Ross -
The following is from one of my favorite tech sites:
http://liutaiomottola.com/
Given: String diameter = .011, Unit Weight = .00002680lbs/in, Least ultimate tensile strength of string material = 350,000 psi, String length = 24", Frequency of G# = 415.3hz.
The interactive calculations indicate that the Breaking Strength of the string should be 33.26 lbs. Mottola recommends tensioning a string at approximately 80% of the breaking strength of the string which would = 26.6 lbs. The tension of an .011 at that frequency would be 27.6 lbs. This seems to be a "ballpark" figure and doesn't raise any red flags with me. Note that I also assumed a string length of 24". Any ideas as to why you should be breaking strings when the math says that you should be pretty much OK? I've used his methods to determine string diameters for my "home-brew" copedent on my old Dekley. No string breakage.
If you're an "egghead" like me and enjoy digging into stuff like this, then Mottola's site has a wealth of info on a bunch of things. He refers the reader to D'Addario's site for info like the Unit Weight of the string. He also provides a chart of note frequencies.
Will dive into the 'net when I have time and see if I can find that paper that I spoke of.
Richard
Changer Finger Design
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richard37066
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Ross Shafer
- Posts: 189
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Re: Changer Finger Design
Hi Richard,
I get the sweats and break out in hives at the thought of sitting down to a pile of math equations...so I think we differ a bit there.
I believe the breakage I experienced was primarily due to the extra stress riser added by running over a roller just in front of the bridge. Plug 440 hz into the calculator (The A note that string gets pulled to) and your margin of safety goes down , plug in longer scale lengths like 24.25 (pretty common on steels) and that margin gets slimmer. Even at 24" as your example shows the G# is already over the 80% safety margin Mottola suggests. Pulling that to an A takes it further over the 80% (30.9 lbs at 24" scale 440hz). Plug in a 25" scale (the scale I'm going for with 440 and the math says we're over the breaking tension....in practice though my current design works fine...I also tested the current design at a 25.5" scale with no breakage (I turned the machine off at around a half million cycles on that test if I recall correctly).
Another thing to consider is that a string does not stretch equally over it's entire length as the changer pulls it. This is easy to see if you use a marking pen to mark the string along its length. The string will move more at the end that is pulled initially, it averages out over the full length pretty quickly, but the breakage I was having typically occurred at the moment the pedal was depressed. I'm guessing that this tendency causes a spike of high tension between the ball of the string and the stress point/riser and pop goes the weasel before the tensions averages out.
I'm not a trained engineer and don't even play one on TV, so I may well be fulla bulla. Bottom line....the current design works great and I'm going with it.
I get the sweats and break out in hives at the thought of sitting down to a pile of math equations...so I think we differ a bit there.
I believe the breakage I experienced was primarily due to the extra stress riser added by running over a roller just in front of the bridge. Plug 440 hz into the calculator (The A note that string gets pulled to) and your margin of safety goes down , plug in longer scale lengths like 24.25 (pretty common on steels) and that margin gets slimmer. Even at 24" as your example shows the G# is already over the 80% safety margin Mottola suggests. Pulling that to an A takes it further over the 80% (30.9 lbs at 24" scale 440hz). Plug in a 25" scale (the scale I'm going for with 440 and the math says we're over the breaking tension....in practice though my current design works fine...I also tested the current design at a 25.5" scale with no breakage (I turned the machine off at around a half million cycles on that test if I recall correctly).
Another thing to consider is that a string does not stretch equally over it's entire length as the changer pulls it. This is easy to see if you use a marking pen to mark the string along its length. The string will move more at the end that is pulled initially, it averages out over the full length pretty quickly, but the breakage I was having typically occurred at the moment the pedal was depressed. I'm guessing that this tendency causes a spike of high tension between the ball of the string and the stress point/riser and pop goes the weasel before the tensions averages out.
