Headshell weight

[Amber Audio]

If you find out three pieces of info there are a couple of calculators that will give you an idea if the cart is likely to perform OK in your tonearm.

1. Cart weight.
2. Tonearm effective mass (with headshell if removable).
3. Dynamic Compliance adjusted for 10Hz.

If your cart shows Dynamic Compliance at 100Hz you multiply by 1.7 - this is a quick and dirty method but will give a reasonable guide.

Google will sometimes bring up tests of carts by guys like Steve Miller with actual measured Dyn Comp numbers and there are test records that can help dial in a cart.

Loads more to it and you can read up about the complexities/minutiae/mitigations and math equations, but the 2 calculators below will give a good idea if things will work and sound decent. Vinyl Engine and Hoffman are good places to search for info as well as pfm obviously.

http://korfaudio.com/calculator

Cartridge Resonance Evaluator - Vinyl Engine

www.vinylengine.com

Below is a calc on each site.

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[Avon]

The table shown by @Amber Audio above shows that 9Hz is the "ideal" resonance frequency for an arm / cartridge assembly. So quoting the dynamic compliance at 10Hz would seem like a meaningful figure to give. But why then would some manufactures quote it at 100Hz? I don't see what possible use that figure could have.

The word dynamic implies the measurement is made when the cantilever is moving at the quoted frequency. So "static" implies it's measured at 0Hz. Again, why would anyone need to know that figure?

 

[Amber Audio]

AIUI

Japanese companies use 100Hz because it shows how well the cart will track related to the cart compliance and the vtf applied.

The USA/EU 10Hz figure is related to the cart/arm resonance ideal/sweet spot figure, somewhere between the range 7-12Hz and 10 is a nice round number

Dunno what use the Static Compliance at 0Hz figure is - it’s like a spring with a weight on top of it compressing it fully.

Here’s a table with lots of info - about 700 cart/arm combo stats from mag tests

Phono Cartridge/Tonearm Resonance

Sorted by Cartridge Cartridge,Tonearm/Turntable,Resonant Peak (dB),Resonant Frequency (Hz),Notes Accuphase AC-2,Wheaton Tri-Planar II tonearm,7 Acutex M315 III STR,Rotel RP-500 turntable,12,10 Acutex M320 III,SME 3009 tonearm,8.8,as measured by High Fidelity Acutex M320 III STR,SME 3009 tonearm,...

docs.google.com

 

[Eoin]

This interests me as well - but the graph thingy that Tony L has put up means nothing to me without some explanation of how to understand it..

No Crystal Clear English in the hi-fi world.

I do find it irritating that no one explains anything in a way that can be understood.
That would take away their power base though.

It’s easy enough. Google the effective mass of your arm. Check the weight of the cartridge and mounting screws.

Add this together.

Check what the compliance is quoted as for you cartridge.

Go into Tony L’s chart above with that total mass number and the compliance number.

If you’re in the blue band you’re golden.

If not you want a different cartridge.

For an easy example my old SME series III has an effective mass of 3g. Let’s put a Linn Troika on it.

Troika 7g and 10cu compliance. Screws 2g

Total mass 12g

Go into Tony’s chart and it’s not in that blue band. If you look at the diagonal lines that’s the resonant frequency, looks like it’s about 13/15hz maybe. So that’s too close to the lower end of the audio band where it’ll start flinging itself about.

If you wanted it smack in the middle of the good band looks like it wants about 20g mass, and can take a lot more before it’s too far the other way. So we want +8g

Quick check shows an SME V has an effective mass of 10-11g and an RB300 of 11.5g so they’re both looking about right. A Linn Ittock is 12g so they’re all perfect. Or if I really wanted to I could add a headshell weight to the III and that would have the same effect.

Back to the light SME III I’ll try a Shure V15 III instead. 6g and compliance is 30cu

Mass then is 11g in the chart and with 30cu I’m now in the blue band, but maybe even towards the back of it, looks like I want even a bit less mass again. Funny enough SME supplied nylon plastic screws just for this which probably take 1.5g off it and back towards that band centre.

Hope that makes sense ok.

Bottom line is if you’re considering a cartridge just stick the numbers into an online calculator and it’ll say if it’s OK. if it’s not it’ll either wobble around on warps or it’ll resonate at low audio frequencies

 

[Avon]

Japanese companies use 100Hz because it shows how well the cart will track related to the cart compliance and the vtf applied.

Interesting. So given two different cartridges (different masses and compliances), both of which would result in the same 9Hz resonance, then the one with the higher 100Hz dynamic compliance ought to track better?

 

[Amber Audio]

Interesting. So given two different cartridges (different masses and compliances), both of which would result in the same 9Hz resonance, then the one with the higher 100Hz dynamic compliance ought to track better?

Unknown, too many variables, even the same model cart has batch variances.

All you can do is take each cart and set it up as best you can after reading up or get someone who knows to do it for you (by the time you buy all the setup tools you’re several hundred quid down - if you only do 1 cart every few years makes sense to pay a dealer).

