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Ring & Pinion Gears & their Ratios. 
RPM & Road Speeds versus Ratios. 
Speedometers & Odometers W ratios.  
Instrument numeral & pointer colors, calibration, etc.
Airheads; slash 2; pre-/2.

Copyright 2018, 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 AirLore, Technical Tips.

For the /5, see:
http://velobanjogent.blogspot.ca/2011/04/bmw-motometer-instruments-twin.html

For detailed information on repairing rear wheel splines on twin-rear-shock Airheads, and detailed information on repairs to the ring gear splines, etc, see: http://bmwmotorcycletech.info/rearwhlsplines.htm


Speedometer & Tachometer parts and service work:

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

To purchase replacement for the flexible printed circuit board, including LED lamps conversion:   http://katdash.com

Airhead instrument pod overhauls, repairs, parts, etc. Speedometers, Tachometers, can even fix the threaded insert areas.  Highly recommended!   Terry Vrla; 776 SE 3rd Ave; Hillsboro, OR 97123; (503) 421-5782

For ODOMETER gears, all models:
http://www.odometergears.com/products/BMW/R+&+K+Motorcycles/42

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

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! ....well known for his driveshaft repairing, ...he also has the small rubbery button that fits over the button on your odometer on later models...a hard to find item. 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 tire 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 when loaded, it contacts the pavement, and the heavier the load, the less round, and the less the effective radius.  There is also an 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 in total width, but sometimes in diameter.   Tire pressure & temperature has an effect, so does the rim width; but those are usually small effects.   There is one considerably larger effect, the slippage of tire rubber at the road surface. You do not have to, and usually do not, feel the normal slippage, it is always occurring to some extent except when the motorcycle is not moving.  Because it is the rear tire that drives the motorcycle, and it slips even in normal easy-going, the resultant instrument reading varies with which wheel has the speedometer-odometer drive.  Manufacturer's often try to compensate for that, of course ...but, it almost always results in the speedometer reading equal to or higher than actual speed due to most company policies on never having the speedometer read slower than you are actually moving.  The odometer is usually very accurate; or, may read very slightly higher.

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 Airheads that was ever used as standard, is only about 15 mm in the worst case I know of (that is 47 mm difference in circumference, about 2 inches).  The actual rolling circumference usually differs by only about 2%.

BMW has used 3.25-19, 3.25-18, 90/90-21, 90/90-18, and 100/90-19 front tires.  Rarer is that some were shipped with 3.50-18 front tires.

For the rear, BMW has used, 3.50-18, 4.00-18, 130/80-17, 120/90-18, and 140/80 tires.  The difference between the extreme's in circumference, is ~3.0 inches.  That is ~3.7% difference.  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; some are actual test data.  Keep in mind the variables. 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.

In all of the above, I have used standard rim width sizes.  The rim width size variations that BMW has used has a rather small effect on rolling circumference. It's primary effect is, with the roundish shape of the tire, to change the rubber footprint SLIGHTLY.

The values in the AIRHEADS chart, well below, are theoretical rpm & speeds, for original stock size tires, at recommended original inflation pressures, loads, etc.  Where available, I suggest you use the Kph W figures and YOU convert to W Mph figures, & disregard BMW's Mph ratio figures, as those W figures are shown charted here with BMW's own original errors.

It is unlikely that you will have exactly the same results for rpm and speed as in the table, due to accumulated errors including instrument calibration, tires, other tolerances, etc.  It is my belief that BMW did NOT chart for actual on the road, but under some factory controlled setup or calculations, and it is also my belief that you will always have a higher rpm on the road, for a given true 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 by BMW!

NOTE 2.  BMW speedometers are notorious for reading high?
Yes!  (but the 0-85 mph speedometers are often very accurate).  So, what is going on?   BTW: All odometers are usually quite accurate.

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 had bulletins on this, the last one, #2756, is 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 for YOU to check the calibration of your speedometer and odometer are, in no specific order of accuracy, mile posts and stopwatch; radar gun; GPS.

