This is not intended to bust anyone's chops, or to call anyone stupid, or right, or wrong. It's just applied mathematics, "shop math," and it's useful.
This is just to show that anyone can figure out the displacement of an engine; and to show you how easy it is to do it, right here on your computer keyboard. Even if you majored in "smokin' in the boys room," nowum sain?
It came up on another thread about what was the egg-ZACKT displacement of the K-model, specifically the KHK, called "55 cubic inches, or 883 ccs." Is it? Or is it 888ccs? Or, as Harley liked to "round it up" in their publicity, 900ccs?
All you have to remember to do this for any engine, are two things:
1.) "Pi," which is the ratio of the circumference of a circle to its diameter, is the number 3.14159, or rounded, 3.1416. (It's a number that can be calculated out to an infinite number of decimal places, but when NASA scientists were working on their old slide rules in the 1960s to put Project Apollo astronauts down in a specific spot on the moon, 186,000 miles away, they relied on Pi as "3.14159." It was close enuf for them, and for Neil Armstrong and Buzz Aldrin).
I said you have to remember two things. First is that Pi is 3.14159. The second thing is:
2.) The formula for the volume of a cylinder. That's "Pi times r squared, (half the bore times half the bore, times Pi) times the stroke." Of course, you have to know the bore and stroke of the engine, and you have to know the shop math to be able to convert fractions to inch decimals, like "1/4 inch equals 0.25 inches," and "7/16 inch equal 0.4375 inches." (typo, sorry! edited: 03-09-2011 Thanx Paps!) You can Google up any kind of table of equivalents. And to do your calculations, you can even type your numbers right into the Google input line, and it will act like a calculator and give you the mathematical answer. I never knew that until I tried it. You <ctrl c> and <ctrl v> the numbers back into the line as you get them, down on the screen, and you don't even need a pocket calculator! Just leave a space between each number, and use "+," "-," "x," "/" and "=" for the symbols.
Given a specified bore & stroke of 2.75 (2 3/4") x 4.5625 (4 9/16) inches,
the displacement of a "55 cubic inch" KHK is
actually 54.1985634 (rounds to 54.20 c.i.)
How do you figure that out?
First, you need the area of the top of the piston; the "area of a circle" formula is "Pi times r squared." Remember that: "Pi times radius (r) squared." The first calculation is "radius squared." and "radius" is half the bore diameter.
Given the cylinder bore = 2.75
Divide it by two: 2.75 / 2 = 1.375
Half the bore (r) = 1.375" (1 3/8")
Equals the radius = 1.375
"r squared," then, is:
1.375 x 1.375 =
radius squared = 1.890625 (that represents nothing, by the way, it's an "intermediate" number.)
Multiply that by the other known constant, "Pi," which is 3.14159.
So, 1.890625 x "Pi" (3.14159) = 5.93956859
= area of the bore, 5.9395 square inches.
That's how many square inches there are on the top of your piston.
Times the stroke: (Given: 4.5625, or 4 9/16") The surface area of the piston times the length of the stroke, or the "volume of one cylinder" equals:
5.93956859 x 4.5625 = 27.0992817
= volume of one cylinder, (rounds from 27.099 to): 27.1 cubic inches.
Two cylinder engine, so, times two cylinders:
27.10 + 27.10 = 54.20
54.20 = the cubic inch displacement of the engine.
So, what's that in metric, in cc's?
1 liter = 1000 c.c.
1 liter = 61.02 c.i.
1 Cubic Inch = 16.387064 Cubic Centimeters
54.20 divided by 61.02 = 0.888233366
Which (carry the decimal), converts to 888.2833 cc's.
or 16.387064 x 54.2 = = 888.178869 (888.18) cc's. That's the design displacement of the KHK.
You can do it for any engine.