Equation for calculating static compression ratio and breakdown of the volumes involved in total chamber volume.
Compression Ratio: The Big Squeeze
One of the major design parameters to decide on when building any engine is the static compression ratio. The appropriate compression must be designed into the engine early in the planning stages, and numerous factors will affect it. These include desired fuel octane, type and amount of power adder, cylinder head material and design, camshaft profile, and planned engine use (street, drag race, road race, etc.), among others. Here, like many other areas of an engine, entire books can be written on the topic.
Theory aside, the crucial thing from a do-it-yourself perspective is how compression ratio is calculated. Compression ratio is defined as the ratio of the volume of air (actually air/fuel mixture if you want to be technical) inside the cylinder when the piston is at top dead center to the volume inside the cylinder when the piston is at bottom dead center. The volume of the cylinder at top dead center (TDC) consists of the so-called total chamber volume. The volume of the cylinder at bottom dead center (BDC) consists of the total chamber volume plus the swept volume of the cylinder.
An idealized cross-sectional representation of a piston at top dead center. The important volumes that must be known for accurate compression ratio calculation are: combustion chamber volume (yellow); head gasket volume (blue); deck clearance volume (orange); piston valve relief pocket volume (purple); and volume above compression ring (crevice volume, green). When combined, these volumes yield the total chamber volume.
The swept volume of the cylinder is easy to calculate. It's simply the displacement of one cylinder and is computed as bore area times stroke. The total chamber volume is a bit more difficult to deal with as there are a few different volumes involved, which we've attempted to show pictorially in Figure 2.
The combustion chamber volume, shown in yellow, is the familiar "combustion chamber cc" that cylinder head manufacturers quote. The stock LS1 cylinder head, for example, has a 67cc combustion chamber volume. This is the main volume involved when the piston is at TDC, but there are other smaller volumes that come into play.
The head gasket volume, shown in light blue, is equal to the compressed thickness of the head gasket multiplied by the circular area cut out in the head gasket. Typically, this area is of slightly larger bore than the engine's cylinder. Head gasket manufacturers do things this way primarily so that a single gasket will work for a range of finished cylinder sizes.
The deck clearance volume, shown in orange, comes into play because almost without exception, the face of the piston does not sit exactly flush with the engine block deck surface when at TDC. While in the graphic we've shown a piston sitting slightly down into the cylinder, in reality nearly all LS1 pistons actually protrude above the engine deck surface, giving these engines a so-called negative deck clearance. The calculation is the same, but we'll just be adding in a negative number instead of the positive number we'd use if the LS1 was a positive deck clearance engine.
The piston valve relief pocket volume, shown in purple, is the valve relief cc discussed by piston manufacturers. We've actually shown it pictorially as a full dish for clarity. This is one of the main specifications one looks at when shopping for pistons.
Equations for calculating the various volumes that comprise the total chamber volume.
Finally, an oft-overlooked volume is that which exists above the piston's top compression ring, which we've shown in light green. As pistons are always slightly smaller in diameter than the cylinders they occupy, a very small ring-shaped volume of air exists encircling the very top portion of the piston. This volume is often very hard to figure out, too, as when the engine is actually running, the piston can expand with heat to close this area up further--not to mention that piston manufacturers rarely quote the vertical distance between the face of the piston and the top compression ring. Therefore, this volume, sometimes called crevice volume, is often simply assumed to be 1 cc.
By looking up specifications for the cylinder heads, head gaskets, and pistons you're shopping for, as well as knowing whether your block will be decked or not, you can mix and match these parts to come up with the desired compression ratio for your engine. In our case, we wanted to stay below a static compression ratio of 11 to 1. This decision was based on our goals of a naturally aspirated engine that would be able to run on pump gas, but also have a moderate amount of nitrous injected into it at some point in the future when the yearning for even more horses hit us. As the factory LS1's compression ratio is only 10.1 to 1, we knew a compression increase like this would pay excellent dividends in efficiency and, hence, power production.
That said, here's how our compression ratio was calculated. We'll perform all of our calculations in English units and do the appropriate conversions from metric. The simplest calculation is the swept volume of one cylinder, and its equation can be seen in Figure 1. It's simply 1/8 the total displacement of the engine, and in our case is calculated as:
Swept volume = 3.14159 x (3.903 / 2) x (3.903 / 2) x 4.000 = 47.85713 cubic inches
Moving up top, let's take a look at our deck clearance. To find out how far the face of our piston is protruding from the cylinder bore, we'll need to sum up the distances between the centerline of the crankshaft main bearing and the piston face. These distances are half the crankshaft stroke, the connecting rod length, and the piston's compression height (the distance from the centerline of the piston pin to the face of the piston).
This gives us:
Height of piston face = (4.000 / 2) + 6.125 + 1.123 = 9.248 inches
As stated in the last issue of GMHTP, we chose not to perform any decking of the block, therefore our block retains the stock LS1 deck height (the distance from the centerline of the crankshaft main bearing bore to the block deck surface) of 9.240 inches. Subtracting the height of our piston face from this:
Deck clearance = 9.240 - 9.248 = -0.008 inches
We see that our piston protrudes 0.008 inches from the cylinder bore, giving us the negative deck clearance typical of Gen III engines. To get the deck clearance volume, we simply multiply this number by circular area of the cylinder bore as per the equation shown in Figure 3:
Deck clearance volume = 3.14159 x (3.903 / 2) x (3.903 / 2) x (-0.008) = -0.095714 c.i.
Head gasket volume is found in a nearly identical manner. All we need to know is the compressed thickness of the head gasket and its bore. For our Cometic MLS gasket, these values are 0.051 inches and 3.910 inches respectively. Therefore, as per the equation shown in Figure 3:
Head gasket volume = 3.14159 x (3.910 / 2) x (3.910 / 2) x 0.051 = 0.612369 c.i.
Our Lunati pistons have a valve relief pocket volume of 8 cc, which converts to 0.488190 cubic inches. Our ET Performance cylinder heads' combustion chamber volume is 62 cc or 3.783472 cubes. Assuming a 1 cc (0.061024 cubic inch) crevice volume, we can now sum up the total chamber volume as per the Equation shown in Figure 1:
Total chamber volume = 3.783472 + 0.488190 + 0.612369 - 0.095714 + 0.061024 = 4.849341 c.i.
Using our compression ratio equation seen in Figure 1, our static compression ratio is then computed as:
CR = (4.849341 + 47.85713)/(4.849341) = 10.869 to 1
This meets our stated goal exactly: a compression ratio of just below 11 to 1! Of course, when actually going through the process of selecting pistons, cylinder heads, and head gaskets, you'll have to rearrange these equations and solve for the unknowns you're interested in; but hopefully, we've pointed you in the right direction.