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Math to show WHY under-hang tonearms sound superiors

tabarddn51

tabarddn51

Super Member
A couple of weeks ago I was asked to show the above math for the above. As I do not want to clog up the Under Hang thread with discussion's about this detail, I decided to post it on a separate thread.

''Designer Akimoto-san’s primary argument is this: the offset angle added by Baerwald to almost all tonearms today is fundamentally flawed in that it magnifies side-force variations to an unacceptable level. Let’s use some elementary vector force mathematics to look at this in a bit more detail.


Side force at any particular tonearm position is given by the formula

µW*tan(α+?), where

µ is the friction coefficient between the stylus and groove,

W is the stylus tracking force (or VTF)

α is the tracking error angle and

? is the offset angle

The ideal situation is where µW, representing the total friction force of the stylus, does not favour either wall of a groove. This would meana side force of 0; in other words, the formula tan (α+?) should give a null value. Any other value given by tan (α+?) will mean that some part of the total stylus friction force is vectored towards the wall of the groove closer to the label (or the left wall if you are looking at a stylus head-on).

Baerwald alignment advocates aligning a 25° (24.63° to be exact) offset tonearm to achieve 3 maxima and 2 minima, points where the lateral tracking error (LTE) is the highest and zero respectively. At the highest point of LTE, Baerwald calculations give a tracking angle error of 1.5° (whether the angle is positive or negative does not matter, LTED is the same).

At the point of minimum tracking error angle (α=0) the side force will be: tan (24.63) which is 0.45846925. At the maximum tracking error angle (α=1.5°) the side force is tan (24.63+1.5) which yields 0.49054437. This means that almost exactly half of the total stylus friction force is given over to pushing against the side wall without any anti-skating correction. Anti-skating is the brute use of force to cancel off the effect of a non-zero tan (α+?), which is neither elegant nor ideal. It’s like this: imagine a car in one of its gears (we don’t know which gear and that changes every second) and wants to move forward; to make it stay still, we have two choices; use a fixed force on a rope to pull it backwards, or shift the gearbox to neutral. The question “which is preferable?” is almost a no-brainer, the former having problems of wear, lagging response times, insufficient or over use of force, & c.

So a straight tonearm with no offset is like shifting the car to neutral gear. Even if we take a worst case scenario of a 10° tracking error angle, tan (10) will still only yield 0.18, which is way better than the best case in an offset arm.''
The full article can be found here

Cheers
 
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A straight arm with no offset angle is fundamentally flawed even more.. that is why no one use it since Loefgrens paper
 
tabarddn51 said:
A couple of weeks ago I was asked to show the above math for the above. As I do not want to clog up the Under Hang thread with discussion's about this detail, I decided to post it on a separate thread.

''Designer Akimoto-san’s primary argument is this: the offset angle added by Baerwald to almost all tonearms today is fundamentally flawed in that it magnifies side-force variations to an unacceptable level. Let’s use some elementary vector force mathematics to look at this in a bit more detail.


Side force at any particular tonearm position is given by the formula

µW*tan(α+?), where

µ is the friction coefficient between the stylus and groove,

W is the stylus tracking force (or VTF)

α is the tracking error angle and

? is the offset angle

The ideal situation is where µW, representing the total friction force of the stylus, does not favour either wall of a groove. This would meana side force of 0; in other words, the formula tan (α+?) should give a null value. Any other value given by tan (α+?) will mean that some part of the total stylus friction force is vectored towards the wall of the groove closer to the label (or the left wall if you are looking at a stylus head-on).

Baerwald alignment advocates aligning a 25° (24.63° to be exact) offset tonearm to achieve 3 maxima and 2 minima, points where the lateral tracking error (LTE) is the highest and zero respectively. At the highest point of LTE, Baerwald calculations give a tracking angle error of 1.5° (whether the angle is positive or negative does not matter, LTED is the same).

At the point of minimum tracking error angle (α=0) the side force will be: tan (24.63) which is 0.45846925. At the maximum tracking error angle (α=1.5°) the side force is tan (24.63+1.5) which yields 0.49054437. This means that almost exactly half of the total stylus friction force is given over to pushing against the side wall without any anti-skating correction. Anti-skating is the brute use of force to cancel off the effect of a non-zero tan (α+?), which is neither elegant nor ideal. It’s like this: imagine a car in one of its gears (we don’t know which gear and that changes every second) and wants to move forward; to make it stay still, we have two choices; use a fixed force on a rope to pull it backwards, or shift the gearbox to neutral. The question “which is preferable?” is almost a no-brainer, the former having problems of wear, lagging response times, insufficient or over use of force, & c.

So a straight tonearm with no offset is like shifting the car to neutral gear. Even if we take a worst case scenario of a 10° tracking error angle, tan (10) will still only yield 0.18, which is way better than the best case in an offset arm.''
The full article can be found here

Cheers
Click to expand...
I've always believed that side forces are more important than given credit for, and tracking error less. This is an interesting design. I do wonder, given the materials we have today to keep mass low, why a shorter arm is preferred. Seems counter productive. I do think more reviews and measurements are needed to reach any final conclusion.
 
