MC's thoughts are a minor consideration in thinking about the magnitude of the skating force. The most important cause of the skating force (after friction) is the tracking angle error, which is varying in terms of degrees of angle, all across the surface of an LP. And it is never zero, for any of our conventional pivoted tonearms that have an offset headshell, even at the two null points you can achieve if you align the tonearm according to any of the known algorithms.
The movement of the stylus in the groove generates a friction force. If the vector direction of that force were to be straight back along the cantilever, and if the cantilever were to align with the arm wand going all the way back to the pivot, there would be no skating force, regardless of the tortuosity of the grooves or the ups and downs of the music signal. But that never happens with our pivoted tonearms; there is always an angle of error. That generates the side force. If you want more on this subject, I will try to help, but otherwise, I don't want to put anyone to sleep. Think of the little red wagon you had when you were a kid. It had four wheels and a pull handle that was attached to the axle of the front pair of wheels. Remember what it was like to try to keep the wagon alongside of you while you dragged it down the street? There was an aberrant side force that you had to correct for. That's the same idea as skating force.
MC, do you read what you write? "OMG sorry but it has nothing to do with the angle of the cantilever. The
skating force that pulls the arm towards the center is a result of not
being tangential. It has nothing to do with the offset angle of the head
shell, or the cartridge, or the cantilever, or the stylus, or any of
It is the cantilever that must be tangent to the groove, but even then, in a conventional pivoted tonearm which has headshell offset, you won't have zero skating force even at the two null points. First you disagree with me, and then you repeat pretty much what I said, using different words. The magnitude of the skating force has a great deal (not "nothing") to do with headshell offset angle and the cantilever. But headshell offset angle is the dominant cause of the skating force only at the two null points, where the cantilever IS momentarily tangent to the groove, but there is still a side force owing to the fact that the pivot point is offset. At all other points on the surface of the LP, the cantilever/stylus is not tangent to the groove, and this plays an additive role in determining the magnitude of the force, in the vector algebra sense.
Everything to you is simple, except sometimes you are wrong in your simple explanations, so maybe not so simple on those occasions. On this occasion, you and I are not really at odds, but you cannot see it. Or, to paraphrase something that Einstein actually did say, a hypothesis to explain a phenomenon should be simple as possible, but not simpler.
Dear Mijo, The friction force is independent of surface area. The formula is f = uN, where f is the friction force, u (Greek letter "mu") is the coefficient of friction between the two bodies in contact and varies according to the materials of which they are made, and N is the "normal force", which is the force by which the two bodies are pushed against each other, in this case gravity. However, I do agree with you that a groove-less LP does not mimic the actual skating force generated when one plays a record.
MC, In your efforts to be flippant, to pretend everything in the world is simple and that you uniquely understand the simplicity, and to belittle others, you are truly annoying even me, who doesn't give a rat's patootie. I could refute your refutations of stuff I wrote, but I won't bother. Suffice to say, it is not that you are wrong but that you are always half right, yet you claim to be completely right.
Stylus overhang, along with headshell offset angle, was posited (by Baewald and Lofgren back in the early 40s, probably) in order to make it possible for there to be two null points on the playing surface of an LP. "No overhang, no skating" is flat wrong. An underhung tonearm with zero headshell offset does generate skating force everywhere on the surface of an LP, except at the single null point. Why do you insist upon your too simple explanations of nearly everything?
You were correct to fault me for my sentence: "Yes, if you can draw a straight line from stylus tip, through the
cantilever, that intersects the pivot point, then you have zero skating
force." Because I neglected to say that at the condition described the cantilever must be tangent to the groove. THEN you have zero skating force. That's a description of an underhung tonearm with zero headshell offset angle at its single null point on an LP. MF is not at all my guru when it comes to the physics of playing an LP. He is often parroting something he was told and is sometimes wrong. In this case, he was being too simple, like you.
MC, Yes, if you can draw a straight line from stylus tip, through the cantilever, that intersects the pivot point, then you have zero skating force. And to Larry, yes the reason conventional pivoted tonearms that are mounted so the stylus overhangs the pivot and which incorporate an offset headshell NEVER exhibit zero skating force is because, even at either of the two null points (where the cantilever IS tangent to the groove walls), the offset headshell alone creates a skating force. But no, MC, not every pivoted tonearm exhibits a skating force at all times. Underhung tonearms, of which there are only a few, that have zero headshell offset, will give only one null point on the surface of an LP, but at that one null point, the skating force is momentarily absent, because the tonearm meets the criterion stated in my first sentence. (Pivoted tonearms that incorporate complicated mechanisms for maintaining tangency to the groove at all times are not part of this discussion.)
Mijo, "mu", the coefficient of friction is non-negotiable and is not dependent in any way upon surface area. Testpilot got it right. It is a constant for any two materials. There are tables showing coefficient of friction for a wide variety of material pairs. Someone else mentioned velocity. No, friction force is not dependent upon velocity, either. Also, can you say where you got the idea that a stylus tip gouges a grooveless LP? Before you go quoting the "tremendous" pressure of a stylus tip on vinyl, which is arrived at by extrapolating the teeny-tiny surface area of a stylus tip to a square inch and multiplying the VTF accordingly, I doubt the validity of making that extrapolation. But I am open to contrary evidence that I might be wrong.
In my opinion, the reason that running the stylus on a grooveless LP does not mimic the skating force generated while playing music is that in the process of negotiating the tortuous groove, the stylus tip is constantly subjected to acceleration and deceleration (acceleration = change in stylus velocity, as someone else mentioned; deceleration = negative acceleration). Each tiny acceleration requires a Force (F = ma), because the stylus tip has mass, pulling the stylus in the same direction as that of friction. That force is adding to the friction force in a way that does not happen when there are no grooves and no music.