NOTE 4.  If you are really anal, you can have someone measure the radius of the tire, bike on tires (not side-stand nor center-stand, and do it on a level surface), while you and passenger seated on bike, bike pointed straight ahead, and 100% balanced straight up, preferably with the help of another person.  The bike MUST be very square to the surface!   Your 1st buddy measures the CENTER of rear axle to the floor on both sides, precisely. Doing it all this way is somewhat inconvenient, compared to having your feet help balance the bike, but you get the full effect of loading.  You adjust the lean of the bike with help of buddy #2, 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 divided by 7 ....and that will give the working circumference close enough to the actual in-use number (except for slippage).

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, which is miles per hour.

Rearrange this formula to find any of the values, like you learned 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 Paralever models have a limited number of gear ratios available.    3.36 was popular on the ST, G/S, R80RT & late R65;  3.00 (33/11) was on the late R100RS and RT.   For the R80GS, R80R, R100GS, and R100R, you will likely find only the 3.20 and the 3.09.

NOTE 6.   This section is for the dual-pod, which is NOT the R45, R65, ST, GS, G/S, and R80R and R100R.  BMW used different colored dials and pointers depending on model/year.  BMW used different plastic covers for the speedometer-tachometer and lights pods. There have been some anomalies, that may not agree with the below information:

The 1974 only had white squares all around
1974-1977 (/6 series and first /7) had the Hi beam indicating lamp at the bottom of the tachometer face.  Pointers are orange into mid-1977, and markings were in white.  In 1974 only there was a white surrounding area inside the rim edge.   While there was both a /6 and a /7 in 1977, the dial markings were white for all of them. The oil lamp was AMBER color, and the turn signal lamp was also AMBER, located at the bottom of the tachometer face.  The brake failure lamp is the top lamp in the center lamps group, then came the neutral lamp, GEN lamp, Oil lamp.
The /7 series had the turn lamp on the top, and just below it is the Oil lamp.  Neutral lamp is second from the bottom.  The bottom lamp is the Brake Failure lamp.  Dial markings are green, pointers are white.
1978 was the transition year for the electronic tachometer; and BMW changed the numbers and text from white to green, but a white pointer.
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 Federal 55 mph speed limit years.

Hints: 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 usually be off, however.   If the speedometer is driven by the front wheel and not the rear (powered) wheel, the over-all accuracy CAN be more accurate, particularly due to slippage being greatly reduced, which varies by amount of horsepower in use.


Transmission ratios used on Airheads (1970 through 1995 models).
(ratios used on pre-1970 models are in a table chart at the end of this article).

Gear 4 speed ratio 5 speed ratio Comments
1st 3.896 4.400

There was only one standard (non-racing) transmission for the 4 speed transmission for the /5; and only one standard (non-racing) transmission for the 5 speed transmission from the /6 to end of production in 1995.  There was no "sidecar" ratio transmission available, as usually offered or shipped with sidecar models, pre-1970.

2nd 2.578 2.860
3rd 1.875 2.070
4th 1.500 1.670
5th 1.500
 



The following chart is for the Airheads, which means /5 and later, through the end of Airhead production in 1995.  A table, below this one, covers pre-1970 models.

Most all of the figures are the BMW bulletins figures & are not necessarily correct with regards to Mph/Kph if you do the conversion, as earlier mentioned, because BMW wrongly converted correct Kph to Mph in an applicable bulletin.  BMW's original chart used 101 Kph to be 55 mph.  The correct speed is 62.6 mph for that conversion.  You should convert from Kph, to Mph.   Assuming correct speedometer ratio shown/real, and correct rear drive ratio, you can do a comparison with a GPS on a flat straight road; and, you can use some method to check your tachometer, such as with a photo tach checker or pulse counting equipment, or my own posted method of using a flourescent light strobe and 6 marked lines on the alternator rotor end.  See:  http://bmwmotorcycletech.info/tach.htm


WHAT'S with the "W....." thing??...

