The experienced engine builder (Harley-Davidson, Mopar, or Ferrari) knows that the “advertised” compression ratio (suggested by the owner’s manual, piston manufacturer, etc.) is only one of several factors involved in determining how much pressure is developed in the combustion chamber.
    This article discusses briefly how to roughly calculate how changes in either cam timing, compression, or both affect low-speed torque and response. Some of the more important factors are:

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Theoretical or mechanical compression ratio (“advertised”, or nominal), including corrections made for changes in combustion chamber volume due to piston compression distance, valve reliefs in piston dome, combustion chamber and/or bore, alternate gasket thickness, head, cylinder and/or case milling, etc.

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Intake valve closing point (generally the 2^nd number in the cam timing data, given in degrees after bottom dead center, or ABDC)

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Internal geometry of the motor

    This last factor is not fully appreciated by most mechanics. The crank-pin is offset from the sprocket & pinion shaft axis by exactly ½ the stroke length. The geometric relationship between the rod and the crank-pin is one not generally understood, but which plays a key role in the motor’s breathing and overall power characteristics.
    The ratio of rod length to stroke length is almost always between 2.2:1 on the “long” end, and 1.4:1 on the “short” end. 99% of all motors fall between these 2 extreme limits, with most standard production designs between 2.0:1 and 1.5:1.

    The percentage of mixture captured, compressed, and burned in the cylinder at a specific point of intake valve closure partially depends on the motor’s rod ratio. The piston’s motion during flywheel rotation is not symmetrical: the piston speed before & after TDC is faster than before & after BDC, but the difference is not constant - it varies with the rod ratio. Two motors with the same stroke, but different rod lengths, will not have the piston in the same place at the same point of flywheel rotation. The only 2 exceptions are 0° (TDC) where both strokes are zero, and 180° (BDC) where both strokes are equal & nominal.
    The long-rod motor will have the piston closer to TDC than the short-rod motor at any point between 90° BTDC & 90° ATDC. The short-motor will have the piston closer to BDC than the long-rod motor at any point between 90° BBDC & 90° ABDC.
    Short-rod motors (“n” = 1.5 to 1.7:1) have slower piston movement upwards away from BDC on the compression stroke, and will capture more mixture at the same point of intake valve closure. This makes them more tolerant of extended (late intake closing) cam timing.     Longer duration cams generally need more static compression. The usual cam functions (also known as valve events) are Intake Opening Point, Intake Closing Point, Exhaust Opening Point, Exhaust Closing Point, Overlap, Lobe Separation Angle, and Valve Lift. The only one which affects cylinder pressure directly is the Intake Closing Point - where the intake valve has just closed ABDC at the beginning of the compression stroke. Intake valve closure after BDC (present in all modern cams) always causes some of the intake mixture to be compressed backwards out of the cylinder by the rising piston at very low speeds. Late (radical) intake valve closure causes some mixture to escape even at moderate speeds, reducing cylinder pressure during the operating range (at the lower end of the torque curve). The point in the engine’s RPM range where this reversion stops and full-stroke capture (or more!) occurs is frequently the torque peak, and depends on many factors, including cam timing, port efficiency, mixture velocity, manifold runner & port cross-sectional area & volume, etc. I have no method of applying math to these factors - too complex!
    If you have (or plan to install) a long-duration cam, you can (and should) regain some of this lost pressure by raising the compression ratio, but the 2 effects do not always “cancel each other out” - you can't get something for nothing. Even though a higher compression ratio will give you back a higher pressure gauge reading, the power may still be lower, at least at low to moderate speeds.
    The error lies in the fact that a smaller volume of mixture being compressed to a higher ratio. Even though the pressure gauge reading taken during cranking or idling is higher, the total of cylinder pressure times the actual mixture volume captured may still be lower (compared to the original milder cam and moderate compression ratio).
    As a note: the gas present in the combustion chamber @ TDC is presumed to be non-combustible exhaust gas remaining from the previous cycle, and is therefore not included in the mixture volume for our purposes. At high engine speeds (under certain conditions) overlap does cause this remainder to be partially combustible, but this is not true at cranking to moderate engine speed.
    In short, a cam change can't be “cured” completely by raising the compression ratio, but it’s still an excellent idea. The “V/P Index” , which is the subject of this Tech Paper, will not predict maximum torque or power, but still provides useful information about conditions present in the motor at cranking speed. These same conditions generally affects low-speed response & flexibility, knock-resistance, etc. for spark advance settings, sprocket size choices, etc.
    Another useful purpose is to anticipate the effect of higher elevation on cylinder pressure. Perform a calculation (as described below) first, then another substituting a lower value than 14.7 psi for “Atmospheric Pressure” . Compare the results to estimate how much adjustment to the nominal compression ratio is needed to (partially) compensate for the lower air density.

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V/P Index     A reasonable estimate of the relative effects of compression ratio, rod ratio, and intake valve closing point at cranking speed can be made by use of a simple formula. Although a “power” (exponent) is used in the formula, most pocket and on-line calculators have a function to permit a fractional exponent to be entered (use Microsoft “Calculator” in Win95, etc. It has this feature - to use it, select “Scientific” view). Try it out - it’s not that difficult!     

Given:

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Atmospheric pressure = 14.7 psi (pounds per square inch, or 29.92 inches of mercury). This is a constant for our purposes here at sea level, but should be adjusted downward for extreme elevations.
To convert psi to In. hg, multiply by 2.036; to convert In. hg to psi multiply by .0491.

