The focus of this
discussion is to explore the benefits of 4-valve head design versus a
conventional 2-valve head. The specific
area of focus is *airflow capacity* of the intake valves and it’s effect on engine
performance.

The ratio of
intake air velocity to the speed of sound in the intake gases is referred to as
the Mach Index (Z). Airflow studies
have shown that as the Mach Index values exceed .6, volumetric efficiency (Ve)
falls rapidly. The Mach Index number is
defined as:

_{} where

Z = Mach Index

A_{p }=
Area of the piston

A_{i }=
Intake valve area x # of intake valves

D = Intake Valve
diameter

s = Mean Piston
Speed

a = Velocity of
Sound in intake gases

C_{i} =
Mean Valve Flow Co-efficient

If we can
calculate the maximum airflow through a valve (or valves) before we exceed Z
.6, we can then calculate how much potential power a given engine design has.

For this
discussion, I’ll use the geometry for the 1981 Euro 635CSi engine for our
2-valve engine. It’s bore size and
piston area is virtually identical to the 1985 Euro M5 engine from which we’ll
utilize the 4-valve geometry. The
various specifications are as follows:

Bore – 93.36mm

Intake valve –
46mm x 1

Intake Valve –
37mm x 2

Rearranging our
Mach Index formula, we can solve it to find maximum ‘s’ without exceeding Z
.6. Because this is a theoretical
example designed to show the difference in and effect of airflow between 2 and 4-valve
head designs, a number of experience-derived numbers will be utilized. Hence, we will assume the following:

a = 1200 ft/min or
366m/sec

C_{i} =
.3 (though real-world values vary from <.3 to >.4)

s = Z / _{} = .6 / _{} = .6 / .0375 =
16m/sec

Maximum Mean
Piston Speed for our 2-valve engine is 16m/sec or 3150ft/min.

Calculating the
formula with the 4-valve head A_{i} we obtain the following:

s = Z / _{} = .6 / _{} = .6 / .0290 =
20.7m/sec

Maximum Mean
Piston Speed for our 4-valve engine is 20.7m/sec or 4075ft/min, an increase of
29%.

Rated Power (HP at
a given engine speed) can be calculated as follows:

P = _{} where

P = Horsepower

A_{p }=
Area of the piston

BMEP = Break Mean
Effective Pressure in psi

s = Mean Piston
Speed

BMEP is Indicated
Mean Effective Pressure – Friction Mean Effective Pressure – Pumping Mean
Effective Pressure of a given engine.
It takes into account the energy consumed by the engine itself in
frictional losses and pumping work (pushing exhaust gases etc.) Once again, as this is a theoretical
exercise concerned only with airflow, the BMEP value will be based on values
gleaned from real-world data collection.

For our 2-valve head:

P = _{} = 205hp

For our 4-valve head:

P = _{} = 265hp

For argument’s
sake, let’s check out what happens when we hotrod our 2-valve head with a larger
47mm valve.

Max s rises from
3150 to 3287ft/min, and power from 205 to 214hp.

While the preceding discussion was based strictly on
mathematical formulas, these formulas have evolved over time based on hundreds
of thousands if not millions of hours of real world testing of the internal
combustion engine. The examples clearly
show a horsepower increase in the order of 29% as predicted by the 29% increase
in airflow.