bring with it a fresh new set of problems, if it fails to act ideally.
     Why might a belt fail to act ideally? There are many reasons. Most designers of belt drive turntables aren't even aware of all these problem areas for belts, so naturally their turntable designs haven't even addressed these problems, and thus produce haphazard performance results. Even the best designers of belt drive turntables, fully aware of all these problems, have to tiptoe through a minefield of engineering tradeoffs and compromises. They have come to know, all too well, that belt drive brings a whole new area of problems, and is not simply a panacea for the ills of rigid drive coupling.
     To start with, let's just scratch the surface by merely mentioning two problem areas where things might go wrong with belt drive. First, the belt might slip slightly in going around the smaller diameter, faster spinning motor pulley. Then the 1 inch red portion of belt would not correspond to exactly 1 inch of the motor pulley circumference. And then, when this red 1 inch portion of belt arrived at the platter rim and drove exactly 1 inch of the platter rim circumference, it would not be faithfully communicating an accurate speed ratio between the motor and the platter, so the platter would rotate at the wrong speed.
     Second, the belt might physically distort along in its length dimension, so that the red portion is not precisely 1 inch long at all times. How could a belt possibly distort along its length dimension? Simple. Remember that the whole point of using a belt in the first place was to exploit its elasticity along its length dimension, to absorb and filter out the kick and coast vibrations and speed irregularities of the multipole motor. An elastic belt is elastic, by definition, precisely because it is willing to distort its length dimension in response to applied stretching forces.
     If the belt distorts its length dimension at all, then we can't count on any given 1 inch red painted portion staying precisely 1 inch long at all times. Suppose, for example, that the belt stretches for some reason as it goes around the motor pulley, so that the red painted portion stretches to become 3/2 inch long. Then this red painted portion leaves the motor pulley and starts on its journey toward the platter rim. Suppose that the stretching forces are no longer present for this part of the journey, so that the red painted portion resumes (shrinks back to) its normal length of 1 inch. In this scenario, the belt would incorrectly, unfaithfully communicate what should be equal circumferential travel between the motor pulley and the platter rim; it would fail in its primary responsibility of communicating and translating 1 inch of circumferential rotation by the motor pulley into 1 inch of circumferential rotation at the platter rim. In this scenario, it would have required 3/2 inch of circumferential rotation at the motor pulley, to produce 1 inch of circumferential rotation at the platter rim; or, to put it another way, 1 inch of circumferential rotation by the motor pulley will produce only 2/3 inch of circumferential rotation at the platter rim. Thus, the platter rim would be driven at only 2/3 of the correct speed, thanks to the mere fact that the elastic belt stretched its length dimension for a little while, at some point, along its journey.
     The belt is wholly responsible for translating motion from the motor pulley to the platter rim, and thus becomes wholly responsible for the speed (including speed constancy) of the platter. If you look at the belt in action, you'll see it moving along its length dimension, as a continuing parade of 1 inch portions (one we painted red, the rest not) marches by. The speed of this motion gets imparted to the platter, to become the speed of the platter and the speed of the record groove, hence the time axis dimension of your musical waveform.
     Thus, the belt can be viewed as a literal metaphor for the time axis dimension of the music signal. As you watch the belt length move by, so are you also watching the progressive unfolding of the time axis dimension of the music you are listening to. For music to be rendered clearly and cleanly (distortion free) by the turntable, we know that the time axis dimension must unfold at a perfectly constant and steady speed. This essentially requires that, as we watch the belt moving by, we can see that it is moving at a constant speed along its length.
     So far, so good. Most turntable belts probably seem to move at a pretty constant speed. But that's not all that is required. As we saw just above, the belt length as such must also remain perfectly constant, without elastic stretching. If it stretches, then 1 inch of circumferential motion at the motor pulley no longer becomes exactly 1 inch of circumferential motion at the platter rim, which messes up the reduction ratio, which messes up the turntable platter speed.
