buildandclick.com sells a computer program to assist in designing 2 stroke pipes.  Apparently you type in some information and it can tell you the sizes of expansion chamber and such. Haven't read any reviews on it.

More pics from Wikipedia search on Engineering Acoustics/Sonic Supercharging of 2 Stroke Engines! Believe it or not Wikipedia has a lot of useful info to figure out design and proportions.  I copy and pasted it here if anybody is interested.


For a 2 stroke engine the tuned pipe is the section of the exhaust system that begins at the exhaust port and ends at the end of the converging section. A tuned pipe is made of between 3 and 4 characteristic sections depending on the desired effect. The figure below depicts cross sections for 3 typical configurations of tuned pipes as well as a straight pipe:

The purpose of straight and tuned pipes is to utilize the pressure waves originating from the exhaust port to assist the breathing of the engine. This is achieved by designing the pipe in such a way that positive and negative reflected waves arrive back at the exhaust port at an instant when a low or high pressure is desired. This is beneficial for two stroke engines because unlike four stroke engines, they do not have dedicated intake and exhaust strokes and valves.
The following picture labels the various elements of a two-stroke engine which are referred to in this Wikibook page.

Furthermore; abbreviations will help as well:
In order of accensding crank angle
TDC - Top Dead Center, 0 deg
EPO - Exhaust Port Open
TPO - Transfer Port Open
BDC - Bottom Dead Ceneter, 180 deg
TPC - Transfer Port Close
EPC - Exhaust Port Close
For introductory material on 2 Stroke Engines please see the following links:
[Wikipedia 2 Stroke Engines]
[HowStuffWorks 2 Stroke Engines]
Straight Pipe:[edit]

The goal of a tuned straight pipe in this application is to use the reflected negative pressure waves from the open end of the pipe to help draw out the exhaust gases. By selecting the appropriate length of the pipe, the reflected rarefaction wave arrives at the exhaust port just as the transfer port opens thus assisting the flow of fresh mixture into the cylinder, and exhaust gases out of the cylinder. The figure below illustrates this action. In the figure, even though the piston has reached bottom dead center (BDC), fresh mixture continues to enter the cylinder because the rarefaction wave causes P2 to be smaller than P1. A key point to note is that the velocity with which the pressure and rarefaction waves travel down and up the exhaust pipe is for the most part independent of the engine operating frequency (RPM). Due to this fact, the conclusion must be made that for a given pipe length there is an optimal RPM for which the waves will arrive producing the greatest benefit for the breathing of the engine. At this optimal RPM, the engine breathes significantly better and hence produces a noticeable increase in output power. This effect is quantified by calculating the ratio of fresh mixture to exhaust gases within the cylinder as the compression stage begins at EPC. If the rarefaction wave is very large, it is possible that fresh mixture is pulled into the exhaust pipe while both transfer and exhaust ports are open. This phenomenon is known as short circuiting the engine and produces undesired effects such as a decrease in fuel economy and an increase in release of volatile organic compounds. These negative effects can be mitigated by designing the exhaust system such that either no fresh mixture is pulled into the exhaust pipe (i.e. perfectly tuned straight pipe) or further utilizing the exhaust pressure wave to inhibit short circuiting. For performance two-stroke engines, the second solution is most often employed by means of a tuned exhaust pipe known as a tune pipe.

Tune Pipe:[edit]

With a converging-belly section-diverging type tune pipe the goal is to have the diverging section create a returning rarefaction wave and the converging section create a returning pressure wave. The belly section acts as an appropriate time delay between the returning waves such that the pressure wave arrives at the exhaust port after the transfer port has closed. This pressure wave pushes the excess fresh mixture in the exhaust pipe from a short circuit, back into the cylinder. Here the short circuited fresh mixture is actually desired since this allows the returning pressure wave to "super charge" the cylinder giving it more fresh mixture than if the cylinder were filled at ambient pressure. This is a similar result to turbo-charging or super-charging a four-stroke engine. If the mixture contained within the cylinder before combustion occurs were allowed to expand to ambient pressure, its volume would be larger than the displacement of the engine. This phenomenon is quantified as volumetric efficiency; it is calculated as the ratio of the ambient pressure volume of the fresh charge, divided by the displacement volume of the engine. The operation of a two-stroke engine equipped with a properly tuned pipe is shown in the animation below, for a step by step description of the process, please follow the link below the animation.
There are exhaust manufacturers now that are mating up tuned pipes to tuned (ported) engines to get the best possible 'supercharging effect' at given rpm's. In the past a tuned pipe would have been tested on a stock engine but the length and shape of the pipe will differ on a 'tuned' engine because of the way it is able to rev higher .
Two-stroke engine operation
Tune Pipe Design Geometry:[edit]

The most basic form of a tune pipe is shown in the figure below with corresponding wave equations.

