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In Reply to: RE: Question posted by Tre' on September 09, 2020 at 18:01:38
that doesn't sound right Tre` ... isn't the effective mass determined by the driving force across the cantilever point, weight, and balance? it's weight in motion ... damping adjusts the parametersno?
with regards,
Edits: 09/09/20
On the vinyl Engine's "Cartridge Resonance Evaluator" page, the weight of the cartridge and mounting hard ware is added to the effective mass of the arm in order to calculate the resonance. Adding a weight to the head shell would be (in terms of the CRE) the same as using a heavier cartridge or heavier mounting hardware.
Tre'
Have Fun and Enjoy the Music
"Still Working the Problem"
no doubt, and a handy online tool for determining resonance
however, please see the link in re: tone arm mechanics
it's a PDF showing the formulae for calculating the effective mass of tonearm / cartridge combos ... note that tracking force etc. are taken into account because the assembly is in motion
I think you addressed the OP's basic inquiry just fine, but technically there's a bit more physics involved ... I'm not a guru on the subject by any means, but your response seemed like an over simplification
best regards,
4.3 seems to back up my point.
"One myth that I have heard repeatedly is that to get the total effective mass, you must add the tracking force to the normal effective mass. This ^^^would be true^^^ if and only if you got that tracking force simply by adding a mass ^^^right to the cartridge^^^...."
Until proven otherwise I still say if you add weight directly above the diamond, the weight (in grams) is added (directly, without reduction) to the effective mass of the arm for purposes of calculating the resonance frequency.
Adding a weight, such as the one pictured, where the weight is not directly above, but slightly behind the point directly above the diamond, then math would have to be done to determine what percentage of the total weight is added to the effective mass of the tonearm/cartridge system. Being close to the end of the tonearm makes me think that most of the weight is added to the effective mass.
Now if I turned this weight around so that some of the weight extended beyond the diamond then it would add more than it's own weight to the effective mass of the tonearm/cartridge system. That is to say, if 1.5 grams (of the 3.5 gram piece) were sitting beyond the diamond, that 1.5 grams would add more than 1.5 grams to the total effective mass of the arm. The part sitting behind the diamond would add less than it's own weight to the effective mass but not by much.
Sorry about all the words, I hope it's not too muddy. :)
Tre'
Have Fun and Enjoy the Music
"Still Working the Problem"
'The part sitting behind the diamond would add less than it's own weight to the effective mass but not by much'
providing the tone arm is rebalanced with the counter weight for proper tracking this would almost have to be the case I would think because it's part of the assembly as a whole and it's mass is moving in counter direction
agree?
with regards,
Adding mass at one end forces us to add a little more mass at the other end.
Tre'
Have Fun and Enjoy the Music
"Still Working the Problem"
"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 counterweight further back away from the pivot, in order to counterbalance 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"
is 1011 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(rē/Lē) + (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 precalculated 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 momentofinertia for a point mass:
.........
Consequently, the units of the momentofinertia would be mass times distance squared, eg., Kg * m ^{ 2 } or grams * mm ^{ 2 } . Once you determine the momentofinertia of a tonearm about its pivot, you can find effective mass simply by dividing the momentofinertia 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 momentofinertia 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 momentofinertia as the actual tonearm's momentofinertia, that point mass would be equivalent to the actual tonearm's effective mass.
Best regards,
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 online calculator you linked to is so valuable
best regards,
...:
Sorry, I just could not resist!
Later Gator,
Dave
that's some mass right there!
Later Gator,
Dave
coupla penny's taped to the engine should improve tracking
regards,
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