Two-Stroke Expansion Chamber Design
© 1998 Vincent Crabtree
Updated 26th December 2009
Introduction
This document gives details of how to determine the dimensions for two stroke exansion chambers. This is the Empirical method as described in the books ‘The Basic Design of the Two Stroke Engine’ and ‘Design and Simulation of Two Stroke Engines’; both by Professor G.P. Blair of Queens University Belfast, for two and three stage diffuser (diverging cone) expansion chambers
If you dont care about how it works, you can jump to the Online calculator directly, but a little knowledge is a dangerous thing.
If you find this document interesting, you are well advised to read at least one of the books mentioned above, since they contain the author’s academic lifetime of knowledge on the two-stroke engine and are highly relevent for anyone interested in two strokes in general.
Before you continue, you should be very familiar with the operation of a tuned, two stroke expansion chamber. If not, search around for the animations on how the shape of a two-stroke expansion chamber works. This is summarised below:-
The section from the cylinder to the belly (the header and diffuser) generates a (relative) negative pressure through the cylinder exhaust port - this helps draw out the spent mixture.
The instant the top edge of the exhaust port is uncovered by the descending piston, a positive pressure pulse passes into the expansion chamber. This is travelling at the speed of sound, defined below, based on temperature and gas density.
As the cylinder pressure blows down, the moving pressure pulse reaches the section where the expansion chamber starts to diverge (the diffuser), reducing pressure at the exhaust port even more. This allows maximum transfer of mixture through the transfers into the cylinder, and effective scavenging.
As the piston is rocking about BDC, the moving pressure pulse has now reached the exhaust belly. At this stage, we are waiting for the inertia of the mixture passing through the transfers to finish filling the cylinder and scavanging.
As the boost ports are closing, we now want to prevent fresh charge exiting the exhaust port. By now, the exhaust pulse is travelling into the converging (plugging cone) section of the expansion chamber. This send a higher pressure back at the exhaust port, stuffing spilled mixture back into the cylinder and preventing further fresh spillage.
Once the piston has closed the exhaust port, the pressure pulse is passing through the stinger. The stinger bleeds of the gas in the cylinder, maintaining the temperature at the right value for everything to work properly. Too hot, and you will melt a piston. Too cold, and the chamber gas will be too cold, and work at too slow an engine speed.
This requires the exhaust gas temperature inside the chamber to calculate gas velocity. The method presented by Blair in his books assumes an average gas temperature over the whole chamber, and from this calculates a tuned length which is at some point on the plugging (converging) cone. The various sections of the chamber are then described as fractions of the tuned length, regardless of the transfer action. This is a simple way to get you started, based on the engine state of tune.
In reality, the gas at the back of the chamber will be cooler than the gas at the front. You can tweak the the dimensions by measuring the gas temperature at various points in your chamber, then alter the chamber lengths to be better suited than the values the formula can give. This approach usually requires two iterations:-
First design using formulas which get you in the ball park. This chamber is ran on the engine and expansion chamber gas temperatures measured at several places. This does not necessarily have to fit the bike too well.
Second design uses the actual temperatures plugged in from above, and gets you infront of the goal posts. If you run part 1 on a dyno, you also get extra information which can allow you to tweak certain characteristics of the pipe.
Common Ground
basic data obtained from engine parameters is required.
