Cranks and Rods 101
An intense look at crankshaft stroke and its affect on mean piston speed, inertia, and controlling the massive, destructive forces at work inside an 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?The video above shows two engines, one with a short stroke crankshaft, and the other with a considerably longer stroke. Note that both pistons reach top dead center and bottom dead center at the same time, but the piston in the longer stroke engine (left) has to move significantly faster.
â€œRather than focus on mean piston speed, look at the effect of inertia force on the piston,â€ suggests Dave Fussner, head of research and development at K1 Technologies.
Letâ€™s first review the definition of mean piston speed, also called the average piston speed. Itâ€™s the effective distance a piston travels in a given unit of time, and itâ€™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
Thereâ€™s a simpler formula, but more on the math later. A pistonâ€™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.
There are formulas to calculate the piston speed at every degree of crankshaft rotation, but thatâ€™s usually much more information than needed by most engine builders. Traditionally they look at the average or mean piston speed during the crank rotation, and they possibly will calculate the maximum piston speed.
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. Letâ€™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. Letâ€™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. Hereâ€™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 youâ€™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, weâ€™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 didnâ€™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 hereâ€™s a basic formula that engine builders have often used that doesnâ€™t require rod length:
Maximum Piston Speed (fpm)=((Stroke x Ï€)/12)x RPM
Letâ€™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 pinâ€”which is why Fussner suggests looking at the inertia force.
â€œInertia is the property of matter that causes it to resist any change in its motion,â€ explains Fussner. â€œThis principle of physics is especially important in the design of pistons for high-performance applications.â€
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 donâ€™t doubleâ€”they quadruple.
â€œOnce started on its way up the cylinder, the piston with its related components attempt to keep going,â€ reminds Fussner. â€œIts motion is arrested and immediately reversed only by the action of the connecting rod and the momentum of the crankshaft.â€
Due to rod angularityâ€”which is affected by connecting rod length and engine strokeâ€”the piston doesnâ€™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,â€ says Fussner.
â€œThis 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.â€
If you donâ€™t consider the connecting rod, thereâ€™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. Letâ€™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 RadiusÃ·Rod Lenth
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