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In Reply to: RE: How Important is Stylus Shape? posted by flood2 on February 02, 2016 at 16:20:27
Going from a 1.8mm thick LP to a 0.76mm LP with a 10.5" arm (273.4 Eff Length) will yield a SRA difference of 0.2 deg....unless my math is wrong. Not worth it to me to adjust VTA between LPs. Enjoy the music.
Follow Ups:
It depends on the shape of your arm - if it is straight then yes. If a J or S shape, then the distance used is not the effective length - you form the triangle that lies on the plane and calculate the length of the side that the headshell axis is on and take that distance... which is much shorter!
Regards Anthony
"Beauty is Truth, Truth Beauty.." Keats
Interesting! I see your point!
However, it doesn't matter whether it's a straight arm or a J or S shaped arm as long as it's an offset tonearm. Then, rather than using the effective length directly in the calculation you would use the cosine of the offset angle times the effective length. For example, the true change in SRA would be determined by the following equation:
1) Delta_SRA = Asin{Delta_Thickness / [cos(offset) x effective_length]}
The above method would yield a change in SRA that is slightly greater than the following method:
2) Delta_SRA = Asin(Delta_Thickness / effective_length)
The change in SRA would be about 0.013-degrees greater using the first equation versus the second equation with the numbers given in miner42 's post.
That is an excellent deduction. I hadn't thought of it before.
Best regards,
John Elison
John, Anthony: I must have still been busy thinking about that in some corner of my mind, 'cause when I woke up from the nap I just had, I had an additional thought: Namely that the effective length times the cosine of the offset angle should only apply, if it's an arm design with "angled pivot" (i.e. on which the pivot axis for vertical motion is angled to be perpendicular to the "headshell angle" to avoid rolling) - whereas for an arm design without angled pivot (e.g. SME M2) me thinks it would rather have to be the effective length divided by the cosine of the offset angle, wouldn't it?
Greetings from Munich!
Manfred / lini
Hi Manfred
So if we go back to the original point of my post, it was to explain the arm height compensation required to compensate for different record thicknesses to achieve the reference SRA.
It is easier to consider the J/S arm to see the reason for the effective length not being the length you use. Unless the arm axis and effective length lines are coincident, the effective length is an imaginary line going from the pivot to the stylus tip. The headshell is mounted on the arm such that the central axis is at an angle (i.e the offset angle) to this imaginary line. So if we want to calculate the arm height adjustment based on a measurement of the implemented SRA, we need to form a plane in the form of (right-angle) triangle which has the (imaginary) effective length line as the hypotenuse. The adjacent side (with respect to the offset angle) on which the headshell lies on is the length we must use for calculating the arm height compensation when we raise and lower the arm.
Using the Technics arm as an example, the effective length is 230mm and the length used for calculating the arm height adjustment is 161.25mm which is the adjacent side of the triangle on which the headshell is aligned with. The effective length is incorrect to use since the SRA is measured on a line which is not on the effective length line; if we consider the headshell/pivot plane it is with respect to the adjacent side.
Regards Anthony
"Beauty is Truth, Truth Beauty.." Keats
> effective length is 230mm and the length used for calculating the arm height adjustment
> is 161.25mm which is the adjacent side of the triangle on which the headshell is aligned
Since offset angle is 22-degrees and the tonearm bearing is aligned to this offset, wouldn't the length used for calculating the arm-height adjustment be Cos(22-degrees) x 230 = 213.25-mm?
Yes that is correct. In hindsight, my example was probably a bad one to use to illustrate the point - my dimension was copied out of my spreadsheet which I did years ago and I forgot that this is specific to the Technics arm - I have referenced the correction with respect to the headshell flange i.e 213.25mm-52mm = 161.25mm. Your calculation would indeed be correct for a normal arm where the headshell is part of the arm pipe or at least parallel to the arm pipe.
Although there is considerable variation in the tilt angles, the Technics headshell is designed to be tilted upwards (by +0.63°) to approximately correct for the arm height scale being with respect to the undeflected cantilever. I have therefore referenced to the headshell flange at the end of the S-pipe so that the arm height can be adapted to match any headshell (irrespective of the tilt angle of the headshell in question) to bring it back to the reference tilt angle so that the arm height scale is correct.
So to clarify, yes, in the *general* case, the correct length is (effective length) * (cos(offset angle)).
Regards Anthony
"Beauty is Truth, Truth Beauty.." Keats
Anthony, John: Tried to make a little illu for your guys to show what I mean - just had MS Paint at hand and I'm not exactly a great illustrator, though, so please excuse its lousiness...
Anyway, to make it a bit simpler I picked an arm design with the headshell sticking out to the right for the illustration, so that the tip is on the actual arm axis and the virtual and the actual arm axis are the same (at least in 2D as seen from above) and "headshell angle" and offset angle also are identical:
So, the way I understood Anthony's point way above, is that we have to heed what we're referencing to, which shouldn't be the angle of the arm axis to the record surface, but rather of the yellow line to the record surface - and I'd agree with that. However, my point would be, that this would only be arcsin (height change / (effective length x cos (offset angle))) for the arm with "angled pivot" on the right, but arcsin (height change / (effective length / cos (offset angle))) for the arm with non-angled pivot on the left. No?
