Engine Math for Engine Builders - Engine Builder Magazine
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# Engine Math for Engine Builders

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ngine building is a numbers game. Whether you like math or not, you often have to use it when figuring things like engine displacement, airflow, compression ratios and valve lift. Knowing how to calculate these values and how to use the numbers to match pistons, cylinder heads, cams, carburetors and valve train components can help you avoid mismatched components, interference problems, engine-damaging detonation, poor throttle response and lost power. And it can make you money.

Let’s start with displacement. If you’re building a motor with the same bore and stroke as an original stock motor, displacement should be the same as before because nothing has changed. A small block Chevy V8 with a 4.000˝ bore and 3.480˝ stroke crank will displace 350 cubic inches. Replace the stock crank with one that has a longer 3.750˝stroke and the engine will displace 372 cubic inches. And if you also bore out the cylinders an extra .030˝ you end up with a 383.

Why is it important to know an engine’s exact displacement? If you’re building a performance engine for a racing application that limits displacement, you don’t want to break the rules. More importantly, knowing displacement allows you to calculate airflow. That information, in turn, comes in handy when sizing a carburetor or throttle body, choosing a camshaft and determining the best intake port volume for a set of cylinder heads.

MEASURING BORE
AND STROKE

To calculate displacement, you first have to calculate cylinder volume. The volume of a cylinder is 3.14 (“pi”) times half the diameter squared (times itself) multiplied by the height of the cylinder.

Volume = 3.14 x (diameter/2) x (diameter/2) x height

This formula works for any type of cylinder, and it can be rewritten in a slightly different version that is slightly easier to use for a piston cylinder:

Cylinder Volume = bore x bore x 0.7854 x stroke

To make this calculation, you first have to accurately measure the bore and stroke of the engine. Bore can be measured with a bore gauge. Measure the width of the bore at the top, middle and bottom of the cylinder, then average the results (add the three measurements together then divide by three). This will give you the average bore diameter.

You can also check for an out-of-round bore by measuring bore diameter twice at top, middle and bottom of the cylinder. Make the first measurement holding the bore gauge in an east-west orientation, then rotate it 90 degrees and measure again in a north-south orientation. If the two numbers differ, you have an out-of-round bore. Stock engines can usually tolerate a couple thousandths of distortion, but performance engines should have as little bore distortion as possible (0.0005˝ or less!).

Checking bore dimensions will also tell you whether or not the block has been bored or honed to oversize. This bit of information is absolutely essential to correctly match replacement pistons and rings to the bores.

Measuring cylinder bore diameters (all of them) will also tell you if the bores need to be reconditioned. Bores that are out-of-round or have excessive taper (more wear at the top than the bottom) will not seal well, leak compression and burn oil. Excessive taper (more than a few thousandths in a stock engine, and even less in a performance engine) will flex the rings in and out with every stroke and increase the risk of ring breakage at high rpm.

Stroke is the distance the piston travels from the bottom to the top of the cylinder. Stoke is measured by rotating the crank so the piston is at Top Dead Center (TDC). The crank is then rotated 180 degrees to move the piston to Bottom Dead Center (BDC). The distance traveled is stroke.

You can also measure stroke on the crankshaft itself. Rotate the crank on a support stand so one of the rod journals is all the way up. Position your measuring tool on the top of the journal, then rotate the crank so the journal is all the way down. The distance between the two positions is stroke.

Once you have the bore and stroke numbers, you can calculate cylinder volume (also called “piston displacement”) using the cylinder volume equation:

Here’s an example using a stock Chevy 350 V8 with a bore diameter of 4.000˝ and a stroke of 3.480˝: 4.000 x 4.000 x 0.7854 x 3.480 = 43.73 cubic inches per cylinder.

CALCULATING ENGINE DISPLACEMENT

To calculate engine displacement in cubic inches, multiply the cylinder volume times the number of cylinders.

Engine Displacement = Cylinder Volume x Number of Cylinders

Chevy 350 example: 43.73 x 8 = 349.8 cubic inches, which everybody rounds up to 350 cubic inch displacement (cid).

ENGLISH-METRIC CONVERSION FACTORS

If you work on import engines or late model domestic engines and prefer to use metric dimensions, your units of measure will be millimeters (mm), centimeters (cm) and liters (L) instead of inches. The basic math equations are still the same but the end result will be cubic centimeters (cc) or liters of displacement instead of cubic inches.

Example: In metric measurements, a Chevy 350 V8 has a bore of 101.6 mm and a stroke of 88.39 mm (see conversion factors that follow).

