How fast would a piston have to move


hey, some of you technicions out there, can you tell me how fast a piston would have to move at 5000 RPM if you have a 3 inch stroke? I realize that it slows down and stops at the top and bottom of the stroke.


Okay, every revolution it moves up 3 inches and down 3 inches. 6 inches times 5000 revolutions = 30,000 inches per minute. That’s 500 inches/second average speed. Getting the actual peak speed is more difficult. It seems like it would be around 707 inches/sec when the piston is at the midpoint of its travel?


Piston speed, measured in feet per second, is the limiting factor in reciprocating piston engines. That’s why racing engines use short strokes and lots of cylinders…
"4000 ft/min used to be an astronomical speed, achieved only by the most exotic of racing engines. Now there are production cars that reach and even exceed this piston speed. I think modern advances in metalurgy are the reason this has become possible, and better design and production techniques are certainly a contributing factor. Modern engines use piston designs that are both stronger and lighter than even state-of-the-art racing engines used just a few years ago. Inertia has decreased, and piston, rod, and crank strength has increased to allow properly designed and built engines to run these speeds with excellent reliability and durability.

I also think friction has a lot to do with this limit. I have read articles that talk about engines having a dramatic and steeply curved increase in friction once piston speeds begin to climb much past 4000 ft/min, resulting in a point beyond which the gains of performance reach an equlibrium with the increased power loss created by the friction. Modern lubricants have extended this ceiling somewhat, but only to a degree."


Piston motion is sinusoidal, with a trigonomic component as well (i.e. the connecting rod being angled at 90/270 deg). For a “true” sinusoidal motion, velocity will be maximum at the midpoint, and acceleration will be minimal. (Basically, if a sine wave is the poisition, the cosine is velocity, and sine (again) is acceleration.

I’m uncetain if assuming true sinusoidal motion woud be a sufficiently accurate approximation.

Also, W/R/T piston speed: since combustion is a burning, not an explosion, it would seem pointless to have peak piston speeds in excess of the speed of sound at cylinder temperatures: the piston would just “outrun” the pressure wave attempting to exert force.


Well, I don’t understand anything you said, but are you sure that “combustion is a burning, not an explosion”??


An explosion occurs when something burns very quickly. I think that I would classify this as a controlled explosion.


I think Tardis got it exactly right. If the average is 500 inches/second, then the peak velocity would be 500 X (square root of 2) = 500 X 1.414 = 707. This assumes the piston’s position is sinusoidal over time (I don’t know if this is exactly true, but it must be close). That lets us use the ‘root mean square’ (RMS) equation for a sine wave, average = peak/(sqrt 2). Same equation used when stereo power is rated in watts (RMS).


Tardis, See If This Is Correct.

To continue with your calculations, dividing 30,000 inches by 12 gives 2,500 feet per minute. Multiply 2,500 by 60 (minutes in an hour) to get 150,000 feet per hour.
Divide 150,000 by 5,280 (feet in a mile) to get 28.40909 MPH (miles per hour average speed).

Now 28 MPH doesn’t sound fast, until you consider that the piston is going from zero and back to zero, averaging 28 MPH 600,000 times (one trip from top to bottom and one trip from bottom to top, each revolution, times 5,000 per minute makes it 10,000 trips in a minute times 60 minutes )in that hour.

Try going from a stop to well over 28 MPH (28 is just the average speed) and back to a stop in 3 inches! There’s got to be some serious acceleration taking place.


P.S. I had to rewrite some of this to reflect that 28 MPH is just the average. I believe just over 40 MPH is peak speed.


Texases, That’s Just A Hair Over 40 MPH Peak Speed In Just One 3" Stroke?


P.S. If I figured it correctly, that trip takes just six-thousandths of a second and the 40 MPH is reached mid-way through in 1 1/2", after just 3-thousandths of a second.


The 30,000 inches/minute is only the average speed of the piston. Since the the circular motion of the chankshaft should give speeds that follow a sine wave, you need to multiply the average by the squareroot of two to get the peak speed. (I think that is right, I am an EE, not an ME.) So, your peak speed would be 28.4 MPH x 1.414 = 40.2 MPH. It should speed up until it gets to this speed at the center of its travel (1.5 inches), and then start slowing down until it hits the end of travel and starts the whole process over again.