I'm not a trained engineer and don't even play one on TV, so I may well be fulla bulla. Bottom line....the current design works great and I'm going with it.
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richard37066
- Posts: 517
- Joined: Sat Dec 11, 2010 11:44 am
- Location: Gallatin, Tennessee, USA
Re: Changer Finger Design
Ross -
http://www.deepdyve.com/lp/elsevier/vib ... 8M9nvwZJ/8
After about two hours of "googling" all manner of phrases, I finally found it. Managed to get a 5-minute "freebee" look at the paper. Obviously didn't have the time to hassle with the math but the reading and ogling some of the math confirms my statement above. It would appear that the "wrapping" of the string (under vibration) saps a tad of energy from the vibrating string. The larger the radius of the "obstacle" (changer, bar?) the greater the amount of energy lost. Didn't want to spend the big bucks to buy the entire paper but, it would appear that, if one did the math, it would show a dramatic reduction in lost energy (greater sustain) with a decrease in the radius of the "obstacle".
What the paper did not address was the fact that a string does not always vibrate in a vertical or longitudinal direction. It precesses all over the place. My question would be: - how much energy is lost due to "scraping" during the longitudinal mode of vibration. After all, this is the mechanism that causes those "grooves" that folks worry about sanding and polishing out when they become obvious.
As we've both acknowledged, there should be a point of diminishing returns: - How small would the radius be before we broke strings every five minutes! When a finger is activated, the side of the string resting on the finger is shortened and compressed while the outer portion Is elongated - stretched. If one does this often enough it is the same as taking a coat hanger and bending it back and forth a zillion times. It's gonna break sooner or later.
For mere mortals such as we, it would appear that some simple experimentation is the shortest way to an answer. Your magic machine would appear to be ideal if you could adjust the amount that the string is stretched for each radius/diameter of the "finger". It would have to be the same distance for each value of radii. Crank it up and see how long a string lasts before it takes the deep six.
Hope I've helped a little bit.
Richard
OOPS. Didn't know that you were going to pull that G# up to an A. It changes everything as you quickly found out.
http://www.deepdyve.com/lp/elsevier/vib ... 8M9nvwZJ/8
After about two hours of "googling" all manner of phrases, I finally found it. Managed to get a 5-minute "freebee" look at the paper. Obviously didn't have the time to hassle with the math but the reading and ogling some of the math confirms my statement above. It would appear that the "wrapping" of the string (under vibration) saps a tad of energy from the vibrating string. The larger the radius of the "obstacle" (changer, bar?) the greater the amount of energy lost. Didn't want to spend the big bucks to buy the entire paper but, it would appear that, if one did the math, it would show a dramatic reduction in lost energy (greater sustain) with a decrease in the radius of the "obstacle".
What the paper did not address was the fact that a string does not always vibrate in a vertical or longitudinal direction. It precesses all over the place. My question would be: - how much energy is lost due to "scraping" during the longitudinal mode of vibration. After all, this is the mechanism that causes those "grooves" that folks worry about sanding and polishing out when they become obvious.
As we've both acknowledged, there should be a point of diminishing returns: - How small would the radius be before we broke strings every five minutes! When a finger is activated, the side of the string resting on the finger is shortened and compressed while the outer portion Is elongated - stretched. If one does this often enough it is the same as taking a coat hanger and bending it back and forth a zillion times. It's gonna break sooner or later.
For mere mortals such as we, it would appear that some simple experimentation is the shortest way to an answer. Your magic machine would appear to be ideal if you could adjust the amount that the string is stretched for each radius/diameter of the "finger". It would have to be the same distance for each value of radii. Crank it up and see how long a string lasts before it takes the deep six.
Hope I've helped a little bit.
Richard
OOPS. Didn't know that you were going to pull that G# up to an A. It changes everything as you quickly found out.