Cylinder volume is 101.6 x 101.6 x .7854 x 88.39 = 71,6607 cubic millimeters. Multiply by .001 and you get 716 cubic centimeters. Multiply by 8 (number of cylinders) and you get 5728 cc. Multiply by 0.001 to convert to liters and you get 5.72 liters, which everybody rounds off to 5.7L.

Here are the formulas for converting English and metric measurements:

• To convert millimeters to inches, multiply by 0.03937.

• To convert inches to millimeters, multiply by 25.4.

• To convert cubic inches to cubic centimeters, multiply by 16.387.

• To convert cubic centimeters to cubic inches, multiply by 0.0610.

• To convert cubic centimeters to liters, multiply by 0.001.

HOW CHANGES IN BORE & STROKE CHANGE DISPLACEMENT

Changing the bore or stroke of an engine will opbviously change the volume of the cylinders and overall engine displacement. Let’s say you overbore a Chevy 350 .030˝ to obtain a new bore diameter of 4.030˝. Do the math and the volume of each cylinder now becomes 44.389˝.

The change by itself isn’t much but when you multiply it by eight cylinders, you gain 5 cubic inches of displacement (355 cid). Such a change is not enough to significantly alter airflow or compression (only a 1.4 percent change).

If you mill the surface of the block to decrease deck height .010˝, you will also reduce cylinder volume slightly (to 43.60 cubic inches) and overall engine displacement to 348.8 cubic inches, a loss of only about one cubic inch. Again, this is not enough to cause any concerns unless you are running really tight deck clearances and are concerned about piston interference with the head.

But let’s say you’re building a 383 stroker motor. Now the increase in displacement over the stock 350 with an overbore and longer stroke is 33 cubic inches, or 9.4 percent. That means the induction system and cylinder heads have to flow almost 10 percent more air than before to deliver the same performance. That, in turn, means you need heads with larger ports (more intake runner volume), a slightly larger carburetor, and or a camshaft with a little more lift and duration to take full advantage of the extra displacement and airflow.

AIRFLOW &

VOLUMETRIC EFFICIENCY

Internal combustion engines are sometimes referred to as air pumps because that’s what they do. The volume of air that a naturally aspirated four-stroke engine can theoretically breathe is its displacement times engine speed (RPM) divided by 2.

Theoretical Airflow = (RPM x Displacement)/2

Example: Our stock 350 Chevy could potentially flow up to 875,000 cubic inches of air per minute at 5,000 RPM.

Airflow is usually specified in Cubic Feet per Minute (CFM) rather than cubic inches, so dividing 875,000 cubic inches by 1728 (the number of cubic inches in a cubic foot) gives us a theoretical airflow of 506 CFM. A 600 CFM carburetor should handle that nicely.

Airflow in CFM = (RPM x displacement)/2 x 1728

Now, let’s rev the engine up to 8,000 RPM and see what happens. The engine is now attempting to pump 810 CFM of air, so you need a much bigger carburetor to take full advantage of the increased airflow.

Of course, an engine won’t really breathe its maximum theoretical airflow because “Volumetric Efficiency” drops off as RPMs go up due to momentum and restrictions in the induction system and cylinder heads.

Volumetric efficiency is important to know because it can help you more accurately size a carburetor or throttle body to the engine’s airflow requirements, and more accurately match the port volume of the cylinder heads to the rpm range where you want the engine to develop peak torque and horsepower.

A carburetor that’s too small will restrict airflow at higher engine speeds and prevent an engine from achieving its peak power potential. By comparison, a carburetor that’s too large for the motor, or a multiple carburetor setup (two four barrels or three deuces) can flow more air at higher rpms but may cause poor throttle response at lower speeds because air velocity and intake vacuum are not high enough to generate a strong signal through the carburetor’s metering circuits.

The same considerations also apply to choosing heads with the optimum intake port volume and flow characteristics. Smaller ports are better for smaller displacement engines because smaller ports increase air velocity for better low speed throttle response and torque. Larger port volumes that flow more air, on the other hand, are necessary for engines designed to make high rpm power. Even so, a set of heads with huge cfm numbers may not deliver the performance you would expect if their flow capacity is a mismatch for what the engine actually requires or is capable of using.

The real world volumetric efficiency of an engine can be measured on a dyno. Actual airflow at any rpm divided by the theoretical airflow times 100.

Volumetric Efficiency = (actual airflow/theoretical airflow) x 100.

Most engines can breathe close to 100 percent volumetric efficiency at low rpms with full throttle. A closed throttle or part throttle creates a restriction that reduces efficiency. Efficiency also drops off sharply as engine speed increases.

