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In Reply to: RE: Question posted by Tre' on September 10, 2020 at 10:14:25
"As someone else wrote, adding mass to the headshell most certainly DOES increase the effective mass of the tonearm, by a factor roughly equal to the added mass, in grams. (As you move down the tonearm toward the pivot, the effect of adding mass at any point on effective mass lessens proportionately.) Adding mass to the headshell will also cause you to need to move the counter-weight further back away from the pivot, in order to counter-balance the added mass and achieve the same VTF. Doing that ALSO will increase the effective mass of the tonearm, by a factor equal to the square of the change in distance from the pivot to the center of mass of the CW, times the mass of the CW. "
Tre'
Have Fun and Enjoy the Music
"Still Working the Problem"
Follow Ups:
is 10-11 grams effective mass. That is because the effective mass of the arm changes depending on where the counter balance is.
Tre'
Have Fun and Enjoy the Music
"Still Working the Problem"
Here's another quote. I think the math is probably correct but the posters final point seems to be counter to what SME says, unless he thinks 1 gram is not "significant".
"So effective mass in not mass - it's inertia! In fact, even the common measurement (in metric grams) is a misconception. This is brought to you here, by the tonearm manufacturers, as a curtsy to the layman. Effective mass, like any inertia, is measured in Kg/m/s2 (that is kilograms per meter per second squared). Since we're talking very small mass here - everything is divided by 1000 and so we're actually dealing with grams per millimeters per second squared. The general em formula relationships are manipulated such that we're left with grams only - but nevertheless it's Inertia!!!. Keeping that in mind it's easier to regard effective mass for what it is.
Another misconception is the relationship between 'effective mass' and mass. If you add 1 gram to the tip of the tonearm you do not add 1 gram of effective mass to the tonearm No way Jose!. You do not add a 1/3 or a half - none of it catches here. So, how much do you add? Well, that cannot be described in English, it can only be described in a math equation. This is what it looks like:
M(kg) = m(r²/L²) + (Z/3)
m is the counter weight mass
r is the counter weight distance from the pivot
L is the effective length (pivot to stylus tip)
Z is equal to twice the mass of the front end of the tonearm at the effective length. Your headshell mass is part of 'Z'.
M is the effective mass and the whole thing is in kilograms but it doesn't matter. This is just to demonstrate why the relationship between mass and effective mass is not as straight forward as one might think.
L (the leverage or effective length) will affect the importance of the real estate the most. In other words - the tip of the tonearm is the most strategic location where mass can affect inertia. Adding just a tiny amount of mass to that specific location might, just as well, be equivalent to the total effect the counterweight has on the effective mass of the tonearm. It's that important! This is where 'r' vs 'm' in the formula kicks in.
Having said that... movements of the counter weight back and forth across the back of the tonearm seldom changes effective mass by any significant amount. It's typically punched in and pre-calculated into the specs of the tonearm and it's a generic part of the given effective mass."
I added a 3.5 gram weight to the top of the head shell on my SME to get the resonance down. It made a large difference in the sound.
I could measure the resonance frequency, then take it off and measure again. That would show how much effective mass was really added.
I probably won't. I'm too lazy. :-)
Tre'
Have Fun and Enjoy the Music
"Still Working the Problem"
> Effective mass, like any inertia, is measured in Kg/m/s 2 (that is kilograms per meter per second squared).
Maybe not! ....Here's what the article "The Mechanics of Tonearms" says about the mass moment-of-inertia for a point mass:
.........
Consequently, the units of the moment-of-inertia would be mass times distance squared, eg., Kg * m 2 or grams * mm 2 . Once you determine the moment-of-inertia of a tonearm about its pivot, you can find effective mass simply by dividing the moment-of-inertia by the tonearm's effective length squared, eg., I / mm 2 = grams .
This means that effective mass is measured in grams. Effective mass is not the same as inertia. Instead, it's the same as the tonearm's moment-of-inertia divided by its effective length squared thereby yielding mass and only mass.
Another way to think about effective mass is if you imagine a tonearm whose mass is zero and you place a point mass directly over the stylus that produces the same moment-of-inertia as the actual tonearm's moment-of-inertia, that point mass would be equivalent to the actual tonearm's effective mass.
Best regards,
John Elison
There are a few posts in this blog discussing cartridge matching and some measurements, I found it interesting. scroll down to the Jan 8 one to start.
http://korfaudio.com/blog
When I decided to try an SPU Royal N on my Schröder I bought the Nifi News test record to see if I was getting a reasonable resonance using the brass cartridge mounting plate on my arm. Before fitting the SPU a tested the existing combination of a Transfiguration proteus and aluminium mounting plate, the brass one adds ~5g over the ali one. With the trans I got a wobbly at 7Hz and warbling from around 16Hz and down, no visible reaction to the virticle tracks. On the face of it this would suggest that Transfiguration quoted their compliance at 100Hz but I'm not sure they do, the cartridge was 5 years old at this point.
With the SPU and brass mount in place I set the arm horizontal and the VTF to 3g with the magnet gap to the thickness of the rather thin business card I found gauged the gap to where it had sounded best with the proteus. There was again warbling over a range of tracks but only a hint of a wobble when going from the 12 to 10 Hz tracks but not on the 11Hz virticle track. I then spent a couple of weeks optimising the parameters by ear and retested This time there was a wobble at 7Hz as I saw for the proteus, which had also set up by ear.
I found the above blog when I was trying to find an explaination for what I'd observed, thier introduction of damping into the equations might hold the solution.
Ortofon always measures dynamic compliance at 10-Hz. However, to the best of knowledge, all Japanese cartridges specify dynamic compliance at 100-Hz.
An arm/cartridge resonance frequency of 7-Hz is probably okay. Theoretically, it shouldn't go below 8-Hz for optimal performance, but my arm/cartridge resonance frequency is 7-Hz and it sounds just fine to me. Therefore, as long as your turntable sounds good and you don't get any cartridge mistracking, you're probably in good shape. You're also right about cantilever damping helping you achieve adequate performance from a slightly low arm/cartridge resonance frequency.
Good luck,
John Elison
'added a 3.5 gram weight to the top of the head shell'
well we've certainly seen lots of coins taped to head shells 'back in the day' ... at least I have anyway
so, the guys at 'Cart Chunk' advocate for measuring in dynes rather than grams with inertia already accounted for ... but one second for disc playback covers a lot of record grooves ... yeah it's complicated and I'd rather not go through the math either ... which is why the on-line calculator you linked to is so valuable
best regards,
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