Speed of sound in a Gas (Pressure Wave Velocity) The main parameter involved in expansion chamber design is the speed of sound, since this governs the speed of the pressure pulses that we use in the chamber.  | Where:-
Tkis Exhaust gas temp, Kelvin
R is 287
g is 1.4 a0 is in m/s |
| Tuned Length of ExhaustBlair's formulae assume that the tuned length of the exhaust is to a point on the plugging cone, and is given by the formula below.  | Where:-
Lt is tuned length, mm
A0 is in m/s
Qep is exhaust duration, degrees |
|
Brake Mean Effective Pressure - Engine State of Tune If we want to guess the exhaust gas temperature based on engine state of tune, then we need to determination an index of state of tune. This is usually a function of the engine’s state of tune or BMEP. This value BMEP for an engine is used in several of the expansion chamber design parameters, and is calculated as shown.  | Where:-
kW is engine power, kW (1bhp=746W)
SVCC is swept volume, cc
Rpm is engine speed, rpm
BMEP is in Bar |
| Average Exhaust Temperature Once the engine BMEP is determined, the exhaust average temperature can be calculated from the formula shown. This is an empirical measure based on readings taken during dyno run tests. From the table by John Robinson. | Bike | BMEP, Bar | Mean Ex Gas Temp, °C |
|---|
| Grand Prix Racer | 11+ | 650 | | Enduro | 8 | 500 | | Roadster | 5 | 350 |
|
Effective Exhaust Diameter (EXD)This is the diameter of a pipe whose area matches that of the exhaust port. For rectangular ports, this is shown below ignoring corner radii. For multiple/bridged ports, you will have to measure this.  | Where:-
EXD is effective diameter, mm
Width is port width, mm
Height is port height, mm |
|
Exhaust Coefficients
There are several coefficients used in the design of the expansion chamber – these are a function of the engine’s state of tune.
| Bike Style | BMEP, Bar | K0 | K1 | K2 |
|---|
Enduro | 8 | 0.7 | 1.125 | 2.25 |
Motocross | 9-10 | 0.65 | | |
GP Racer | 11+ | 0.6 | 1.05 | 3.25 |
Note these engines use petrol, and are in the range 50cc upto about 500cc per cylinder. These web pages have been copied (without credit) for use with glow-plug engines and also in university projects in India amongst others. It is doubtful these equations would work on non-motorcycle engines or engines running fuel other than petrol, since the exhaust gas temperature is much lower, and the engine speed is much higher. If the person who copied the pages would have emailed me asking for permission I could have told them this, but there you go.
Two Stage Diffuser Expansion Chamber Dimension Calculation
A diagram of a typical two-stage diffuser expansion chamber is shown above. Note that the length of the plain pipe section LP01 includes the length of the exhaust port, i.e. LP01 is measured from the piston face.
Dimension Calculation - Two Stage Diffuser
The following table gives the dimension for the two-stage diffuser expansion chamber section diameters.
| D1 = K1.EXD | D3 = K2.EXD | D4 = K0.EXD |
|---|
 |
The two-stage diffuser expansion chamber section lengths are given in the next table
| LP01 = 0.10LT | LP12 = 0.41LT | LP23 = 0.14LT |
|---|
| LP34 = 0.11LT | LP45 = 0.24LT | LP56 = LP45 |
|---|
Three Stage Diffuser Expansion Chamber Dimension Calculation
A poorly drawn diagram of a typical three-stage diffuser expansion chamber is shown above. Note that the length of the plain pipe section LP01 includes the length of the exhaust port, i.e. LP01 is measured from the piston face.
The following table gives the dimension for the three-stage diffuser expansion chamber section diameters.
| D1 = K1.EXD | D4 = K2.EXD | D5 = K0.EXD |
|---|
 |  |
Notice that two extra parameters are required for diameter calculation. These are given next.
Notice also that an extra Coefficient has been introduced. This Coefficient Kh is called the horn coefficient, with typical values between one and two. Small values of Kh are best suited to GP engines with narrow power bands, larger values are for wider more flexible engines.
The next table gives the dimensions for the three-stage diffuser expansion chamber section lengths.
| LP01 = 0.10LT | LP12 = 0.275LT | LP23 = 0.183LT | LP34 = 0.092LT |
| LP45 = 0.11LT | LP56 = 0.24LT | LP67 = LP56 |
End Note
This document has provided formulae from the books mentioned in the introduction. The author cannot express how useful these books are for two-stroke design. All formulae are presented ‘as is’ with no warranty of suitability or correctness.
I would be interested in hearing from any builder who uses the data presented here for construction of their own expansion chamber.
Any constructive criticism and pointers gratefully received..
First Published 22nd March 1998. (Word Doc. )
HTML'ized 27th March 1998.
Typo updated finally 29th July 2003. Streamlined 7th Aug 2007
Individual sections added 31st Aug 09