Greetings from Munich!
Manfred / lini
I agree with your equation for the tonearm with the angled vertical bearing, but I can't wrap my mind around the other equation due to the additional complexity resulting from the change in azimuth when arm-height is changed.
Why wouldn't the equation simply be:
Arcsin [height change / effective length]
The fact that azimuth will also change makes it difficult for me to isolate SRA from azimuth. The more I think about it, the more I'm inclined to think the equation for the change in SRA might remain
Arcsin [height change / (effective length x Cos(offset))]
even though the arm-bearing is not aligned to the offset angle. It's just that there will also be a change in azimuth. I just can't seem to get an accurate picture in my mind of this situation, though.
Hi Manfred
Regardless of straight or bent arm, the Adjacent side of our triangular plane is the correct length to use for referencing arm height. Unless you have a tangential tracking arm the headshell axis is not coincident with the arm axis. Note also that with SME type straight arms, it is an illusion that the stylus lies on the arm axis since the mounting hole to tip distance varies from cartridge to cartridge so the effective length is still a virtual line just like the headshell reference axis.
Regards Anthony
"Beauty is Truth, Truth Beauty.." Keats
Oh, man! That's too difficult to think about right now, although I don't think it would ever be the effective length divided by the cosine of the offset angle. Then, again, I can't really wrap my mind around it at the moment, so you could be right. It just doesn't seem intuitive to me, though.
I think we should move on to something more musical. If you don't address an issue when it's on Page 1 or Page 2 at the latest, it's just too hard for me to wrap my mind around it when it reaches Page 4. ;-)
Best regards,
John Elison
John: I wonder whether that's already correct enough, if one strives for exactness - but I must confess, that I find it quite hard to wrap my brain around a close to real world model...
Anyway, I think for a more correct and universal formula one would also need to consider the initial angle of the arm - and then also need to compensate for the vertical distance between the tip/record surface and the vertical pivot on non-OPS-arms (to use Dual's term (Optimum Pivot System) for an arm design with the vertical pivot axis lowered to tip/record surface level, foremost to minimise warp-related scrubbing...). I.e., if effective length = tip to horizontal pivot distance, that's practically already a 2D projection "as seen from above/below", but in reality we're usually rotating an "L" and not a "[", so that the actual radius would be a bit larger... And exactness freaks might even additionally want to consider tracking force over height level. ;)
But actually I think for a decent approximation the simplified formula (angular change = arcsin (height change / effective length)) will already do the job well enough...
Greetings from Munich!
Manfred / lini
Whatever works for you is fine with me. Personally, I don't even worry about changes in VTA from different thickness records. However, if I did, I'd use the equation that comes closest to the truth. I own a powerful programmable calculator so it doesn't bother me to throw a few more numbers into the mix. In fact, I just bought a brand new HP Prime calculator, which is probably the most powerful handheld calculator in the world.
Best regards,
John Elison
*lol* Neither do I, John. But I tend to regard wasting some thoughts on the theoretical side as a bit of a workout for the brain, which can't really harm, even if the matter doesn't really seem all too practice-relevant to me.
Oh, and nice calculator, btw. Are there as many games for it as for the Casio FX-CG10/20? ;)
Greetings from Munich!
Manfred / lini
..you made my day! :)
I've been on hold most of the afternoon trying to sort out an insurance claim on a large cracked window in the house....and then my RGP contact lenses suddenly cracked into 3 pieces whilst cleaning.
I'm scared to touch my records now in case something breaks there too!
Seriously though...
As you pointed out, the actual angular shift in SRA appears miniscule with the change from thin to thick discs. I firmly believe, after extensive experiments, that astonishingly small adjustments to have an audible effect WHEN ONE IS NEAR THE SWEETSPOT. I'm talking about fractions of an arc which, based on the calculations you just presented, are TINY adjustments in arm height which are beyond belief and certainly beyond anyone eye-balling.
Once one has dialled in as close to the optimum by measurement first, the only fool proof method to fine tune I found was to use test tracks (as in music or voice material) on the inner grooves and use sibilance or some HF rich material such as high hats where one can listen for clean sounds (a clean "tssssss" sound) . I am literally adjusting in 0.01mm amounts and testing for the smooth sounds. I can consistently hit the sweet spot now according to my measurements. A small error of 0.1mm in arm height results in an obviously "gritty" quality to sibilants and cymbal sounds with the MicroLine and Stereohedron. I can only imagine how difficult the Replicant 100 would be given that the bearing radius is 33% longer than the two mentioned tips.
I wish test tones would have been produced to make this process easier to do consistently. The IEC IMD 4:1 test tones at 60Hz and 4kHz for setting VTA are not much use - one needs another higher frequency tone in the upper presence band to examine the amplitude of the sidebands. However it is real to me! The subjective result is a clean soundstage and silky smooth highs.
For this reason, I think that exotic tips are an "undertaking". Without this level of attention to setup, the true potential of the tip is never realised.
Regards Anthony
"Beauty is Truth, Truth Beauty.." Keats
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