When you’re building an engine, it’s nice to be armed with the facts necessary to do it successfully. Much of engine building is about math – machining dimensions, compression and rod ratios, bore sizes, stroke, journal diameters, carburetors, port sizes, dynamic balancing, and all the rest of it. Without math, you cannot successfully build an engine. What follows are quick facts that will help you in your Ford engine building.
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CUBIC INCH DISPLACEMENT
Cubic inch displacement is simply the volume displaced by the cylinders of your engine. So, if we calculate the volume of one cylinder, and multiply that figure times the number of cylinders, we have the engine’s displacement.
The formula for a cylinder’s volume is:
Pi x r2 x S = Volume of one cylinder
Where Pi is a mathematical constant equal to 3.14159; r is the radius of the cylinder, and S is the stroke. If you think back to your high school geometry, you’ll remember that a circle’s radius is half the diameter. In this case, the diameter is equal to the bore (B), so 1/2B = r. Plug that in, and our formula becomes:
Pi x (1/2B)2 x S = Volume of One Cylinder
We can simplify this further by plugging in the numerical value for Pi, then doing some basic algebra that doesn‘t necessarily need to be covered here – but trust us: the equation before is equal to this equation:
B x B x S x 0.7854 = Volume of One Cylinder
To determine the engine’s displacement, factor in the number of cylinders (N):
B x B x S x 0.7854 x N = Engine displacement
So, let’s use this to figure out the displacement of a Ford engine that has a 4-inch Bore and a 3-inch Stroke:
4.000” x 4.000” x 3.00” x 0.7854 x 8 = 301.59 ci
Ford rounded 301.59 up to 302 ci, or 5.0L. (Note: One liter is equal to about 61 cubic inches.)
CALCULATING COMPRESSION RATIO
An engine’s compression ratio is the ratio between two volumes: The volume of the cylinder and combustion chamber when the piston is at BDC, and the volume of the combustion chamber when the piston is at TDC. But there’s more to consider than just cylinder volume and head cc’s. To get the engine’s TRUE compression ratio, you need to know these volumes:
- Combustion Chamber Volume ©
- Compressed Head Gasket Volume (G)
- Piston/Deck height (D)
- Piston Dish Volume (P) or Dome Volume (-P)
- Cylinder Volume (V)
When the piston is at BDC, the total volume is all of these volumes added together. When the piston is at TDC, the total volume is all of these EXCEPT the Cylinder Volume (V). So … true compression ratio is this:
V + D + G + C + P / D + G + C + P
Combustion chamber volumes for stock heads and aftermarket heads are typically available from the manufacturer. If you cant find the info or if you’ve modified the combustion chambers, you’ll have to measure the volumes (using a plastic deck plate, burettes, and a graduated cylinder) or have your local machine shop do it for you.
Converting cc’s to ci’s
Combustion chamber volume,dome volume, and dish volume are generally measured in cc’s, not cubic inches. To convert cc’s to cubic inches, divide the measurement in cc’s by 16.4.
Compressed Head Gasket Volume
Compressed head gasket volume is simply the volume of the cylinder hole in the head gasket – think of it as a very shallow cylinder. So, its volume is computed the same way you compute cylinder volume:
B x B x Gasket Thickness x 0.7854 = Compressed Head Gasket Volume
In this case, the gasket’s compressed thickness is .038 inches, so …
4.000” x 4.000”x .038” x 0.7854 = 0.4775232ci
Piston/Deck Height Volume
Piston/Deck height volume is the small volume at the top of the cylinder that is not swept by the piston. Measure piston/deck height with a dial indicator. Bring the piston to top dead center (TDC) and measure the distance from the top of the piston to the deck of the block. This is normally somewhere between .008 and .025-inch. If the block deck has been machined, say .010-inch, then deck height will be smaller.
Once again, this volume is a shallow cylinder. Compute its volume by plugging the piston/deck height measurement (D) into the cylinder volume formula:
B x B x D x 0.7854 = Piston/Deck Height Volume
In our example, this measurement was .015 in, so we plug in that value to compute piston/deck height volume in cubic inches.