Justme, what I objected to in MC’s generalization was his saying “no overhang, no skating force”. I believe that is a direct quote from his post. The fact is that any pivoted tonearm, whether it overhangs the spindle or not will generate a skating force. The one exception is for in underhung tonearm, or a tonearm where the stylus does not reach the spindle. Such tonearms are built with zero head shell offset angle. In that case, when the stylus tip is at its single null point on the surface of an LP, for that instant only, there is no skating force. Everywhere else on the LP there is a skating force, even with an underhung tonearm. I don’t disagree that when you have the stylus overhang the spindle, per se that will cause a skating force. It’s the Pythagorean Theorem.
Clear thinker, I do apologize for being so pedantic, but your point #1 is blatantly incorrect. In fact all of our pivoted tonearms mounted so the stylus overhangs the spindle WILL generate a skating force even at the two null points, because of headshell offset angle. I am not sure I understand your point #2, because the null point is defined by the exact spot where the stylus contacts the surface of the LP, so the stylus can never “overhang” a null point. Or perhaps you are being facetious, for which I cannot blame you.
This is a complex topic, whether you like it or not. It seems that when I focus on one aspect, you assail me for not focusing on another aspect. So this is useless. I did NOT ever say the "spindle" caused the skating force, for god's sake. When we use the term "overhang" we are referring to pivoted tonearms that are set up such that the stylus tip overhangs the spindle. I mentioned the spindle for the benefit of anyone who might be trying to follow the logic or who might not be familiar with the meaning of "overhang". That is the context in which I used the word "spindle". I would like to add with respect to your last post, that when I first discussed the mechanism of the skating force, you got after me for talking in terms of the cantilever and not mentioning the rest of the tonearm system. Now here you can be caught out for talking about the stylus alone. The stylus can be thought of as a single point on the surface of the LP. As such, the "stylus" can never be tangent to anything. For tangency, you need two objects that have at least 2-dimensionality. The point in space has only one. The cantilever, on the other hand, can be thought of as a straight line, which can exhibit tangency to a circle (the LP groove). I believe you understand this topic almost as well as I do. Why do you need to include ridicule in your rejoinders?
MC, It's a matter of vector algebra, adding the various force vectors results in a net side force that can only pull the stylus toward the spindle (in the case of an overhung tonearm), because the stiffness of the arm wand prevents movement in the actual direction of the major net force, which is toward an ever-moving point that is always pointed to the rear but to the inside of the pivot (with a pivoted, overhung tonearm). With an underhung tonearm, the direction of the side force actually changes from pulling the tonearm inward to pushing it outward, after the stylus passes through its single null point, where there momentarily is zero skating force.
"Each and every point on a circle is the same distance from the center.
Therefore the vector pointing towards the center is zero." It's not that the two statements are wrong. It is that the two statements have nothing to do with each other. Moreover, an LP groove is actually spiraling toward the spindle or the label, so each and every point is NOT the same distance from the center. And there is a net vector force toward the spindle; we call it the skating force. (I know we agree on that, but you seem to lose sight of it once in a while.)
The ball on a string goes off into space on a straight line tangent to its circular orbit, when you let go, because you were applying a force that kept it circling, until you let go of the string. That is called a centripetal force. Because as Newton tells us, "every object persists in its state of rest or uniform motion in a straight line, unless it is compelled to change that state by forces impressed upon it".
You wrote, "The motion of each point on the circle breaks down into a vector that is
pointed straight ahead, ie tangentially, and straight towards the
center. Each and every point on a circle is the same distance from the
center. Therefore the vector pointing towards the center is zero." What?
The reason why overhung tonearms can never have zero skating force can be shown by the Pythagorean Theorem. As you say, tangency to the groove is what we are talking about, but we need tangency to the groove where the friction force generated at the stylus tip has a vector that passes back through the pivot point. Then and only then do we have zero skating force. Consider an underhung tonearm with no headshell offset angle that can achieve zero skating force at its single null point. In that one moment, the distance from the pivot through the tonearm/cartridge is one side of a right angle triangle (side a). The distance from the stylus tip to the spindle is another side of a right angle triangle (side b). And the pivot to spindle distance would be the hypotenuse of the right angle triangle, side c. Pythagorus told us that for any right angle triangle, c-squared = a-squared + b-squared. But if you have an overhung stylus, side a (tonearm effective length) is always larger than side c (P2S). So you can never achieve even a null point, let alone zero skating force, with an overhung tonearm, UNLESS you invoke a headshell offset angle. The founding fathers of cartridge alignment handed down to us a headshell offset angle, so as to achieve two null points across the surface of an LP. But they didn't give us any condition that satisfies what we need for zero skating force, because headshell offset per se causes a skating force.
Just to point out that there is a good argument to be made in favor of a high horizontal effective mass for producing accurate base response. I am not coming down either way on this subject, but certainly there is a school of thought that is contrary to mijostyn’s ideology.
So, the discussion has come around to the idea that high effective mass in the horizontal plane, relative to vertical effective mass, is at least theoretically a good idea. How does one know that 25g is too high? What is the typical horizontal compliance of most cartridges? While reading the preceding posts, I remembered that some pivoted tonearms place outboard weights right at the pivot point, extending out on either side at a 90 degree angle to the arm wand. These weights are added in order to increase horizontal effective mass, and I have read at least one thread, a few years ago, wherein the benefits were said to be evident. M Fremer has popularized the idea that horizontal mass should not be so high, for what that is worth. It seems logical to me that when the stylus is trying to trace the heavy horizontal modulations of a bass response, you want the stylus/cantilever to move whilst the arm stays as still as possible.