Equation for Displacement

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Dirgle

Conjurer of Boost
Mar 30, 2005
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You affect displacement with Bore, Stroke and Number of Cylinders.

Bore is affected by the size of the piston, and Stroke is affected by the radius of the crankshaft, and well, I’m sure you understand the number of cylinders.

Contrary to popular belief changing the length of the rod, or height of the deck, does not affect any of these three, bore, stroke or cylinder count. All the rod does is connect one, (piston) to the other(crank), that is it.

The equation is:
Total Engine Displacement (cc) = (.0031416 / 4) x Bore x Bore x Stroke (mm) x Number of Cylinders

The measurement used on bore and stroke is millimeters (mm)

1JZ
Bore = 86 mm
Stroke = 71.5 mm

(.0031416 / 4) * 86 *86 * 71.5 * 6 = 2491.98 cc

2JZ
Bore = 86 mm
Stroke = 86 mm

(.0031416 / 4) * 86 *86 * 86 * 6 = 2997.35 cc

7M
Bore = 83 mm
Stroke = 91 mm

(.0031416 / 4) * 83 *83 * 91 * 6 = 2954.19 cc

Now there has been much debate on what exactly changes the displacement between the 2JZ(3.0 liters) and the 1JZ(2.5 liters) some believe it’s the rods and that the cranks are identical, the equation proves this is not possible.

Since Bore is the same (2JZ=86, 1JZ=86) this indicates that the circumference of each piston is identical, and cannot change the displacement. The number of pistons for each is 6 so this cannot change the displacement. This leaves ONLY stroke, And as was discussed earlier the ONLY thing that can affect stroke is radius of the crankshaft. This is a physical constant. It will never change over time by math or magic, science or sorcery. Because the stroke is different the crankshafts MUST therefore be different. This is a mathematical absolute, so ordered by the laws of physics. And they are different, 7.25mm different to be exact. The 2JZ crankshaft is 7.25mm longer, from main bearing journal centerline to crank throw centerline, than the 1JZ crankshaft. They may be identical in the crank throw degreeing and counterweight placement, but they are different in the radius.

This is an absolute FACT, mathematically proven and sound. The cranks are different.(period)

P.S. IJ reminded me in an earlier thread about listing the number of cylinders also changing displacement, I had forgoten to list it with the things that cahnge displacement but it was still in the equation. I had spaced it out in my earlier post because it was so obvious that I over looked it, so thanks IJ.
 

figgie

Supramania Contributor
Mar 30, 2005
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Curious

why did you use the calculations you did (and most websites use) instead of doing the basic calculation of volume of a cylinder? (pi*(r^2)*h) multiplied by number of cylinder?
 

Dirgle

Conjurer of Boost
Mar 30, 2005
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I thought about using that one, but after digging around a little I actually found web sites using various versions of the one I stated above. So I took it and modified it a little for ease of use. I chose that equation format because the numbers are easy to find, plug in and calculate it. Most people already know the numbers to use this equation right off the top of there heads.
 

Dirgle

Conjurer of Boost
Mar 30, 2005
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(pi*(r^2)*h) multiplied by number of cylinders

To do this equation we need to change our unit of measure from Millimeters to Centimeters since we want to end up with Cubic Centimeters (CC's)

7M
Bore = 83 mm -> 8.3 cm
Stroke = 91 mm -> 9.1 cm

Easy enough

Now the equation
(pi*(r^2)*h) * y

pi = 3.1416
r = 4.15 (radius of the bore, 8.3cm is the diameter, so divide that in half to get the radius 4.15cm)
h = 9.1 (height or stroke length, simple , it’s 9.1 cm)
y = 6 (number of cylinders)

Let's plug them in: (for simplicity I'm going to round everything to the nearest ten thousandths)

Start here:
(3.1416*(4.15^2)*9.1) * 6

Step 1: 4.15^2 =17.2225

(3.1416*(17.2225)*9.1) * 6

Step 2: 3.1416 * 17.2225 = 54.1061

((54.1061) * 9.1 ) * 6

Step 3: 54.1061 * 9.1 = 492.3655

(492.3655) * 6

Step 4: 492.3655 * 6 = 2954.193

7M = 2954.193 cc

So there you have it, that's how the equation works, I think my version is a little simpler, but you can get there with this one.
 

Orion ZyGarian

Jeff Lange wannabe
Apr 2, 2005
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www.suprastore.com
2954.1919394141816870984890115018

Theoretically is the correct displacement from the factory lol

Jeff: actually, I think what I was doing is leaving everything as mm instead of converting to cm by dividing by 10.

An even easier way for the equation is to remember that except for triangular/pyramidal and otherwise crazy prisms/three dimentional shapes like spheres, you just calculate the area of the base and multiply by the height. Since all of this is multiplication, the only "order of operations" to concider is the squaring of the radius.

83mm bore = 8.3 cm, 91mm stroke = 9.1 cm

Area of the base times height times 6 instances

Area of the base of a cylindrical prism is just a circle, Pi R^2. The bore is the diameter, and half of the diameter is the radius, which is 4.15, square of that is 17.2225. Multiply that by ~3.1416926 (using the computer's calculator, I can use the Pi button which is caried out to 31 decimal places for extreme precision) and you get 54.106079476450214049422875668531, multiply that by the 9.1 cm height and you get the number of cubic centimeters per cylinder: 492.36532323569694784974816858362. Since we have 6 cylinders, multiply that by 6 to get your 2954.1919394141816870984890115017 exact displacement in ccs.

So maybe it wasnt as easy as I made it sound, but that way you dont have to get lost and confused in multiple parentheses if you dont like parenthetical documentation. Or my big ass words.
 

thagr81_us

Boost Junkie
Apr 11, 2006
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You use the number .0031416 as pi divided by 1000 due to the unit conversion factor correct? From going to mm^3 to cm^3. So basically a factor of 10, three times correct (10^3)? Just making sure that's where you logic is coming from...
 

Eriol

New Member
Mar 31, 2005
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IJ. said:
Or you could be a lazy bastard like me and click this! ;)

(I try to use a bare minimum of formulas these days if I can help it!)

Hehehe... my university is making me take a ton of math, so the easiest way for me, like Orion, is to simply think of it as (area of each cylinder)*(number of cylinders). :)

Edit for clarification: when I say "area of each cylinder," I mean an imaginary cylinder that corresponds to the movement of the piston -- the "displacement" of the piston.
 
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