This pipe consists of an expansion chamber which serves to create both the returning rarefaction and pressure waves. From reference [1], we know that wave speed in the pipe is effectively independent of engine RPM and largely dependent on temperature of the gases in the pipe. This means that a tune pipe with basic geometry operates optimally for only one specific RPM, as the engine RPM deviates from this optimal value the timing of the arrival of the returning waves is less optimal for the volumetric efficiency. The relation between the volumetric efficiency and the engine RPM is characterized qualitatively by the following graph:

Although the basic tune pipe performs the desired task of increasing the volumetric efficiency, the narrow RPM band width for which increased power is available reduces the practicality of the basic pipe since engines are typically required to operate within a wide range of RPM. One way to broaden the effective RPM band width of a pipe is to taper the pipe at sections of increasing and decreasing cross section. To understand how this works, we can represent a tapered section as many small step increases/decreases in cross section. Each step will produce transmitted and reflected waves in the same way as the basic geometry; however, the overall effect is weaker waves with longer wave lengths arriving back at the exhaust port. Although the waves have smaller peak amplitudes, the effect on volumetric efficiency is greater due to the longer interaction times of the waves with the cylinder and crankcase. If the number of steps increased to n diverging steps and m converging steps, the equations shown represent the plane waves as well as the transmission and reflection factors for each change in cross section.


The graph below shows qualitatively how pressure at the exhaust port varies with crank angle for both basic and tapered pipe geometry.

The important differences to notice in the graph are the relative magnitudes and durations of the positive and negative pressure waves arriving back at the exhaust port at TPO and EPC. In this graph, if we pin down the waves with respect to time along the horizontal axis and then we increase or decrease the RPM, the effect will be that the positions of the port timing will no longer match up with the same positions of the waves. This is due to the fact that, as mentioned above, the wave speed is independent of RPM. In more detail if we increase the RPM it would have the effect of shrinking the port timing scale while keeping EPO in the same position. If we increase the RPM, the port timing scale expands with EPO remaining in the same position.
Looking at things the other way around, if we change some aspects of the pipe geometry we can see how they change wave propagation in the pipe and hence operation of the pipe with respect to the engine.
Length of the pipe between the exhaust port and the diverging section (L1) - this length set by the difference in crank angle between EPO and TPO and the desired effective RPM range of the pipe. Making the section longer would fit a lower RPM range or a greater difference between the crank angle of EPO and TPO.
Length of the belly section - this length is set by the difference in crank angle between TPO and EPC and the desired effective RPM range of the engine. This length and L1 are interdependent since the crank angles are also interdependent, (e.g. EPC=(0-EPO)).
The angle of the diverging/converging sections - changing this angle from steep angled cone (interior angle > 90 degrees) to a shallow angle cone (interior angle < 90 degrees) has the effect of broadening out the wave length. This increases the effective band RPM band width of the pipe since there greater flexibility of crank angle for which an appropriate pressure will at the exhaust port. This also has the effect of decreasing the maximum attainable volumetric efficiency of the pipe since the peak pressure amplitude is diminished by spreading out the waves energy over a longer wavelength. Note that if the diameter of section L1 and the belly section are kept constant, changing the angle and changing the length of the diverging/converging section is geometrically the same.
The ratio of the cross section of section L1 and the belly section - the ratio is largely dependent on the desired angle and length of the diverging/converging sections and the minimum diameter desired to avoid impeding the flow of the exhaust gases.
Further Investigation[edit]

For further investigate of the operation of two-stroke engines with tuned exhaust pipes it is most appropriate to analyze actual test data. For this we can go to the TFX website where they demonstrate their testing and data analysis software, or read the paper referenced below titled "Exhaust Gas Flow Behavior in a Two-Stroke Engine.

are these programs free to use? and also how do i find out the diameter of a the pipe i want to make? im thinking about making a pipe and im interested in this process

I did a little digging for some reviews of the literature available on this subject. Came across somebody who posted comments on threewheelerworld.com about several books so I added this. It will list the books name, & give a description of the book. Hope it helps.

2 Stroke engine performance resources. Books, and other things.

I'll try and get the ball rolling in here with a list of books I currently own on 2 Stroke engines, and 2 stroke engine performance tuning. I started reading these about a year ago now and I've learned so much in just the short time already its mind boggling. Anyone interested in doing their own engine porting, or taking the time to learn the intimate secrets of 2 stroke engines should take the time and read each of these books.
Two Stroke Tuners Handbook by Gordon Jennings: This is in my opinion, hands down THE BIBLE of 2 stroke engine tuning. Written in the early 1970's by Cycle magazine writer and engine tuner extrordinare you can learn more about a 2 stroke engine from this book then you can imagine. I have read it cover to cover 7 times so far and I STILL pickup something new that he mentions every time. Important topics covered are Port/time area formulas and how to calculate them, cylinder head design and improvement, crank case volume, crankcase pressure, transfer port angles and heights, rotary valves, piston port engines, exhaust and intake resonance, efficiency, complete with formulas. Even though this is just the tip of the iceberg for the treasure trove of information this book holds it is very very easy for a person to read and understand. By following the information in this book you can make even the slowest slug of an engine run like it was designed for a motoGP track. Even if you only have elementary understanding of the 2 stroke engine and how it works, you can jump right in with this book and have everything laid out for you in easy to understand and comprehend terms. Highly recommended as the first book to read on the subject! ISBN: 0-912656-41-7

