Piston area ? 1

[Rat5]

Consider 2 engines with a 90mm bore.
One has a flat piston
The 2nd has a spherical piston

Will the one with the spherical piston make more torque because there is more piston area ? Or are you supposed to use projected ( so bore) area for this calculation ?

 

[RodRico]

We're talking about piston engines in which compression and expansion result from the linear motion of a piston. An ideal spherical combustion chamber is only spherical at the instant of minimum volume. At other times, it's a cylinder with hemispherical ends. In contrast, a cylindrical combustion chamber formed by flat surfaces is always a cylinder. I decided to explore the two mathematically.

I defined the minimum volume of a cylinder having flat ends with a bore of 4 inches and a minimum clearance of 0.1 inches. I then calculated the surface area and volume of the cylinder at both the minimum volume and at a volume 10x larger. Next, I defined a spherical combustion chamber having the same minimum and maximum volumes and calculated the surface area. The result is below.

At min volume, the spherical chamber bore is only 31% of the cylindrical chamber with only 19% of the area.
At max volume, the spherical chamber height is 932% of the cylindrical chamber height with 97% of the area.

Heat transfer is a function of temperature difference, surface area, and time. The spherical chamber starts with less surface area, but its stroke is 9x larger and it has about the same surface area at maximum volume. The amount of heat transferred thus depends on how quickly combustion occurs; it will lose significantly less heat during very rapid HCCI combustion but its performance will be less impressive in a diesel cycle. It also has only 31% of the ring circumference, but for any given RPM, the rings are sliding much more quickly due to a 932% longer stroke, so ring friction (which dominates FMEP) will likely be higher at a given RPM.

It's important to note the above discussion relates to an ideal spherical chamber that can't actually be built. First, there must always be some minimum clearance between the piston and head to account for mechanical tolerances, and this means the chamber can't be perfectly spherical. Furthermore, the edge of the piston can't be infinitely thin as in a hemisphere due to loads and the need for ring lands. These practical considerations move the spherical chamber closer to the cylindrical chamber.

In the end, I suppose a spherical chamber may make sense for a long stroke HCCI engine running at low RPM, but I think it's a poor choice for high revving, high horsepower, engines using traditional combustion.