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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 based on my own theories. 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. And I recommend a maximum belly diameter as 2.55 times that diameter (but you can use any size you want and see how different sizes affect the final power graph). The formula I use agrees with the experiment done by Gordon Jennings with different header diameters for a DT250 where he found the best size for maximum power.
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 see how different diffuser designs result in different return wave shapes and amplitudes. 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 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 12 times the header area it is just not recommended to expand that far.