Gobbledygook. Pseudoscience and poor pseudoscience at that. That is not maths. The equations are way more complex than that and Baerwald doesn't resort to analogies of car gearboxes halfway through his explanations to prove his equations.

See it for what it is. Nonsense spouted in the name of selling the product. Nothing more and certainly not maths to prove this theory of side forces.
 
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tabarddn51 said:
A couple of weeks ago I was asked to show the above math for the above. As I do not want to clog up the Under Hang thread with discussion's about this detail, I decided to post it on a separate thread.

''Designer Akimoto-san’s primary argument is this: the offset angle added by Baerwald to almost all tonearms today is fundamentally flawed in that it magnifies side-force variations to an unacceptable level. Let’s use some elementary vector force mathematics to look at this in a bit more detail.


Side force at any particular tonearm position is given by the formula

µW*tan(α+?), where

µ is the friction coefficient between the stylus and groove,

W is the stylus tracking force (or VTF)

α is the tracking error angle and

? is the offset angle

The ideal situation is where µW, representing the total friction force of the stylus, does not favour either wall of a groove. This would meana side force of 0; in other words, the formula tan (α+?) should give a null value. Any other value given by tan (α+?) will mean that some part of the total stylus friction force is vectored towards the wall of the groove closer to the label (or the left wall if you are looking at a stylus head-on).

Baerwald alignment advocates aligning a 25° (24.63° to be exact) offset tonearm to achieve 3 maxima and 2 minima, points where the lateral tracking error (LTE) is the highest and zero respectively. At the highest point of LTE, Baerwald calculations give a tracking angle error of 1.5° (whether the angle is positive or negative does not matter, LTED is the same).

At the point of minimum tracking error angle (α=0) the side force will be: tan (24.63) which is 0.45846925. At the maximum tracking error angle (α=1.5°) the side force is tan (24.63+1.5) which yields 0.49054437. This means that almost exactly half of the total stylus friction force is given over to pushing against the side wall without any anti-skating correction. Anti-skating is the brute use of force to cancel off the effect of a non-zero tan (α+?), which is neither elegant nor ideal. It’s like this: imagine a car in one of its gears (we don’t know which gear and that changes every second) and wants to move forward; to make it stay still, we have two choices; use a fixed force on a rope to pull it backwards, or shift the gearbox to neutral. The question “which is preferable?” is almost a no-brainer, the former having problems of wear, lagging response times, insufficient or over use of force, & c.

So a straight tonearm with no offset is like shifting the car to neutral gear. Even if we take a worst case scenario of a 10° tracking error angle, tan (10) will still only yield 0.18, which is way better than the best case in an offset arm.''
The full article can be found here

Cheers
Click to expand...
“The ideal situation is where µW, representing the total friction force of the stylus, does not favour either wall of a groove. This would meana side force of 0”

Isn’t this what anti-skate is for?
 
curtisw99 said:
“The ideal situation is where µW, representing the total friction force of the stylus, does not favour either wall of a groove. This would meana side force of 0”

Isn’t this what anti-skate is for?
Click to expand...
None of that "explanation" is serious. Matter of fact I'd call this thread an embarrassment for the original poster. Imagine being sufficiently deluded to post that drivel as proof of anything. Made himself a laughingstock.
 
tabarddn51 said:
A couple of weeks ago I was asked to show the above math for the above. As I do not want to clog up the Under Hang thread with discussion's about this detail, I decided to post it on a separate thread.

''Designer Akimoto-san’s primary argument is this: the offset angle added by Baerwald to almost all tonearms today is fundamentally flawed in that it magnifies side-force variations to an unacceptable level. Let’s use some elementary vector force mathematics to look at this in a bit more detail.


Side force at any particular tonearm position is given by the formula

µW*tan(α+?), where

µ is the friction coefficient between the stylus and groove,

W is the stylus tracking force (or VTF)

α is the tracking error angle and

? is the offset angle

The ideal situation is where µW, representing the total friction force of the stylus, does not favour either wall of a groove. This would meana side force of 0; in other words, the formula tan (α+?) should give a null value. Any other value given by tan (α+?) will mean that some part of the total stylus friction force is vectored towards the wall of the groove closer to the label (or the left wall if you are looking at a stylus head-on).

Baerwald alignment advocates aligning a 25° (24.63° to be exact) offset tonearm to achieve 3 maxima and 2 minima, points where the lateral tracking error (LTE) is the highest and zero respectively. At the highest point of LTE, Baerwald calculations give a tracking angle error of 1.5° (whether the angle is positive or negative does not matter, LTED is the same).

At the point of minimum tracking error angle (α=0) the side force will be: tan (24.63) which is 0.45846925. At the maximum tracking error angle (α=1.5°) the side force is tan (24.63+1.5) which yields 0.49054437. This means that almost exactly half of the total stylus friction force is given over to pushing against the side wall without any anti-skating correction. Anti-skating is the brute use of force to cancel off the effect of a non-zero tan (α+?), which is neither elegant nor ideal. It’s like this: imagine a car in one of its gears (we don’t know which gear and that changes every second) and wants to move forward; to make it stay still, we have two choices; use a fixed force on a rope to pull it backwards, or shift the gearbox to neutral. The question “which is preferable?” is almost a no-brainer, the former having problems of wear, lagging response times, insufficient or over use of force, & c.

