The sting is in the tail

The sting is in the tail

In much the same way that an Atac chamber sitting close to the cylinder can influence the efficiency of the exhaust pipe at rpm just under the start of and into the engine`s power band, so too can the tail pipe, however, the tailpipe additionally affects events at peak torque rpm. They both influence the amplitude of a pressure wave moving through the length of the exhaust system. Again, it is a little counter intuitive in that lower pressure in the pipe, achieved with a `larger` diameter tail pipe renders the pipe less efficient at low rpm, thus reducing power losses and so, average power increases. When the return pressure wave arrives back at the cylinder too early at lower engine rpm, this wrongly timed stuffing action plays havoc with several aspects of the scavenge process, resulting in power loss thus delaying the start of transfer mixture flow.
Paradoxically, these two elements are at the extreme ends of that same exhaust pipe. It might be suggested that between these two extremities is an internal chaos of differing pressures, gas densities, temperatures and movements, even flow reversals. For instance, gas temperatures, therefore density, do in fact vary enormously and there can be differences of more than 200*c existing at any one time in a single engine cycle. Waves in an exhaust pipe travel at the local speed of sound, which in turn are temperature dependent, so they can vary from 200m/s to 600m/s depending on it being an expansion wave or compression wave.
A typical race scenario would be that at peak torque rpm at full chat the engine produces exhaust gas in proportion to the quantity of fuel burned. Hot gases pass into the exhaust pipe driven by combustion pressure and can only exit through the tail pipe. Pressure rises in the exhaust pipe until it reaches its maximum level at which point the tail pipe cross area should be capable of flowing as much exhaust gas at maximum velocity as the engine produces per second during each combustion cycle. Just as flow rate increases with pressure, at the same time, resistance to flow increases with gas velocity, through friction and turbulence.  This then poses the question, how can that quantity of exhaust gas be determined and what diameter of tail pipe is required to cope with that mass?
Both of these questions are tied to the amount of power the engine in question produces, thus the quantity of generated exhaust gas is directly proportional to the generated horse power.
It is self-evident that a Bantam race set-up will make way less engine power than the RS Honda and that in turn, less than a GP Aprilia. It follows then that tail pipe diameters will vary to reflect these disparate power numbers even though all cylinder capacities are of 125cc. Depending on which published drawing you look at, the Aprilia tail pipe diameter is nominally 23.3mm.  
What response could be expected to a reduction in pipe diameter, or to be more precise, a greater flow restriction? This would cause a higher average pressure in the exhaust pipe, hence less gas expansion and higher temperature of the gas in the pipe reflecting a higher speed of sound and higher resonance frequency.
Creating too much restriction however will severely heat up the cylinder and piston crown as well as the fresh transfer mixture waiting in the transfer ducts. As mentioned previously, a small diameter restriction will increase mean pipe pressure so, if the blowdown time/area from exhaust to transfer port openings is insufficient this increased pressure will make much worse the consequences of exhaust gas diluting and pre-heating the transfer mixture.