Most stock engines have a volumetric efficiency of only about 75 percent at maximum rpm, and only about 80 percent at the rpm where they develop peak torque. A naturally aspirated racing engine with a hot cam, well-flowing heads, big valves, and smooth flowing intake and exhaust systems can often achieve 90 percent volumetric efficiency at peak rpm, and up to 95 percent volumetric efficiency at the rpm where it makes peak torque.

Obviously, the higher an engine’s volumetric efficiency, the more air it can pump and the more power it can make. One hundred percent volumetric efficiency can’t be achieved at all rpms in a naturally aspirated engine so that’s where turbochargers and superchargers come into play.

An engine with a forced induction system can far exceed the volumetric efficiency of any naturally aspirated engine. The higher the boost pressure, the more air is forced into the engine and the higher the volumetric efficiency.

Adding a turbo to a small displacement engine can make that engine perform like a much larger engine.  Think of all the turbocharged two-liter engines that are now used in many late model cars. Many of these engines are making 250 to 300-plus horsepower, which is equivalent to a larger 3.0L V6 or even some V8s.

CALCULATING

COMPRESSION RATIO

Compression is another number that’s important to know, but is harder to calculate. Basically, compression is the volume of the cylinder divided by the volume of the combustion chamber in the cylinder head. If the piston volume is ten times the chamber volume, the engine has a compression ratio of 10 to 1.

Compression = (cylinder volume + chamber volume)/chamber volume

When a piston comes up on its compression stroke, the volume of air and fuel in the cylinder is compressed and squished into the small cavity created by the combustion chamber in the head. The larger the cylinder volume and the smaller the chamber volume, the higher the compression ratio.

Most stock engines have a compression ratio of at least 9 to 1, and many late model naturally aspirated engines have compression ratios as high as 10.5 or 11 to one. Race engines burning alcohol or race gas can handle even higher compression ratios, up to 14.5 or
15 to one.

We’ve already covered how to calculate cylinder volume, so all that’s needed for this step is to measure the volume of the combustion chamber. Combustion chambers are odd-shaped so the only way to accurately determine the actual displacement of a chamber is to fill it with a liquid (colored water, rubbing alcohol, light oil, etc.) using a calibrated cylinder (called a “burette.” This is called “CCing” the head because the burette is usually calibrated in cubic centimeters (cc).

The combustion chamber is measured by turning the head upside down and installing the valves and spark plug. A flat clear piece of plastic (Plexiglass or Lexan) is then placed over the chamber. Vaseline is typically used to seal the valves and the plastic cover to the head. The burette is inserted through a small hole in the plastic cover until the chamber is full and there are no air bubbles. You then note how many cc’s of liquid it took to fill the chamber.

Comparing the measured displacement of the chamber against the specs for a stock head will tell you if the head has been milled or modified. A smaller displacement would indicate a milled head.

Once you have the chamber volume, you need to add in the space created by the deck clearance between the top of the block and the piston. This formula will convert the measurement in inches to cc’s:

Deck clearance volume = deck clearance x (bore/2) x (bore/2) x 3.14 x 16.387

You also have to add in the space created by the thickness of the head gasket (again using inch measurements that will be converted to cc’s):

Add up the chamber volume, deck clearance volume and head gasket volume in cc’s and you get the total chamber compression volume above the piston.

Now you have to add or subtract some volume depending on the type of pistons used (dished, flat top or domed). With a flat top piston that has no valve reliefs, no corrections are needed. With a dished piston, add the volume of the recessed area in the dish (which should be provided by the piston manufacturer). With a domed piston, subtract the volume displaced by the dome (also available from the piston manufacturer).

Okay, now you can finally calculate the compression ratio of the engine. Add up all the numbers for everything about the piston (chamber volume, deck clearance volume, gasket thickness volume, and plus or minus piston volume) and divide that into the cylinder volume displaced by the piston. Make sure you convert the combustion chamber cc’s to cubic inches before you divide if you are using cubic inches for the cylinder volume, or convert the cylinder volume from cubic inches to cubic centimeters so you are using the same units of measure for compression volume and cylinder volume – otherwise the compression ratio won’t make any sense.

WHY COMPRESSION MATTERS

Compression affects power, the octane requirements of the fuel and ignition timing. Higher compression ratios increase the thermal efficiency of an engine and allow the engine to capture more of the heat energy that’s released during combustion. That’s one reason why high compression diesel engines are more fuel efficient than gasoline engines. But strange things can happen inside a combustion chamber when heat and pressure interact with the air/fuel mixture.

Detonation (spark knock) can occur if the temperature and pressure in the chamber are too great for the octane rating of the fuel. Detonation is an erratic form of combustion that spawns multiple flame fronts instead of a single expanding flame balloon. This causes a sudden and sharp rise in combustion pressure that hammers the piston and can damage the piston, rings and rod bearings. It also hurts power.