Figure 1.12 Nondimensional velocity vs. crank angle for

      If we neglect terms of , and use the trigonometric identity , the piston velocity can be approximated as

(1.39)

      The acceleration is found by differentiating Equation (1.39) with respect to time

      (1.40)

      Note that the velocity and acceleration terms have two components, one varying with the same frequency as the crankshaft, known as the primary term, and the other varying at twice the crankshaft frequency , known as the secondary term. In the limit of an infinitely long connecting rod, i.e., , the motion reduces to a simple harmonic at a frequency .

      The reciprocating motion of the connecting rod and piston creates accelerations and thus inertial forces and moments that need to be considered in the choice of an engine configuration. In multicylinder engines, the cylinder arrangement and firing order are chosen to minimize the primary and secondary forces and moments. Complete cancellation is possible for the following four‐stroke engines: in‐line 6‐ and 8‐cylinder engines; horizontally opposed 8‐ and 12‐cylinder engines, and 12‐ and 16‐cylinder V engines (Taylor 1985).

      Scaling of Engine Performance

The performance characteristics of three different diesel engines are compared in Table 1.1. The engines are a four‐cylinder 1.9 L automobile engine, a six‐cylinder 5.9 L truck engine, and a six‐cylinder 7.2 L military engine. Comparison of the data in the table indicates that the performance characteristics of piston engines are remarkably similar when scaled to be size independent. As Table 1.1 illustrates, the mean piston speed is about 12 m/s, the bmep is about 15 bar, the power/volume is about 40 kW/L, and the power/mass about 0.5 kW/kg for the three engines.

Table 1.1 Performance Comparison of Three Different Four‐Stroke Turbocharged Diesel Engines