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In Reply to: Re: Question to Brian: Difference between Baerwald and Löfgren alignment posted by bkearns on December 14, 2001 at 08:16:01:
Hello Brian,thank you very much for the detailed answer.
>>>I can’t read German, so what follows is only guessing.<<<
I can read German so I guess I will take the task one day to crawl through it; a first try showed that the whole papaer is not an easy one although verbal explantions are comparatively easy to understand, but the author expects the reader to go through the math.>>>As far as I can figure out, they both derived the same
result for minimizing the peak tracking distortion:
Löfgren was first. When I looked through Löfgren’s
paper, and Barewald’s paper, I was surprised at how
similar the equations were and I did wonder– but who
am I to accuse the dead of plagiarism!<<<
Nor would I. I always found it very comfortable to know that two powerful minds independently arrivesd at the same result. Also, I do not object against good plpagiarism as the plagiator crosscheck and validates his predecessor's work.What I loathe is bad, foolish plagiarism where the plagiator does not fully understand what he is copying and skips important details or worse, doesn't find hidden flaws and copies the flaws with the rest. :-) the railworm story ...
>>> Löfgren also proposed a method for minimizing the
average tracking distortion. However, he only gave the
solution in terms of linear offset. If the optimum linear
offset for minimum peak distortion is used (93.445mm), the
minimum average distortion occurs when the null radii are
70.29mm and 116.60mm. However, I cannot think of any
a-priori reason why the linear offset should be the same for
minimum average distortion as minimum peak distortion.<<<It is not the same, fiddling with the spreadsheet showed me that the values are very close but not the same.
>>>John Elison independently calculated the null radii for
minimizing average distortion, using a numerical method, and
this method coincidentally gave almost the same null radii
as those above (70.15mm and 116.23mm). So it seems that it
is correct to use the same linear offset for either method.
I was very surprised by this coincidence!<<<Well, I would say that the difference drowns in the measuring accuracy. So we can take the smae value.
>>> For whatever reason Baerwald seems to have been credited
with the former method, ie minimizing peak distortion. <<<So do I and son will any engineer do who likes classical music. IMO, it is quite foolish that records start at the outer groove; ususally biggest stylus excursions happen at the fierce finale, at the inner groove where distortion is much more critical.
>>> It is also possible to calculate the arm parameters from
the preferred null radii (since the null radii are not
dependent on the arm parameters). The following two
equations, give the necessary relationships.1: Linear Offset = Effective Length times sine of offset
angle = average of null radii2: Square of Effective Length - Square of Mounting distance
= product of null radii.In other words, once you have selected a pair of null radii
and selected one arm parameter, the other two parameters
come directly from the two simple formulae above.I find this method preferable.<<<
I agree.
I learned very late about the Löfrgern/Baerwald stuff. I wrote my diploma thesis on TT and tonearm design and as I did not find any relevant literatur back then (before the internet age), I had to derive the whole problem myself. I also settled on known null radii, presuming they are the same of any arm length. May this is of interest to you, so here it goes:
outer null (m) : 120.9
inner null (n) : 66.0
Effective length (b) : 250
tonearm pivot (P)
platter spindle (S)
stylus tip locations (T1 and T2)S sits on b and divides b into x and b-x
mounting disctance (x) : ??
overhang (b-x): ??
offset angle (90°-gamma): ??I used the law of cosines, for that I needed the angle gamma. Two triangles P-S-T1 and P-S-T2 canbe drawn and for each triangle a cosine law equation can be written.
[1; P-S-T1]:
x^2 = m^2 + b^2 - 2*m*b*(cos gamma)
[2; P-S-T2]:
x^2 = n^2 + b^2 - 2*n*b*(cos gamma)[1 and 2, x^2 eliminated and solved for cos gamma]:
(m^2 - n^2)/(2*b*(m-n)) = (m + n)/(2*b) = cos gammaIn this example cos gamma is 0.3738 , so gamma is 68.0498° and offset angle is 21.9502°. To get x, cos gamma is put in eq.1 or eq.2.: x = 233.496 , so overhang is 16.5035 .
With same effective length, 60.33 as innermost groove and 146.06 as outermost groove, the Baerwald spreadsheet yields null radii 66.00 and 120.90; offset angle is 21.951 and overnhang is 16.504. Apart from rounding errors the same results.
Somehow I think, I know more now about pivoted tonearm geometry than I never need to know :-) remember, I am stuggling with a linear tracking tonearm design. Have a look!
Greets,
Bernhard
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Follow Ups
- Thanxalot! attached: my homebrew tonearm geometry calculus. - dice45 08:37:38 12/15/01 (0)
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