It used to be that back in the early 60s-70s determining tail pipe size was seen to be a function of cylinder exhaust duct outlet area with no indication of how that figure was arrived at, prior to that there didn`t seem to be any specific direction of tail pipe thinking. Indeed, the dimensions for the very first Bantam exhaust pipe I ever made was taken from an article in the February 1961 `The Motor Cycle` magazine, the author being Herman Meier. He was engaged by BSA to develop a competition Bantam and these tuning articles were based on some of his experiences there and of course his own depth of two stroke knowledge. My own 1962 edition of the book `Speed and how to obtain it` also features those articles, plus, by way of a small digression, a basic introduction to thermodynamics, both are well worth a read. The tail pipe specified in the drawing was a whopping 1-3/8 ”(35mm) diameter and 1-3/4”(44mm) long, so little help to engine efficiency was gained from that monster tail piece! Upon completion, the box was affixed to a suitable length of standard D1 exhaust pipe.
Actually, I made the rear cone a little longer and used a 1”diameter tube 6”long, for no more informed reason than I thought it looked better, what did I know back in 63?
The first published reference I have of the area ratio between exhaust port and pipe is by way of an article of 1967 written by Gordon Blair and published in the `Motorcycle sport` magazine. With the extensive testing facilities available at Queens University any data published at the time had the stamp of authority and was based in reality. Even so, the area ratio was no more precise than 2, meaning that the tail pipe for a race engine should be half that of the initial front pipe.
Tuning horizons changed in 1970 when SAE in Detroit published the results of a joint collaboration between Blair and Johnson of Queens University entitled `Simplified Design Criteria for Expansion Chambers for Two-cycle Engines`. Here at last was a scholarly document with enough raw data to get home tuners designing their own exhaust pipes. But of course, there were just as many problems left unanswered than were explained, sadly it seemed the holy-grail still remained to be discovered, nonetheless two stroke tuners worldwide were universally grateful.  
A whole plethora of tuning books were subsequently published each offering the tantalizing prospect of real answers, such authors were Jante, Jennings, Graham bell, Robinson, Sher, Dixon, Bacon and many more, missing from all these was any meaningful insight into tail pipe sizing, relying on a fraction of the header pipe size these being in the range of .55 to.70, depending on the end use. One scholarly tome devoted a whole two sentences to the subject of tailpipes despite beginning the topic by warning that the diameter has a `critical` effect on flow resistance! I suspect that a certain amount of plagiarism took place amongst the two-stroke design and tuning literati on this particular subject.
Blair referenced tailpipe diameters rather loosely to the bmep of the engine in question, good Bantam race engines would all fall into the range of about 8 bar their respective categories being enduro and motocross and an area of .65 of the initial duct/header pipe in question.
1990 saw the publication of Blair`s mighty work entitled `Basic Design of  Two Stroke Engines` some 675 pages of pure two stroke technology. Nothing on the scale of this book had ever been seen before. Associated with the book was a suite of 24 basic computer programs on diskette referencing chapters of the book`s content and were available, at the modest cost of £40, for all to use. Crucially the book also contained hard copy of the source codes for these programs. So not only could you read the book but enter data from your own engine and get results displayed on the computer screen.
The overwhelming number of tuning programs available on the internet today use this source as the basis for their software, as well as countless tuning articles and books.
One important piece of information which emerged from this work at Queens was the suggestion that, “In a racing pipe, where maximizing the plugging pressure gives the highest trapping efficiency, there seems little point in having the first down pipe diameter much more than 1.05 times the port area, for in unsteady gas flow, the larger the pipe, the lower the pressure wave amplitude for the same mass rate of gas flow “. At last, here was made available some relevant data to connect the exhaust port area to duct outlet area to tailpipe area. This data was never suggested to be optimal, being no more precise than very well informed guidance to get designers, engineers and tuners alike, into the `ball-park`.
The last few decades have seen a lot of improvement in exhaust port area and duct design technology with ducts getting smaller in area and volume with cooling water flowing around the internal duct walls.
As far as I am aware it was Helmut Fath who introduced the innovation that now is common practice when designing tailpipe configuration. The placing of an insert linking the reverse cone to the tail pipe with an internal diameter of the desired cross area, the tail pipe bore is then a couple of mm bigger again with the silencer bore larger again. Fath came up with the insert idea, which is in effect a de Laval nozzle, when working with the Hondas of Freddie Spencer and trying to get the tail pipe/silencer lengths to fit the machine. Being able to eliminate the adverse effects of differing pipe lengths solved a major installation headache. Apparently the opposition couldn`t work out why one pipe was so much longer than another with no apparent reduction in performance. Hither to, tailpipes offered impedance to flow and the pressure pulse exiting the pipe end hit the atmosphere, altered in sign and attempted to reverse flow further messing things up. The Fath innovation enables tuners of today to remove tail pipe and silencer influence from pipe calculations altogether.

Cheers for now you guys, stay vigilant. Regards,   Trevor