There are no standards as such and people disagree about what’s important, some pay minute attention to VTA/SRA, others don’t pay much attention to them cos the differences in angles are too small to matter.

 

[Avon]

If you increase the mass, you must also reduce the compliance.

 

[Pine Marten]

I had a Landrover series 3 swb that was just like the first example. I remember my Dad having a huge Vauxhall in the 60's, could have been a Cresta just like example two. It was the only car which made my brother and I carsick.

Same here, I think of it as a car, if the car has hard suspension (low compliance) and low mass it will not absorb bumps and bounce down the road, if it has soft suspension (high compliance) and high mass it will bottom out and be syrupy. The suspension and weight of the car needs to be balanced.

 

[andyr]

NOTE - due to similar logic, using a heavier CBW reduces effective mass/inertia of the tonearm. Taking an extreme and unrealistic example - double the mass and you will halve the distance pivot to CoG, so one quater of the contribution due to distance, mutiplied by doube the mass.

Inertia is a measure of how resistant a body is to being disturbed either from rest or continuing in its steady motion - a measure of "stability", if you like.

Wow! Thank you for this insight, Vinny.

I had actually thought it would increase the eff mass ... but your explanation shows me I had it wrong.

Given 2 simplistic scenarios:
1. a mass of 242gm situated 48mm from the pivot (ie. the CoM of the c'weight is 48mm) and
2. a mass of 370gm situated (ie. CoM) 30mm from the pivot

... is it possible to calculate how much the eff mass of an arm (24gm) will be reduced, in scenario #2?

 

[Vinny]

is it possible to calculate how much the eff mass of an arm (24gm) will be reduced, in scenario #2?

Yes - very simply - the reduction is entirely down to the change in the contribution of the CBW - everything else remains the same.
The complication is in working out where the decimal point has to be because, as ever, the hifi industry does not choose simple units, but has aimed for simple low numbers around 10.

Your example gives inertia of -

1. 242 x 48 x 48 = 557568 gmm^2
2. 370 x 30 x 30 = 333000 gmm^2

Your examples are not unrealistic (although they don't produce the same turning moment - weight times distance, but close) so I have not looked up where the decimal point should be, but would bet that the numbers are actually 5.5 and 3.3, so the reducton in effective mass is 2.2g.
You need to check that my educated guess is correct. Conventionally, this is calculated using kg and metres - that is where part of the complication about decimal points comes in.

 

[andyr]

Yes - very simply - the reduction is entirely down to the change in the contribution of the CBW - everything else remains the same.
The complication is in working out where the decimal point has to be because, as ever, the hifi industry does not choose simple units, but has aimed for simple low numbers around 10.

Your example gives inertia of -

1. 557568 gmm^2
2. 333000 gmm^2

Your examples are not unrealistic (although they don't produce the same turning moment - weight times distance, but close) so I have not looked up where the decimal point should be, but would bet that the numbers are actually 5.5 and 3.3, so the reducton in effective mass is 2.2g.
You need to check that my educated guess is correct. Conventionally, this is calculated using kg and metres - that is where part of the complication about decimal points comes in.

Thanks very much, Vinny!

Logically, I think the position of the dp can only be (as you suggested): 5.5 and 3.3 - leading to a reduction in eff. mass of 2.2gm.
(It doesn't make sense if it's only 0.22gm!)

2gm reduction is what I had guessed ... and this makes my ZYX 'Ultimate Airy' / 12" Univector combination even better suited than what they were before (with the original c'weight setup)!

 

[Avon]

How would that calculation work if I added a weight at the cartridge bolts, but kept the same counterweight? The counterweight has to move back of course.

 

[Vinny]

How would that calculation work if I added a weight at the cartridge bolts, but kept the same counterweight? The counterweight has to move back of course

The change in CBW position would probably be irrelevant/tiny.
The simplest but good approximation to the change would be to measure pivot to centre of bolt hole distance and weigh the different bolts. (Don't forget to double-up - two bolts)
The calculation wouldn't be far out at all, but the difference would be slight as the only thing changed is the mass of the bolts.

I have never weighed bolts (you'd need something like a tracking force scales to do a good job), but they must be no more than a gramme. Say they are at 9 inches from the pivot and and weigh 1g total- that gives an effective mass of

1 x 228 x 228 = 51984gmm^2

Using my educated guess at decimal point position from above, that is an effective mass of just 0.52g.
So for every g you add to the bolt position(s), you would add something like 0.52g effective mass.

All of this is just a guide and significanec of changes will to some extent depend on the EM of the tonearm as a whole - changing the EM by that on an arm with nominal 8g and 25g EMs, for instance, are likely to be somewhat different.

If you wanted to calculate for the CBW, the calculation is exactly as above.

Try, and have a listen!!

The calculation does indicate that using over-long bolts, as I have had to do on occasion, will have pretty much minimal or no effect.