4.000” x 4.000” x .015” x 0.7854 = 0.188496ci
Piston Dome/Dish Volume
The last bit of information we need is the volume of the piston dome or dish (dish includes valve reliefs, too). Because the dishes or domes are irregularly shaped, it’s necessary to either measure the volume using burettes and graduated cylinders, or you can usually get the measurement from the piston manufacturer. If the piston is domed, the dome reduces the amount of volume in the combustion chamber, so its volume is subtracted. If the piston is dished, the dish increases the volume of the combustion chamber, so its volume is added. In this example, our 302 has flat-top pistons with valve reliefs that measure 2cc in volume. That 2cc increases the cylinder volume, so we give it a positive value. If the pistons were domed, the dome would reduce the cylinder volume, so we’d give it a negative value. Either way, the volume has to be converted from cc’s to ci’s:
This diagram shows all the volumes you need to know to calculate an engine’s true compression ratio: Cylinder volume (V), piston dome (-P) or dish volume (P), piston/deck height (D), compressed gasket volume (G), and the combustion chamber volume (C). The compression ratio is the volume of the piston and combustion chamber (V + P + D + G +C) when the piston is at bottom dead center, compared to the volume of the combustion chamber (P + D + G +C) when the piston as at top dead center.
cc / 16.4 = ci 2cc / 16.4 = 0.121951ci
This Tech Tip is From the Full Book, HOW TO BUILD BIG-INCH FORD SMALL BLOCKS. For a comprehensive guide on this entire subject you can visit this link:
LEARN MORE ABOUT THIS BOOK HERE
SHARE THIS ARTICLE: Please feel free to share this article on Facebook, in Forums, or with any Clubs you participate in. You can copy and paste this link to share: https://www.diyford.com/big-inch-ford-small-block-engine-math-reference-guide/
So, let’s check the true compression ratio for that 302ci engine, assuming it has a combustion chamber volume of 63cc, a compressed head gasket thickness of .038-inch, and a piston/deck height of .015-inch. Here’s what we’ve figured out so far:
V = Cylinder Volume: 37.6992ci (calculated)
C = Combustion Chamber Volume: 63cc (3.8414634ci) (measured)
G = Compressed Head Gasket Volume: 0.4775232ci (calculated)
P = Piston Dish Volume: 0.121951ci (measured)
D = Piston/Deck Height Volume: 0.188496ci (calculated)
Now (finally!) we’re ready to calculate our true compression ratio, using the formula we developed earlier:
V + D + G + C + P / D + G + C + P
Plug in the values (all in ci):
37.6992 + 0.188496 + 0.4775232 + 3.8414634 + 0.121951 / 0.188496 + 0.4775232 + 3.8414634 + 0.121951
42.328634 / 4.629434
That gives us a true compression ratio, for this engine, of 9.1:1.
CHOOSING THE RIGHT CARBURETOR
Seems a lot of folks specify a larger carburetor than they actually need. Here’s an easy formula that will put you on target every time, as long as you’re honest with yourself about where your engine’s going to operate. We want to look at cubic inches and the best volumetric efficiency (VE). With street engines, volumetric efficiency is typically around 75 to 80%. Boost the performance and VE goes up to 80 to 95%. The best indicator of engine performance is an engine dynamometer. This formula will calculate the required carb size for your engine:
VE (Volumetric Efficiency) x CI x Max RPMs / 3456
For example, we’ve built a 460 that performing strong on the dyno. The dyno figures tell us 85% VE. On the street, we figure the max RPM this engine will see is 5,500 rpm. So, if we plug in the numbers, we get:
0.85 x 460 x 5,500 / 3456
Do the math, and we end up with 622.25115. In this case, we’d opt for a 650cfm carb.
CALCULATING HORSEPOWER AND TORQUE
Horsepower and torque are words we hear a lot in the automotive realm. Which do you believe is more significant to power output? It may surprise you to learn that torque is the more significant number. Did you know horsepower and torque are the same at 5,252 rpm on any engine? That’s because Horsepower is derived from torque. Here’s a good formula to remember:
Horsepower = RPM x Torque / 5,252rpm
If you do a little cross-multiplying, you can also rearrange this equation to compute torque from horsepower:
Torque = 5,252rpm x Horsepower / RPM
HORSEPOWER AT THE DRAGS
Approximate horsepower and torque can be determined with a simple quarter-mile pass at the drag strip. Begin by weighing your vehicle – you can find scales at a farm coop (anyplace that sells grain or feed by the truckload) or truck weigh station along the interstate. Then make several quarter mile passes and calculate an average top mph. Then make the following calculation:
Horsepower = Weight x 0.4 x 1/4-mile MPH / 282
Assume your car weighs 3,000 pounds, and your average quarter-mile time was 100mph. Plug in the numbers and we get …
3,000 lbs x 0.4 x 100 MPH = 425.53191 HP / 282
If you know what RPM your engine was turning as you went through the traps, you can also figure out the torque your engine generates. If we went through the traps at 6,000 rpm, we can calculate torque is determined by doing the following formula:
5,252 x 425 HP = 372 ft-lbs. of torque / 6000 RPM
Save yourself the cost of a dyno and do the calculations yourself. Remember, these calculations are approximate.
Written by George Reid and Posted with Permission of CarTechBooks
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