How A Two Stroke Expansion Chamber Works
by Michael Forrest

This site contains both well known pipe info and details never before discussed. Please don't dismiss this page as just another regurgitation of common knowledge. Near the end you will be presented with the latest and best software for design and analysis of 2 stroke pipes.

Two strokes can function with significantly better power if they are aided in these 4 ways: 1) pulling in extra intake charge up from the crankcase into the cylinder, 2) pulling in extra intake charge from the carburetor into the crankcase, 3) preventing the intake charge from escaping through the exhaust port  (so it can be used for combustion), 4) boosting the compression at top RPM for a faster burn and more power. An expansion chamber does just that. But at what part of the powerband it does it is dependent on how far from the engine the diffuser cone and baffle cone are. That is because the pressure wave (created when the exhaust suddenly enters the exhaust pipe) travels at a certain speed, so many meters per second. When the wave enters the diffuser cone the sudden expansion causes a reverse traveling suction wave which, when it arrives back at the cylinder matches the crankcase suction in order to prevent sucking exhaust gas from the cylinder into the transfers, and/or helps to pull up gasoline/air mixture from the crank into the cylinder. When the ongoing pressure wave in the pipe hits the baffle cone the sudden contraction of the wave causes a reverse pressure wave which, when it arrives back at the cylinder, prevents the escape of intake charge if the wave arrives between the time the piston closes the transfer ports and closes the exhaust port. 

I used to think that explanation was just speculation until I studied professor Blair's work. In his "Design and Simulation of Two Stroke Engines", in chapter two entitled "Gas Flow Through Two-Stroke Engines", he gave the results of tests with pressure waves in pipes that proved the above explanation. For more detailed info on this go to the bottom of this page.

I have made an Excel file for analyzing the dimensions of an expansion chamber to see if they are in harmony with the cylinder port timing and desired peak RPM of the engine. (An Excel file automatically does calculations and displays/graphs the results when information is entered into the correct data "boxes".)

The Hidden Action of Expansion Chambers:

Primary Action

The main action of an expansion chamber is the creation of reverse waves (returning to the cylinder) that happen from the main pressure wave in it expanding and then contracting at the diffuser and baffle cones. The wave is first created when the exhaust blasts into the exhaust port. Graham Bell wrote that "changes in cross-sectional shape [area] affect pulse wave energy" which is another way of saying that the bigger the change in pipe area, the stronger the return wave from that area is. My Excel file, sheet 2, calculates the percentage area change along the diffuser and baffle every 10mm of their length. Putting the calculated numbers into sheet 3 will result in a graph of the return waves:

Wave Speed
The speed of the pressure wave in the expansion chamber is directly dependent on the temperatures inside the pipe. It would be very straightforward but what complicates things is that the farther from the cylinder, the less the temperature. It changes with jetting, load, exhaust port timing, and RPM (higher causes higher temps). For designing you should be precise and measure it yourself because a 40 degree C variation causes a typical difference of 250 RPM in the end of pipe powerband. For precise pipe calculations you can drill a 1.8mm (.07") pinhole in the header about 6 inches from the piston, insert a thermocouple (attached to a meter), and read the peak temperature when you are riding at top of powerband RPM going up an inclined surface with the meter taped to your gas tank (with foam in between the two to insulate the meter from engine vibrations). Don't take any reading till the engine is at maximum temperature since that affects EGT. But you can use my pipe calculators estimation of the temperature to design a near perfect pipe and later adjust the header length to match the desired pipe powerband of RPM. Temperature isn't super critical. The difference between 605 C and 645 C header only requires a header length difference of 10mm (.4").
Factors affecting temperature--> more compression gives less temperature (because the mixture burns quicker. a compression ratio of 7:1 is 40 C hotter than 9:1), alcohol content in the gasoline lowers temperature, richer fuel/air mixture gives hotter temperature, higher elevations give less temperature, colder ambient temperatures give less temperature, non-squish band heads give more temperature (due to a longer burn), and the larger the exhaust port duration the greater the temperature will be.

