Engine displacement is the most common math calculation. Displacement is the size or volumetric capacity of an engine expressed in cubic inches, cubic centimeters, or liters. Here in America we typically work in cubic inches while the rest of the world uses the metric system. I discuss appropriate conversions later in this chapter. Displacement is determined by a calculation involving the bore diameter and the stroke length times the number of cylinders. The result is the actual swept volume of each cylinder and the total swept volume of the engine assuming 100 percent volumetric efficiency. Please note here that the actual swept volume is not the total volume of each cylinder since it does not include the volume of the combustion space above the piston at top dead center (TDC). These separate volumes allow you to calculate the engine’s compression ratio (described in Chapter 3.)
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Cylinder Bore Diameter
Cylinder bore diameter is a primary component of the engine displacement formula. Without a convenient comparison, any cylinder bore seems substantial to the eye, but even small changes in diameter relative to a fixed stroke length will produce an increase in engine displacement. Bore size is a major concern for any competition engine build because it dictates valve size and ultimately the breathing capability of the engine. Many engine builders feel that the breathing gains from a larger bore outweigh any friction penalties that may accrue from larger pistons with more skirt surface and potentially increased ring drag. A bigger bore also provides more piston area for combustion pressure to work against, but it also creates a greater distance for the flame front to travel and more surface area to cool the flame.
Street engines are one thing, but some racing series actually limit the bore size and bore spacing. These are typically cost measures designed to curtail the use of more expensive cylinder blocks with revised bore spacing, allowing larger bores while retaining desirable cylinder wall thickness and stability. Sprint Cup engines are a good example. The displacement is limited to 358 cubic inches with a maximum bore of 4.185 inches. Cup engines previously operated with a bore spacing of 4.400 inches, but NASCAR allowed a bore spacing increase to 4.5 inches to accommodate larger bores, bigger valves, and revised valve geometry—all in attempt to level the playing field among various brand competitors. If the cylinder bore is not specified, you must choose a bore dimension that best suits your particular application as defined by air flow and combustion chamber requirements, compression ratio, flame travel, and other factors, including a stroke length that also accommodates your operational requirements.
Precise bore measurements are taken with a dial bore gauge. Dial bore gauges typically read to an accuracy of ± 0.0005 inch and many are accurate to ± 0.0002 inch. It is no slight to any machinist for a customer to check their work, but it is important to recognize that your instruments may read different. That may be okay as long as your measurements fall within the acceptable tolerance. The best way to ensure the accuracy of any bore measurement is to set the tool according to a known standard prior to taking your bore measurements. If you have a favored machinist, you might also want to take some of your instruments by his shop and compare sample measurements with his tools.
Stroke length is the companion factor in the cylinder displacement formula. Adding stroke length increases displacement relative to a fixed bore size. Stroking, an early hot rodding trick, has found particular favor in many latemodel engine builds seeking to maximize displacement. With the exception of high-performance applications, stroke lengths usually remain fixed with the factory length as it is much easier and more practical to increase the displacement via bore enlargement. And in the case of your typical engine rebuild, the primary concern is to restore cylinder sealing with new oversized pistons and rings. A simple bore-and-hone job is all that’s required. Stroke increases often require block modifications to provide clearance for the rods and rod bolts, and require the purchase of new pistons with the appropriate pin location to accommodate the new stroke length. In either case, the displacement formula can be manipulated to calculate displacement or to find the required bore or stroke when the desired displacement and one of the dimensions is known.
To calculate an engine’s displacement you must first find the swept volume of an individual cylinder based on the bore and stroke dimensions. The bore is the diameter of the cylinder and the stroke is the distance that the piston travels up and down in the cylinder. (Stroke is actually a function of the length of the crankshaft throw, but it is commonly referenced by the travel of the piston top.)
In almost every case you will already know the size of the engine and the bore and stroke dimensions, but calculating engine displacement with precision allows you to determine the amount of “rounding” the factory has applied to the stated displacement. Sometimes they round up; sometimes they round down. In practice, a more useful reason is the ability to brainstorm various engine configurations to suit a particular racing class that specifies a displacement limit, or to calculate the displacement effect of over-boring on an engine rebuild.
