When the exhaust port cracks open, gases still under a considerable pressure burst out into the exhaust tract, forming a wave front that moves away at a high speed down the port and headed for less confined quarters. After travelling a comparatively short distance, this wave reaches the first part of the expansion chamber proper, which is a diffuser (commonly called a megaphone). The diffuser’s walls diverge outward, and the wave reacts almost as though it had reached the end of the system and is, reflected back up the pipe toward the cylinder with it’s sign inverted. In other words, what had been a positive pressure wave inverts, to become a negative pressure wave. The big difference between the action of the diffuser and the open end of a tube is that the former returns a much stronger and more prolonged wave; it is a much more efficient converter (or inverter) of wave energy.
As the initial wave moved down the diffuser, the process of inversion continues apace, and a negative pressure wave of substantial amplitude and duration is returned. Also, overlayed on this the effect of inertia on the fast-moving exhaust gases, and the total effect is to create a vacuum back at the exhaust port. This vacuum is very much stronger than one might suppose, reaching a value of something like minus-7 psi at its peak. Add that to the plus-7 (approximately) psi pressure in the crankcase working to force the fresh charge up through the transfer ports and this will help understand how the transfer operation is accomplished in such a very short time. Obviously, too, this combined pressure differential of almost one atmosphere is very helpful in sweeping from the cylinder the exhaust residue from the previous power stroke. It’s all like having a supercharger bolted on over at the engine’s intake side-but without the mechanical complication.
Years ago, the exhaust system ended right behind the diffuser. Those devices did a job in clearing exhaust gases from the cylinder, and helped the fresh charge up from their crankcase. But their vacuuming effect was very much a mixed blessing: their problem was that they did not know when to stop vacuuming, and would pull a sizable portion of the fresh charge right out of the cylinder. Horsepower being a more or less a direct function of the air/fuel mass trapped in the cylinder at the onset of the compression stroke, this aspect of the pure megaphone’s behavior was highly undesirable.
Here, our original wave reaches the cure. Following the diffuser, and after perhaps a couple of inches of straight-walled chamber, the wave encounters a converging cone that effectively constitutes a closed end to the expansion chamber. A part of the wave energy will already have been inverted by the diffuser sent back to the cylinder, but there is enough of it’s original strength left to rebound quite strongly from that closed end, and it reflects with its original, positive, sign. In due course of time, this wave arrives back at the exhaust port itself, stalling the outflow of the fresh charge. Indeed, it will momentarily reverse the flow there, stuffing what might have otherwise been lost back into the cylinder. The net result of all this activity on the part of the expansion chamber-first pulling and then pushing at the fresh charge to hold it in the cylinder-is a big boost in power.
As mentioned earlier, the expansion chamber is not purely a sonic-wave device. Back at the closed end of the chamber there is an outlet pipe, and it is too small to keep the pressures inside the chamber equalized with atmospheric pressure. Consequently, there is an abrupt pressure rise inside the chamber, toward the end of its operating cycle, that is felt at the engine’s exhaust port and plays a very large part in preventing charge loss.
This entire process can work wonderfully well, and it can also fail miserably if the various elements of the expansion chamber are not dimensioned properly. All of the various waves and pressure sucking and surging about the exhaust port must operate in agreement with the engine’s requirements. When they disagree, the result is worse than can be obtained at much lower price paid in time and money with the stock muffler. As it happens, the motions of those waves are stubbornly tied to the exhaust gas temperature, and supremely indifferent to what the engine would prefer in terms of their arrivals. The time intervals between the initial wave departure, and the return of it’s reflected components is a function of wave speed, and the system’s lengths. Thus as wave speed is subject only to the laws of physics and exists as something one must simply use without altering, the task of designing an expansion chamber for some particular application is to establish lengths, diameters and tapers that will use the pulsations within the exhaust system to the engine’s benefit.
We may start by determining the proper length through the entire system back to the expansion chamber’s closed end. That task requires that we know the speed at which sonic waves travel within the chamber, and therein lies a great difficulty. As noted previously, these wave’s velocity are determined largely by the factor, temperature of the gases through which they are propagated-and that factor, temperature, varies continuously in the course of a single operating cycle. Exhaust gases emerge from the cylinder at about 1200. F and have very nearly (about 800. F) the same temperature back in the outlet pipe. But expansion within the chamber itself cools them (prior to recompression and re-heating back in the baffle cone) to perhaps 500. F or less in the midsection, and a wave does not move as rapidly through those cooler gases. It is possible to calculate fairly exactly the temperatures at all points throughout the system, but that would be a very complex thermodynamic problem.
