Hi gang ... still confused over effective arm mass. I see nowhere to find the actual bare arm shaft weight (mass). All Inertia calculations only use eff mass.
I'm obviously missing something.
Zene
I'm obviously missing something.
Zene
Effective mass is the mass as seen by the stylus.
It's actually a measure of the tonearm's moment of inertia, i.e., its resistance to being accelerated by the moving stylus.
It's actually a measure of the tonearm's moment of inertia, i.e., its resistance to being accelerated by the moving stylus.
The bare arm shaft weight helps you calculate the effective mass. The cartridge sees the effective mass. If you know the effective mass then you can determine how the cartridge will respond on the tonearm. So the bare arm shaft weight is irrelevant unless you're designing a tonearm.
I'll try to explain how effective mass is calculated in the case of a simplified tonearm arrangement. I will assume that the "arm shaft" mass is negligible compared to both that of the cartridge and the counterweight, each of which I'll treat as a point mass.
As we shall see, the single largest contributor to the total effective mass of the tonearm is the cartridge. This is because of the overwhelmng dependency of the moment of inertia (I) of a point mass (m) on the square of the distance (r) from the pivot, according to the formula I = mr^2.
To understand the above, let's look at a simplified tonearm where the cartridge of mass 5 g is 20 cm from the pivot and the counterweight of mass 100 g is 1 cm from the pivot.
I (cartridge) = mr^2 = 5 x 20^2 = 5 x 400 = 2000 g cm^2
I (counterweight) = mr^2 = 100 x 1^2 = 100 g cm^2
It can clearly be seen that, because of the r^2 dependency, the moment of inertia of the cartridge dominates, and that of the counterweight is neglible by comparison.
Now, the total moment of inertia of the simplified tonearm is 2100 g cm^2, but how do we convert this into an effective mass?
The first question is where should this effective mass be located? The obvious answer is at the stylus tip which is 20 cm from the pivot.
Taking the equation I = mr^2 and making m the subject, we get: I/r^2 = m.
So for our total moment of inertia of 2100 g cm^2 we can calculate the effective mass 20 cm from the pivot as 2100/20^2 = 2100/400 = 5.25 g.
Remember folks, that's the simplified version of the calculation! 😉
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@zmajz
Thanks for the diagram which extends my simplified two point mass model to include the mass of the "arm shaft" itself.
However, the end result is the same: m = 1/r^2, i.e., effective mass = total moment of inertia/square of distance of stylus from pivot
I had hoped, by including some numbers, to explain why the single largest contributor to the total effective mass of the tonearm is the cartridge.
Thanks for the diagram which extends my simplified two point mass model to include the mass of the "arm shaft" itself.
However, the end result is the same: m = 1/r^2, i.e., effective mass = total moment of inertia/square of distance of stylus from pivot
I had hoped, by including some numbers, to explain why the single largest contributor to the total effective mass of the tonearm is the cartridge.
Does this help to explain why tone arm internal cabling is so small and light ?
If so, then would using a different, heavier or lighter, internal cable alter how the assembly reacts ?
If so, then would using a different, heavier or lighter, internal cable alter how the assembly reacts ?
No, UserAbuser, the mass of the internal cabling would make an insignificant contribution to the total moment of inertia of the tonearm - even less than the tonearm wand itself.
The wiring has to be thin and flexible so as not to hamper the movement of the tonearm when it emerges at its pivot.
The wiring has to be thin and flexible so as not to hamper the movement of the tonearm when it emerges at its pivot.
Effective tonearm mass seems to be another severely overrated by engineers parameter. A very successful recent tonearm has an effective mass of 60g and no one is complaining 🙂
Nice diagram, @zmajz!
@Galu, if you look up known tonearms, you'll find most have effective mass in the range of around 4 to 40g. https://www.vinylengine.com/tonearm_database.php
A common eff. mass for tonearms is around 9-12g, like many SME & Technics tonearms. A Fidelity Research FR64 S is 36g (!). https://www.vinylengine.com/library/fidelity-research/fr-64.shtml. SME 3009 SIII is among the lightest, only 5g eff mass. https://www.vinylengine.com/library/sme/series-iii.shtml
Also, for many tonearms (like for the FR64S), you have to add the mass of the replaceable headshell. The lightest start at 6-7g + wires and screws/bolts. 9-10g is common, and 13-15-17g is not unusual at all. To use FR64S as example with a 13g headshell+1g wires/screws, total eff. mass is about 50g, excluding cart. Contribution of a 5g cart will therefore vary, but will rarely contribute more than 50% of eff. mass.
