Piston speed generally refers to the average or mean speed of the piston as it moves up and down in the cylinder bore during each crankshaft revolution. Since the piston actually comes to a complete stop at the top of the stroke (TDC) and at the bottom of the stroke (BDC), its speed and acceleration at any given point is always changing. The piston is always accelerating from or decelerating to zero speed. The formula for mean piston speed yields an average speed based on two times the stroke (up and down for one revolution), times the engine speed (RPM) divided by 12 to convert to feet per minute (fpm). To simplify the formula, divide the numerator and the denominator by 2.
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Piston Speedfpm = stroke x RPM ÷ 6
Let’s work an example for a 302 Ford that has a stroke of 3 inches and a maximum engine speed of 6,000 rpm.
Piston Speedfpm = 3 x 6,000 ÷ 6 = 3,000 fpm Note that if you did not simplify the formula, the answer still comes out the same. It is the distance the piston travels in one minute. To convert the answer to MPH, multiply the answer by 60 to get feet per hour.
Then divide by 5,280 to get miles per hour.
MPH = (mean speed x 60) ÷ feet per mile
MPH = (3,000 x 60) ÷ 5,280 = 34.09 mph
Maximum Piston Speed
You can get a very close approximation of maximum piston speed (ignoring rod center-to-center length and rod angularity) with the following formula. Multiply the stroke by pi and divide by 12 to get feet per revolution. Then multiply by the maximum engine speed to get the maximum feet per minute. This speed occurs about mid stroke, where the connecting rod is ninety degrees to the crankpin. Before that point the piston is accelerating; after it the piston is decelerating. When the piston is exactly at either top or bottom dead center it is stopped and there is no acceleration. Using the formula for mean piston speed we calculated 3,000 fpm or 34.09 mph for our 302 Ford. Now let’s find the maximum piston speed at 6,000 rpm.
Maximum Piston Speed = MPS
MPSfpm = (stroke x π ÷ 12) x RPM
MPSfpm = (3.00 x 3.14 ÷ 12) x 6,000 MPSfpm = (9.42 ÷ 12) x 6,000 = .785 x 6,000 = 4,710 fpm
MPSfpm x 60 ÷ 5,280 = MPH
4,710 x 60 ÷ 5,280 = 53.52 mph
Mean piston speed has long been used as an indicator of component durability under severe service. It is a good rule for evaluating engine potential and it is even more instructive if you calculate maximum piston speed since one of the axioms of engine performance dictates that power comes from engine speed. The more power strokes per minute, the more power available to do work.
Consider the 2000 Ferrari Formula 1 engine that has a stroke of 1.6-inch. At 18,000 rpm that’s a mean piston speed of 4,800 fpm and a peak speed over 7,536 fpm, or more than 85 mph at mid-stroke. Potential disaster for a big block Chevy, but the Formula 1 engine enjoys the luxury of very exotic materials and very small pistons that have much less mass to accelerate.
The most important consideration is the instantaneous piston acceleration and the staggering loads placed on the piston, piston pin, and connecting rods and rod bolts. These are the most highly stressed components in the engine. Since an engine’s ability to make power is closely tied to the RPM it can turn, every effort is made to lighten valve train components to combat valve float. But the real limit turns out to be piston mass and piston acceleration. A typical 350 Chevy piston weighs 1.3 to 1.6 pounds. Special racing pistons weigh in at less than a pound, but imagine trying to accelerate one to 6,800 fpm (350 Chevy at 7,500 rpm) max piston speed at mid-stroke and then slam it to a dead stop and reverse direction in about 13⁄4 inches (stroke/2). At TDC the piston is headed for the moon and the rod has to stop it and yank it back the other way. That’s enough to pull the piston pin right out of the piston and it does on occasion. It also exerts similar loads on rod bolts and rod caps. Since acceleration (load) is greatest just after TDC, lets calculate the maximum acceleration of a 350 Chevy piston at 7,500 rpm using the stock stroke of 3.48 inches and the stock rod length of 5.7 inches. The formula is:
Max Acceleration = (rpm2 x stroke ÷ 2,189) x 11⁄3
MA = (7,5002 x 3.48) ÷ 2,189 x 11⁄3 = 195,750,000 ÷ 2,189 x 11⁄3 = 89,424.39 x 1.3333333 = 119,232.5 ft/sec2
That’s insane acceleration for a 1.5-pound object that is not a cannon projectile. And because they are captured by the ring grooves, the piston rings are along for the ride; slamming up and down within the ring grooves trying desperately to maintain a seal with the cylinder wall. Is it any wonder that they experience ring flutter at very high engine speeds? Hence the practice of using the tightest ring grooves possible without seizure and the thinnest and lightest rings that have minimal inertia. Try working that formula on the previously mentioned Formula 1 engine and you’ll find that the instantaneous acceleration is far beyond the normally accepted limit of 150,000 ft/sec2. How do they do it? The pistons are changing direction more than 150 times per second. It seems far beyond the physical limitation of the components involved, but then Formula 1 uses some very light and very strong exotic materials.