Header Diameter
This is the pipe that connects the cylinder to the diffuser cone. Gordon Jennings said its cross sectional area should be 15%-20% larger than the exhaust port area for maximum peak power, and 50% greater for motocross bikes (for a wider powerband). Most pipe builders just keep the same stock header diameter. My expansion chamber calculator lets you do whatever you want to but gives recommendations for header and belly diameter. What I don't like about his advice on headers is that it essentially disassociates its size from the size of the engine displacement and exhaust port blowdown area (which is the only part of the exhaust port I consider because all of the exhaust typically exits before the exhaust port is 3/4 open). This topic of header size is important because both Graham Bell and Gordon Jennings give belly diameter recommendations that are 2.5 times that of the header. So they keyed off the header. The right diameter header is best for power because too narrow creates a slight restriction to outflow of exhaust charge. And too wide reduces the strength of the trailing wave which needs to be strong to help pull up intake charge through the transfers.
My pipe calculator uses a multiple of the exhaust port open area at the end of the exhaust pulse which jives pretty much with a lot of quality engines.
Flared Header
Most headers on high RPM MX and GP bikes are divergent up to 2 degrees. That is to say that they get larger with more distance from the cylinder. This theoretically aids exhaust gas flow at high RPM but reduces the diffusers return wave strength by reducing the diffuser cone angle(s). This loss of diffuser wave strength in the example below lowered the average power by 38% (from 6.3 to 3.9). 



If it does help evacuate the cylinder pressure faster then the exhaust pulse time would be lowered. On my pipe calculator I changed the formula to lower the exhaust pulse time by 10% and the effect it had was to change the graph a little but it maintained the same power loss. I then tried a 1 degree header and the result was only a 19% power loss.



So I'm skeptical of any advantage of a flared header but I admit I have no personal experience doing a back to back test between a straight and a flared header on a high RPM bike.

Header Length
This length determines when the diffuser and baffle return waves will arrive back at the cylinder so it has to be in agreement with your target peak RPM since the baffle waves timing sets the limit for how high the engine will rev. The correct distance depends mostly on the peak RPM you want. Shortening it allows the engine to rev higher. For a open classed motocrosser reving to 7,000 RPM one inch of length affects the powerband by approximately 100 RPM, and for an engine reving to 10,000 RPM one inch changes it by 300 RPM. Its best length is discussed in the section about secondary waves.


The Diffuser (expanding/diffusing) Cone
As long as the primary pressure wave is traveling along the diffuser it is creating a vacuum (negative pressure) wave that returns to the cylinder. The extra vacuum either helps to suck in extra intake charge from the crankcase into the cylinder, or it prevents the suction into the crankcase of exhaust gases (due to crankcase vacuum) as the piston rises. Extra fuel/air contributes to a stronger/longer combustion for more engine power. Also less dilution of air/fuel by exhaust gases leads to a more powerful combustion due to a higher percentage of oxygen. This is what causes an expansion chamber to give more power than a header/muffler combo w/o diffuser or baffle cones.

* pipe powerband: the RPM range where the horsepower is increased due to the effect of the baffles return pressure wave.

Diffuser Angle(s)
The two main considerations are: how many milliseconds long the return wave has, and what the shape of the diffuser is (whether it is a single cone or if multiple cones then what waveshape do they create so that it matches the type powerband you want). Greater angle of diffuser sections means the diffuser will be shorter. Jennings wrote in his Two Stroke Tuners Handbook that multi-coned diffusers cause a higher return wave peak which increases power. I would add that stronger return waves are more likely to suck out fresh intake charge from the cylinder unless the transfers have a good design so that they are good at directing the intake charge towards the back of the cylinder away from the exhaust port. Also a strong return wave may suck out too much intake charge if the front transfers are very close to the exhaust port. You can tell by looking at the pattern the intake flow leaves on top of the piston. (see example). The diffuser angles should also be in relation to crankcase compression ratio because a high ratio (1.5:1 or more) has more need of a strong vacuum wave from the diffuser to counter the crankcase suction as the piston rises after BDC. Otherwise some exhaust gas gets sucked back down into the crankcase. The advantage of a multi-coned diffuser: Since the main factor affecting the strength of the return wave is the percentage change of cross sectional area (every 10mm) then a single angle diffuser cone for my 55cc engine ended with a 6.5% area change (for the last 10mm distance of the cone) whereas a 3 stage cone I designed, although the belly cross sectional area was 9 times that of the header, ended up with a strong 9.1% area change at the end. A 2 or 3 stage diffuser causes the percentage area change to be more evenly spread out along the length of the diffuser instead of having very strong changes at the beginning (15.5%) and very weak changes at the end (6.5%).


Here's the return waves for the 3 types of diffusers:


Click here to read more about diffuser cone angles.

Maximum Cross Sectional Area of Diffuser
Former recommendations was that the maximum diameter at the end of the diffuser (at the belly) shouldn´t be any more than 2.5 times the beginning header inner diameter. This is equal to an area 6.25 times that of the cross sectional area of the header. But that was back when they used single coned diffusers. Now with the use of multi-coned diffusers (with increasing angles) we are able to counter the loss of return wave generation efficiency at diameters more than 2.5x. My pipe calculator now uses Boyles Law as part of the computation to accurately determine return wave generation even for bellys larger than 2.5 the header diameter. My pipe calculator suggests using 2.75 times the ideal header diameter (which it also computes).

