My new alignment template generator

[Graeme Dennes]

If I could add a couple of points to an interesting discussion.

As a background note re null points. Null points are based on (ie, are calculated from) the inner and outer groove radii selected for alignment optimisation purposes. They are outputs only. They are not the drivers of the optimisation process, but the consequences of it.

Of course, they may be specified for use in an alignment procedure or for when using a particular alignment tool, but their specifying does automatically pre-determine the values of the inner and outer groove radii (from which the null points were calculated).

As a background note re the Stevenson A alignment. Stevenson's goal was to minimise (in fact to make zero) the weighted tracking error (WTE) and the resulting distortion at the specified inner groove radius. In and of itself, this was a worthwhile outcome. However, under the Stevenson A alignment, the WTE and the distortion occurring over about 75 percent of the record playing time is greater than that which occurs under the Löfgren A alignment for the same conditions (ie arm length and groove radii). Further, the Stevenson A alignment is only significantly better than the Löfgren A alignment during the last 3-4 mm of the record playing surface (usually less than one minute of playing time).

Plotting the WTE of these alignments will confirm the above. It is primarily for these reasons that the Stevenson A alignment was never going to be broadly accepted and adopted.

Practically, this leaves us to choose between the Löfgren A and Löfgren B alignments, although the Löfgren A alignment still continues to be the most widely adopted alignment standard.

Graeme Dennes

[Conrad Hoffman]

Graeme, I want to thank you for your excellent paper. Though I've drawn many templates in CAD, the math eluded me somewhat until your analysis. You did, however, provide a legend for everybody's math except your own (unless I missed it)! Not being terribly good with math, I have a question. I was able to rearrange the Löfgren A formula such that I could input pivot-to-spindle and groove radii, for the desired output. I was unable to do that for the B alignment and the Stevenson, so I went with a brute force numerical method. It works fine, and we have so much computing speed that there's little penalty, but I'm curious if there's a simple solution?

[Graeme Dennes]

Conrad, thank you for your kind words regarding my 1983 analysis. I'm very pleased to know it's been able to assist you.

Re the notation: it can be found on page 65 of the current (February 2008) release.

At the time I wrote the analysis (1983), I had no access to quality publishing tools, and so unfortunately it ended up being hand written, which I was never happy about. I have considered rewriting it using modern software tools, but perhaps little or nothing will now be gained from an information viewpoint. However, it does remain on my job list!

Now, to your most interesting question re how to determine the overhang d (and arm length L) given we supply only the mounting centre M and the groove radii R1 and R2. You mention you have done this for the Löfgren A solution, but not for the Löfgren B solution. This is how I would do both calculations.

For Löfgren A:

1. Calculate Löfgren's a^2 term using EQN (4) on page 3 of my paper. (Note that my Ra^2 term is equivalent to his a^2 term.)

2. Ra = SQRT(L^2 - M^2), and Ra = SQRT(R01.R02) = SQRT(a^2) from page 68 of my paper.

So L^2 - M^2 = a^2

so L^2 = M^2 + a^2

3. The Solution:

Arm length L = SQRT(M^2 + a^2)

and overhang d = L - M

So given M, R1 and R2, we can calculate arm length L and overhang d for the Löfgren A alignment.


For Löfgren B:

1. Calculate Löfgren's a^2 term using EQNS (16) and (17) on page 7 of my paper. This is the a^2 term for use with his B solution.

2. Substitute this value for a^2 into Step 3 of the Löfgren A solution above to find the L and d values for the Löfgren B alignment.

Hoping this will be of assistance.

Graeme Dennes

[Conrad Hoffman]

Goodness, that was so easy it makes me look the complete fool. My only excuse is that I was working from several sources of formulas- thanks!

[Conrad Hoffman]

For anybody still reading, I have a somewhat insane idea. First, though I really like arc templates, there are significant error sources in the use of any template (see post above concerning axial forces on the cantilever). Let me quote myself from my readme file:

"Remember, the goal is to have the cantilever correctly aligned while playing a record, not sitting on an alignment template. Read that again- it's important!"

