How an Expansion Chamber Works
by Michael Forrest

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. Thankfully for you I have measured all along the pipe to get generic percentages (of the temperature halfway down the header) for all the different sections of the pipe. As a beginning temperature I measured it halfway down the header which falls within the standard 4-6" that tuners use. Blair wrote that the average temps for GP is 650, MX is 600, enduro 500, street is 350. It changes with jetting, load, exhaust port timing, and RPM. For designing you should be precise and measure it yourself because a 35 degree variation causes a difference of 400 RPM in the calculations. For precise pipe calculations you can drill a 1.8mm (.07") pinhole in the header, 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 guess at the temperature, design a near perfect pipe, and later adjust the header length to match the desired pipe powerband of RPM. I think you could use 600 as the temp if your peak RPM is at least 10,000 and you sometimes ride at peak RPM (which incurs the highest temperature). If you entered 625 as your mid-header temperature then you would be within 2.5% of 600 and/or 650. If the perfect pipe for your engine needs a 430mm header and you were 2.5% off then the difference in length would be 15mm (.6"). Guessing at the temperature means you'll need to test different header lengths before welding the body of the pipe to it. I use automotive hose although it only lasts one run before getting too out of shape due to the heat. But one run is all you need for each test length. You can also use sheet aluminum cut out from a cooking pan rolled into a tube. 5 lengths will need to be tested; -25mm, -12mm, 0, +12mm, +25mm (-1", -.5", 0, +.5", +1"). "0" gives you the header length (from piston to diffuser) that the Excel file says you need. Factors affecting temperature--> more compression gives less temperature (because the mixture burns quicker), alcohol content in the gasoline lowers temperature, richer fuel/air mixture gives hotter temperature, higher elevations give less temperature, colder ambient temperatures give less mid-header temperature, non-squish band heads give more temperature (due to a longer burn), and the longer 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 half way 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 too much suction following the pressure pulse and causes more air/fuel loss from the cylinder. And too wide doesn't assist in pulling up intake charge through the transfers. 
What type of powerband you want should influence your choice of header diameter you choose. Larger diameter headers will present a greater pipe volume. Following the exhaust pulse will be a negative pressure that will be minimalized the greater the pipe volume is. So a smaller than normal header diameter will allow more post-exhaust suction which has both good and bad effects. The good aspect of its influence is that it helps pull up intake charge through the transfer ports right as they open. This can be important when the transfer duration or blowdown  is small for the intended RPM. The bad aspect is that the suction will cause the intake flow to be less toward the rear of the cylinder and more toward the exhaust port. This causes some loss of intake charge out the exhaust port. To know what is happening you need to see the intake flow pattern left on the top of the piston. It depends a lot on how close the transfers are to the exhaust port and whether or not their direction of flow is well toward the rear.
My idea on how to correctly size the header diameter is that it should be done by a formula using engine size, compression ratio, and open port area at the end of the exhaust pulse exiting the cylinder. But I've never been able to find a formula that seems right for all sizes of engines so my spreadsheet just uses .7 times the cylinder bore (which is what most manufacturers use) and then the maximum belly diameter as 2.55 times that diameter.
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.  

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 length should be so that the beginning of the diffuser wave returns to the cylinder between the exhaust pulse end and the end of the exhausts negative trailing wave.


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. From around 2500 RPM to peak RPM this vacuum wave returns when the transfer ports are uncovered and the 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 diffuser and baffles return pressure waves.

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. Also the transfers roof angle comes into play as the more horizontal they are, the more likely the intake charge can be sucked out the exhaust port instead of heading up to the spark plug. 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%).


Click here to read more about diffuser cone angles.

Maximum Cross Sectional Area of Diffuser
According to Graham Bell 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. My recommendation after much study of different engine/pipe/dyno results is to use 6.5 times the area instead which is 4% bigger.

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 a minimal return wave strength. 10.3 psi is a typical exhaust pressure peak in the header which is the beginning absolute pressure in this graph. 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 times the header area it is just not recommended to expand that far. Previously the maximum recommended was 2.5 times the header but there just isn't a black and white cutoff point. Version 22 of my expansion chamber calculator makes use of Boyles Law to calculate accurate return waves and you can experiment with different belly sizes to see what the power/powerband differences are.


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 virtual 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 only because it's causing a longer effective belly section at the expense of the diffuser and baffle lengths. Look at the graph below to see how the end of the diffuser wave and the beginning of the baffle wave are extended weak areas of wave strength which looks almost the same as if the belly were much too long (much longer than the actual 90mm the pipe had). The belly width was 129mm when it should of been no more than102mm.


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 two graphs showing the difference in pipe powerbands for 2 belly lengths with a single cone baffle. You can see how a longer belly has peak power 500RPM earlier in the powerband and a more linear rise in power. The purple graphs are the pipe power graphs.



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 its main 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 that power dip with a boost bottle). Making a 2 or 3 cone baffle with lesser angles gives more power at the beginning of the powerband (and less at the end of it). Most racing bikes just use a single angle cone. My expansion chamber calculator ECcalc is useful for calculating the baffle return wave length and shape.
Here's some graphs showing the changes of pipe power from different baffle angles. Take note of the last graph which is from a baffle with 3 cones of increasing angle. This is best for enduro bikes because its peak happens 750RPM earlier than the 13.6° baffle and has about the same peak power.



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 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.

Stinger/Silencer
The stinger acts as a bleed off valve for the pipe. It controls the amount of average pressure in the pipe. More pipe pressure adds to the baffle wave and detracts from the diffuser wave. So too narrow or too long a stinger will 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 from .1 psi to .5 psi which my Excel file does a good job of calculating diameters and lengths to approximate that range. Although the formula in my Excel file now calculates the minimum and maximum stinger sizes for 3 different lengths of stingers 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. 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. This graph shows how too much pipe pressure can negate the diffuser wave at peak RPM when the back pressure is excessive. Notice that the -5psi diffuser wave is reduced to 0 psi by the 5 psi back pressure:


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. But if the carb and reed are good then a little back pressure can give you a little more horsepower. How I analyze a reed valve is by using my fingernails to hold open the reeds and measure the opening height and width (which multiplied together gives the area). The trick is in estimating how much pulling force happens at the reeds as the piston rises to create a vacuum. 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.

Click here to read about matching the peak power RPM of the pipe with the engine.

My Expansion Chamber Calculator "ECcalc", how to use it, how to obtain it, and comparison to a free calculator.

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.

Two examples showing how accurate ECcalc20 is compared to dyno graphs.

Pipe Design forum where you can discuss pipe design with myself and others.

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.

Pipe Design Questions & Answers

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