Belly
The belly exists to keep the diffuser and baffle waves from overlapping too much which would cause a canceling of their pressure differences. You can see in the graph below (calculated using Boyles Law) that as the belly width increases there is a more minimal pressure change and therefore weaker return wave strength. 10.3 psi is a typical exhaust pressure peak in the header which is the beginning absolute pressure in this graph. (Absolute pressure is psi + 14.7) (The pipe functions with absolute pressures whereas we humans think in terms of relative pressures.) It is the pressure changes in the exhaust wave going thru the pipe that cause the secondary waves to return to the cylinder. The more pressure change, the stronger the return wave is. So although there are pressure changes all the way up to 4.5 times the header diameter it is just not recommended to expand that far. Using multi-coned diffusers I wouldn't recommend going over 3 times the header diameter.


If the belly is too wide then that causes the end of the diffuser and the beginning of the baffle to be "dead zones" that cause very minimal return wave strength and so in essence lengthens the belly. That is why some people think that having a wide belly widens the powerband (at the expense of peak power). Well, it does but sometimes because it's causing a longer virtual belly section at the expense of the diffuser and baffle lengths which does widen the powerband at the expense of peak power.

With most bikes there is limited space which sets the maximum diameter of the belly and so the diffuser and baffle have to be designed to accommodate the belly diameter. It is always parallel-walled. When designing a pipe it is always best to make variations to it and note the results at the power graph. Below are 3 graphs showing the difference in pipe powerbands for different belly lengths with a single cone baffle. The shortest belly gave the best peak power but the need for the powerband to be wider than each gears RPM range is more important than peak power. After you upshift you want to be within the pipe powerband.



The Baffle Cone
The purpose of the baffle is to create a return wave so that at high RPM the return wave arrives back at the cylinder before the exhaust port is closing in order to increase cylinder pressure. Without it the piston will push intake charge out the exhaust port as it rises. Providing a pressure to match or exceed the pressure created in the cylinder by the ascending piston (~5psi) is the reason for the baffles return wave as well as increasing dynamic engine compression. Doing both things increases engine power at high RPM. Unfortunately, at all engine RPM except near peak RPM, the return wave returns when the transfers are open and tends to push exhaust gas and/or intake charge back down into the crankcase from the cylinder via the transfers which limits mid range engine power. But if you want an engine with explosive power on top then you have to have a strong baffle return wave. The baffle should be designed to match the bikes RPM range of the needed powerband which takes precedence over the peak power you want. A longer baffle due to a lesser angle will allow a slightly wider pipe powerband, but another advantage is less power loss when the engine RPM is just below the RPM range of the powerband.
Tuned length
The perfect location for the baffle, in distance from the piston, needs to be set to match the desired peak RPM of the desired powerband. The header, diffuser, and belly set its length from the piston. But if the baffle uses many cones of differing angles then using a formula can't accurately determine the tuned length because a formula doesn't take into account the modified baffle wave shape (due to multiple cones).
Angle
For a single angle baffle cone the steeper the angle the stronger the baffle return wave and the stronger the supercharging effect. Lesser angles cause less peak power but don't restrict pre-powerband power as much as a steep angle and so are better for trail bikes and street bikes (although you can eliminate most of that power dip with a boost bottle). Making a 3 cone baffle with increasing angles gives more power at the beginning of its pipe powerband. It is normally better for large bore engines or trail/street bikes. A 3 cone baffle with decreasing angles gives more power near the end of the pipe powerband. It is normally better for race engines. Click here to read more on this subject.

Ratio of Diffuser Angle to Baffle Angle
Others have written that the diffuser angle needs to be half that of the baffle angle but that is a crude generality that doesn't apply here because all the best of my pipe designs have multiple cones for diffuser and baffle which complicate the situation. All that really matters is the return waves and so I will speak in regards to them. If the diffuser wave peak strength is too weak in relation to the baffle wave peak strength then you will have that horrible pre-powerband engine drop in power that is common with race bikes (that are intended to only be ridden within their pipes powerband). I had a pipe do that on my 100cc street bike and it was completely annoying. It ruined my riding experience until I redesigned the pipe to not do that (by increasing the belly diameter and the diffuser angles). I wouldn't recommend allowing that to happen with any pipe design for an enduro or street bike. If your ride has that problem then you can also try lessening the pipe back pressure caused by the stinger (if it's smaller than what ECcalc recommends on sheet 2) by increasing the stinger diameter. Back pressure adds to the baffle wave and detracts from the diffuser wave strength which increases the pre-powerband power dip.