Sine is a trigonometric function derived from the study of triangles. Think sine, cosine, tangent. The formula variables determine the sine wave shape. A sine “wave” is simply the results of the sine formula charted on a cortesian coordinate chart.

Were it not for the smoothing (damping) effects of the rotating flywheel and harmonic damper, the pulses in the waveforms caused by the cylinders firing would make it not a sine wave, but I think it’s safe to call it one.

I’d argue that the explosion isn’t controlled, simply that some of the energy is converted into piston movement, the rest into heat and light. Once the combustion process is initiated by the addition of the heat energy, it takes on a life of its own.


The crank and slider motion in a typical engine is not sinusoidal. The exact formula for speed is too complicated even for engineers to make sense out of it. So they approximate it as the sinusoid of speed plus the sinusoid at 2x the speed. There’s also the sinusoid for 4x, 6x, … of the speed, but they are insignificant.

But the sinusoid at 2x the speed is why a big inline 4 needs balance shafts to spin at 2x the speed. The counterweights on the crank do not spin that fast.


My understanding of what constitutes an “explosive” is something that burns in excess of the speed of sound. Nitroglycerine (explosive velocity 7700m/s) is an explosive; I do not believe a fuel/air mixture ever is.


Envision in the link that the circling dot is the crank portion of the crankshaft to which the bottom end of the connecting rod is attached, circling at a constant rate. Envision a piston connected a fixed distance from the crank portion of the crankshaft and moving only in the Y axis, immediately in line with the “zero” of the Y axis. I’d say that the piston’s movement charted is sinesoidal. Wouldn’t you?


Well, I think you guys covered the situstion pretty accuratley. Now the reason I asked the queation is that I believe that 5000 rpms puts a keck of a strain on everything, but espedially the rod and main bearings. I know that engines have been inprobed much over the years but still beleive high speed shortens the life on an engine. In another post called “am I driving my car too hard?” several people said that the higher the RPM, short of the redline, the better the engine performed and the “happier” the engine was.
I looked up “explosion” in dictionary and one of the answers was " a large-scale, rapid, or spectacular expansion or bursting out or forth"


FWIW, definition #5 says an explosion is: “the burning of the mixture of fuel and air in an internal-combustion engine.”

I tried to web search “when is burning an explosion?” and got nowhere. Your definition is well conceived, though.


MB, I only meant it is controlled expansion because it is inside the engine.


IMHO, the “redline” is not really a well defined rpm. What I mean is that if the redline is “5000 rpm” it does not mean that the engine will live forever at 4999 rpm and the sky falls at 5001 rpm.

The rpm where the engine is “happiest” at depends on the trottle opening. When you barely open the throttle, the ideal rpm is much lower than when the throttle is wide open.

You may have noticed that the less gas you give a car, the sooner an automatic transmission shifts into high gear. The engineers who designed the transmission know what they are doing.

One more thing, some of the most vocal experts in this world are really know-it-alls.


The “am I driving my car too hard?” thread is about a 2009 Acura TSX, which has variable timing. That means when you get the RPMs up into the higher end, not only do you get more torque as you would expect, but the cams shift to “power mode” where the adjusted timing exploits those higher RPMs for even more power, all without sacrificing reliability. If you never get the RPMs up, the timing never shifts, and you might as well not have one of the VTEC engines that are available in the 2009 Acura TSX.

If the “am I driving my car too hard?” thread was about a 20-year-old Ford Escort, you would be right, but that thread is about a car that comes with either a 4-cyl. 16-valve, DOHC i-VTEC engine or a V-6 24-valve, SOHC VTEC engine. Both engines thrive in high RPM ranges because the engineers who designed them expected them to be driven that way.


All This Was About Piston Travel And High RPM? I’d Worry More About The Crankshaft Flexing And Main Bearing Wear.

Just be sure you have an engine designed for it with lots of bearings and maybe even roller bearings.