# Intake Valve Lift

As a good estimate, you can use the formula below. For more details, read below the picture.

intake valve lift = (0.15)(bore)

Pictured above are some valves on the left and the valves in their place in the engine on the right. The valves factor in to the amount of air that gets into the cylinders.

## What you do:

Choose a lift that gives you the power you want at the rpm you want.

Factors to consider:

How it all works:

This is a picture of a cam. The lobes on the cam are the egg shaped bumps. These lobes have lift and duration specifications that you dictate. The lift is how high the lobe on the cam will lift the valve. The duration is how long, in crank degrees, the valve will be lifted.

Intake valve lift is determined by the height of the intake lobe on the cam. When you set the lift, you are setting the height of the intake lobe on the cam. Intake valve lift, intake valve diameter and intake valve duration determine air velocity in the intake system. High lift, large diameter and long duration all cause the engine to breath better at high rpms, but also cause the air to move slower at lower rpms, which reduces power at lower rpms. Low lift, small diameter and short duration all cause the air in the intake system to go faster, which increases power at lower rpms, but chokes air flow when the air velocity reaches the speed of sound. The speed of sound is 767.58 mph (miles per hour) or 67547.4 fpm (feet per minute).

Since the cam rotates 1 time for every 2 times the crank rotates and cam duration is measured in crank degrees, the HiPerMath equation for intake cam degrees is:

intake cam degrees = __intake valve duration__

2

Next, we calculate the angle from the x-axis to the point at which lift begins. We call this angle "theta".

theta = 90 - __intake cam degrees__

2

Next, we calculate the x and y values of the point at which lift begins, using the angle we just calculated:

x = 0.5cos(3.14/(180 / theta))

y = 0.5sin(3.14/(180 / theta))

Next, we calculate the b-value for the equation y = ax^{2} + b, which is the equation
for a parabola. We use a parabola because it closely represents the shape of a cam lobe.

b = intake valve lift + 0.5

The 0.5 in the equation above is the radius of what is called the cam base circle. The cam base circle is the minimum radius the lifter will rest on.

Now that we have values for x, y and b, we can calculate the a-value for the equation
y = ax^{2} + b :

a = -(y - b) / x^{2}

Now that we have the a and b values for the equation, we plug in -0.4, -0.3, -0.2, -0.1, 0, 0.1, 0.2, 0.3, 0.4 for the x values (since the x values for our parabola will range from -0.5 to 0.5, to get values for y:

yn4 = -a(-0.4^{2}) + b

yn3 = -a(-0.3^{2}) + b

yn2 = -a(-0.4^{2}) + b

yn1 = -a(-0.1^{2}) + b

y0 = -a(0.1^{2}) + b

y1 = -a(0.1^{2}) + b

y2 = -a(0.2^{2}) + b

y3 = -a(0.3^{2}) + b

y4 = -a(0.4^{2}) + b

We calculated values for y above because we are going to use them in the distance equations below where we calculate the distance from (0,0) to (x,y) and subtract the radius of the cam base circle:

d1 = &radic ^{2} + yn4^{2})

d2 = &radic ^{2} + yn3^{2})

d3 = &radic ^{2} + yn2^{2})

d4 = &radic ^{2} + yn1^{2})

d5 = &radic ^{2} + y0^{2})

d6 = &radic ^{2} + y1^{2})

d7 = &radic ^{2} + y2^{2})

d8 = &radic ^{2} + y3^{2})

d9 = &radic ^{2} + y4^{2})

Now we calculate the average lift:

average intake lift = __ d1 + d2 + d3 + d4 + d5 + d6 + d7 + d8 + d9__

9

Next we calculate average open intake valve area:

average open intake valve area = average intake lift x intake valve size x 3.14

Now we can calculate the air velocity, in fpm (feet per minute) through the intake valve, during the time it is open, at any rpm we want:

air velocity through intake valve in fpm = __0.327 x number of cylinders x 2 x stroke x rpm x 3.14 x (bore / 2)__^{2}

average open intake valve area x 12

Finally, we can put 67547.4, which is the speed of sound in fpm, in place of "air velocity through intake valve in fpm", solve the equation for rpm and find out what the maximum rpm is from that result! The HiPerMath equation is below:

maximum rpm = __ 67547.4 x average open intake valve area x 12 __

0.327 x number of cylinders x 2 x stroke x 3.14 x (bore / 2)^{2}

We just found out how much this cam allows the engine to breath!

Now for the equations about the air separating from the surface of the valve and the effects of the air separation.

As stated at the top, in "Factors to consider", air separation begins to occur when the lift of the valve is higher than 15% of the bore. So:

lift height at which air separation occurs = 0.5 + bore x 0.15

For convenience, let "lift height at which air separation occurs" = "lift separation height".

Next, we find the x and y values on the cam lobe at which the lift is higher than the
"lift separation height" calculated above. We
use the distance formula, which is x^{2} + y^{2} = distance^{2} and
the parabola formula, which is y = -ax^{2} + b. By substituting the right part of the
parabola equation in for the y part of the distance formula:

x^{2} + y^{2} = distance^{2}

x^{2} + (-ax^{2} + b)^{2} = distance^{2}

Now we expand the (-ax^{2} + b)^{2} part

x^{2} + a^{2}x^{4} - 2abx^{2} + b^{2} = distance^{2}

x = square root of {(2ab - 1) / 2a^{2} - square root of {[lift separation height^{2} / a^{2}] - b^{2} / a^{2} + (2ab - 1)^{2} / 2a^{4}}

We only want the positive x value from the above equation.

Next we get the angle at which this lift occurs by using the fact that x = rcos(angle), which means angle = arccos(x/r):

angle at which air separation occurs = arccos(x / lift separation height)

Now we can get the total degrees on the cam lobe during which air separation occurs:

total air separation degrees = 2(90 - angle at which air separation occurs)

Finally, we calculate the coefficient that will be applied to air flow, since some of it is wasted due to air flow separation:

wasted air flow coefficient = 1 - __2(total air separation degrees)__

(duration / 2)

Definitions:

fpm = feet per minute

rpm = revolutions per minute