Snowbum's BMW Motorcycle Repair & Information Website

Let T = the tach reading
Let M = miles per hour
Let C = circumference in INCHES
Let S = small number in the rear end teeth ratio
Let L = large number in the rear end teeth 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 the formula to find any of the values, like you learned in  school in algebra 101.

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 (disregarding slippage, etc).

17.  PISTON TRAVEL vs CRANKSHAFT ROTATION IN DEGREES; MARKING FLYWHEELS, etc.:

On a BMW Airhead, you might be presented with a cut-down flywheel, with one or more markings gone.  It is easy to calculate for the needed markings, no need for piston travel versus crankshaft movement & cosine calculations.   You simply measure the exact flywheel diameter (where the marks will go) & multiply that by 22 divided by 7; or directly measure the measuring surface circumference of the flywheel.   Each degree of crankshaft/flywheel is 1/360th of the total circumference.  All you need to do is find Top Dead Center very precisely (perhaps the OT mark is still intact??), a rather easy job with a piston stop & degree wheel; then mark TDC on the flywheel.  (BMW uses OT).  Then each degree from that, advanced or retarded, is a known measurable distance (degrees) on the circumference.  You can mark the flywheel for such as Z or F and S; or, for whatever you need.    If you are doing camshaft measurements, you start with OT, use a degree wheel mounted at the crankshaft (perhaps onto the bolt holding the rotor in) ....but you need a dial indicator at the valve stem, and the valve is at the cam manufacturer's specified lift.  BMW uses 2 mm.  This website has a how-to -article, step-by-step, on using a degree wheel for basics:   https://bmwmotorcycletech.info/F,OT,S,Z.htm

Things are very different when you need to know or use the distance a piston is lowered from TDC, in degrees of crankshaft movement.  Perhaps you want to set the piston downwards a certain amount, and this can be in degrees of crankshaft movement; or, the typical and more complex problem, you need to set the piston down a certain amount but can't have a dial indicator work properly through the spark plug hole ....etc.

Movement of crankshaft versus piston movement is not a straight-line function.

Nearly all the time, the job is set the ignition timing, perhaps on a bike that has no timing marks that are or can be used with a stroboscopic light.    This happens on a classic K-bike, and also on many two-stroke engines, & some other engines.    Perhaps the specification for ignition timing function is based on degrees of crankshaft movement; or, usually, piston movement, typically inwards from top dead center.   You may need to know how to do the calculations.  The following information is normally used for 2 stroke engine timing purposes, but has some uses on other engines.

When measuring piston movement per degree of crankshaft rotation, the distance the piston moves is a cosine function ...I will show the actual formula below.
...but, first, here, is the simplified ...but usually adequate method:
Using the manufacturer's published stroke, multiply by the cosine of the number of degrees, to equal the piston stroke distance.  You can use your scientific function calculator, or a table of cosine functions. It is easy to transform the results into markings on the flywheel.   This can also be used for determining ignition timing.

The actual accurate-enough calculation is more complex:
    v=(1-cos(a))*r+(r*sin²(a))/(4*K)

In the above formula:
v = piston travel in mm
a = degrees of crankshaft rotation
r = half stroke in mm
K = L/(2*r); which is generally about 2
L = conrod length, meaning the distance between axes; this is in mm

I previously published the actually even more complex super-precise trigonometry & confused the heck out of some folks even more!

So, here is a website page with a bit of Javascript to get "accurate enough" information, by simply plugging information into a table; which will then do the calculating for you: http://www.dansmc.com/mc_software2.htm

NOTE:
BMW's larger Airhead engines have a 70.6 mm stroke, which is 2.78".
9° is 0.9877; or ~8.889 mm.
BMW R45 & R65, only, have a shorter stroke, of 61.5 mm, which is 2.42".

18.  Oil viscosity is often given in cST or SUS; seldom are both given for the same product.  Here is how to convert one to the other. The conversion formula varies, depending on the rated SUS value.   Other, less accurate formulas exist, & are usually plenty good enough.  Below is the quite accurate method:

SUS between 32 and 99; use this formula:  Cst = 0.2253 x SUS - (194.4 ÷ SUS)
SUS between 100 and 240; use this formula:  Cst = 0.2193 x SUS – (134.6 ÷ SUS)
SUS greater than 240; use this formula:   Cst = SUS ÷ 4.635

For very considerably more on oil see my oil articles, and regarding viscosities of specific brands and versions of oils, see: https://bmwmotorcycletech.info/viscosity.htm