This is a short short discussion regarding the speedometer "ratio" (the tiny numbers located on the lower center area of the speedometer face, except most /5 models and prior to /5 models).  W stands for a not easily fully-translatable German "Wegdrehzahl".  It translates into something akin to road speed coefficient.  On a practical basis, W....   is equal to revolutions divided by either Kmh or Mph.  The next paragraph explains what this means.   The speedometer W number should match the rear drive ratio, per the chart below.

If you intend to use these W 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).  A W ratio of 1.112 really means 1112 turns of the speedometer cable per mile.  It might be expressed as W=1.112 or W=1112. Speedometer gear ratios can be shown in literature in these various ways.  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 Kph, or 1 per minute.   If the W=  number is under 1.00, the value is for a speedometer calibrated in Kph; if over 1.00, it is for Mph.     Many speedometers have both Kph and Mph calibrations, the larger numerals are the one's that the W factor applies to. Note that there may be no printing of W numbers on the face of older speedometers, from the /5 to earlier.

BMW's habit was to have the speedometer cable rotate the same number of times for rear wheel rotations.  Only the gears in the speedometer were changed, to have Kph and Mph. If you are quite anal, and understand what and how the rear drive (unless using a speedometer drive from a front wheel) ratio works with simple mathematics with the speedometer ratio and, perhaps, the transmission output drive to the speedometer, you can calibrate any speedometer, perhaps modify it for any specific rear drive ratio, etc.  For the Airheads, BMW elected to use the same worm drive gears/ratio at the transmission output flange, for all models.

Speedometers may not conform to precisely the W figures shown.  In motorcycle shipments to some countries, requirements for more precise accuracy (usually less optimism on speed) means that a slightly different W figure is used in the instrument.   It is 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 the reason some books show different speedometer ratios.   I suspect BMW did this just to make minor corrections in instrument readings.   There are also ERRORS in some literature on what W values were in use, and why.  This got particularly a mess of fun and games when the fact that BMW made a different set of gears for the transmission innards, and these were not universally used, back when BMW made sidecar rigs.  In other words, BMW, pre-Airheads, had a sidecar transmission ratio gears, and solo (no sidecar) transmission gear set.  All, back then, were 4 speed, but 4th gear was always the same. This is clearly shown in a small chart quite aways below in this article. For the Airheads, things became more standardized, and there were fewer combinations required, basically just one speedometer W number for each rear drive ratio offered. Fewer rear drive ratios were offered later on too. Any competent speedometer technician can change a particular instruments actual W number.

The ratio between Mph and Kph speedometer ratios is always 0.621.    1 Kph is 0.621 Mph.

There may be errors in some literature, particularly with Mph ratios, wrongly converted from Kph. NOTE THAT IN MY CHART, I AM USING W RATIOS AS THEY ARE USUALLY PRINTED ON THE SPEEDOMETER FACE.  IN A FEW INSTANCES, THOSE HAVE NOT BEEN PUBLISHED OR NOT AVAILABLE TO ME, SO I HAVE DONE THE CONVERSION FOR YOU....AND THAT INCLUDES SHOWING THE LITERATURE ERRORS BY LISTING MORE THAN ONE VALUE.   THERE MAY BE A 1 DIGIT +- ERROR BETWEEN WHAT BMW PRINTS ON THE FACE OF THE SPEEDOMETER, AND THE ACTUAL CONVERTED CALCULATION USING 0.621. FOR THE EXACT W RATIO FOR Mph, DIVIDE THE Kph W NUMBER BY 0.621.

Ring
Gear
Ratio & 
teeth

 

RPM,
55
mph

RPM,
70
mph

MPH,
7200 rpm

Speedo
 ratio,
 Mph

Speedo
 ratio,
 Kph

Notes:
Speedometer ratio in Mph is always the as shown Kph ratio divided by 0.621.
 

