Ford Small-Block Rebuild: Engine Math

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’svolumeis:

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 may 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 4.9L. (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 (C)
• 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

 

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 cylinder 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 is at top dead center.

 

Combustion Chamber Volume

Combustion chamber volumes for stock heads and aftermarket heads are typically available from the manufacturer. If you can’t 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 to ci

Combustion chamber volume, dome volume, and dish volume are generally measured in cc, not cubic inches. To convert cc to cubic inches, divide the measurement in cc by 16.4.

cc/16.4 = ci

 

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 = 0.4775232 ci

 

 

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 inch, 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 = 0.188496 ci

 

 

 

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 combustionchamber, so its volume is added. In this example, our 302 has flat-top pistons with valve reliefs that measure 2 cc in volume. That 2 cc 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:

cc / 16.4 = ci 2 cc / 16.4 = .121951 ci

 

So, let’s check the true compression ratio for that 302-ci engine, assuming it has a combustion chamber volume of 63 cc, 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: 37.6992 ci (calculated)

C=Combustion Chamber Volume: 63

cc (3.8414634 ci) (measured)

G=Compressed Head Gasket

Volume: 0.4775232 ci (calculated)

P=Piston Dome Volume: .121951 ci

(measured)

D=Piston/Deck Height Volume:

0.188496 ci (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:

37.6992 ci + 0.188496 ci + 0.4775232 ci + 3.8414634 ci + .121951 ci

0.188496 ci + 0.4775232 ci + 3.8414634 ci + .121951 ci

 

42.328634

4.629434

That gives us a true compression ratio, for this engine, of 9.1:1.

 

Choosing the Right  Carburetor Size

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 percent. Boost the performance and VE goes up to 80 to 95 percent. 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 302 that’s performing strong on the dyno. The dyno figures tell us 85 percent 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:

.85 x 302 x 6,000

3456

 

Do the math, and we end up with 445.66 cfm. As you can see, there are probably a lot of engines running around with too much carburetor.

 

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

                           5,252 rpm

If you do a little cross-multiplying, you can also rearrange this equation to compute torque from horsepower:

Torque = 5,252 rpm x Horsepower

RPM

 

Estimating Horsepower at the Drags

Your car’s 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 co-op (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 100 mph. Plug in the numbers and we get . . .

3000 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 by doing the following formula:

5,252 x 425 Hp    = 372 ft-lbs. of torque

6000 rpm

These calculations are approximate, but close enough to make a good guess at your engine’s output.

Written by George Reid and Republished with Permission of CarTech Inc