Many racing applications find it beneficial to use the largest bore possible in order to gain more piston surface area and unshroud the valves to promote more efficient breathing. For example, a 4.125–inch bore typically promotes better breathing than a 4.00–inch bore because it provides a more efficient flow path for the intake charge. If you are displacement limited, you can use a variant of the displacement formula to calculate the appropriate stroke required by your bore selection or vice versa. More about this later.
To find total displacement, begin by calculating the volume of a single cylinder and then multiply the result by the number of cylinders in the engine. The formula for the volume of a cylinder requires the use of pi, a mathematical constant (see sidebar “How the Displacement Formula Works” on page 15) that allows the calculation of the area (or volumetric difference) between a square (or a box) and a circle (or a cylinder). Pi divided by 4 gives you another constant to complete the basic displacement formula as follows:
Pi (π) = 3.1415927
Cylinder Volume = pi ÷ 4 x bore2 x stroke
Pi ÷ 4 = 0.7853982 (commonly rounded to 0.7854)
Hence, 0.7854 becomes the constant that helps us calculate cylinder volume.
The formula for displacement is: Bore2 x stroke 0.7854 x number of cylinders
Let’s work an example: If a 327 Chevy engine has a published bore of 4.00 inches and a 3.25-inch stroke, the calculation becomes:
4.002 x 3.25 x 0.7854 x 8 = 326.726 ci
While infrequent, sometimes you will find that an engine’s dimensions are listed with a common fraction. In the case of our Chevy example, it is often referred to as having a three-and-a-quarter-inch (31⁄4) arm or crank. Since engine math works in decimal notation, you need to convert that fraction to a decimal. The following chart shows the most common examples.
1/32 . . . . . . . . . . . .0.031
1/16 . . . . . . . . . . . .0.0625
1/8 . . . . . . . . . . . . .0.125
1/4 . . . . . . . . . . . . .0.250
3/8 . . . . . . . . . . . . .0.375
1/2 . . . . . . . . . . . . .0.500
5/8 . . . . . . . . . . . . .0.625
3/4 . . . . . . . . . . . . .0.750
7/8 . . . . . . . . . . . . .0.875
1 . . . . . . . . . . . . . . .1.000
For our 327 Chevy with a 31⁄4-inch crank we note that 1/4 inch equals 0.25 inch, so the stroke in decimal notation is 3.25 inch; hence the following calculation:
4.002 x 3.25 x 0.7854 x 8 = 326.726 ci
In this case Chevrolet rounded up to 327 ci because the decimal is more than 326.5, or closer to 327 than 326. Manufacturers don’t always follow this practice. They sometimes round in the opposite direction even if the decimal doesn’t require it. This is frequently done to differentiate among engine families or newer models.
Calculating Overbore Displacement
Suppose we decide to overhaul our 327 Chevy. An examination reveals excessive cylinder wear and a noticeable ridge at the top of each bore above the area of piston ring travel. We decide to install new pistons that are 0.030-inch oversize. What will the displacement be on our newly rebuilt 327-ci engine? This is easy to calculate by plugging the new bore value (a variable) into the standard displacement formula:
4.0302 x 3.25 x 0.7854 x 8 = 331.645 ci
While this would normally round up to 332 ci, for some unknown reason this particular overbore is commonly called a 331 on a Chevy small-block. Strangely, substituting for a 0.060-inch overbore yields 336.601 ci, which is commonly called a 337. Go figure.
Calculating Bore and Stroke Relationships
The next two formulas are most useful for brainstorming engine combinations that have a displacement limit. Why is this important? Most often, it allows you to calculate a stroke length to suit a desirable bore size for a fixed displacement set by a racing sanctioning body. This is critical to keeping your engine size within the maximum allowable displacement.