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. Orange pointer.  1978 began with green numerals white pointer. 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; orange pointers. 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, orange pointers.  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; orange pointers. 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; orange pointers.   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
1.276

1.277

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.
I think this should be 1.429

0.888

R45S, 35 hp model at 7250 rpm

4.25
34/8

 

     

1.575.  I think this should be 1.562

0.970

R45

             

In general, pre-1978 had white numerals and orange pointers. 1978 models came to USA with green numerals & lines, then white pointers. 1978 had electric tachometer with some changes in the instrument pod terminal wiring.

MORE NOTES:

      Some numerals & pointers had different colors, depending on where sold.  Some few had tick lines of different colors.    

Not shown are a few ratios used by the factory & never sold. 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 R75/5 racing. There was a 4.50 ratio (36/8) for competition.

Some speedometers had small differences in W ratio, depending on Country; and what accuracy was specified by that Country.



The BMW /2 and pre-/2 series had a very different set of rear drive gear ratios from the Airheads (although the 2.909, 32/11 was also used on the pre-/2 version of the R60). Some were specifically for sidecar use. Here, /2 can mean earlier than the /5 models, even though these may not be true /2.   The below chart is all I have at the moment.

25/8       3.13

 

This was standard on the R69S.

35/11   3.181

 

This was standard on the R50/2; in some places.  Also the R50 pre/2.

27/8     3.375

 

Also used on the R50/2; usually found on motorcycles with US forks and 3.50-18 tire.

32/9     3.556

W=0.95 for Kph; 1.52 for Mph, could be error.

R67 to R67/3

25/7     3.571

 

Used on the R50S, 1960 to 1962

27/7     3.857

 

Sidecar use, 1956 to 1967; R60/2

35/9     3.889

W=0.95 for Kph; 1.52 for Mph, could be error

R51/2; R51/3; R68

25/6     4.167 

 

R26 and R27

26/6     4.33

 

Sidecar use 1960-1969; R50/5 and R69S, using 3.50-18 tire.

35/8     4.375

W=1.1 for Kph; 1.76 for Mph

R67 and R67/2 with sidecar

     
27/6       4.50   R25/2; R27

32/7     4.571

W=1.15 for Kph; 0.84 for Mph

R51/2; R51/3; R67/3 with sidecar, R68

24/5     4.800 R25/3 with sidecar

36/7      5.14

R25/2 with sidecar
 

26/5      5.20

 

Optional ratio for R26 and R27 

 

 



The /2 era motorcycles had two different 4 speed transmission gear sets available, one was specifically for sidecar rigs.
The sidecar transmission was often shipped with sidecar rigs from the factory, but, according to what I THINK I found out, that was not always done.

Gear Standard Ratio Sidecar transmission Ratio Comments
1st 4.17 5.33  
2nd 2.73 3.02  
3rd 1.94 2.04  
4th 1.54 1.54  
  4200 RPM, 4th, 104 Kph, 66 Mph, 8/25 rear ratio R60/2 Sidecars usually had 7/27 rear drive  
  4200 RPM, 3rd, 84 Kph, 52 Mph, 8/25 rear ratio
 
   

 

Here is an on-line calculator for various tires.  It works for motorcycle and cars and truck tires.  You may find it useful someday:
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 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.
10/21/2016:  Metas, scripts, layout, clarity of 2 explanations.
01/21/2017:  Expand on needle and markings colors for instruments.
04/10/2018:  Revise article; reducing excessive html, colors, fonts.  Clean up layout. Add 10pxl margins. Improve some explanations.
05/02/2018:  Begin major revision.  Add extensively more W values and improve W description. Add more /2 and pre-/2 era rear drive ratios.  Add transmission ratios charts and information on changes with sidecar rigs from the factory.  Add pre-/5 information on the two 4 speed transmission ratio setsl  Reduce HTML, fonts and colors changes, but improve emphasis a/r.  Fix T-A-L link.

Copyright 2018, R. Fleischer

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Last check/edit: Sunday, October 21, 2018