Two Stroke performance tuning by A. Graham Bell: This is a great follow up to Jenning's book. Its a little bit more technical, and novices of the 2 stroke engine may have a hard time comprehending some of the concepts but sarge on through the book and you will learn a great many things ranging from Exhaust pipe formulas, port maps and layouts, power valves, extensive information on reed valves and operation, intake stuffers and their purpose, tips and tricks for lubrication and cooling to give your engine better life, and a more up to date look at carburation and ignition systems then Jennings book has. Its info ranges from Dirtbikes, to MotoGP machines, to carts, to trials bikes. ISBN: 1-85960-619-9

Two Stroke Tuning by Roy Bacon: This book has a lot of info already well covered by the two previously mentioned books, but it also has a few things that they don't cover well. One is crankshaft splitting and rebuilding in detail with several diagrams, and what to do if you happen to press it together slightly off. The other is information on porting, and improving your stock reed cage and intake tract. Grahams book touches on this briefly, and the info in this book adds to it. The back of the book has some pretty good info on how to read Lectron carb metering rods, and how to tune them. That info is hard to come by. Its also got a pretty interesting index of specifications for many motorcycles and dirtbikes. Information ranging from stock timing, carb settings, clearences, and wear tolerances. Not a very good stand alone but a great additional resource. ISBN: 0-8518-4039-6

Two stroke Exhaust Systems by Roy Bacon: This is a very small book that is almost like a pamphlet but still has some good info. It ranges from the different type of 2 stroke exhaust pipes which are a plain pipe, pipe and megaphone, pipe and expansion box, and the current day resonant pipe. You'll get educated on things like negative and positive pressure waves, exhaust temperature varying pipe efficiency, pipe construction, mounting, and maintenance. No ISBN. Printed by Lodgemark Press.

The High Performance Two-Stroke Engine by John C. Dixon: This book is probably the most detailed and **** book out of the list. It is also consequently the most mathematically complex out of the books listed here also. There are others (Such as Gordon P. Blair's Design and Simulation of two stroke engines) that are more technical, but I have not read them yet. Its got formulas for everything and even ventures into the very serious realm of calculating and anticipating the fluid/air dynamics inside of the engine as they are happening. There is an entire chapter on head dome designs and how they should vary dpending on the types of fuels being burnt, and what the engines specific use will be. A nifty chart with different types of fuels or additives to use in the engine for different applications IE anti detonation additives for a gasoline base, methanol 10%, acetone 10%, benzol. Easier starting, Propylene oxide 5%. To sum this book up, its got every topic all the previous books mentioned in the most ****, geeky way possible. There are calculations, and limits for every single part of the 2 stroke engine and this book will explain them all to you with a performance first attitude. Not for the faint of heart when it comes to 2 stroke engines!ISBN: 1-84425-045-8

Two stroke high performance engine design and tuning by Cesare Bossaglia: This book is rare, and almost not worth mentioning because of that. First printed in 1968, although not that much older then Jennings book this one just “feels” like a lot of the info is outdated. However, the best part about this book are the numerous obscure designs and ideas people had for 2 strokes back when it was at the start of its hey-day. Even though this book is old, it is almost an engineers reference. It goes over a few topics not covered in other books such as bore and stroke proportions, balancing, theoretical analysis including the forces exerted onto engine components like the crankshaft, piston, connecting rod, and wristpin and how increasing an engines power levels effects the forces applied to these parts. A large portion of the book is focused on the larger industrial type 2 stroke engines, although there is a lot of info about smaller motorcycle based engines. Tons and tons of pictures and illustrations, probably more then all the other books put together. I've read this book once, and some of it is difficult to understand because of the translation from Cesare's native language and also because some of the things its talking about have absolutely no place in todays engines and its difficult to understand the usage of such ideas and theories without being able to imagine it. Read this book when your ready to really think outside the box on your next engine build, you'll have so many crazy ideas you wont even know where to start. No ISBN: Lodgemark Press.

I'm still constantly looking for books relating to this subject I've not yet read. The 2 main ones I'm missing out on right now is Gordon P. Blair's Design and Simulation of the two stroke, and MIT Professor Heywood's book. I will obtain these in time, study them, and then add a review of their content to this thread. If anyone else have a book not mentioned here and has throughly read it, feel free to post your overview and thoughts of what you learned from it.

http://3cyl.com/mraxl/manuals/bell/performance-tuning-graham-bell.pdf

Graham bells' book for free!

I read this article about water injectable jackets on a pipe to affect sonic travel, this would allow for people to tune their pipe on the fly by either removing from or adding water to the pipe. Thought it was very interesting, and thought it was worth sharing. Maybe somebody could contact them about doing a pipe design for an LT. That would be awesome! Did I misunderstand the article on this link? 

http://www.factorypipe.com/t_pipetuning.php

2 Stroke Engine Diagrams and Animation that breaks each part of a cycle down and allows you to see the concept of a 2 stroke, as well as a quick class about sounds role in the design of a pipe.

http://www.2strokeengine.net/2strokeenginetuning/2strokeengineanimation.php