How the Rotary Pulse Jet compares with an IC Piston Engine:1

The area shown at the top of the drawing is an additional volume that remains even when the piston is at the very highest point, a location called TDC for Top Dead Center, which will mean more in our second drawing. The space above the piston at TDC is carefully designed. In this specific case, it has a volume of around 6.3 cubic inches.

Most superficial descriptions of automotive engines then say that the gas-air mixture is ignited at that moment and that the even higher pressure of the exploding gas drives the piston down, turning the crankshaft. Reference is usually even made of 'advancing the timing' of the ignition spark, so it occurs maybe 10° or 20° BEFORE TDC, so the explosion has a moment to build up its full power by the time it gets to TDC. If you look at this drawing for a while, you should be able to see that that is impossible! If the explosion (and all its effects) occurred exactly at the moment shown in this drawing, at TDC, the crankshaft would not be given any rotation at all! Virtiually the entire force of the explosion initially acts to try to drive the piston, connecting rod and crankshaft downward, out of the bottom of the engine, without giving it any rotation at all! (When this actually happens, VERY bad things tend to happen to the engine!)

All actual internal combustion engines rely on KEEPING that explosion pressure for as long as possible! In Calculus terms, the total effect regarding rotating the crankshaft is the Integral of the net force actually applied to the crankshaft by that connecting rod for as long as there is explosive pressure inside the cylonder. In an engine that is operating properly, contributions to this Integral begin at the instant of ignition and end when the exhaust valve begins to open. The instantaneous force applied as torque in rotating the crankshaft continuously changes during this "power stroke". It actually begins with a slight negative contribution since ignition is timed to occur before TDC, but not much pressure yet develops since the flame is still spreading inside the cylinder. The contribution becomes exactly zero at TDC, and then quickly rises as the internal burning and pressure continues and the leverage angle at the crankshaft improves. Eventually, the piston goind down reduces the presssure, and engine cooling also does, and good design times the exhaust valve to begin opening about when productive torque is no longer available.

So, from a truly accurate (Physics) perspective, a VERY complicated graph of resultant torque would first need to be determined, and then that graph would be Integrated to determine actual engine torque generated, at that engine speed and under those conditions of spark advance and the rest. Such analysis is rarely actually done, and nearly always, simply experimental measurements of real engines is found by experiment to learn these things.

You might note that the pressure must be maintained within the cylinder throughout the entire power stroke for decent performance. This explains why an engine loses much of its power once the piston rings are worn (and therefore leaking pressure) or the valve seats become worn or distorted (and therefore leaking pressure). If the engine actually just relied on the instantaneous effects of the explosion, worn rings or valves would be of minimum importance, but the fact that the basic design relies on HOLDING the pressure before actually using it make those components extremely important.

It turns out to be sort of fortunate that the "speed" of the explosion of the gasoline-air mixture is relatively slow! Under the conditions

It is very well established that the explosion, and therefore the heat created, causes the gases in the combustion chamber to obey standard rules of Chemistry, such as the Ideal Gas Law. Because of the sudden heat, the gases try to expand immediately, but they cannot, so the pressure in those hot gases greatly and rapidly increases. Very consistently, the explosion pressure in an internal combustion engine rises to between 3.5 and 5 times the compression pressure. Since our example engine had a compression pressure of 120 PSIA, this results in a momentary explosion pressure that peaks at around 500 PSIA.

Since the piston is 4" in diameter, the top surface of it is just PI * (4/2)² or around 12.6 square inches. Each of those square inches experiences the 500 PSI pressure, so the total force then instantaneously applied to the top of the piston is 12.6 * 500 or around 6300 pounds.

Because of the geometry of the situation when the crankshaft has progressed 10° after TDC, the force diagram indicates that this downward force must be multiplied by (approximately) the sine of 10°, in order to determine the tangential force applied to the crankshaft. Approximately, because the connecting rod is no longer parallel with the axis of the cylinder bore, the actual angle being slightly higher, and an exact angle is easy to calculate with a thorough analysis. For now, 10° will give an approximate result for our purposes.

Therefore, the tangential (rotative) force actually transferred to the crankshaft is around 6300 * sin(10) or 6300 * 0.174 or around 1100 pounds. Since this force is applied to the throw of the crankshaft, at 1.75" radius from the centerline of the crankshaft, the torque transferred to the crankshaft is therefore 1100 * 1.75" or 1100 * 0.146 foot or 160 foot-pounds of torque. This calculation is in ball-park agreement with the published maximum torque curves for such engines, at 1500 rpm.

Notice that the radial force applied to the crankshaft (bearings) is around 6300 * cos(10) or around 6200 pounds! At that moment, the vast majority of the power of the explosion is trying to drive the crankshaft down out of the engine, without rotating it! And in seriously trying to abuse the bearings! Without engine oil, under pressure, in the bearings, they do not last long with 6200 pounds force against them!

In traditional automotive thinking, this sort of makes sense! As long as the piston rings do not leak too much and the valves do not leak too much, then those expanded gases inside the combustion chamber cannot escape. That means that, until the exhaust valve starts to open, all the pressure will act to push the piston downward. In order to get the most total power, it makes sense to keep that pressure acting as long as possible. This means that having the maximum pressure developed as soon as possible after TDC gives the most possible available degrees of productive crankshaft rotation. The benefit of this is seriously affected by the fact that, as the piston moves downward, the volume inside the combustion chamber increases, so the pressure drops. From a beginning pressure of 500 PSI in our example, at the later instant when the crankshaft had rotated 45° the volume has increased such that the pressure drops to around 200 PSI (without any leakage) and by the time the crankshaft has advanced 90° the pressure is down to around 125 PSI. The AVERAGE pressure during this 90° of rotation is referred to as Mean Effective Pressure (mep) and is commonly around 200 for common engines under power. (This description is for best conditions, fairly high power and revs).

(The contents of this page are taken from C. Johnson's web-site:The Physics of an Automobile Engine

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