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Thread: Calculating Engine Displacement

  1. #1

    Calculating Engine Displacement

    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.
    Last edited by Sarge; 03-09-2011 at 11:30 AM. Reason: grameur/ went back over the numbers today and cleaned them up
    Sarge, Gerry Lyons, Fla.
    AGENT ORRNGE Survivor. So far.
    The Friendly Fire that Keeps on Burnin'.
    F.O.G. member:
    "It's a 1937, and the downside is, it's out of warranty"

  2. #2
    Join Date
    Nov 2007
    Puget Sound, America

    Re: Calculating Engine Displacement

    You bored, Sarge?
    52 HydraGlide
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  3. #3

    Re: Calculating Engine Displacement

    How about Laplace transforms or logarithmic decrement Good God you all

  4. Re: Calculating Engine Displacement

    Or you can use the little displacement calculating wheel, mine also does gear ratios- it's kinda like a round sliderule

    2000 Indian Chief
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  5. #5

    Re: Calculating Engine Displacement

    I guess I thought someone would benefit from knowing "the way" and how simple it really is to figure out your displacement if you were just reminded of the rules.
    So many Americans raised today on Nintendo and American Idol don't have a clue of how to work "Pi times r squared," if they could remember it, especially that the first step is to square the radius; half the bore diameter, before getting into the first part. "It's too complicated!"
    Everyone wants to use a shortcut today. (edit.). Ich gibt!
    Last edited by Sarge; 11-17-2009 at 06:47 AM.
    Sarge, Gerry Lyons, Fla.
    AGENT ORRNGE Survivor. So far.
    The Friendly Fire that Keeps on Burnin'.
    F.O.G. member:
    "It's a 1937, and the downside is, it's out of warranty"

  6. Re: Calculating Engine Displacement

    That's nice information. Nice thread and posts too..
    Thanks for sharing with us.
    Stay Connected.

  7. #7

    Re: Calculating Engine Displacement

    Must have snowed in sunny fla!

  8. Re: Calculating Engine Displacement

    Thanks for the info Sarge. A lot of us "old timers" have been doing it that way for a long time and I agree with you that a lot of people look for short cuts. Also some people think that if they bore the cyls. .020 they have increased the ci by a significant amount. I've heard comments like,it was a xx ci but I bored it .020 so its a lot bigger now. Do the math.

  9. #9

    Re: Calculating Engine Displacement

    7/16" is .4375" Sarge.

  10. #10

    Re: Calculating Engine Displacement

    Thanks, Paps. I went back over it and I saw the typo you pointed out. Luckliy, it was just a decimal number that I threw out there, but 7/16" is decimal 0.4375. Thanx for pointing that out.
    That's a pleasant surprise, kinda, when you realize that new people are reading through our threads as old as this one and still deriving benefit from them; something which we only hear about when they reopen one with a new post, as was done here.

    Buzz's forum here is a knowledge gold mine, a regular encyclopedia of the subject of old American motorcycles, in many ways, thanks to many, many people including yourself, Paul.
    Sarge, Gerry Lyons, Fla.
    AGENT ORRNGE Survivor. So far.
    The Friendly Fire that Keeps on Burnin'.
    F.O.G. member:
    "It's a 1937, and the downside is, it's out of warranty"

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