Stinger/Silencer
The stinger acts as a bleed off valve for the pipe. It controls the amount of average pressure in the pipe. So too narrow or too long a stinger will increase the back pressure and decrease the diffuser wave too much. The pipe pressure caused by the stinger increases with RPM so that the highest pressure is at top RPM which is why it hurts the diffuser wave the most there, more so than at mid RPM.
I never believed that the length of a tube would have much affect on its ability to flow air through it till I blew into two tubes of the same diameter but different lengths and could feel the difference of resistance to flow between the two. Then I looked for a good flow calculator and found one that works good. We can use these input parameters: diameter stinger interior in inches (which is mm/25.4), GPM=cc above exhaust port (or 72% of engine size) x 1.5 thermal expansion x .00027 conversion factor cc to gallons x RPM), length of stinger in feet (mm/304.8), .001 specific gravity for air, .168 cP viscosity for exhaust, no couplings, results in a calculation of psi difference from beginning to end of pipe. Experimenting with stinger diameters and using the flow calculator I concluded that a good range of stingers would provide about .1 psi which my spreadsheet does a good job of calculating diameters and lengths to approximate that. Although the formula in my pipe calculator now calculates a recommended stinger diameter for any length of stinger you may want to double check the results at the flow calculator site. For more on stinger sizing click here. Flow restriction from the silencer, if not a completely flow-through design, contributes to total exhaust restriction and to back pressure which restricts the engine a bit. For example my Suzuki 100 gained 10kph more top speed when the silencer was removed. Excessive exhaust restriction also adds to engine heat.
If the stinger originates at the side of the belly, and not the end of the baffle, then the exhaust pulse loses its bark and bite for a much more silent exhaust system (a whopping 84% quieter according to my decibel meter). Although my computer mic doesn't capture the sharpness of the exhaust note exiting a standard stinger, you can watch this video to see and hear how quieter the exhaust is when it exits the belly. Gordon Jennings wrote that a belly stinger adds a little bit of mid range power without losing any high RPM power. His belly stinger was the stinger pipe stuck up into the pipe so that its beginning was at the same distance from the piston that the beginning of the baffle was. Just be sure to weld a little support connecting the inner stinger to the belly so that it won't break its weld from being moved up/down by you hitting bumps at speed. Here is what he wrote on the subject:

Click here to see a belly stinger "channel" before being welded to my pipe. I cut off the previous stinger and had it welded to the belly stinger channel. Then the end of the baffle cone was welded shut. Click here to see the end product.
The graph below shows how too much pipe back pressure can elevate the whole system of return waves. This is from one of Blairs research papers with a 172cc engine. Note also how the EGT at the belly changes with stinger differences:


My experience tells me that if the intake of an engine is restricted with too small a carburetor or too small a reed valve then it's best to have a big diameter stinger for no back pressure. (Also a free flow silencer.) Here is the formula for determining correct carburetor size:
Carb throat inner diameter = K x square root of (engine cc x (peak power RPM/1000))
K for piston port intakes is .9 and for reed valve intakes .8 is its value.

Secondary Waves
When the returning diffuser wave and baffle wave gets to the cylinder some of their energy is expended (if the exhaust port is open) and the rest bounces back into the exhaust pipe. Those sound waves return a second diffuser wave from the diffuser and a second baffle wave from the baffle. And then the process repeats over and over many times till all the waves energy is expended. All these waves following the primary diffuser and baffle waves I call "secondary waves" because they are of secondary importance to the primary diffuser and baffle wave. The secondary diffuser waves increase the primary diffuser wave and lower the primary baffle wave. The secondary baffle waves decrease the primary diffuser wave and increase the primary baffle wave. The graph below on the left shows the waves occurence in relation to the timing of TC (transfers closing) and EC (exhaust closing) from 7500 RPM to 10500 RPM in milliseconds after exhaust opening. It's beneficial to pipe power to have positive pressure at EC and negative pressure at TC. The position of the secondary waves in relation to TC~EC depends on the header length. The longer the header, the later those waves occur. So we can manipulate when they occur by either lengthening the header and shortening the diffuser, or shortening the header and lengthening the diffuser. You mostly have to accept when the secondary baffle waves occur because you have to change the pipes tuned length (and peak RPM) to change when they occur. In the example below the middle of 8D (the mid point of any sine wave is the strongest) crosses EC around 9400 RPM which would lower engine power from about 9300 to 9500 RPM. Its middle also crosses TC at 8900 RPM which would increase power around 8800 to 9000 RPM. The graph on the right shows the waves occurence in relation to the beginning and end of the exhaust wave. When a secondary wave crosses its center then it changes its peak pressure which then affects the peak pressures of the diffuser and baffle wave which affects engine power. Secondary diffuser waves decrease the exhaust pulse strength, and secondary baffle waves increase its strength. In the example below the middle of 5B crosses the middle of the exhaust pulse zone at 9250 RPM to lower it and therefore lower engine power for about 250 RPM (around 9250).