     The solution to this problem might seem easy: simply employ a belt that doesn't have elastic stretch along its length dimension. Indeed, some string drive turntables approach this design extreme. However, there's a big fly in the ointment. Remember that the whole point of introducing the belt drive concept was to filter out the kick and coast problem of multipole motors. A belt that doesn't have elastic stretch can't do this. So then what's the point of introducing belt drive in the first place?
     The only way that a belt can filter a multipole motor's kick and coast problem is by distorting its length dimension, by elastically stretching and then collapsing. In other words, the only way that a belt can cure the speed inaccuracies of a multipole motor's kick and coast problem is by introducing its own new inaccuracies, which arise from its distortions of its length dimension. From the frying pan into the fire?
     Let's take a moment to take a micro-look at the way in which belt stretching speed inaccuracies develop, so we can appreciate the many dimensions of these gremlins and their intractable nature.
     Imagine you're holding a rubber band between your two hands, so that it is fully extended but not yet stretched. The rubber band is now at (or just a hair longer than) its natural rest length. Now imagine that you give this rubber band a sudden pulling jerk. This rubber band will stretch. Its length will increase.
     Each pole of a multipole motor supplies the same kind of sudden pulling jerk. This jerk, if rigidly coupled directly to the platter, would produce a spike of temporary speed increase, resulting in the kick and coast speed irregularity problem.
     But what happens if, instead of rigidly coupling this jerk directly to the platter, we couple this jerk to an elastic belt? The elastic belt will stretch, just as the rubber band did. Its length will increase.
     Now, what happens when a belt's length increases? As we saw above, length changes in a belt will distort the faithful transmission of motion from motor pulley to platter rim, distorting the ratio between the two, thus distorting the speed of the turntable, and therefore distorting your music. In particular, if a belt becomes longer after leaving the motor pulley, this can produce a slower speed for the turntable.
     Thus, in response to the sudden jerk from each pole of a multipole motor, an elastic belt distorts your turntable speed. But then how can a belt be helping anything? Who needs two distortions instead of one? The answer is that two distortions can be advantageous if they offset or cancel each other out (remember the pre-distorted groove of Dynagroove?).
     How do these two distortions offset each other? Each sudden jerk from a multipole motor tends to increase the turntable speed, while each distorted stretch in belt length tends to decrease turntable speed. In other words, a belt's length-changing, speed-distorting response to each sudden motor jerk actually works to distort the turntable speed in the opposite direction from the motor jerk itself, thus helping to cancel out the speed increase variations that would be caused by each kick from a multipole motor.
     If a second distortion is to offset and cancel out a first distortion successfully, then it must match that first distortion exactly, being as it were a mirror image of it. Since speed is a time based phenomenon evaluated instant by instant, and since our goal here is to maintain constant speed instant by instant, it follows that the two distortions should match and offset each other instant by instant. But that would be a very difficult, perhaps impossible design engineering job for the turntable designer.
     The first distortion, the jerk from the motor pole, has a complex waveform shape that changes instant by instant. The waveform of this jerk depends on the physical contour of the motor's poles as they come together and then drift apart, on the magnetic strength of the poles, etc. The design engineering ideal might be to have the belt's elastic characteristics perfectly matched to the complex characteristics of a particular motor's jerks, such that, instant by instant, as the motor's jerk waveform increased speed, the elastic belt would stretch the precise amount of length needed to slow down the speed by precisely the same amount. Then the two offsetting distortions could track each other perfectly, instant by instant. To accomplish this, the belt's dynamic acceptance characteristics, showing how it responds in real time, instant by instant, to changes in jerk waveforms, would have to be evaluated, and would have to be perfectly matched to the jerk waveform of a particular motor.