The NHRA for example, always rounds up to the next largest number, so anything greater than the stated engine size would make your engine illegal. At Bonneville, the SCTA publishes an engine displacement range, which savvy racers push to the limit in each class. A C-class engine, for example, can range from 306.00 to 372.99 ci. They won’t round up to the next inch, but your calculation had better not exceed 372.99 by any margin. Most people shoot for about 1 ci less, just to provide a safety margin. So if you are building a C-class Bonneville engine with a small-block Chevy and you feel that a 4.125-inch bore will breathe better than a 4.00-inch bore, what stroke length will you need to meet the 372.99-ci limit?
Stroke Length when Bore is Known
If you know the bore size and the final displacement you can use them to calculate the stroke length. This is useful for brainstorming bore and stroke combinations where you wish to examine various possibilities for achieving a desired displacement.
Stroke = displacement ÷ (bore2 x 0.7854 x number of cylinders)
Stroke = 372.99 ÷ (4.1252 x 0.7854 x 8) = 3.4887 inches
What this tells you is that you could use a standard 400-ci Chevy bore dimension (4.125-inch) with a standard 350 Chevy (3.48-inch stroke) crankshaft to stay under the limit. A 350 Chevy stroke is 3.48 inches, which computes to 372.055 ci; a little close for comfort, but possible if you maintain your dimensions carefully. This would keep your crankshaft expense in check by using an off-the-shelf crank size.
Let’s say you want to further aid the engine’s breathing and piston area by increasing bore size to 4.155 inches.
Stroke = 372.99 ÷ (4.1552 x 0.7854 x 8) = 3.4385 inches
That’s an odd crank size that requires special grinding. Sure, a crank grinder could make it, but you have to weigh the potential airflow benefit versus the crank grinding cost plus the expense of purchasing pistons with a pin bore height that matches the odd stroke and your desired rod length. In some cases, engine builders use this same calculation to see how much they can shorten the stroke to gain more RPM potential with less piston speed. In either case, the formula for finding stroke allows you to brainstorm ideas on paper before you lay down cold cash for parts.
Bore when Stroke is Known
Some times you have a particular stroke in mind and you want to calculate a bore dimension to suit a given displacement. I recently had occasion to brainstorm some small-displacement Chevy V-8 combinations that had a cubic inch limit of 260.99. My first thought was to use a small-displacement block from a 283 or a 305. I knew the stroke lengths for both of them, but I couldn’t recall the bore diameter of the 305 and I didn’t have a handy reference. Fortunately, I was able to calculate it by using the formula for finding an unknown bore dimension when the stroke is known.
To work the formula, do the math inside the square root symbol first, then enter the result into your calculator and press the square root key to get the answer.
Bore = √[displacement ÷ (0.7854 x stroke x number of cylinders)] In the case of a 305 Chevy, the stroke is 3.48 inches, the same as a 350. By plugging in the known variables, you calculate the unknown bore dimension as follows.
Bore = √ [305 ÷ (0.7854 x 3.48 x 8)] = 3.734 inches bore diameter
305 ÷ (0.7854 x 3.48 x 8) = √13.948 = 3.734
I was then able to use that dimension to calculate a stroke that would yield 260.99 ci. To do this, I went back to the formula for finding stroke.
Stroke = displacement ÷ (0.7854 x bore2 x number of cylinders)
Stroke = 260.99 ÷ (0.7854 x 3.7342 x 8) = 2.979 inches
Neither dimension is convenient. The bore is too small to breathe well and the stroke is an odd number that will have to be specially ground. After further consideration, the logical choice is a 4.00-inch-bore block, which is readily available. It offers the best breathing, and with the stated displacement limit, there is no way around having to get a crank ground to the required stroke dimension. Using the 4.00-inch-bore dimension the stroke requirement computes as follows.
Stroke = 260.99 ÷ (0.7854 x 4.002 x 8) = 2.596 inches
The interesting thing here is the temptation to round off the stroke to 2.600 inches. Let’s see what happens when we plug that into the displacement formula.
Displacement = 4.002 x 2.600 x 0.7854 x 8 = 261.38 ci
Uh-oh! Busted for an oversize engine.
Let’s try the exact stroke figure we calculated previously.
Displacement = 4.002 x 2.596 x 0.7854 x 8 = 260.978 ci
You can’t get much closer to the displacement limit than that, but it’s a little too close. A more comfortable choice would be to shorten the stroke to 2.585, which yields roughly a 1-ci safety margin.