So a straight tonearm with no offset is like shifting the car to neutral gear. Even if we take a worst case scenario of a 10° tracking error angle, tan (10) will still only yield 0.18, which is way better than the best case in an offset arm.''
The full article can be found here

Cheers
Click to expand...
I just wanted to capture the original post in case he decided to delete it or change it. This post is proof that there is nothing scientific about the method and that it is a hoax pushed mainly by this poorly informed individual.
 
What do you get when you cross nonsense with pseudoscience?

Nonscience.

This thread is exhibits A through to Z in the emerging field of Tonearm Nonscience.
 
what about the timing error between the two groove walls with a purely straight pivoting arm? That would really screw up the imaging and staging while playing a record. A perfect linear arm would be the preferred choice. But unfortunately nothing is perfect in this world. But I do prefer my Old Rabco linear arm over the SME, Grado, Ortofon, ESL, VPI, and Lexicon tone arms I have had in the past and the VPI arm I have now.
 
Hi, Well I read through the formula & his notes, he said an 8'' arm is the minimum length for U/H & 15'' arm is preferred.

The underlying statement that Akimoto-san is saying is that any mechanical A/S is detrimental to the S/Q of all arm/cart combinations.

I have tried both arm lengths, well mine were 14.5'' & 8.25'' set to U/H, they both sounded better that my 12.5'' arm set to Lof A then B (prefer B);
The longer 14.5'' arm has slightly bloated bass line, whereas the 8.25'' arm had a crisp bass line & is certainly the best overall for S/Q, but only by a fraction. Cart used was a Ortofon MC25FL (re-tipped with Boron cantilever & M/Line stylus). No tracking problems or distortion was heard in any of the configurations. Stlus was set to 80mm nul point -5mm

So tell me why has Michael Fremer Apr 15, 2025 (I'm fairly sure he has read the Baerwald calculations) just advised in a review of the V/Labs 9'' (no commensal association from my side) Hi used 3 different T/T & 3 carts ( Lyra Helikon SL and Titan i, and the Transfiguration Phoenic)
''Sound
Multiple variables were at work, so it was difficult to determine what was producing the Viv Lab Rigid Float 9's consistent sound quality. However, the three cartridges all sounded more lush, more full bodied, more richly textured than they do in more traditional tonearms.''

Cheers
 
It's called second harmonic distortion. Well known to be very pleasing to the ear. Most listeners prefer the addition of(even substantial amounts of) second harmonic.

Exciter (effect) - Wikipedia

en.wikipedia.org en.wikipedia.org
 
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Psychoacoustic Enhancers

Paul White looks at the different ways in which the leading enhancers produce their results, and offer some practical advice on where the various types work best.
www.soundonsound.com www.soundonsound.com


Enhancers

Psychoacoustic enhancers are a frequent topic of enquiry here at the SOS office. Hugh Robjohns provides the answers to some of the most common questions.
www.soundonsound.com www.soundonsound.com
 
It pays to know a little about psychoacoustics before assigning virtue to additional even order distortion. It always holds the possibility to sound good even if it is a deviation from accurate reproduction.

Hence "fuller bass". You're hearing the fundamental plus an additive of the second harminc. "Richer' is another way of putting it. 'Voluptuous" all of these descriptors would fit the bill.
 

Psychoacoustic Enhancers

Paul White looks at the different ways in which the leading enhancers produce their results, and offer some practical advice on where the various types work best.
www.soundonsound.com www.soundonsound.com

QUOTE

"The secret of the harmonic enhancement principle is that only a very small amount of the processed signal needs to be mixed back in with the original, and when this is done properly, music appears more detailed, with better separation between individual sounds."
 
tabarddn51 said:
The ideal situation is where µW, representing the total friction force of the stylus, does not favour either wall of a groove.
Click to expand...

The groove with audio info is a zig-zag line, so the stylus gets constantly pushed either towards the center of the record or outwards. Even with a straight groove (as in not-concentric) equal pressure/friction occurs only in the moment when the stylus movement changes from inwards to outwards and vice versa. So, not favouring either wall of the groove throughout the whole lenght ain't gonna happen.
 
borchee said:
The groove with audio info is a zig-zag line, so the stylus gets constantly pushed either towards the center of the record or outwards. Even with a straight groove (as in not-concentric) equal pressure/friction occurs only in the moment when the stylus movement changes from inwards to outwards and vice versa. So, not favouring either wall of the groove throughout the whole lenght ain't gonna happen.
Click to expand...
He has been informed of this umpteen times on the many and varied threads he has started on many different forums touting this technique. The fallacy that this method eliminates side thrust has become a dogma which some seem to only want to shut their minds to any fact which undermines this belief system.

There is no science underpinning it just a following originating in Japan.
 
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