An intense look at mean piston speed, inertia, and controlling the massive, destructive forces at work inside your engine.
Engine builders have long calculated the mean piston speed of their engines to help identify a possible power loss and risky RPM limits. This math exercise has been especially important when increasing total displacement with a stroker crankshaft, because the mean piston speed will increase when compared to the standard stroke running at the same RPM.
But what if there was another engine dynamic that could give builders a better insight into the durability of the reciprocating assembly?
“Rather than focus on mean piston speed, look at the effect of inertia force on the piston,” suggests Dave Fussner, head of research and development at Wiseco Pistons.
Let’s first review the definition of mean piston speed, also called the average piston speed. It’s the effective distance a piston travels in a given unit of time, and it’s usually expressed in feet per minute (fpm) for comparison purposes. The standard mathematical equation is rather basic:
Mean Piston Speed (fpm)=(Stroke x 2 x RPM)/12
There’s a simpler formula, but more on the math later. A piston’s velocity constantly changes as it moves from top dead center (TDC) to bottom dead center (BDC) and back to TDC during one revolution of the crankshaft. At TDC and BDC, the speed is 0 fpm, and at some point during both the downstroke and upstroke it will accelerate to a maximum velocity before decelerating and returning to 0 fpm.
The mean piston speed takes the total distance the piston travels during one complete crankshaft revolution and multiplies that by the engine RPM. Piston speed obviously increases as the RPM increase, and piston speed also increases as the stroke increases. Let’s look at a quick example.
A big-block Chevy with a 4.000-inch-stroke crankshaft running at 6,500 rpm has mean piston speed of 4,333 fpm. Let’s review the formula again used to calculate this result. Multiply the stroke times 2 and then multiply that figure by the RPM. That will give you the total number inches the piston traveled in one minute. In this case, the formula is 4 (stroke) x 2 x 6,500 (RPM), which equals 52,000 inches. To read this in feet per minute, divide by 12. Here’s the complete formula:
(4 x 2 x 6,500)/12=4,333 fpm
You can simplify the formula with a little math trick. Divide the numerator and denominator in this equation by 2, and you’ll get the same answer. In other words, multiply the stroke by the RPM, then divide by 6.
(4 x 6,500)/6=4,333 fpm
With this simpler formula, we’ll calculate the mean piston speed with the stroke increased to 4.500 inch.
(4.5 x 6,500)/6=4,875 fpm
As you can see, the mean piston speed increased nearly 13 percent even though the RPM didn’t change.
Again, this is the average speed of the piston over the entire stroke. To calculate the maximum speed a piston reaches during the stroke requires a bit more calculus as well as the connecting rod length and the rod angularity respective to crankshaft position. There are online calculators that will compute the exact piston speed at any given crankshaft rotation, but here’s a basic formula that engine builders have often used that doesn’t require rod length:
Maximum Piston Speed (fpm)=((Stroke x ?)/12)x RPM
Let’s calculate the maximum piston speed for our stroker BBC:
((4.5 x 3.1416)/12)x 6,500=7,658 fpm
By converting feet per minute to miles per hour (1 fpm = 0.011364 mph), this piston goes from 0 to 87 mph in about two inches, then and back to zero within the remaining space of a 4.5-inch deep cylinder. Now consider that a BBC piston weighs about 1.3 pounds, and you can get an idea of the tremendous forces placed on the crankshaft, connecting rod and wrist pin—which is why Fussner suggests looking at the inertia force.
“Inertia is the property of matter that causes it to resist any change in its motion,” explains Fussner. “This principle of physics is especially important in the design of pistons for high-performance applications.”
The force of inertia is a function of mass times acceleration, and the magnitude of these forces increases as the square of the engine speed. In other words, if you double the engine speed from 3,000 to 6,000 rpm, the forces acting on the piston don’t double—they quadruple.
“Once started on its way up the cylinder, the piston with its related components attempt to keep going,” reminds Fussner. “Its motion is arrested and immediately reversed only by the action of the connecting rod and the momentum of the crankshaft.”
Due to rod angularity—which is affected by connecting rod length and engine stroke—the piston doesn’t reach its maximum upward or downward velocity until
about 76 degrees before and after TDC with the exact positions depending on the rod-length-to-stroke ratio,” says Fussner.
“This means the piston has about 152 degrees of crank rotation to get from maximum speed down to zero and back to maximum speed during the upper half of the stroke. And then about 208 degrees to go through the same sequence during the lower half of the stroke. The upward inertia force is therefore greater than the downward inertia force.”
If you don’t consider the connecting rod, there’s a formula for calculating the primary inertia force:
0.0000142 x Piston Weight (lb) x RPM2 x Stroke (in) = Inertia Force
The piston weight includes the rings, pin and retainers. Let’s look at a simple example of a single-cylinder engine with a 3.000-inch stroke (same as a 283ci and 302ci Chevy small-block) and a 1.000-pound (453.5 grams) piston assembly running at 6,000 rpm:
0.0000142 x 1 x 6,000 x 6,000 x 3 = 1,534 lbs
With some additional math using the rod length and stroke, a correction factor can be obtained to improve the accuracy of the inertia force results.
Crank Radius÷Rod Lenth
“Because of the effect of the connecting rod, the force required to stop and restart the piston is at maximum at TDC,” says Fussner. “The effect of the connecting rod is to increase the primary force at TDC and decrease the primary force at BDC by this R/L factor.”
For this example, the radius is half the crankshaft stroke (1.5 inch) divided by a rod length of 6.000 inches for a factor of .25 or 383 pounds (1,534 x 0.25 = 383). This factor is added to the original inertia force for the upward stroke and subtracted on the downward movement.
“So, the actual upward force at TDC becomes 1,917 pounds and the actual downward force at BDC becomes 1,151 pounds,” says Fussner. “These forces vary in direct proportion to the weight of the piston assembly and the stroke to rod length and they also vary in proportion to the square of the engine speed. Therefore, these figures can be taken as basic ones for easily estimating the forces generated in any other size engine.”
“We know a common measure used for many years to suggest the structural integrity danger zone of a piston in a running engine is mean piston speed,” sums up Fussner. “As the skydive instructor told his student, it’s not the speed of the fall that hurts, it’s the sudden stop. And so it is with pistons. So rather than focus only on the mean piston speed, let’s decide to also consider the effect of inertia force on the piston, and what we can do to reduce that force. And if that is not possible, make sure the components are strong enough to endure the task we have set forth.”
This article was sponsored by Wiseco. For more information, please visit our website at wiseco.com