Here's the crazy idea. How 'bout you set up a camera above the template target and take a photo, hopefully nicely resolving the cantilever and target, with the stylus resting correctly on the target, and hopefully aligned as best as you can get it. Next, without moving the camera or table, you remove the template and play a record. When the stylus reaches the place in the viewfinder where the target was, you snap another photo. Now you overlay them and compare the cantilever angle. If the difference in angle is consistent, one could then adjust the template to compensate, or just adjust the cartridge and repeat the photo process until the correct result is achieved.

What do you think? When I have some time I may try this, but if it has some major flaw, maybe somebody will point it out to me.

[Conrad Hoffman]

I haven't done exactly what I've described above, but here are some photos that I think illustrate the problem, at least with very compliant cartridges like my OM30-

First, this is what happens when the stylus is first lowered onto a template, or even a non-rotating record:

IMO, the problem is caused by the increase in effective length as the cantilever deflects upwards. Something has to give, and because the arm pivot isn't in line with the cantilever, the arm moves away from the spindle, deflecting the cantilever as shown. It also twists it slightly. (BTW, I'm of course not suggesting that the pivot should be in line, just that this is the result of the geometry we use.)

Next, if one applies a few grams rotational pressure to the platter, everything straightens out. I applied a bit too much, and I'm off target as a result:


Finally, here's a shot of the cartridge playing a record, taken at the same location as the previous targets. Anti-skate is being applied, but everything is still about as one would expect:


From this, I'd have to say that aligning to the cantilever with high compliance cartridges is problematic. IMO, this is probably a worst case situation, but the error sources are real. It seems that either a bit of pressure on the platter is necessary (risky and hard to be consistant), or one is better off aligning the cartridge body. For less compliant cartridges, or where the geometry somehow prevents the cantilever from deflecting, aligning to the cantilever makes a certain amount of sense.

Comments? Am I crazy?

[doktorgigi]

Glad to see some interest! I don't have any problem changing Baerwald to Löfgren A, but called it Baerwald because that's the most popular name and I didn't want to clutter up the screen with a dual name. I used the wonderful Graeme Dennes paper to sort out the formulas and, as he says, if Löfgren wrote the only paper on alignment, we'd still be doing things exactly the same way.

I learned something interesting while experimenting yesterday. When the stylus is off the record or template, the cantilever forms an angle to the arm. You knew that. When the stylus is on the record or template, the angle is reduced. You knew that too. What I hadn't thought about was that this increases the effective length of the arm slightly. Not much, not enough to really measure, but enough to put axial force on the cantilever. Because the arm pivot isn't in line with the cantilever, the cantilever will be deflected in the cartridge body towards the spindle. IMO, this makes aligning to the cantilever more problematic, especially with high compliance cartridges. Once friction is overcome, say playing a record, or if the template had zero friction, the cantilever re-centers.

What do people have to say about this- I'm far from being any expert on the topic?

hi I'm a newebie at all of this, but thanks for the protractor, looks gr8!

re: your question, I believe the RS-A1 tone arm tries to address your issue of inward deflection amongst other things... kinda cool but scary looking in terms of use. double unipivot! definitely out of the box thinking.

http://www.sakurasystems.com/articles/rs-a1.html

[Conrad Hoffman]

Wow, you don't see an arm like that every day! Very interesting, though the static vs dynamic issues I'm thinking about are somewhat different that what they've addressed.

[Graeme Dennes]

To add a note to my post above dated 27 January:

For the Löfgren A solution, the null radii are dependent only on the selected inner and outer groove radii, and are given by the equations shown at paragraph C on page 67 of my analysis (2008 release). Baerwald was the first to explicitly state the null radii equations. I presume Löfgren also knew of these because his 'a squared' term at EQN 4 on page 3 of my analysis is the product of the null radii equations shown on page 67. Also, the page 67 equations are correct only when L, beta and d are optimum, ie, have been calculated according to the Löfgren A alignment.

