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**Formulas & Conversion Factors**

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© Copyright, 2003, 2017, 2018, R. Fleischer

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

1. Torque (for nuts, bolts, fittings, etc):

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. Volume and mileage:

cubic inches x 16.39 = cc

liters x 61.02 = cubic inches

cubic inches ÷ 231 = gallons

Imperial gallon x 1.2 = U.S. gallon Note: The Imperial gallon is same as UK gallon.

See item #11, below.

mpg x 0.354 = km/l

km/l x 2.825 = mpg

3. Pressure:

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. Distance or length:

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. Temperature:

(F°-32) x .56 = C°

(C° x 1.8) + 32 = F°

6. 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.

7. 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

also see my tools article: https://bmwmotorcycletech.info/tools.htm

8. Velocity:

mph x 1.467 = feet per second

kph x 0.621 = mph

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

10. mph = (rpm x rolling radius of the driven tire in inches) ÷ (168 x the overall gear ratio)

11. Weights/quantities:

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.

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.

Kilometers per liter x 2.825 = mpg

Miles-per-gallon = 0.354 x km/L

12. 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).

13. 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)

14. The formulas to calculate gas flow, resonance, 1st order reversion, intake & exhaust diameters, and flow & reversion, are all available from me.

15. Modern internal combustion engines produce ~ 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.

16. 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 the 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. Which axle to use depends on which wheel is actually driving the speedometer. If the engine is not that wheel, then do separate calculations for each wheel.

The formula for determining the relationships, suitably simplified for rear wheel drive, 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). 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

19. How to find the approximate belt length needed:

1. Add the large and small pulley diameters together. Example: 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.

20. Nothing here yet

Revisions:

11/10/2017: All prior revisions since 04/11/2003 incorporated this date; plus, go through entire article, greatly reduce excessive HTML, excessive fonts, colors, etc. Improve clarity on a few items. Check that links work.

11/19/2018, and then later on same date, corrected: In 2. on the Imperial gallon, add note that an Imperial gallon __is not__ the same as the U.S. gallon, and, the reference is to #11, not #12.

**© Copyright 2018, R. Fleischer**

Last check/edit: Monday, July 22, 2019