Even though I cannot provide you with formulae, or even anything other than generalized comment, I can give you at least some indication as to what combinations of time-areas/angle-areas work best in specific instances: Exhaust system characteristics are, for example, very closely related to both exhaust port and transfer port time-areas. In a motocross engine, where power range is more important than maximum power, you would want an exhaust system that provides a relatively weak but extended duration resonant pulse (which means that it would be effective over a very broad engine speed range) and, relatively speaking, a low exhaust port time-area value in combination with a high transfer port time-area. In fact, if the engine in question is a single-cylinder 400, or something in that general displacement range, then you probably would select a transfer time-area at the very top of the range, and an exhaust time-area established at the bottom. That is to say, a transfer port time-area of 0.00010 sec-cm2/cm3 and an exhaust port time-area of 0.00014 sec-cm2/cm3. This combination of time-areas provide an exhaust timing that borrows minimally from the working stroke, which maximizes broad-range torque, and it gives the negative wave returning from the exhaust system a better opportunity of finding the transfer port still open –meaning that this negative, or scavenging pulse will be able to help pull the fresh charge up from the crankcase. Relatively large transfer port time-areas also give the fresh charge conditions allowing it to make its way up into the cylinder even if there is little or no assist from the exhaust system. The sole disadvantage of the condition described is that it does appear to permit a somewhat greater degree of mixing between residual exhaust gases and the incoming charge, as well as an enhanced tendency toward short-circuiting.
Road racing engines represent an entirely different situation, as they respond best, being tuned for maximum power and with power range a secondary consideration, to a maximum value for exhaust port time-area and a minimum transfer port time-area. At least, that will be the case when the engine in question is fitted with a typically road-racing expansion chamber exhaust system, which returns very strong but short-lived scavenging and plugging pulses to the cylinder. Also, for reasons that will be discussed later, road racing engines' scavenging is aided by high crankcase pressures resulting from strong, albeit narrow-band “supercharging” effects of sonic wave activity in their intake tracts. With the extractor effects of the exhaust system and the ramming effects on the intake side combining to aid cylinder charging, maximum power is obtained by upper-limit exhaust port time-areas (to make best use of the exhaust system) and lower-limit time-areas on the transfer side to minimize charge dilution and short-circuiting.
Carried to its extremes, the described combination of sharp, powerful pulses from the exhaust system and low-limit transfer port time-area can elevate, and narrow, an engine's power band to a remarkable degree. The two-cylinder, 350cc Yamaha TR3, for instance, has an exhaust port time-area value of 0.000148 sec-cm2/cm3 and a transfer port time-area of 0.000081 sec-cm2/cm3, and these numbers represent very nearly the maximum and minimum time-area values within their respective ranges. Power output from this engine must be in the order of 63-65 bhp, but the power is developed over such a narrow range that a 6-speed transmission with ultra-close ratios is required to hold it within limits. I am informed by a very good source that the latest Yamaha 250cc TD3 has an even narrower power band, and that the most skilled of riders has considerable difficulty keeping it on the power curve under actual racing conditions. My suggestion to
Shown here in graph form is the relationship between time-area and angle-area over a range of engine speeds.
those who have this machine, and the difficulties, is to increase the engine's transfer port time-area slightly. An increase in the transfer-open duration of only 4- to 6-degrees would probably broaden the TD3's effective power band enough to make the machine very much easier to ride, reducing maximum power by perhaps two bhp and adding about three or four bhp at the lower limit of the present range. The same applies to all two-stroke engines: increases in transfer port time-area tend to depress the power peak, but add to the power curve at lower engine speeds.
It should be understood, however, that excessive transfer port time-area, in combination with the wrong exhaust system, can lead to serious instability in running - yielding a major drop in peak power without adequate compensation in power range, and a power curve marked by humps and hollows. Thus, while engines exist in which exhaust/transfer time-area imbalances (relative to the values presented here) have not prevented quite good power outputs, such imbalances may be regarded as extreme-example anomalies more interesting for their value as curiosities then as patterns from which to work. In most engines the correct approach will be to establish time-area values that fall within the ranges suggested here, and to make adjustments within those ranges according to the conditions for which the engine is intended. Road racing engines for which 6-speed and/or close ratio gear sets are not available should be biased toward the “motocross” end of the time-area spectrum; small displacement motocross engines which commonly are coupled to fairly close-ratio, 5-speed transmissions should be biased toward the road racing specification simply because the horsepower thus gained has become a competition necessity- even though a rather peaky motocross engine is no joy to a rider.
EMPHASIS ON AREA
Taking each port individually, there is every reason to make any port as wide as possible, acquiring the necessary time-area value in this manner instead of extending the port-open duration. Reasons for moderating this approach do exist, however, in the interaction between ports and in the effects exaggerated exhaust port widths have upon pistons and rings. These reasons are discussed in detail in the chapter titled, “Scavenging”, but I will I include a brief reminder here. Atoo-wide exhaust port will cause rings to snag and break, or wear very rapidly, and if the widening brings the exhaust port window's sides too near the transfer ports, there will be an increased tendency toward short-circuiting of the incoming charge. Obviously, excessive widening of the transfer ports can also result in ring-trapping and/or charge short-circuiting. You should also understand that widening an engine's exhaust port, increasing its time-area value without actually increasing its open duration, has much the same effect as obtaining the same increase by raising its height and thus increasing both time and area: that is to say, widening the exhaust port increases the engine speed at which maximum power is realized, while reducing low-speed power. And the same pattern is to be observed in increases to transfer port time-area, though in the opposite direction. These effects should become familiar to you, particularly as regards the exhaust port, for any increases in exhaust time-area should begin with widening the port to the maximum tolerable to the piston and rings, moving on to the business of raising the top of the exhaust port only after the limit for width has been reached. There is good reason for taking this approach, for while increases in exhaust port time-area, gained by whatever change in the port-window's shape, certainly will have the same general effect, increasing width to get more time-area has a much less narrowing effect on the power band than increases in height.