Displacement = 4.002 x 2.585 x 0.7854 x 8 = 259.87 ci
You can see from this exercise how you can use the displacement formula, bore formula, and stroke formula to model theoretical combinations that meet your requirements. Once you settle on a bore and stroke combination that meets your displacement limit with the best possible breathing, piston area, and RPM capabilities, you can move on to selecting the best connecting rod length and piston pin height to match. These handy formulas make it all happen on your calculator and on paper before you spend a dime on parts. And, if you enter the variables into a computer spreadsheet (discussed in Chapter 13), you can save and print all your theoretical combinations for quick review whenever you wish.
Bore/Stroke and Rod/Stroke Ratios
Another thing to consider during your brainstorming sessions is the bore/stroke ratio and the rod/stroke ratio. These ratios tell you several important things. If an engine has the same dimensions for bore and stroke it is said to be square. If the bore is greater than the stroke, the engine is over-square. An under-square engine would have a stroke length greater than its bore dimension. Lowspeed under-square engines are often thought to promote more torque, but in practice, the difference is minimal and can’t compete with the superior breathing of an oversquare combination. While a larger bore may have slightly higher friction properties, it more than overcomes the difference with the improved breathing offered by a larger bore size that permits larger valves and more efficient air/fuel charge entry into the cylinders. The bore/stroke ratio is simply the bore dimension divided by the stroke.
B/S ratio = bore ÷ stroke
For example, a Chevy 350 engine has a standard bore/stroke ratio of 1.15:1,
B/S = 4.00 ÷ 3.48 = 1.15:1
Any number above 1.0:1 is over-square. A larger bore permits larger valves. Consider the following examples based on three different Chevy small-blocks:
Displacement 283 ci 350 ci 400 ci
Bore 3.875 4.000 4.125
Stroke 3.000 3.480 3.750
B/S Ratio 1.29:1 1.15:1 1.1:1
With the highest ratio, the 283 looks okay on paper. It is efficient for its displacement and stroke length, but the small bore restricts valve size. The 350 has a lower B/S ratio, but its bore permits much larger valves than the 283 so breathing is more efficient. The 400 is almost square at 1.1:1, but it is the most desirable from a breathing standpoint because it can accept monster valves without shrouding or restricted breathing. It’s one more thing to consider when you are planning your optimum combination.
Another relationship to consider is the rod/stroke ratio. This is the rod center-to-center length divided by the stroke. A rod/stroke ratio of 1.9 to 2:1 has always been considered beneficial because it reduces the angle of the rod to the cylinder wall, thereby lowering the sideloading on the cylinder wall and the piston skirt. That’s why the short rod (5.565 inches), long stroke (3.75 inches) Chevy 400 small-blocks experienced higher cylinder wear. The rod angularity was too great. A 302-ci Chevy (with its 5.7-inch rod and a 3.00-inch stroke) has a rod/stroke ratio of 1.9:1. Compare that to the Chevy 350 and 400 small blocks shown in the following chart.
R/S Ratio = rod length ÷ stroke
Displacement 302 ci 350 ci 400 ci
Rod Length 5.7 5.7 5.565
Stroke 3.00 3.48 3.75
R/S Ratio 1.9:1 1.64:1 1.48:1
A longer rod and higher rod/stroke ratio is also purported to improve power by “parking” the piston at TDC for a fraction longer than a short rod ratio. This allows more time for peak cylinder pressure to build before the piston starts downward on the expansion cycle. Comparative dyno tests suggest this benefit to be less substantial than theory promises, at least at street engine speeds. However, the durability benefits of improved rod angularity are more apparent. In any case, you may want to compute the bore/stroke ratio and the rod/stroke ratio of any combination you design and consider the implications.
If you are dealing with metric dimensions, you are looking at bore and stroke dimensions measured in millimeters (mm) and engine displacement stated in cubic centimeters (cc) or liters (L). The formula for displacement works the same way, but you divide the result by 1,000 to obtain cubic centimeters.