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Georg
- Posts: 457
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Re: Changer Finger Design
Richard,
in your mind, should we then contribute the improved sustain some players claim they get by using a bigger/heavier (1" or even a 1 1/4") bar, only to the increased weight compared to that of a regular 7/8" bar?
To me this indicates that those players do not push the bar down very hard when they play, and instead rely much on the bar's own weight. I do push the bar rather hard down while playing, and get best overall sustain with a light (Zirc) 7/8" bar.
For my own contraption I am designing in an around 3mm diameter fixed bridge-point, while rollers over which the the keyhead end changer will pull the strings will be around 20mm in diameter. With a shallow string-angle over those rollers -- may go down to less than 5 degrees -- the bending action that breaks strings should be minimal. String-stretching force will be the same or ever so slightly higher than that of any 24.25 scale keyed PSG, so no advantage there.
I think I can get away with a string-angle over the rollers as small as the string-angle under the bar during play IF I see the need for it, without getting any rattling. Sustain should IMO be the same in open tuning as with the bar on the strings, so having rollers with about the same diameter as a bar should work fine in that respect. As the entire keyhead/changer will be attached to the backbone of the neck -- that's what makes the string-angle over those rollers adjustable, I may even have to dampen those rollers to tune down / reduce sustain without the bar.
in your mind, should we then contribute the improved sustain some players claim they get by using a bigger/heavier (1" or even a 1 1/4") bar, only to the increased weight compared to that of a regular 7/8" bar?
To me this indicates that those players do not push the bar down very hard when they play, and instead rely much on the bar's own weight. I do push the bar rather hard down while playing, and get best overall sustain with a light (Zirc) 7/8" bar.
For my own contraption I am designing in an around 3mm diameter fixed bridge-point, while rollers over which the the keyhead end changer will pull the strings will be around 20mm in diameter. With a shallow string-angle over those rollers -- may go down to less than 5 degrees -- the bending action that breaks strings should be minimal. String-stretching force will be the same or ever so slightly higher than that of any 24.25 scale keyed PSG, so no advantage there.
I think I can get away with a string-angle over the rollers as small as the string-angle under the bar during play IF I see the need for it, without getting any rattling. Sustain should IMO be the same in open tuning as with the bar on the strings, so having rollers with about the same diameter as a bar should work fine in that respect. As the entire keyhead/changer will be attached to the backbone of the neck -- that's what makes the string-angle over those rollers adjustable, I may even have to dampen those rollers to tune down / reduce sustain without the bar.
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richard37066
- Posts: 517
- Joined: Sat Dec 11, 2010 11:44 am
- Location: Gallatin, Tennessee, USA
Re: Changer Finger Design
Georg -
I place little credence in anecdotal "evidence". I have no doubt that, when some people change their bar to a larger diameter, they are anticipating a change and, thus, their imaginations tend to fulfill their anticipations. I'll ask the same question that I've asked for ages:- Did you actually measure any change and what are the numbers?
In spite of the implications contained in the paper that I referenced, above, everything is still very much up in the air. The paper, and one's intuition, says that the effect, as described, is real but one must remember that the paper is primarily theoretical. Nothing has been MEASURED that is directly applicable to the PSG.
You will recall that, some many months ago, I roughly measured the break angle of the strings over the roller bridge on the PS210 from the patent drawings. It was in the neighborhood of 7°. Whether Gene Fields took into account the bending/breaking action of the string over the roller is open to question. The "rattling" that you mention is also a function of the picking force that the player uses. With small "break angles" and a pair of "gorilla hands", rattling can become a problem since the down force on the roller/under the bar is minimal. Ditto with bar pressure. I tend to play with a light touch thus I most probably would not run into that problem.
Everyone should know that maximum sustain of a vibrating string is realized only on a monochord having infinite mass and well-defined terminations. We have to take a couple of giant steps backwards from that ideal when attempting to apply the concept to the PSG. The fact that you tend to press down considerably with a smaller bar indicates to me that you are increasing the break angle under the bar by a small number of degrees thus negating the possibility of inducing "rattling". Having seen you play - in my old music room - I know that you tend to be "heavy-handed" therefore you must apply greater pressure to the bar so as to get out of that "rattling" mode. That is your own personal playing technique and, I think, not open to question.
