- Piston Velocity and Acceleration -
The subtle effects of rod length
The study of piston velocity and acceleration provides some interesting insights into the operational challenges presented by a reciprocating engine. The following graph shows a plot of the piston travel (blue line) as a percentage of distance from TDC as the crankshaft moves through 360° of rotation. The graph also shows the instantaneous piston velocity (green line) and piston acceleration (magenta line) for one full crank rotation. The magnitude values are shown as percentages of the maximum calculated value. These graphs were calculated for an engine with a 4.0 inch stroke and a 5.91 inch rod length. All specific numbers quoted in this explanation are for that case.
(Note: If you still believe that installing longer connecting rods will increase an engine's stroke, there's no need for you to go any further here.)
NOTE: All the calculations and explanations on this page and the previous page assume zero piston pin offset. A non-zero offset will slightly alter the calculations, SLIGHTLY being the operative word.
Figure 1
PISTON POSITION
You already know that if you position a crankshaft so that a given piston is at its Top Dead Center (TDC) location (absolute maximum upward motion), and then rotate the crankshaft 180°, the piston will be at the bottom of its stroke (Bottom Dead Center, BDC). It is less obvious, however, that during the first 90° of that 180° rotation the piston moves significantly farther than it does during the second 90°. Note that the blue line in Figure 1 above shows that during the first 90° of rotation, the piston travels 60% of its stroke. This characteristic is explained in detail on the previous page.
PISTON VELOCITY
The green velocity line (Figure 1 above) shows the relative speed of the piston (as a % of maximum) at any point during one rotation of the crankshaft. Velocity with a "plus" sign is motion TOWARD the crankshaft; velocity with a "minus" sign is motion AWAY from the crankshaft.
Note that at TDC and again at BDC, the piston velocity is zero. That is because the piston reverses direction at those points In order for the velocity to go from a "plus" number to a "minus" number, it must be zero at some point.
Note also that the maximum piston velocity in this case occurs at about 73° before and after TDC, not at 90° as you might think. The velocity line also shows that the piston velocity at any rotation point after TDC and before max velocity is greater than at the same number of degrees before BDC. For example, compare the velocity at 30° after TDC (62%) with the velocity at 30° before BDC (34%).
The value of the maximum velocity varies directly with engine RPM. For the configuration used in this example (4-inch stroke, 5.91" rod length), at 4000 RPM, the peak piston velocity of 4402 feet per minute.
This asymmetric velocity profile is a result of the same geometry characteristics which cause the dissymmetry in piston motion (described above). The position of maximum piston velocity depends on the relationship between connecting rod length and stroke length, known L/R ("L over R", rod length divided by stroke length). (The graph is repeated below for easy reference.)
As the rod gets shorter with respect to stroke, two interesting things happen which can have dramatic effects on cylinder filling: (1) the point of maximum piston velocity moves closer to TDC, and (2) the piston moves away from TDC faster, creating a stronger intake pulse. The location of maximum piston velocity influences the design of camshaft lobe profiles (especially intake) in order to optimize the intake event in a particular speed range.
Figure 1 again
MEAN PISTON SPEED
There is another piston velocity which is used more as a "rule-of-thumb" in engine evaluations. It is called "mean piston speed", which is a calculated value showing the average velocity of a piston at a given RPM in an engine having a known stroke length.
Keeping in mind that the piston travels a distance equal to twice the stroke length every revolution, Mean Piston Speed (MPS) is calculated by:
MPS (ft per minute) = RPM x 2 x stroke (inches) / 12 (inches per foot) = RPM x stroke / 6
The Mean Piston Speed for the example engine (4.00 inch stroke, 5.91 inch rod, 4000 RPM) is:
4000 x 4 / 6 = 2667 feet per minute.
For purposes of rules of thumb, it is generally agreed that for an engine in aircraft service, 3000 fpm is a comfortable maximum MPS and experience has shown that engines having an MPS substantially exceeding that value have experienced reliability issues.
