Reflecting On Exhaust Waves

As I hung the coffee-filter holder on its hook I must have disturbed the nearby milk pitcher, for the two of them began a fascinating dance. At first, both were swinging in opposite directions. But because their natural (swinging) frequencies were slightly different after a few seconds they were swinging together. Then, after more seconds, they were swinging in opposite directions again. This made me think of the problem of engine synchronization on multi-engine prop planes: As the slightly differing rpm of the engines came into and out of step, a kind of throbbing wahhh-wahhh could be heard. Evidently the pilots heard it too. Presently, the rpm differences were zeroed out and everything became smooth.

And then I thought of the late Professor Blair, who brought mathematics to the analysis of two-stroke exhaust pipes. One evening in 1976, with Bushmills Irish whiskey between us, I asked him how a small change in exhaust-pipe center-section length could make the big difference in horsepower that is often seen on the dyno.

“That is because the pipe contains not just a single resonance but two,” he said. He went on to note that the major resonance is a wave that is created as the exhaust port begins to open, releasing a pulse of exhaust of perhaps 100 psi. It travels the length of the pipe to the convergent cone at the far end, where it is reflected with no change of sign (it remains a positive wave) back to the exhaust port just in time to stop and reverse the outrush of fresh charge that has meanwhile been looping into the cylinder through the two or more transfer ports.

There is a secondary wave, which bounces back and forth between the divergent cones nearer the front of the pipe and the convergent cone at the rear. It typically makes three oscillations while the primary wave makes one. And this explains why a small change to center-section length can have a big effect on engine power: If the two are nicely in step, their amplitudes add, creating a stronger “stuffing wave” that can pack escaped fresh charge back into the cylinder. If the two are out of step, however, the amplitude of the secondary is subtracted from that of the primary, resulting in a much weaker stuffing wave, less escaped charge pushed back from the head pipe into the cylinder, and reduced engine torque. In this way, a 5mm change to center-section length can have a big effect.

Pipe waves are useful in four-strokes as well, but they are employed differently. When a cylinder’s exhaust valves begin to open, exhaust pressure rushes out into the pipe just as in a two-stroke, but instead of being reflected back to the cylinder by a convergent cone, the exhaust wave’s sign is reversed at every point of pipe enlargement. When the exhaust wave reaches the collector at the end of the head pipe, it expands in all directions, including back toward the cylinder. If this wave—now negative because expansion has reversed its sign—arrives back at the cylinder during overlap (the period when the exhaust valves are about to close but the intakes have already begun to open) its low pressure causes exhaust remaining above the piston (which hovers near top dead center) to enter the exhaust pipe. The low-pressure wave propagates across the combustion chamber to the intake valves where its low pressure invites intake flow into the cylinder to begin, even before the piston has begun to move down on its intake stroke.

These two effects—allowing remaining exhaust gas to leave the cylinder and beginning the intake cycle early—result in a purer, denser fresh charge in the cylinder. This boosts torque. Now the bad news: Because sound waves move at basically the same speed all the time, at some lower engine rpm that helpful negative pipe wave will have come and gone by the time overlap occurs, and now it will be a following positive wave that arrives at the about-to-close exhaust valves. It pushes hot, inert exhaust gas back into the cylinder, and maybe out through the just-opening intakes and into the intake tract. Now, when the piston starts down on its intake stroke, the gas it first pulls in is exhaust. Because this cannot support combustion, the result is reduced torque—the dreaded “flat-spot.”

We’ve all seen sympathetic mechanical vibrations on motorcycles: shift pedals that all but disappear because at a certain rpm they whip rapidly from side to side; luggage racks that buzz; handlebars that put our fingers to sleep; front wheels that rapidly oscillate forward and back on the springiness of the fork tubes. All of these arise when the driving force—the primary or secondary shaking forces from the engine—come into step with the natural vibratory frequencies of various parts.

Motorcycle manufacturers spend big money on sound suppression, so you will find clutch covers with dampers inside them. Panels that were flat in a previous model may be given a curved shape to prevent their acting as “loudspeakers” that turn vibration into sound. Sound sources are identified and the irritating ones are calmed. This engineering specialty is called “NVH” for noise, vibration, and harshness. Ah.