So, how do we find m2 and m3 in the schematic posted by zmajz? Can we measure vertical downforce at Cg1 to aquire m2 (without counterweight m4 attached)? M3 is the smallest contribution, but how to measure? It is also unavoidably included in m2, if m2 is measured as VerticalDownForce@Cg1...
Dagfinn
@Galu, if you look up known tonearms, you'll find most have effective mass in the range of around 4 to 40g. https://www.vinylengine.com/tonearm_database.php
A common eff. mass for tonearms is around 9-12g, like many SME & Technics tonearms. A Fidelity Research FR64 S is 36g (!). https://www.vinylengine.com/library/fidelity-research/fr-64.shtml. SME 3009 SIII is among the lightest, only 5g eff mass. https://www.vinylengine.com/library/sme/series-iii.shtml
Also, for many tonearms (like for the FR64S), you have to add the mass of the replaceable headshell. The lightest start at 6-7g + wires and screws/bolts. 9-10g is common, and 13-15-17g is not unusual at all. To use FR64S as example with a 13g headshell+1g wires/screws, total eff. mass is about 50g, excluding cart. Contribution of a 5g cart will therefore vary, but will rarely contribute more than 50% of eff. mass.
So, how do we find m2 and m3 in the schematic posted by zmajz? Can we measure vertical downforce at Cg1 to aquire m2 (without counterweight m4 attached)? M3 is the smallest contribution, but how to measure? It is also unavoidably included in m2, if m2 is measured as VerticalDownForce@Cg1...
Dagfinn
As I stated, dagfinn, I was using a simplified two point mass model, along with convenient numbers, to illustrate a specific point.
I agree that I really should have said "cartridge + headshell'" and not just "cartridge".
To take a stab at how to obtain m2 and m3 in zmajz's diagram, I would work with the linear density, or mass per unit length, of the arm tube.
I hope that's not seen as a cop out! 🙂
I agree that I really should have said "cartridge + headshell'" and not just "cartridge".
To take a stab at how to obtain m2 and m3 in zmajz's diagram, I would work with the linear density, or mass per unit length, of the arm tube.
I hope that's not seen as a cop out! 🙂
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Depending on the cartridge's Compliance, of which there are many varieties, it is important to consider what arm it works best in.
Higher mass arms work better with stiffer compliance, and vice-versa.
Considering m2 and m3: if the wand of tonearm is made of two parts (as on schematic) than you measure masses (weights) of two parts separately and if it is made as one peace then use formula for calculating moment of inertia that you can find using google... just type moment of inertia in your browser.....
In theory (strictly by the schematics) you can; either with or without counterweight. By measuring the vertical downforce at the stylus' tip, you are left with three uknowns (vertical downforce at pivot/base, m2 and m3).
You also have three equations:
- summ of vertical forces equals zero
- summ of moments at stylus equals zero
- summ of moments at pivot equals zero.
Hi, Partially no true unfortunately.
The Eff Mass of an arm is critical to ensure your arm & cart match so they can achieve an Eff Mass between 8-12hz.
The mass of the arm has no effect on trackability, it is the design (shape) & efficiency of bearing & tolerance in tone arm manufacturing. Tracking Distortion is due to in part the alignment template you choose. Lofgen B being the least distortion & your ability to align your cart correctly.
However if you use the Under-Hang alignment system, then at least your ability to align the arm is largely taken out of the equation.
Cheers
The Eff Mass of an arm is critical to ensure your arm & cart match so they can achieve an Eff Mass between 8-12hz.
The mass of the arm has no effect on trackability, it is the design (shape) & efficiency of bearing & tolerance in tone arm manufacturing. Tracking Distortion is due to in part the alignment template you choose. Lofgen B being the least distortion & your ability to align your cart correctly.
However if you use the Under-Hang alignment system, then at least your ability to align the arm is largely taken out of the equation.
Cheers