Fascinating stuff, but somewhat beyond most of our typical applications so we’re better off calculating some real-world piston speeds and learning how to rearrange the formula to calculate RPMlimits based on an arbitrary piston speed that we don’t want to exceed. Consider the following examples when solved for mean piston speed, the calculation you will use most frequently.
302-ci Chevy with 3-inch stroke at 7,000 rpm
Piston Speed = 3 x 7,000 ÷ 6 = 21,000 ÷ 6 = 3,500 fpm
The generally accepted limit for non-race performance applications is about 3,500 to 4,000 fpm, so the 302 is pretty happy at 3,000 fpm, especially since it came equipped with forged pistons.
350-ci Chevy with 3.48-inch stroke at 7,000 rpm Piston Speed = 3.75 x 7,000 ÷ 6 = 26,250 ÷ 6 = 4,375 fpm
Piston speed increases with RPM, but note that for a fixed RPM, piston speed always increases with stroke. That’s one reason why high-RPM engines generally trend toward shorter strokes. A 350 will rev over 8,000 rpm nervously while the 302 hums along quite happily provided the valve train can keep up.
Calculating RPM Limits
Suppose you have a 427 big block Chevy with big heavy pistons, a heavy piston pin, and standard ring package. You want to determine a safe rev limit that won’t exceed the structural limits of your stock pistons and rods. Just rearrange the formula to solve for RPM.
RPM = (desired piston speed x 6) ÷ stroke
The 427 has a 3.76-inch stroke and we want to impose an arbitrary piston speed of 3,800 fpm.
To meet your arbitrary piston speed limit, you should set your rev limit to 6,100 rpm. Now, do most people rev 427 Chevy’s higher than that? Of course, but if you want to set a limit, that’s how you calculate it. Most engines have considerable latitude with modern components. Consider a NASCAR engine for another example. The displacement limit is 358 ci and builders are limited to a maximum bore size of 4.185 inches. We know they run different configurations for different tracks, but let’s assume the large 4.185 bore for maximum breathing capability. Using the formula for finding stroke, we calculate:
Stroke = [358 ÷ (4.1852 x .7854 x 8)] = 3.25 inches
So what’s the mean piston speed of a Cup engine at 9,200 rpm at the end of the back straightaway?
Piston Speed = (3.25 x 9200) ÷ 6 = 4,983 fpm
Of course they have state-of-the-art lightweight components, but now that you know their limits for a 500-mile race, you can adjust your thinking accordingly. And isn’t it interesting that a Formula 1 engine and a NASCAR engine both make about the same power. The Formula 1 engine is less than half the size of the NASCAR engine and has to rev twice as fast to do it. Note also that the Formula 1 engine actually runs less mean piston speed than a Sprint Cup NASCAR engine. If you think about these relationships, you can’t help but marvel that they are physically possible. And you thought science was boring in high school.
Engine Balancing and Overbalancing
Engine balancing is often thought of as a “black art” practiced by machine shop wizards, but it’s not all that mysterious. Thousands of highly competent engine shops do it every day and rarely experience balance-related engine problems. Balancing has become even more precise with today’s modern computer-controlled equipment. Balancing components within 2 grams used to be commonplace in performance circles, but not anymore. Most high performance engine builders now balance to within 1/2 gram or less for maximum precision and engine smoothness. So what does that mean? Everything in modern performance engines is lighter and potentially more fragile, particularly in a high-speed environment. The slightest imbalance has the potential to crack crankshafts, pound out bearings and pistons skirts, and cause other types of mechanical mayhem.