Happily, in this instance it is possible to arrive at a satisfactory solution to the problem by determining wave speed-by starting with the answer and working back. In short, you can measure a lot of existing expansion chambers known to be effective, and by comparing their lengths, exhaust port timings and the speeds at which the engines develop their power, eventually come up with a figure for wave speed representing a workable average.
Using that high-average figure for wave speed, we can establish the exhaust system’s tuned length by means of the following formula:
Lt = 
Where,
Lt is the tuned length, in inches
Eo is the exhaust-open period, in degrees
Vo is wave speed, in feet per second
N is crankshaft speed, in revolutions per minute
This length is measured from the exhaust port window back to a point slightly more than halfway down the baffle cone at the end of the system
Diffusers should have an 8-degree included taper for maximum energy recovery, and an outlet area 6.25 times that of their inlet. Outlet diameters for diffusers of all inlet diameters may be determined in the following manner:
D2 = 
Where
D2 is the diffuser outlet diameter
D1 is the diffuser inlet diameter
6.25 is the outlet/inlet ratio constant
Although these diffuser diameters, tied to the 6.25 constant, remain the same, diffuser length may be varied, as there are reasons for using diffuser tapers other than 8-degrees. That taper does the best overall job of energy recovery, but it is possible to get a stronger inverted wave with diffuser tapers greater than 8-degrees, at the expense of wave duration. Conversely, one also may extend the wave duration by accepting some diminishing of its amplitude with shallower tapers. Diffusers having tapers of more than 10-degrees return a wave of very brief duration.
The use of two-stage diffusers also facilitates coping with the conflicting requirements of expansion chamber volume and lead-in pipe length. With a longer lead-in pipe or added chamber volume, the overall effect is to increase power output below the power peak- with volume having its most pronounced effect high on the engine speed scale, near the power peak; length added to the lead-in pipe brings about a somewhat more serious drop in maximum power, but also lends a marked increase in low speed torque. These effects tend to modify the choice of diffuser tapers, as a short, steep taper diffuser provides room for a longer lead-in pipe or added chamber volume- both of these tending to offset the power range narrowing influence of such diffusers.
Exhaust waves simply do not like being puffed through anything but a cone; even less do they like a cone that has been dented or notched to clear a frame tube or to provide ground clearance. They can feel every change in cross-section in the containing vessel. They are, however, willing to follow even the most abrupt jog in the system. Sonic waves may be able to feel even the most minute changes in section; they will make any turn built in the system without slowing or losing any of their energy.
The only part of the system we must be careful to provide smooth turns is up at the lead-in pipe and at the entry to the diffuser. Though at such section, gas velocity is very high, and while the wave wont care about sharp jogs, such jogs will have a bad effect on gas flow. Gas flow involves the movement of matter; a wave is just energy, and being without mass, is also without inertia and therefore cares nothing about sharp corners.
Flattening the chamber is not a very good idea, but it can be squared off somewhat without greatly compromising its basic power enhancing properties. Now, with the drive against noise so prominent, any departure from round will be considered poor design practice. Exhaust waves are very strong, and will make even a round section chamber walls ring loudly, just like the engine is shooting marbles out of its exhaust port. These pulses, which are strong enough to set up ringing even in the relatively stiff walls of a round-section chamber, will make any flat areas in the expansion chamber walls pant in and out like a drum-head. This vibration is of course transmitted into the surrounding atmosphere as a hellishly loud noise, and no matter the effectiveness of the muffler added back at the chamber’s outlet pipe, the engine’s overall noise output will nonetheless be very high. The noise source just described can only be minimized by either making the chamber the chamber out of very heavy steel, or by giving it a shape that resists pulsing; the round-section chamber may ring somewhat, but it cannot actually pulse in and out even when made of very light-gauge material. This pulsing of the chamber’s walls has another highly undesirable side effect : it makes the permanent attachment of a bracket or heat shield should be very difficult. Most fasteners will fairly quickly fracture from the severe vibration, leaving the heat shield to drop away- which is bad, but not as bad as when the same vibration fractures a major mounting bracket and the entire expansion chamber comes adrift. For all these reasons, the round-section expansion chamber, although inconveniently bulky at times, is really the best choice.