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Intake valve closing point (ABDC). At cranking speed, intake flow reversal still takes place until the valve is actually closed, so the “paper duration” (nominal) closing point is used for calculations. By the way, at operating speeds the general consensus is that the intake valve is effectively closed (the flow has stopped for practical purposes) at about .050” valve lift.

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Theoretical compression ratio. Click here to review the factors, as described above: .

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Stroke remaining at intake valve closing point, which is determined by the engine’s stroke, and rod to stroke ratio (“n” ). This is calculated by dividing the rod length by the stroke length. To find the rod ratio of most Harley-Davidson engines, click here: .

    Results:

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Corrected (true) compression ratio.

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Cranking pressure, absolute (in psi, zero elevation std.).

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Gauge pressure (in psi, zero elevation std.).

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Corrected cylinder volume (cylinder displacement trapped when the intake valve closes).

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V/P Index*

    *V/P (Volume/Pressure) Index is a mathematically-derived figure, the product of the corrected volume and cranking pressure. It’s a very useful barometer of the motor’s low-speed power, and may be solved with new variables for a “before & after” analysis when modifications are contemplated. Anyone planning a cam or compression ratio change would definitely want to know how much the low-speed flexibility would be affected. Some useful insight may also be derived as to the motor’s tolerance of pump-quality gas (ping & knock resistance). The results of these comparisons are generally quite surprising!     To calculate the V/P Index for a specific motor, you'll need the exact piston position at all relevant flywheel positions from BDC to about 90° ABDC, the compression ratio, and the intake valve closing point.

    If you'd like to calculate piston positions for your own motor, the following formula has been contributed by a reader:

where “SE” is the effective stroke, “S” is the nominal (full) stroke, “R” is the rod length, “A” is the crank-shaft angle in degrees ABDC from 0 to 90°, and “SQRT” (or “SQR” ) is the square root function.
    Be sure to copy the equation very accurately, including the “nested” pairs of parentheses. This should work “as-is” for calculators, but most computer programs will require “A” to be converted from degrees to radians: Radians = Degrees × .017453, or Degrees × Pi ÷ 180.

    To make a V/P Index calculation, find your intake closing point. Unfortunately, most cam manufacturers (including Andrews Products, Sifton, Leineweber, etc.) don't list nominal closing points in their specs - you might try to call them for this info (no, I don't have phone numbers, and I have no cam timing figures). Locate this figure as the flywheel position, and take the stroke from that position to calculate the “effective” cylinder volume (“VE”), which is amount trapped by the closed intake valve; which is always less than the nominal volume (“VN”). Using this, calculate the effective compression ratio (“CRE” ); also lower - the combustion chamber volume is unchanged, but the cylinder volume is less. At cranking speed, the absolute cranking pressure (“CP” ) is a function of the 1.25 power of the effective compression ratio (i.e., for 8:1 compression ratio, use 8^1.25) times atmospheric pressure (14.7 psi @ sea level, etc.). This adjustment (1.25 power) is a polytropic value used in preference to the traditional adiabatic value (1.4) for the ratio of variable heats for air and similar gases at the temperatures present. This compensates for the temperature rise caused by compression, as well as heat lost to the cylinder. 1.25 is not accurate in all cases, since the amount of heat lost will vary among engines based on design, size and materials used, but provides useful results for purposes of comparison.
    To predict a pressure gauge reading subtract 14.7 (or the correct atmospheric pressure at test elevation) to compensate for the fact that a gauge in free air reads “0” , not 14.7 psi, even though atmospheric pressure is always present.
    The V/P Index number is the product of the effective volume times the effective compression ratio, times the number of cylinders, times a correction factor weighted to produce a number roughly proportionate to torque in ft./lbs.

Symbol

Meaning

Definition or Calculation

B

Bore

Piston diameter, in inches

S

Stroke

Full (nominal) flywheel stroke; TDC to BDC measurement (180° rotation), in inches

SE

Stroke, Effective

Stroke measured from intake valve closing point (less than 180°) to TDC [always less than “S” , above]

VN

Cylinder Volume, Nominal

B² × S × .7854 (1 cylinder)

VE

Cylinder Volume, Effective

B² × SE × .7854 (1 cylinder) [always less than “VN” , above]

VC

VC = VN ÷ (CRN - 1). Total volume (1 chamber) above piston @ TDC, in inches.

N

Number of cylinders

(2 in this case)

AP

Atmospheric Pressure

14.7 psi @ sea level (zero elevation); use the correct lower figure for higher elevations

CRN

Compression Ratio, Nominal

CRN = (VN + VC) ÷ VC

CRE

Compression Ratio, Effective

CRE = (VE + VC) ÷ VC [always less than “CRN” , above]

CP

Cranking Pressure (absolute)

CP = (CRE^1.25 × AP)

GP

Gauge Pressure

GP = (CRE^1.25 × AP) - AP. To predict gauge pressure, subtract atmospheric pressure (14.7 psi @ sea level, etc.) from absolute pressure. See above: .

V/P

Volume/Pressure Index

V/P = CP × VE × N × .6% (.6% or .006 is a correction factor to return a useful 2 digit number proportionate to torque)

Note: I have a Q-Basic program (your Windows 95/98/2000 PC already has it, probably in the “DOS” directory) to do all this annoying math automatically for any intake closing point, any compression ratio, etc., including reduction in atmospheric pressure for elevation. I can supply you with a copy of this program tailored to your own motor on disk for $10.00. E-mail me here for details: jdiamond@optonline.net for a copy.