     However, this kind of belt evaluation and belt matching information is not generally available to the turntable designer. And we don't see turntable designers being fussy enough to demand such information. Indeed, most belt turntable designers haven't taken nearly enough care to even try matching their belt to their motor (or to their platter). The operative design principle has instead been: if the belt has the right diameter and a little stretch, then it's good enough to spin my platter round and round. That cavalier ignorance of (or avoidance of) the issue of exact speed control has given rise to a plethora of belt drive turntables which introduce as many new speed regulation distortions from the belt as they eliminated by filtering the multipole motor's kick and coast problems.
     Moreover, even if the detailed dynamic characteristics, of the motor's changing kick jerk waveform and of the belt's response instant by instant, were to be studied, it's possible (indeed probable) that no physically real belt could be built that would truly offset each kick jerk's speed error, instant by instant. In part that's because a belt's length stretching (furnishing the offsetting correction which slows down speed) is triggered by and proportional to force changes from the motor's kick jerks (though the speed of its response to force changes is unknown); however, the motor's own speed error changes (furnishing the error which needs offsetting) are not proportional, instant by instant, to the force changes, but instead are proportional to the integral of the force changes from the motor's kick jerks (velocity is proportional to the integral over time of force)..
     If a turntable design engineer can't get a belt's dynamic acceptance characteristics to exactly match and offset the instant by instant waveform of a multipole motor's jerks, are there at least some compromise design approaches by which he can at least get a belt to approximately match the overall motor jerks, averaged over time? Yes, but they're pretty lame. One commonly available spec for a belt, its static compliance, indicates how much it stretches after a fixed, unchanging force has been applied for some time (the belt's steady state position after all dynamic phenomena have died away). But this static compliance says nothing about the belt's dynamic response, instant by instant, which is what we care about since speed constancy instant by instant is our goal. Static compliance also says nothing about a belt's response to an input jerk waveform that is changing over time, instead of the fixed, unchanging force used to test static compliance. So static compliance is a pretty irrelevant spec to guide the turntable designer.
     If static compliance is the only belt spec available, can the turntable designer utilize it, perhaps for a much cruder, lamer approach to designing a belt drive turntable? One tactic would be to calculate the average over time, within each kick jerk, of the extra force supplied by each kick jerk. The static belt compliance could then be selected to respond with the appropriate amount of stretch to this average extra force, the appropriate amount of length stretch being that amount which would slow down the turntable by just the right amount to offset the average speed increase from each kick. But there's a problem with this tactic. If the belt stretches just enough to accommodate the average extra force of each kick, then it might not stretch enough, quickly enough to accommodate the peak extra force of each kick. Thus, some of the peak extra kinetic energy of each kick jerk might not be converted to belt stretch (i.e. converted to potential energy), but instead will be transmitted by the belt to the platter. In other words, the belt won't completely succeed at filtering out the kick and coast problem of the multipole motor.
     Another tactic would be to select a more compliant belt, which would stretch enough at the peak extra force of each kick to slow down the turntable the appropriate amount to offset the speed increase from the kick. But there's a converse problem with this tactic. The belt might stretch too much, and thus slow down the turntable too much, for those parts of the kick jerk waveform that are at less than peak force level.
     A third tactic would be to look at the total kinetic energy put out by the multipole motor's jerk, summed over time (not evaluated instant by instant), and then try to find an elastic belt with exactly the right static compliance to convert all of this kinetic energy into longitudinal stretch (potential energy). If the belt is not compliant enough, then some of the extra kinetic energy in each kick jerk will not be converted to belt stretch, to potential energy, and thus some of the kinetic kick jerk and coast problem will be passed on by the belt to the platter. On the other hand, if the belt is too compliant to match the particular motor, then it will stretch too much, thereby slowing down the turntable too much.
     It's doubtful that most turntable designers even go to the trouble of trying the above three design tactics, for matching the belt to the motor. It's doubtful that most even bother to try matching the belt's acceptance characteristics in any way to the motor's kick jerk output characteristics.