Löfgren and the later authors used (minor) mathematical approximations to simplify their analyses and results, and the page 67 null radii equations are consistent with the Löfgren A solution.

However, in the strictest (ie no approximation) mathematical sense, the null radii are in fact the roots of the weighted tracking error (WTE) function, (ie, are the radii at which the WTE function is zero). The WTE function is shown at EQN J on page 70 of my analysis, and the no-approximation null radii equations are shown at EQN N on page 71. You'll note that the null radii here are dependent on L, beta and d only, and not groove radii. Any variation in these three parameters will result in a change to the null radii. Also, the null radii given by EQN N are correct for all L, beta and d values, not just the optimum values determined by the Löfgren A solution.

Thus, the null radii calculated from the page 67 equations will be close to, but slightly different from, the theoretically correct null radii calculated from the equations on page 71.

In summary, to calculate the null radii: When using the Löfgren A alignment, the null radii equations on page 67 of my paper are practical and consistent (although the page 71 equations may be used). If using the Löfgren B, Stevenson A, or any other alignment, the page 67 equations do not apply, and the equations on page 71 must be used instead.

Hope this assists.

Graeme Dennes

[Conrad Hoffman]

Yes, that clarifies things- thanks! I changed the program math based on your previous info, though I haven't uploaded it as a new revision. The user wouldn't see any difference, but the code is a lot cleaner. I thought it was just a couple pages, but I checked the editor and that little app is actually about 680 lines of code. I also set my table up with Löfgren B and am pretty sure it's an improvement over "A". Stevenson holds little appeal- I only included it because a significant number of people seem to want it.

Best regards,
Conrad

[andyr]

Hi Graeme or Conrad,

Could one of you confirm for me (who is a relative newbie in terms of understanding the difference between 'Loefgren A', 'Loefgren B' and 'Baerwald') that:

1. 'Loefgren A' is the same as 'Baerwald'?
or
2. 'Loefgren B' is the same as 'Baerwald'?
or
3. Neither?

Thanks,

Andy

[Conrad Hoffman]

1.

(worlds shortest reply)
Regards,
Conrad

[andyr]

1.

(worlds shortest reply)
Regards,
Conrad

Haha - thanks, Conrad.

Regards,

Andy

[Graeme Dennes]

Hi andyr,

Further to your question regarding differences between various alignments, may I refer you to page XV of my analysis on optimum tonearm alignment (2008), located at:

http://www.vinylengine.com/phpBB2/viewtopic.php?t=4854

On that page is shown a graph, which shows the weighted tracking error (WTE) across the groove radii of 146.05 to 60.325 mm, for three alignment strategies. Tracking distortion is proportional to the WTE, as established by Löfgren in 1938.

Now, a closer look at the three plots on that graph may help explain the effects of the different alignment strategies, ie, different offset angle/overhang pairs. After all, the only differences behind the three plots is the differences in the offset angle and overhang values selected for each. Changes to those values will result in changes to the shape of the WTE plot. The null radii are located at those groove radii where the WTE is zero, ie, where the WTE plots cross the zero axis. Areas on the plots with the higher WTE values - note that positive and negative values are treated equally for distortion purposes - will produce the higher distortion at those groove radii, and vise versa.

The Löfgren A alignment provides the minimum overall distortion (ie, the three WTE peaks are minimised and equal), the Löfgren B alignment reduces somewhat the distortion between the null radii but increases the distortion at the inner groove area, while the Stevenson A alignment has small to zero distortion at the very inner groove area, but has the largest WTE (ie distortion) over most (around 75 percent) of the record playing surface.

Of further note is that the WTE for the three alignments over the outer one third of the groove radii (say 115 to 146 mm) are somewhat similar. However, the WTE for the three plots for the inner two-thirds of the record radii are quite different, resulting in different distortion results for that area of the record.

The three plots on page XV are three examples of alignment strategies, and the equations used to obtain the offset angle and overhang values for them are shown in my analysis, courtesy of their authors (Löfgren in 1938, and Stevenson in 1966).

Hope this assists.

Graeme Dennes