PISTON ACCELERATION
Piston acceleration is simply a measure of how fast piston velocity is changing. If velocity does not change, there is no acceleration. Conversely, if velocity changes very rapidly, there is a large acceleration (see Velocity and Acceleration).
The force it takes to accelerate an object is proportional to the weight of the object times the acceleration. From that it is clear that piston acceleration is important because many of the significant forces exerted on the pistons, wristpins, connecting rods, crankshaft, bearings, and block are directly related to piston acceleration. Piston acceleration is also the main source of external vibration produced by an engine.
Figure 2
Acceleration with a "plus" is caused by a force pulling the piston toward the crankshaft; Acceleration with a "minus" sign is caused by a force which is pushing the piston away from the crankshaft. Notice that the magenta total acceleration line (Figure 2 above) has a very different shape around TDC than it does around BDC. At TDC and BDC, the piston is reversing its direction of motion, so piston velocity is zero, but that velocity is changing very rapidly, producing large values of acceleration.
The maximum positive value of acceleration occurs at TDC (1216 "g"). Between TDC and 73°, acceleration is positive but decreasing toward zero (the piston velocity is still increasing but less rapidly). At maximum velocity (73°), the piston begins to slow down. At that point, the acceleration changes direction (from a "plus" number to a "minus" number), and in so doing, momentarily passes through zero.
The maximum negative acceleration (-643 "g") does not occur at BDC, but about 43° either side of BDC. The value of this maximum negative acceleration is only about 53% of the maximum positive acceleration seen at TDC. The acceleration at BDC (-601 "g") is only 49% of the TDC maximum. The acceleration from 73° to BDC is negative, and it is slowing the piston to zero velocity. Therefore, it might be (incorrectly) called deceleration. However, that same negative acceleration is applied to the piston after BDC and is causing its velocity to increase.
The piston motion caused by the vertical component of crankpin movement (explained on the previous page) is called primary motion. The piston motion caused by the horizontal component of crankpin motion is called secondary motion. Recall that as the crank rotates 90° from TDC, the secondary motion adds to the primary motion, and from 90° to BDC, the secondary motion opposes the primary motion. The same is true for the acceleration. The acceleration curve is the sum of the primary (blue) and secondary (green) curves, as shown in Figure 2 above.
The asymmetrical nature of all three curves is a function of the relationship between the length of the connecting rod and the crankshaft stroke. A longer rod with respect to stroke length tends to reduce the asymmetry of motion, reduce the peak acceleration at TDC and increase the peak acceleration at BDC, moving those two peaks closer to the same value.
Contemporary auto engines tend to have rod-length / stroke ratios in an approximate range of 1.5 to 1.9. Note that a rod / stroke ratio less than 1.3 is, for practical applications, not possible due to physical constraints such as the need for piston rings and a wristpin, sufficient piston skirt length, and the inconvenience of having the piston contact the crankshaft counterweight.
Here are two practical examples showing typical values. In a Lycoming IO-360 (and IO-540) the rod length is 6.75" and the stroke is 4.375", for a ratio of 1.543 (close to the low end of the spectrum in contemporary design). At the other end of the spectrum, the connecting rod on a typical (circa 2007) 2.4-liter Formula-1 V8 engine is about 4.01" long (what your average grease monkey would call a "very short rod"). The stroke is in the vicinity of 1.566", for a very large ratio of ratio of 2.56. The following graph (Figure 4) clearly shows the effect of large and small rod/stroke ratios, and the figures in this paragraph certainly reveal the absurdity of discussing rod length as an absolute.
Figure 3
It is clear that the engine with the "long rod" (6.75") has a very small L/R ratio, and produces the green and magenta curves in Figure 3, showing the substantially earlier velocity peak and the distinct reversal around BDC, indicating a substantial secondary vibration component. Compare that to the large-ratio ("short rod") black and blue curves, showing an earlier peak velocity (could that help intake tuning, perhaps ??) and a very clean curve around BDC, showing a substantially-reduced secondary vibration component.