These are the same graphs but with the target zones filled in with orange color.


The latest version of my pipe calculator incorporates the seconday waves with the primary waves which affects the pipe power and RPM range. This adds another degree of accuracy that the "plain" pipe calculators, that only depend on a few basic formulas, don't do. In the return waves graphs below you can see their occurence at 9500 (top right) and 6500 RPM (bottom right).



My pipe calculator uses a method to recommend the best lengths of the pipe sections for the best overall power.


My Expansion Chamber Calculator, how to obtain and use it.

The mathematical basis for the calculations of the return waves in my Excel file.

An example of pipe analysis and redesign.

Pipes built using this method.

My video showing how to make a pipe by hand.

How ECcalc agrees with the real life exhaust pressure graphs from Blair.

Three examples showing how accurate ECcalc is compared to dyno graphs.

Pipe Design Questions & Answers

Questions and comments can be directed to me, Michael, at health@dragonfly75.com
I am the designer/manufacturer of analog CDIs (for the KDX200, AX100, and motorized bicycles)  and I run BioElectric, an alternative health business. I owned my first motorcycle (Penton 125cc) in 1975 and have motocrossed a Husqvarna CR125 and Kawasaki KDX200.


Other spreadsheet calculators I've made:
Squish Velocity Calculator
Crank Balance Calculator
Boost Bottle Calculator
Porting Calculator
Fuel/Oil Ratio Calculator


details from "Design and Simulation of Two Stroke Engines"
by professor Gordon Blair:

Pressure transducers were along the length of the pipes to record the pressure waveforms and the time from their release from the cylinder to when they were sensed. The wave for each test came from a temporary opening of a port, similar to a two stroke port, that was opened releasing the internal pressure and making a pressure wave of around .008 seconds long, similar to what is produced by a two stroke running at 730 rpm if the blowdown is 35 degrees. He lists the wave speed as 343 meters per second, initial pressure as 1.5 bar, and temperature as 293 Kelvin.

Diffuser Cone and its Return Wave
Here is the drawing showing a test apparatus with a diffuser cone:


Here is the graph from page 181 showing the sensor #1 sensing the initial pressure wave, and then the negative (vacuum) return wave, then the return wave bounced back from the closed cylinder port, then the wave reflected back from the diffuser as a positive wave:


What is most important about this test is the recorded time it takes for the wave to travel these known distances. The distance, in meters divided by the wave speed, in meters per second (mps), gives the time of wave travel. (m/mps=time) This test proves that the negative return wave is reflected back all along the length of the walls of the diffuser cone. Doing a graphical analysis of the wave graph I determined the initial positive wave was 7.2 milliseconds wide and that the negative return wave was 8.8ms wide. The increase in width is due to the length of the diffuser, at the end of which is where the last of the positive wave reflects back from. The way to calculate the return timing and length of the negative wave in a 2 stroke expansion chamber is by this formula: WRT1=(D1x2)/SW where WRT1 is the wave return time for the first part of the wave, D1 is the distance from cylinder port to beginning of diffuser, and SW is the speed of the wave which is determined by the temperature and chemical composition of the exhaust gas (and almost impossible to calculate). To figure the return time for the end of the wave is WRT2=((D2x2)/SW)+WW/2 where D2 is the distance from port to the end of the diffuser, and WW is the width of the initial wave which is figured thusly: WW=(60/RPM)xBD/360 where RPM is the top engine rpm, and BD is the blowdown in degrees (exh ATDC - transfer ATDC).

Baffle Cone and its Return Wave
Next we can glean information from his test on the baffle cone:



Doing a graphical analysis of the wave graph I determined the wave action can be determined in the same way as with the diffuser cone except that the return wave is positive instead of negative. The return wave starts its return at the beginning of the cone, and the end of it begins its return at the end of the cone. This effectively defines the return action of the wave in a very specific way, with no room for other theories.
 
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