Calculating Balance Weight
The difficulty with engine balance is that some of the parts go round and round while others go up and down. Getting them to do it harmoniously requires precision engine balancing. Adjustable bob weights are used to simulate the weight of the parts during balancing. Rotating weight includes the big end of the rod, rod bolts and rod bearings, plus a small amount (2 to 3 grams) to simulate the oil between the crank journals and bearings. Reciprocating weight includes the small end of the rod, the piston, piston pins, piston rings and retainers if they are used, and a few grams for the oil that clings to the moving parts. Once all of the component weights are equalized, the bob weights are calculated. A normal bob weight comprises 100 percent of the rotating weight and 50 percent of the reciprocating weight. The crankshaft is electronically balanced with the bob weights attached and normal balance is easily achieved.
High-RPM engines are frequently overbalanced to improve the high-speed balance with less regard to low speed smoothness. The intent is to further smooth the engine’s state of balance in its intended operating range. The trick is to balance the assembly so that any critical imbalance falls outside of this range (either above or below it). To accomplish this, the bob weights are adjusted from the calculated norm. Instead of adding 50 percent of the reciprocating weight, the percentage is often increased to something in the 52- to 54-percent range. If any of this is truly a “black art” it may be in actually determining the optimum percentage of overbalance. Many builders know this from experience, but new combinations often require a highly educated guess. The best approach attempts to err to the conservative side, say, 51 to 52 percent. If the engine’s ultimate performance and smoothness improves within its primary operating range, they may overbalance it a bit more on the next go round.
Normal Balance = 100% rotating weight plus 50% reciprocating weight
The overbalance percentage may cause dramatic vibrations outside of the engine’s normal operating range, but it is of no concern since you don’t run it here for any length of time. Note that overbalancing is a competition engine practice and not something that you would normally do to a street or street/strip engine that has to operate over a broader RPM range. For race engines, it has the potential to save parts and improve performance by reducing vibrations that might be harmful to ring seal, valve train dynamics, and other factors that affect power within a specific power band. It’s just one more trick in the high-performance engine builder’s bag.
Calculating Piston Position
For the purpose of accurate camshaft selection, it is important to know the piston position where the maximum pressure drop is created in the cylinder. If you recall our core mission of maximizing VE, it’s easy to grasp the critical relationship between crank angle and the timing of valve action relative to piston position. For a given rod length, the piston will achieve maximum velocity at some point during the stroke. This point (crank angle) varies according to rod length since stroke length is fixed. You may have heard that a longer rod makes more power, but that’s not necessarily the case. As a rule, changes in rod length tend to move the power peak closer to or farther from the torque peak RPM, depending on the change. When rod length is increased, the horsepower and torque peaks move closer together, but the peak values may not change significantly. Shortening the rod tends to separate the peaks farther, which may or may not be beneficial depending on the application. A longer rod causes the piston to linger longer in the vicinity of TDC and the rate of acceleration and deceleration is diminished. To some small degree this provides a little more time for combustion pressure to rise higher before the power stroke. This is beneficial in high-RPM applications where combustion time is limited. In Chapter 14, note that computerized engine simulation programs pay particular attention to rod length versus crank angle. The important thing to remember is the crank angle where the piston achieves maximum velocity and maximum pressure drop within the cylinder. The intake valve opening at this point must be sufficient to maximize flow. Simulations help you calculate and visualize this point.
For those who wish to calculate piston position in the bore relative to crank angle, keep in mind that the point of maximum velocity will differ according to rod length. Generally this point occurs when the rod centerline is 90 degrees to the crank pin, but the actual crank angle will vary with rod length. Use the following formula to calculate piston position relative to crank angle for any given combination of stroke and rod length.
P = S (1 – Cos C) + (S x S) ÷ L (Sin2 of C)
S = stroke length
L = rod length
P = piston position relative to deck surface
C = crank angle relative to cylinder centerline
Cos C = cosine of angle C
Sin2 = the sine squared of angle C
This formula is valid for any given value of angle C. While longer rods are generally preferred for high-RPM operation where burn time is minimal, shorter rods have higher acceleration rates and less dwell time around TDC. Higher acceleration rates equate to quicker exposure to the pressure drop in the cylinder, which tends to separate the peaks and promote greater efficiency at lower engine speeds. The difference is often subtle, but savvy engine builders use these tools to accurately position the peaks they want relative to specific applications. Moving the peaks closer together may bring more effective power to bear on a super speedway or a Bonneville engine, while separating the peaks may be more useful for a circle-track or road-racing engine where a broader power band is more desirable. In either case, doing the math often helps illuminate the way.
Written by John Baechtel and Posted with Permission of CarTechBooks