by Dr. Randy Herold
Engineer IV, General Atomics Aeronautical Systems
While there are many factors that contribute to an engine’s efficiency, the primary factor that needs to be considered is the engine geometry itself. Not only does the overall size of the engine matter, but the aspect ratio of the engine cylinders—defined by the stroke-to-bore ratio—also matters. To explain why, one must consider three factors: in-cylinder heat transfer, cylinder scavenging and friction.
Simple geometric relationships show that an engine cylinder with longer stroke-to-bore ratio will have a smaller surface area exposed to the combustion chamber gasses compared to a cylinder with shorter stroke-to-bore ratio. The smaller area leads directly to reduced in-cylinder heat transfer, increased energy transfer to the crankshaft and, therefore, higher efficiency.
Cylinder scavenging—a two-stroke phenomenon in which the exhaust products in the cylinder are replaced by fresh air—is also strongly affected by the stroke-to-bore ratio in a uniflow-scavenging, opposed-piston, two-stroke engine. As the stroke-to-bore ratio increases, so does the distance the fresh air has to travel between the intake ports at one end of the cylinder and the exhaust ports at the other end. This increased distance results in higher scavenging efficiency and, as a result, lower pumping work because less fresh air is lost via charge short circuiting.
Engine friction is affected by the stroke-to-bore ratio because of two competing effects: crankshaft bearing friction and power-cylinder friction. As the stroke-to-bore ratio decreases, the bearing friction increases because the larger piston area transfers larger forces to the crankshaft bearings. However, the corresponding shorter stroke results in decreased power-cylinder friction originating at the ring/cylinder interface.
At Achates Power, we have conducted extensive analyses in all three areas in order to correctly identify the optimum engine geometry that provides the best opportunity to have a highly efficient internal combustion engine. In-cylinder simulations have shown that the heat transfer increases rapidly below a stroke-to-bore ratio of about 2, engine systems simulations have shown that the pumping work increases rapidly below a stroke-to-bore ratio of about 2.2 (because of the associated decrease in scavenging efficiency), and engine friction models have shown that the crankshaft bearing and power-cylinder friction values, for the most part, cancel each other out for our opposed-piston, two-stroke engine.
It should be noted here that in an opposed-piston engine—where there are two pistons per cylinder working in opposite, reciprocating motion—the “stroke” results from the combined motions of the two pistons and is roughly double the distance that one of the pistons travels in half a revolution. This fact allows an opposed-piston engine to have much larger stroke-to-bore ratios than an engine with one piston per cylinder without having excessively high mean piston speeds that are detrimental to inertial loading and friction.
For context, below is a plot of power density versus stroke-to-bore ratio of some current four-stroke engines designed for a wide range of applications. Note that all of the engines in the chart have cylinder heads, so the stroke describes the actual piston stroke. The data in the plot show a trend in which engines that require high power density—like those in race cars—have a small stroke-to-bore ratio, and engines that require high fuel efficiency—like those in heavy-duty trucks and marine cargo ships—have a large stroke-to-bore ratio.
The limiting factor in this relationship is the inertial forces origination from the piston motion. To achieve high power density, the engine must operate at a high engine speed (up to 18,000 rpm for the Formula 1 engine), which leads to high inertial forces that must be limited by using a small stroke-to-bore ratio. For applications that demand high efficiency, a long stroke-to-bore ratio is necessary and, again because of the inertial forces of the piston, requires a slower engine speed and lower power density. For the marine application that has a 2.5 m stroke, the engine speed is limited to 102 rpm.
In comparison, the Achates Power opposed-piston, two-stroke engine is being designed with a stroke-to-bore ratio in the range of 2.2 to 2.6. This range of stroke-to-bore ratio values allows us to create a highly efficient internal combustion engine while still having mean piston speeds comparable to engines currently available in medium- and heavy-duty applications. Any opposed-piston, two-stroke engine with a stroke-to-bore ratio below 2 will suffer from high in-cylinder heat transfer and poor scavenging, both of which act to reduce the engine’s overall efficiency.