     In any case, none of these three tactics is truly satisfactory. All give up hope of matching and offsetting the two distortions instant by instant. Thus they give up all hope of attaining truly constant turntable speed instant by instant. Instead, they settle for achieving more nearly constant turntable speed
on the average, over time.
     Unfortunately, that's not the way you listen to music. You listen to music instant by instant, as it flows by, not as some average over time. You also hear distortion instant by instant, if the turntable speed varies instant by instant. What do we mean by "instant"? Assuming a 20 kHz bandwidth, even a flicker of speed irregularity that lasts merely 1/10,000 second could distort your music. Some turntable might have perfect overall average speed over time, but that doesn't help. Its speed has to stay constant each and every 1/10,000 second.
     As a reductio ad absurdum, imagine the worst turntable in the world, with horrible wow and flutter, and thus horrible distortion of your music. It might still have perfectly accurate speed taken on the average over time (for example, all the peaks of horrible flutter might match all the valleys, so that a 30 minute record side is over in exactly 30 minutes). Yet it would sound awful. Obviously, any claim or engineering design goal of achieving speed constancy on the average over time is meaningless. Obviously, we have to insist on the higher standard of achieving speed constancy instant by instant.
     In sum, it's virtually impossible to design a belt drive so that the input acceptance characteristics of the belt truly offset or filter the kick jerks output by the motor, or truly achieve the required goal of speed constancy, instant by instant. As noted, most belt drive turntable designers don't even try.
     But there's another tool at the disposal of the belt turntable designer. Unfortunately, this tool also brings some problematic baggage with it.
     We've concentrated on the input acceptance characteristics of the elastic belt, as it stretches its length in response to each kick jerk from the multipole motor. But the elastic belt also has some output release characteristics.
     After you stretch a rubber band with your hands, it then wants to shrink, and it exerts a force on your hands, trying to get the rubber band back to its normal length. Likewise, an elastic turntable belt stretches in response to each kick jerk from a multipole motor, and then it wants to shrink back to its normal length. In so doing it exerts a force on the other objects in the system, the motor pulley and the platter rim.
     In other words, after the elastic turntable belt accepts the input of being stretched, it then provides an output of trying to shrink back to normal. This process could be viewed as an approximate conservation of energy, a sacred principle of physics. During the stretching phase, the extra kinetic energy of each kick jerk from the motor is converted to potential energy in the form of belt stretch (some energy being lost to heat). Then, when the belt tries to shrink back to normal length, the extra potential energy stored in its temporary stretch is reconverted back to kinetic energy, thus affecting the motion of the platter and the motor pulley.
     To see how this works, it's useful to consider the continuously moving belt as comprising four sections. First, there's the section of belt that wraps perhaps 3/4 around the circumference of the platter rim. Second, there's the section of belt that wraps perhaps 1/2 around the circumference of the motor pulley. Third, there's the section of belt in free air that's travelling from the motor pulley to the platter rim. And fourth, there's the section of belt in free air that's travelling from the platter rim back to the motor pulley. Let's concentrate our attention on what's happening just in this fourth section of continuously moving belt.
     Each pole of the multipole motor supplies a kick jerk which yanks this fourth section of belt, thereby supplying inputs which the belt accepts by stretching. The poles of a rotating multipole motor occur frequently enough so that there are at least several such yanking inputs on this fourth section of moving belt, before that section fully moves onto and beyond the motor pulley. Thus, any given fourth section of belt we might look at has already been yanked and stretched several times.
     As discussed above, when the belt is stretched, the speed of the turntable platter is slowed, compared to what it would have been if the peak speed of the motor pole's kick were to have been faithfully transmitted by a non-elastic belt.
     Now, what happens when the fourth section of belt releases the potential energy of its stretched length and shrinks back to normal length? If you stretch a rubber band between your two hands, it pulls on the constraints at both ends, namely your two hands, as it tries to shrink back to normal length. Likewise, the fourth section of turntable belt pulls on the two constraints at both ends,

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