No conversion is required for the constant (0.7854) because it applies regardless of the unit of measure. To gain a better understanding of it, let’s work the displacement formula for a hot contemporary engine like the 426-hp L99 aluminum small-block in the 2010 Camaro. It has the following dimensions:
Stated Dimensions Calculated Dimensions
L99 Chevy 376 ci, 6.2L 375.129 ci, 6.147L
Bore: 4.06/103.3 mm 103.12 mm
Stroke: 3.622/92 91.998 mm
To convert inches to millimeters, multiply by 25.4 (see Appendix B “Handy Conversion Factors”). This conversion gives an exact number so it is very accurate. To convert from millimeters to inches, multiply by 0.0393701, which does not yield an exact number, but it is close enough.
Let’s work with inches first.
Displacement = 4.062 x 3.622 x 0.7854 x 8 = 375.129 ci
In this case Chevy rounded up to 376 ci. Now let’s convert to millimeters.
Bore = 4.06 x 25.4 = 103.124 mm
Stroke = 3.622 x 25.4 = 91.998 mm
Since converting from inches to millimeters is exact, the figures are dead accurate, but here we’ll round them off because they are rounded in most published accounts. Most often the bore is stated as 103.3 mm and the stroke is quoted at 92 mm.
To simplify our calculations let’s round the numbers by reducing 103.124 mm to 103 mm and increasing the stroke to 92 mm.
Displacementcc = (1032 x 92 x 0.7854 x 8) ÷ 1,000 = 6,132.57 cc
Divide 6132.57 cc by 1,000 to get liters—6.132. So, mathematically the L99 is 6,132 cc or 6.13L (which Chevy rounds up to 6.2L). Note that the cubic centimeters and liters converted from inches are slightly different from those calculated from millimeters.
If your measurements are already in millimeters, you can simplify by converting to centimeters before you work the calculation. This will yield an answer in centimeters without having to divide by 1,000. To convert the bore and stroke dimensions to centimeters, divide each number by 10.
Bore = 103 ÷ 10 = 10.3 cm
Stoke = 92 ÷ 10 = 9.2 cm
Displacement = 10.32 x 9.2 x 0.7854 x 8 = 6,132.57 cc
This is identical to our previous calculation.
If you are brainstorming combinations in metric units, the basic formulas for displacement, bore and stroke still apply. You just have to be careful to keep your units straight and work any conversions properly. (Consult the conversion chart in Appendix B).
You can see that published dimensions do not always match measured dimensions. A tech inspector always goes by the actual measured dimensions in the units called for by the rulebook. If you are dealing with a sanctioning body, always use the units they specify to ensure a legal engine build.
Another convenient conversion to remember is from cubic inches to liters. To convert, divide the cubic inches by 61.024. For our L99 Chevy, the calculated displacement was 375.12/61.024 equaling 6.147 liters (which Chevy rounds up to 6.2L). We already calculated the cubic centimeters at 6,132.57. Dividing by 1,000 yields 6.132L. That is still pretty close to exact, but you can see how rounding and conversion factors can skew the final answer.
There is a formula for calculating equivalent displacement for a non-reciprocating engine such as a Mazda rotary. This helps classify non-reciprocating motors against conventional piston engines.
Equivalent Displacement = SV x 3
SV = the actual swept volume of one single chamber of the rotary engine.
In this case you would substitute the published swept volume since you can’t bore and stroke a rotary engine.
What Is Bore Spacing?
Bore spacing is the distance between the centerlines of adjacent cylinder bores. It helps determines how much you can overbore a cylinder block without weakening the cylinder walls to the point of potential failure. As shown, a small-block Chevy has a bore spacing of 4.400 inches. Note the radius of the adjacent bores in the illustration and you see that there is 0.400-inch between the cylinder bores for cylinder walls and water jacketing. The cylinder walls are typically 0.180- to 0.200-inch thick with very little space for the cooling jacket between them.
The cylinder walls are actually egg shaped in the water jacket and they taper between the bores to accommodate coolant flow. This area is tangent to piston thrust and is not subjected to maximum loading. On large-bore blocks such as the 400 Chevy, adjacent cylinder walls are joined or siamesed with block material to maintain strength.
