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Note that for the automotive/hotrod use-case the most convenient (used by enthusiasts) unit of length for the piston-rod-crank geometry is the inch, with typical dimensions being 6" (inch) rod length and 2" (inch) crank radius. This article uses units of inch (") for position, velocity and acceleration, as shown in the graphs above.
But in reality, the torque is maximum at crank angle of less than α = 90° from TDC for a given force on the piston. One way to calculate this angle is to find out when the Connecting rod smallend (piston) speed becomes the fastest in downward direction given a steady crank rotational velocity. Piston speed x' is expressed as:
The comparison of mean piston speed (black line) with real piston speed (color lines). Diagram shows one stroke from BDC to TDC. Revolution = 1.000 min-1, stroke = 88 mm. The connecting rod ratio l/r varies: 3 - red, 4 - green, 5,5 - blue. The mean piston speed is the average speed of the piston in a reciprocating engine.
The acceleration, or rate of change in piston velocity, is the limiting factor. The piston acceleration is directly proportional to the magnitude of the G-forces experienced by the piston-connecting rod assembly.
The piston or other reciprocating part is directly coupled to a sliding yoke with a slot that engages a pin on the rotating part. The location of the piston versus time is simple harmonic motion, i.e., a sine wave having constant amplitude and constant frequency, given a constant rotational speed.
A fundamental specification for such engines, it can be measured in two different ways. The simpler way is the static compression ratio: in a reciprocating engine, this is the ratio of the volume of the cylinder when the piston is at the bottom of its stroke to that volume when the piston is at the top of its stroke. [1]
In the equations of piston motion, if rod length (L) is made appreciably large compared to crank radius (R), say by 100x or 1000x, then you will see that the waveforms (position, velocity, acceleration) approach sinusoidal... with real world dimensions (e.g. L=6", R=2"), the motion equations contain several components: Simple Harmonic Motion ...
As piston engines usually have their maximum torque at a lower rotating speed than the maximum power output, the BMEP is lower at full power (at higher rotating speed). If the same engine is rated 72 kW at 5400 min −1 = 90 s −1, and its BMEP is 0.80 MPa, we get the following equation: =