We have already noted that the baffled end of most expansion chambers is conical. This cone lends the chamber rather more pleasing lines than it would have been with a flat end, but that is not its reason for being. The reason is that if we end the chamber very abruptly, with a flat plate, the wave reflections away from it will be abrupt : strong but of a duration too brief to provide the desired port-plugging effect except within narrow limits in engine speed a conical baffle on the other hand, extends the wave reflection time (as reflection occurs down its entire length) and, because its effect are thus felt over a wider engine range speed, the engine’s useful power band is broadened. Here, along, gently tapered baffle-cone will extend an engine'’ power range more than a shorter, more sharply tapered cone in the customary trade-off between range and peak power. These tapers should be, in most cases, twice that of the diffuser used in the expansion chamber. The largest taper you should use is 20-degrees; the smallest,14-degrees. And to obtain a particular effect, diffusers and baffle-cones may be "mismatched" in any combination.
Baffle-cones, as stated earlier, reflect over their full length any wave entering them, but there is not an even reflection. What we find is a "mean" point of reflection, which is slightly more than half-way down the baffle-cone’s length. The "tuned length" is actually the distance from the exhaust port window, at the piston face, measured along the exhaust system’s centre line out to this point of mean reflection. This midway point seems to be at the halfway point of the complete cone, which would be half the length of the cone if the cone were complete, right out to a sharp tip, instead of being truncated at it’s small end to make room for the outlet pipe. This point of mean reflection is found either by drawing the complete cone, measuring, and dividing its length in half, or by using the formula:
Lr= 
Where,
Lr is the distance from the baffle-cone’s inlet to the mean point of reflection.
D2 is the baffle-cone’s inlet diameter
A2 is half the baffle-cone’s angle of convergence.
Also, the formula for finding the length of a cone, given its taper, major and minor diameters is as follows :
L=
Where
L is the length
D2 is the cone’s major diameter
D1 is the cone’s minor diameter
A is half the angle of divergence, or convergence
Outlet Pipes:
Having gotten past the business of diffusers and baffle-cones, we can proceed onward to the lengths and diameters of lead-in and outlet pipes. If the rest of the expansion chamber is proportioned properly, the outlet pipes will have a diameter between .58 and .62 times that of the lead-in pipe, and a length equal to 12 of its own diameters. It is simply a pressure-bleed resister, which prevents the free escape of exhaust gases from inside the expansion chamber and thereby creates a back-pressure to enhance the port-plugging efforts of the wave reflected by the baffle-cone.
This outlet pipe is much more sensitive to diameter than length. A particular problem associated with the outlet pipe is that if it is made too small or in diameter, or given too much length, (both tending to over-restrict the chamber’s outlet passage in terms of flow capacity) then there will be a price to pay in terms of overheating. If the outlet is too restricted, engine temperature is greatly elevated. The same will also be observed when the expansion chamber’s baffle-cone is tapered too abruptly. This increase in temperature is especially sharp at the piston crown, which tends to be the power-limiting part in a two-stroke engine. There will be temperatures high enough to darken the underside of the piston crown, due to baked-on oil forming there, when the engine is healthy. The warning sign is when that oil begins to char, which should be watched out for.
The choice of lead-in pipe diameter must be shaped not only by unit cylinder displacement, port timing/area , and according to the application in mind for the engine-but also with an eye towards the lead-in length, and the configuration of the diffuser to which the pipe attaches. For maximum horsepower only, the lead-in pipe should be given a length equal to from 6 to 8 of its diameters, while for a broader power curve up to 11-times pipe diameter should be used. All these lengths are not just from the pipes themselves, but also include the distance from the pipe mounting flange through the port to the piston face. Resistance to flow is increased with length, and this should be offset by giving the gases a larger passage. Ideally, this reduction in resistance would be accomplished by using a lead-in pipe having a slightly-diverging taper (2 or 3 degrees) but that may represent a more difficult job to fabricate.
When testing the finished item, it is important to remember that changing the taper of the baffle-cone changes that part of the power curve past the power peak, while changes in the lead-in pipe length mostly influence the low-revs part of the curve. Increases in volume are effective mostly in adding area under the power curve right at the power peak; reducing outlet pipe diameter will, if the existing pipe is too large, boost power over the entire range, but will require a close watch over piston-crown temperature. Also, each part of the system tends to develop its own individual resonances, and the lead-in pipe, diffuser, baffle-cone and outlet pipe will each have their own little wave system rattling back and forth, with other resonances of lower frequencies occurring in paired parts of the chamber. In most cases, these incidental wave patterns go unnoticed, but some-times they will fall into mutually-reinforcing activity at certain engine speeds and combine to force humps and hollows into what would otherwise be a nice, even power curve. When these do occur, often a slight shifting on lengths is enough to keep them from marching locked-step and interfering the job to be done with the primary wave motions.