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Formulas & Conversion Factors
http://bmwmotorcycletech.info/formulas.htm
72

Copyright, 2013, R. Fleischer



This is not the only place in this website with mathematical formulas & conversion factors.  The most commonly needed ones ARE below!


1. Torque:
       Nm x 0.7376 = ftlbs
       ftlbs x 1.356 = Nm
       Mkp x 7.23 = ftlbs
       inch-ounces = 141.6 x Nm 
       Mkp x 9.81 = Nm

2. cubic inches x 16.39 = cc
    liters x 61.02 = cubic inches
    cubic inches 231 = gallons

    Imperial gallon x 1.2 = U.S. gallon
      See item #12, below.

    mpg x 0.354 = km/l
    km/l x 2.825 = mpg

3. psi x 27.68 = inches of water
    inches of water x 1.868 = mm of mercury
    Kpa x 0.145 = psi
    bars x 14.5 = psi

4. 1 mm = 0.03937 inches
    1 inch = 25.4 mm
     miles x 1.609 = km
     km x 0.62 = miles
    one Km is approximately 5/8th of a mile.

5. (F-32) x .56 = C

6. (C x 1.8) + 32 = F

7. Electricity:
       Resistance in ohms = (voltage by amperes)
       The symbol for ohms is the Greek omega Ω
       Power in watts = amperes x voltage.
       746 watts = one horsepower.

8. Usually interchangeable wrench sizes:
       11 mm and 7/16 inch
       13 mm and 1/2 inch
       16 mm and 5/8 inch
       19 mm and 3/4 inch
       27 mm and 1-1/16 inch

9a.  velocity in mph x 1.467 = feet per second
9b.   kph x 0.621 = mph

10. (horsepower x 5252) by rpm = torque in foot-pounds.

11. MPH = (rpm x rolling radius of the driven tire in inches)   by (168 x the overall gear ratio)

12. Gasoline weighs 6 pounds per U.S. gallon.
      Oil weighs 7.5 pounds per U.S. gallon.
      Kerosene weighs 6.7 pounds per U.S. gallon.
      Water weighs 8.4 pounds per U.S. gallon.

      Miles-per-gallon =  0.354 x km/L
      km/L x 2.825 = Mpg

      U.S. gallon is 3.785 liters; IMPERIAL gallon is 4.546 liters. In both systems 4 quarts are a gallon, but the quarts are  different sized.

      The British beer barrel is 36 gallons, the U.S. beer barrel is 31.5 gallons.

13. Gas velocity through a port in ft/sec =  (piston speed in ft/min by 60)  x   (diameter of piston squared     by the port diameter squared).

14. Mean gas velocity through the valve in ft/sec =    (piston speed divided by 60)   x  [diameter of piston squared], by  (the valve diameter at throat x lift of valve x pi)

15. The formulas to calculate gas flow, resonance, reversion, intake & exhaust diameters, flow & reversion are available from me.

16. Modern internal combustion engines produce APPROXIMATELY 2 horsepower-hours per pound of fuel consumed. If one uses fuel weighing 5.6 pounds per gallon, then you can expect 11.2 horsepower-hours per gallon, which is 8355 watt-hours.

17.  TACH, MPH, RPM, SPEED:
Measure the radius of the tire, bike on tires, not stands, you & any passenger seated on bike, bike pointed straight ahead, balanced straight up, a buddy measuring the CENTER of axle to the floor (double check, by measuring BOTH axles to the floor), multiplied by 2, multiplied by pi, will give the circumference, close enough to the actual in-use number.    A very quick way of getting an accurate pi, is to divide 22 by 7.

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 teeth ratio
Let L = large number in the rear end teeth ratio

Example: you have 37/11 gears (which is 3.36:1 btw).  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  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.

18.  PISTON TRAVEL vs CRANKSHAFT ROTATION IN DEGREES; marking flywheels, etc.:
On a BMW Airhead, you might be presented with a cut-down flywheel, with the markings being 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 diameter & multiply that by pi; or directly measure the 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 as "OT" on the flywheel.  Then each degree from that, advanced or retarded, is a known measurable distance 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 simply go to 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, 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:   http://bmwmotorcycletech.info/F,OT,S,Z.htm
 
Things are very different when you need to KNOW/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, what you need to do 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 simplified 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 just below, but...HERE....is the SIMPLIFIED but adequate method:   
Take the manufacturer's published stroke, multiply by the cosine of the number of degrees, to equal the piston stroke distance.  You can use your calculator, or a table of cosine functions. It is easy to transform the results into markings on the flywheel.   This is also used for determining ignition timing.

The ACTUAL accurate-enough calculation is more complex:
    v=(1-cos(a))*r+(r*sin(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 place 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 larger 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".

19.  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 really 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 particular oils, see:
http://bmwmotorcycletech.info/viscosity.htm

20.  
How to find the approximate belt length

1. Add the large and small pulley diameters together.  10 + 2 = 12
2. Multiply the total amount by 1.6.  (Half of 3.14 (pi) of the sum of the two pulleys).  12 x 1.6 = 19.2
3.  Add twice the distance between the two shafts.  24 x 2 = 48    ;   48 + 19.2 = 67.2
The total will be the approximate belt length.  67" belt




Revisions:
04/11/2003:  add .htm title; edit a few places for clarity and renumber some items/splitting them first.
04/29/2003:  expand #2; remove note in blue at top; clarify minor details throughout
05/07/2003:  add #19
09/27/2003:  add a few conversions
12/23/2006:  add #20 
12/24/2006:  add #21
01/27/2008:  merge #6 into #20, and edit same
04/26/2010:  remove a link
05/31/2022:  clean up
09/28/2012:  Add QR code; add language button; update Google Ad-sense code; clean up article again; re-arrange a few things.
10/09/2012:  Put my more complex calculations information on stroke/piston/degrees back into the article as requested by someone.
2013:  Remove troublesome language button script
02/24/2016:  Increase font size; update meta-codes, clean-up.
06/24/2016:  Update metacodes, scripts, layout, final cleanup.

05/03/2017:  add 20.
                   

Copyright, 2013, R. Fleischer

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Last check/edit: Wednesday, May 03, 2017