I've stated the obvious before: - None of us has a "calibrated" set of ears as regards volume level. The old Fletcher-Munson curves (et al) of the 1950's show how nonlinear our hearing is as a function of not only volume but of frequency as well. Unless and, until, someone does some viable laboratory experiments regarding all of the above, I'll take any statement which smacks of an anecdote with a giant grain of salt.
I've posed this question before but it's worth repeating: - How much "sustain" is enough? If someone did an experiment in which a player was asked to pin down his/her preferred length of sustain then you'd end up with time values which varied all over the lot. The best that could be gleaned from such an exercise would be to plot the results which, most likely, would resemble the ubiquitous "bell" curve. At most, it would be indicative of the average preferred length of sustain. Personal preference then takes over in order to satisfy the individual's taste. This, and a hundred other experiments, has not been done. It's frustrating.
I have no doubt that the instrument that you're designing will be first rate. I also have no doubt that a portion of that design will, eventually, fall under the heading of experimentation. We do - we learn. Forge ahead, my friend.
Richard
I place little credence in anecdotal "evidence". I have no doubt that, when some people change their bar to a larger diameter, they are anticipating a change and, thus, their imaginations tend to fulfill their anticipations. I'll ask the same question that I've asked for ages:- Did you actually measure any change and what are the numbers?
In spite of the implications contained in the paper that I referenced, above, everything is still very much up in the air. The paper, and one's intuition, says that the effect, as described, is real but one must remember that the paper is primarily theoretical. Nothing has been MEASURED that is directly applicable to the PSG.
You will recall that, some many months ago, I roughly measured the break angle of the strings over the roller bridge on the PS210 from the patent drawings. It was in the neighborhood of 7°. Whether Gene Fields took into account the bending/breaking action of the string over the roller is open to question. The "rattling" that you mention is also a function of the picking force that the player uses. With small "break angles" and a pair of "gorilla hands", rattling can become a problem since the down force on the roller/under the bar is minimal. Ditto with bar pressure. I tend to play with a light touch thus I most probably would not run into that problem.
Everyone should know that maximum sustain of a vibrating string is realized only on a monochord having infinite mass and well-defined terminations. We have to take a couple of giant steps backwards from that ideal when attempting to apply the concept to the PSG. The fact that you tend to press down considerably with a smaller bar indicates to me that you are increasing the break angle under the bar by a small number of degrees thus negating the possibility of inducing "rattling". Having seen you play - in my old music room - I know that you tend to be "heavy-handed" therefore you must apply greater pressure to the bar so as to get out of that "rattling" mode. That is your own personal playing technique and, I think, not open to question.
I've stated the obvious before: - None of us has a "calibrated" set of ears as regards volume level. The old Fletcher-Munson curves (et al) of the 1950's show how nonlinear our hearing is as a function of not only volume but of frequency as well. Unless and, until, someone does some viable laboratory experiments regarding all of the above, I'll take any statement which smacks of an anecdote with a giant grain of salt.
I've posed this question before but it's worth repeating: - How much "sustain" is enough? If someone did an experiment in which a player was asked to pin down his/her preferred length of sustain then you'd end up with time values which varied all over the lot. The best that could be gleaned from such an exercise would be to plot the results which, most likely, would resemble the ubiquitous "bell" curve. At most, it would be indicative of the average preferred length of sustain. Personal preference then takes over in order to satisfy the individual's taste. This, and a hundred other experiments, has not been done. It's frustrating.
I have no doubt that the instrument that you're designing will be first rate. I also have no doubt that a portion of that design will, eventually, fall under the heading of experimentation. We do - we learn. Forge ahead, my friend.
Richard