25
34/8

 

     

1.575

0.970

R45

             

In general, 1978 models came to USA with green numerals & lines.  Earlier models had white numerals & lines. 1978 had electric tachometer with some changes in the instrument pod terminal wiring.

 

           

Not shown are some few ratios used by the factory & NEVER sold, even for racing; a FEW WERE used by the factory racing department.   For the 2.812 (31/11 gears) & 2.75 (33/12) ratios: while the books & on-line 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. There was a 4.50 ratio (36/8) for competition.

 


The BMW /2 series had a very different set of rear drive gear ratios. Some were specifically for sidecar use. HERE, /2 means earlier than the /5 models, even though these 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     5.14

 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
08/06/2014:  Clear up some confusion on Euro speedometer ratios
12/18/2014:  Explain why the confusion.
06/11/2015:  Clarity, 33/11, and add note regarding 0.62 ratio between Mph and Kph.
10/15/2015:  Clean up article.  Some further cleanup and added notes on 11/04/2015; re-arrange some of the article.
03/22/2016:  Update metacodes; format, fonts, colors, some minor details.
09/05/2016:  Clean up, slightly, which had white and which green numerals; that all R80/7 were green and Electronic tachs.

Copyright, 2014, R. Fleischer

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Last check/edit: Monday, September 05, 2016