TERMINATOR tonearm (Pt 2) – Ladegaard’s thinking

This is a follow-up to my Terminator linear tracking tonearm post in last Feb.

I mentioned Effective Mass and how it differs significantly in the horizontal and vertical planes.

Poul Ladegaard’s “Tangential Tonearm” experimental work is informative here.

With tonearms generally, Effective Mass is usually targeted at a figure that, in combination with the mass and compliance of the cartridge, results in a Resonant Frequency that is in the region of 8 – 12Hz.

This is intended to be below the lowest reproduced frequency (say 15 – 20Hz) and above any record warp or eccentricity frequency (0.5 – 2Hz).


With most pivoted tonearms, Effective Mass is similar in both the horizontal and vertical planes.  (Except in cases where some horizontal damping is applied.)

However, with linear tracking tonearms, it is common for the Effective Mass (inertia, if you like) in the horizontal plane, to be much greater than in the vertical plane.

This is also the case with the Trans-Fi Terminator linear tracking tonearm.


Poul Ladegaard’s work was the inspiration behind Victor’s Trans-Fi Terminator tonearm.

Vic has kindly drawn my attention to Poul Ladegaard’s research when Ladegaard was prototyping his Tangential Tonearm concepts over a period of 20 years.

In a Ladegaard published article (translated by Thomas Dunker), he explains his reasoning behind his Tangential Tonearm concepts…

 …..a theory about a more optimal and well considered placement of the arm resonances was to be tested in real life. The latter in the attempt to split resonances below 20 Hz in the vertical and horizontal planes with independent responses, thereafter optimizing them separately.

The basis was/is that there is only groove modulation in the horizontal plane at lower frequencies, below about 200 Hz, and that unwanted disturbance from warps on the record exist in the vertical plane. Due to the desire for the best possible transient response, the frequency response in the horizontal plane should be as smooth as possible, with a soft 6 dB/octave roll-off down towards 1-2 Hz, so that the only disturbance from eventual eccentricity can be eliminated.

In the vertical plane the goal is to achieve the best possible roll-off of the warp frequency below 10 Hz. This means that the arm resonance should be between 12 and 16 Hz, and it can very well be undamped, so as to make the roll-off as steep as possible. In real life this means that the effective mass of the arm in the horizontal plane has to be 25-50 times greater than in the vertical plane, where in a light arm it’s typically about 10 grams. The total effective mass of the moving system in the horizontal plane will then be in excess of 250 grams, and depending on its distribution, the total mass can get very high. One experiment was made.

….. Listening tests as well as measurements confirmed the idea.

ladegaard proto 3

Poul Ladegaard’s first prototype

The Trans-Fi Terminator air-bearing, linear tracking tonearm has a very lightweight Tomahawk arm wand with low vertical Effective Mass (~5gm).  However, the entire slider carriage assembly contributes to horizontal Effective Mass which is many times higher (~100gm).

Thus, the Terminator generally fits Poul Ladegaard’s criteria.


With a low compliance Moving Coil cartridge (Koetsu Rosewood) installed, calculated vertical Resonant Frequency is 12 – 12.5Hz.  Calculated horizontal Resonant Frequency is around 5Hz.

Thus, vertical Resonant Frequency is well above record warp frequency range.

And horizontal Resonant Frequency is well below recorded low frequency range (ie. monophonic, horizontal-only groove modulations) & above any record eccentricity resonances.

In use, Bass reproduction and dynamic range are two of the notable things about the performance of the Terminator. Bass is deep and powerful.  And there is no instability with transients (piano, etc).

I am thinking too that the low horizontal resonant frequency contributes to preservation of deep bass harmonics and sense of ‘ambient envelope’.

Thanks Poul and Vic!


Below (copied from Roscoe Primrose’s Ladegaard webpage) are Ladegaard’s graphed test results for:

  1. Resonant Frequency in the horizontal (vandret) plane 2.8Hz and vertical (lodret) plane 12Hz.  Ladegaard’s 3rd prototype used an air-bearing for horizontal sliding movement and a knife-edge bearing for vertical movement – the Terminator uses twin ‘uni-pivot’ points for vertical movement.ladegaard-resonances
  2. The effect or Air Pressure on horizontal resonant behaviour – Ladegaard used a vibrator to examine the effect of varying pump supply voltages – ie. air pressure.  His conclusion at that time was that an air film thickness of just 50 microns (0.002″) is sufficient.  ladegaard-air-pressure

7 thoughts on “TERMINATOR tonearm (Pt 2) – Ladegaard’s thinking

  1. Pingback: Linear tracking tonearm… the Terminator | D a r k L a n t e r n

  2. Pingback: Terminator tonearm – new arm mount | D a r k L a n t e r n

  3. What compliance is used to calculate the horizontal resonance? I don’t think one can use the cartridge compliance, which is relevant only to vertical motion of the cartridge. To me, it makes more sense to know the horizontal resonance frequency + the horizontal effective mass, and work out the horizontal compliance. The horizontal effective mass can be estimated from Moment of inertia about vertical axis through the “pivot”/effective length squared.

    Am I making sense?


  4. Hi Isidore (apologies for delay in replying) – cartridge compliance is determined by the coil-cantilever damper/suspension, so should be similar horiz & vertical I believe.
    As we are mainly interested in LF resonance, then it is horiz Eff Mass that we are interested in (horiz groove excursions, mono bass signal).
    With linear trackers, horiz Eff Mass is typically large, the total moment of inertia of the whole arm assembly but largely determined by the highish mass of the slider carriage.
    Cheers, Owen

    • Hi Owen

      I respectfully disagree. Effective mass is a mathematical analogy introduced for the sake of easy comprehension. I will write up something to elaborate but will take a bit of time. Please bear with me since I am a slow writer.

      While you are waiting, let me entertain you with my controversial idea about antiskate (attached). I am well aware of the two papers that have been cited widely, as well as several others. One showing only the frictional forces acting on the stylus, a subset of those shown in Fig 1 of attachment. The other, put out by Shure, I think, on measuring the skating force on the TONEARM via gadget. Both are, to me, not correct. The latter erred on focusing on the tonearm and not on the stylus. We should realize that the tonearm + (cantilever/stylus) do not form a RIGID mechanical system and cannot be treated as such. The stylus  has to be viewed in isolation before one can apply F = ma. That’s the source of all the wrong ideas that have been widely accepted. It should be simple undergraduate physics.



      • I must apologize for my aforementioned disagreement. I was thinking the moments of inertia of a pivoted arm – their two effective masses are of the same order of magnitude. You are correct that the horizontal effective mass is about 10-20 times that of its vertical counterpart. Hence my silly disagreement.

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