Width is even more important on the intake side of any engine with a piston-controlled intake port, as there are sharp limits to time-area increases gained by lengthening the port-open duration. Piston-port engines have the advantage of simplicity, but are somewhat (sometimes seriously) handicapped by the fact that their intake timing is symmetrically disposed before and after top center. There is, therefore, a strong tendency for the mixture aspirated into the crankcase during the period between intake-opening and top center to be pushed back out during the equal port-open period between top center and intake-closing. This tendency accounts for the extraordinary influence of intake-tract resonance and gas-inertia on the piston-port engine's power characteristics. The combined activities of sonic waves and the inertia of the high-velocity mixture stream can simply overpower the rising pressure in the crankcase created by the descending piston.
Ideally, intake-closing should occur at the precise moment when ramming pressure is at its peak and when that pressure is equal to the pressure inside the crankcase, as this condition will trap the greatest volume of air/fuel mixture inside the crankcase. Unhappily, this ideal can only be realized within very narrow engine speed ranges, as inertia effects diminish rapidly at lower-than-planned speeds and the natural frequency of the intake tract is determined almost solely by its (and the crankcase's) dimensions, which means that it pulses at a fixed rate, and only at one particular engine speed will it truly be working in phase with the motions of the piston. Worse, at very low engine speeds neither sonic-wave activity nor the ramming effects of gas I inertia will be strong enough to prevent the piston from displacing part of the charge aspirated into the crankcase right back out through the carburetor. All of which means that at cranking speeds, when you are trying to start an engine, the total volume of the charge being delivered into the cylinder will be determined by that which the piston displaces between the point at which the transfer ports close and the point of intake opening (which also is intake-closing). For example, in a piston-port road racing engine with transfer-closing at 115-degrees before top center and an intake port opening and closing 100-degrees before and after top center, the volume of gases actually being pumped through the crankcase, per revolution, would be only that displaced by the piston in a mere 15-degrees of crank-angle.
It is entirely possible that in the example given, starting would prove to be impossible unless the engine was actually cranked fast enough to bring it up to the point where intake-tract resonance and inertia began to have some effect. Quite obviously, this example does represent an extreme, but not one I that seriously distorts the condition being illustrated. Yamaha's TR3 racing I engine actually has transfer ports that close 120-degrees before top center and I an intake port that opens and closes 94-degrees before and after top center, leaving only 26-degrees of crank-angle for pumping enough mixture to start the engine. I would think that this is something very near the absolute minimum even for an engine to be started by vigorous pushing of the motorcycle, and it would severely limit any efforts to improve this engine's power range through increases in transfer port-open duration.
Considering the intake-timing limitations imposed by the just discussed, it should be clear that the task of obtaining adequate crankcase filling in high-speed engines is not confined to establishing a suitable time-area value. Engines for motocross are restricted, in terms of port-open duration, by the need for a very broad-range output characteristic, to an intake period of not much more than 160-degrees. More than that virtually guarantees that they will be too peaky to be ride-able, or at least to be effective in terms of competitive laps times on most circuits, no matter what their time-area number may be. Road racing engines have an ultimate limit imposed by the starting problem already outlined. All of which means that you may regard the upper limit of intake-open duration for the former as being about 160- degrees, and about 200-degrees for the latter; about 80- and 100-degrees before and after top center. Exceed those limits, and the road racing engine will not start; the motocross engine's power band will narrow beyond the point of being useful no matter how impressive the maximum power figure may sound.
Intake-tract “tuning” will be vitally important no matter what kind of time-area is provided at the port window, and it is all too easy to get the pulsations out of phase with the piston by altering the intake timing. All alterations in intake timing should be followed with a careful check to determine if matching alteration of the intake tract length is not also required. Although this kind of work should be validated by actually running the engine with a stub exhaust attached, as outlined elsewhere in this book, a preliminary check may be run mathematically, using the formula for finding the resonant frequency of the necked flask formed by the crankcase and intake tract provided in the chapter on crankcase pumping.
For all of the reasons outlined in that chapter, which deals at length with intake-tract tuning, I have little confidence that the use of this formula will provide more than a rough guide as regards an engine's proper tuned intake length, but for some this rough guide may be all the guide they will have. It is better than nothing, if you compare the frequency thus derived for your engine's stock condition with the reality and make appropriate adjustments in the theoretically-obtained numbers for your modifications. It may also help to know that one of the better researchers in the field, Fujio Nagao, of Kyoto University, has verified that maximum air delivery occurs when the intake pipe's natural frequency provides a wave period 75-percent of the intake port open period. With all that, I still am inclined to believe that there is no substitute for actual testing, using a stub exhaust system to isolate intake effects.