When you bore a block you are taking one half the over bore measurement out of each side of the cylinder. On a 0.030-inch overbore, you’re only losing 0.015-inch material overall. Most blocks accept up to 0.060-inch overbore without loss of cylinder wall strength, except for GM’s newer LS-series engines. These use an iron sleeve that can only be over-bored 0.010-inch. In practice it doesn’t matter what kind of engine you have. Your machine shop will be very familiar with the safe boring limits of most engines and can even sonically check the cylinders to determine if they are thick enough to accommodate your desired bore dimension and the final application of the engine.
Some engines (like the 305-ci Chevy, for example) are built with thin-wall castings to reduce engine weight. In theory they will never be subjected to high RPM or racing loads, so thicker walls are unnecessary. These blocks should be sonic-checked prior to any substantial overbore.
In contrast, the old 283 Chevy blocks were known for thick cylinder walls that would accept an overbore of 0.125 inch. This yielded a 4.00-inch bore and the well-known 301-ci hot rod engine of the early 1960s. The factory later duplicated this engine with the 302 small-block for the first-generation Z28 Camaro.
Sonic checking is an ultrasonic procedure that provides accurate cylinder-wall-thickness measurements to support bore and stroke calculations. While most factory and, aftermarket race blocks now come with a factory sonic-check sheet, many builders prefer to verify the sheet and in the case of previously bored blocks, it is wise to determine the thickness of the cylinder walls. Most race blocks now provide cylinders with at least 0.250- to 0.300- inch wall thickness and it is important to maintain as much of that as possible. Sonic checking is not a lengthy process and most shops that perform it regularly have their own sheets for recording the numbers. The sonic checker device comes with standards that are used to calibrate the system prior to use. They have a known thickness and are made in a curved shape to simulate the cylinder bores. Some builders break up old blocks and keep curved sections of broken cylinder walls around to use as real-world calibration samples that can be easily measured for comparison.
Once a unit is calibrated, gel is applied to the sensor and the sensor is held firmly against the cylinder wall at specified locations depending on the type of block. Most builders prefer to check the cylinders at four equally spaced locations starting with the primary thrust surface and working their way around the bore 90 degrees at a time about 11⁄2 to 2 inches down from the deck surface. Once these numbers are recorded, they repeat the same process roughly halfway down the bore. Some even record numbers at the bottom of the bore. When the process is completed the builder and/or machinist has an accurate roadmap of the block’s cylinder wall thicknesses.
The primary, or major, thrust side is located opposite to the rotation of the engine. For clockwise rotation, stand in front of the engine and face toward it. The major thrust surface is the left side of each bank of cylinders; it’s toward the passenger side of the block for every cylinder. That’s where you want the thickest readings—typically 0.300 inch or better, but no less than 0.250 inch for racing.
The minor thrust side is the opposite wall, or the right side of all the cylinders as you face the front of the block. If you have counter-clockwise rotation, or, as in some cases, you are building a reverse rotation engine, the major thrust surfaces all shift to the opposite side. Non-thrust surfaces opposite the wrist pin axis in each bore (front and back side of each bore) are typically the thinnest and some builders actually accept walls as thin as 0.100 inch in this area.
Grab your calculator and fill in the blanks for the following engines. Calculate the displacement for the first three, the stroke for the second three, and the bore for the last three. Compare your answers to those shown below.
1. 1962 Chevy
2. 1968 Dodge
3. 1957 Ford
4. 1970 Plymouth;
5. 1966 Pontiac
6. 1951 Ford
7. 1968 Chevy
8. 1964 Ford
9. 1961 Dodge
Bore x Stroke
4.00 x 3.25 = ___________ ci
4.25 x 3.75 = ___________ ci
3.80 x 3.44 = ___________ ci
4.04 x ___________ = 340 ci
4.09 x ___________ = 421 ci
3.19 x ___________ = 239 ci
__________ = x 3.48 = 350 ci
________ = x 3.78 = 427 ci
______ = x 3.75 = 413 ci
Written by John Baechtel and Posted with Permission of CarTechBooks