 

[Avon]

Thanks. In order to use the weight / compliance tables above, we're normally told to add the effective arm mass to the cartridge mass. For a 9" arm though, your calculation means we should be adding about half the cartridge mass. But then the counterweight distance change does become significant for say a 6g cartridge, which is probably why we don't have to worry about moments of inertia, as they cancel out, fore and aft.

 

[Vinny]

Thanks. In order to use the weight / compliance tables above, we're normally told to add the effective arm mass to the cartridge mass. For a 9" arm though, your calculation means we should be adding about half the cartridge mass. But then the counterweight distance change does become significant for say a 6g cartridge, which is probably why we don't have to worry about moments of inertia, as they cancel out.

The maths is simple, so I would advise doing some as, not having done the sums myself, I doubt that all of your logic is correct. But I could be wrong (Agreed about adding half cart' mass though - give or take, not the actual mass, having actually done that maths.)

Hint - adding a 6g cart' at 228mm would require a very small change in position of a 250-300-350g CBW - the maths is even simpler, just mass x distance, so distance changes in the inverse ratio to the masses (300g CBW would move 4.5mm).

Certainly adding cart' mass to tonearm EM, makes no immediate sense at all - you are adding apples to pears - 2 apples + 6 pears = 8 pears.

One tip for measuring distances for anyone not having some of the expensive kit to do it - use dividers, and a steel rule -
something like this or longer (longer makes them easier to use and hence more accurate - draw them out if uncertain. I paid something like £6 for a 10 inch pair of very acceptable quality).

https://www.amazon.co.uk/dp/B0001P04QY/?tag=pinkfishmedia-21

 

[Vinny]

I would say again, that to some degree this is rearranging deckchairs on the Titanic, getting deep into figures +/- a gramme or less. Although that will depend on tonearm EM to some degree. (The Hadcock is very low at around 6-7g, but how many tonearms are down under something like 10-12g, and how many up around 20g+?)

Your ears should always be your final guide.

 

[Vinny]

Thanks. In order to use the weight / compliance tables above, we're normally told to add the effective arm mass to the cartridge mass. For a 9" arm though, your calculation means we should be adding about half the cartridge mass. But then the counterweight distance change does become significant for say a 6g cartridge, which is probably why we don't have to worry about moments of inertia, as they cancel out, fore and aft.

Curiosity got the better of me.........

Random, but realistic, example - 300g CBW which balances the tonearm without cart', at 40mm from pivot

EM = 300 x 40 x 40 = 480000 gmm^2 (4.8g in hifi speak)

Move the CBW 4.5mm to balance a 6g cart' -

EM = 300 x 44.5 x 44.5 = 594075 gmm^2 (5.9g in hifi speak).

So total EM change for this example - cart' plus CBW, is around (6 x 0.52) + (5.9 - 4.8) = (around) 4.2g (yes, they are additive even though opposite sides of the pivot).

It does show that the online calculator above, isn't really worth much as it does not contain either CBW mass or position for balance of the bare tonearm. In fact it also needs arm length too. The calculations are very simple so why they aren't included............

NOTE - you need actual postion of the CBW to calculate inertia of the CBW, not difference in position.
These calculations work for any 9 inch tonearm, near enough, you just need to know the weight of your CBW and then measure its position. Figures just drop into the above equations as applicable. In fact, you can change the tonearn length too, and recalculate.

There are various places where errors of varying degree will be introduced, the obvious one being that the CoG of the cart' will not be at the effective length in all probability, but slightly less.

 

[Avon]

Very interesting. The problem is that arm manufacturers only give an effective mass figure, so you have to work from that, before buying an arm and cartridge from new. That EM would have taken into account the length of the arm. I was never sure whether it was calculated (as you have done) or actually measured (using a machine).

 

[Vinny]

The problem is that arm manufacturers only give an effective mass figure, so you have to work from that, before buying an arm and cartridge from new.

At the end of the day, it is guide and you can buy a tonearm before a cart'

That EM would have taken into account the length of the arm.

That is a complicated comment to comment further upon. As far as the manufacturer is concerned, the EM is what it is and inescapably includes arm length in the calculations.

I was never sure whether it was calculated or actually measured.

With CAD, it would be the clicking of a key to get a number.
As mentioned above, there is one quick and dirty way to measure tonearm EM yourself - you remove the CBW and place a scales under the headshell, and then weigh the CBW seperately. That much I do remember. The (simple, apart from decimal place position) calculations are over on VE. It did give me a perfectly logical number for a Hadccock.
Calculation long hand can also be done - just measure all the tonearm parts etc. etc., although, again, CAD could do that faster than PDQ. Then just add all of the individual EM figures.
For parallel and square parts this is very simple. Not so for anything with a taper, or being otherwise non-symmetrical, anywhere in it.

 

[paulfromcamden]

@Big Tabs don't worry - you're not the only one reading this thread and scratching your head...