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| What is the cube rule? http://mowrystrings.luthiersforum.com/forum/viewtopic.php?f=10102&t=14314 |
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| Author: | Bruce Dickey [ Wed Oct 31, 2007 11:24 am ] |
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Following another thread on bracing an unfamiliar engineering term the "cube rule" is used. What is that? TIA |
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| Author: | Kent Chasson [ Wed Oct 31, 2007 11:33 am ] |
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The stiffness (deflection) of a rectangular beam is proportional to the cube of it's height (as opposed to a 1 to 1 ratio of width). So a 1/4" x 1/2" brace will be 8 times stiffer than and 1/4" x 1/4" brace. And a 1/2" x 1/2" brace will only be twice as stiff. All things being equal. |
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| Author: | grumpy [ Wed Oct 31, 2007 12:21 pm ] |
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And a 1/2" x 1/2" brace will only be twice as stiff Sigh.... In the above example, a 1/4" wide by 1/2" tall brace will be 8 times stiffer(twice cubed, or 2x2x2) than a 1/4'' by 1/4" brace, but a 1/2" wide by 1/4" tall is only twice as stiff as the 1/4 x 1/4. In other words, double the width of a member, double the stiffness. But double the height, and you cube the stiffness. It's not really called the cube rule, BTW. That's just a catchy term, but it does describe it well. |
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| Author: | Kent Chasson [ Wed Oct 31, 2007 1:01 pm ] |
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I suppose it would have been clearer had it read... And a 1/2" x 1/2" brace will only be twice as stiff as a 1/4" x 1/2" brace. I think, in context, it was pretty clear though. Yet another example of where a simple asking for clarification would be productive if you thought the post wrong or confusing. The exasperated sigh serves no productive purpose and is just the type of thing that sounds belittling, distracts from productive converstaion, and starts arguments. What are you trying to acheive? |
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| Author: | K.O. [ Wed Oct 31, 2007 1:31 pm ] |
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Kent I think accuracy on this is very important. I also think that led to the sigh. I tend to be guided by feel while doing my best to understand the science, if the science is presented inaccurately.... I interpret the sigh as not really wanting to have to correct.... Maybe the <s> is overused some but walking on eggshells when people make mistakes gets really old. I have already said to much and involved myself where it is unneeded most probably with my hat on sideways. YA goofed thicken up the skin a touch. PEACE, Kirby |
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| Author: | grumpy [ Wed Oct 31, 2007 1:52 pm ] |
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I suppose it would have been clearer had it read... And a 1/2" x 1/2" brace will only be twice as stiff as a 1/4" x 1/2" brace. sigh... Yes, but no. And no, but yes. Since you're not clearly stating which is width and which is height, your post is meaningless and confusing to those who wish to understand. Plus the numbers here don't jibe with the ones in your first post, thus creating more confusion. And as Kirby said, accuracy is important here, if you want to understand it, and get it right. Please re-read my last post up there. I state it very clearly and concisely. And accurately <bg> And each sigh was real. I actually let out a real-world sigh.... I didn't read that other thread that is real popular right now, because i can only imagine what it's all about(specially after the other one got closed up). There's only one subject around this place that ever gets that many posts in a thread. Please don't come chasing me around the stump over a silly little expression such as a sigh. What the he** good is a forum if one can't correct an incorrect post? and having to do so twice in 2 days, on the same subject, well, that brings about a sigh. And Hesh, stay out of this <LOL> sigh.... |
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| Author: | Andy Zimmerman [ Wed Oct 31, 2007 2:14 pm ] |
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Mario you are correct. understanding this principle is SO critical to voicing and bracing tops. Bruce definitely needs to grasp it correctly. As I say to students etc, they have to get a mental picture of it to grasp it. You have to know which measurement is the height and which is the width. This is where constructive comments are so useful on this forum. This point is so critical to lutherie |
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| Author: | Bruce Dickey [ Wed Oct 31, 2007 2:22 pm ] |
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Okay, let me restate this so I'm sure I've got it. double the width of a given brace, double the strength double the height of a given brace, cube the strength Wow, that's almost shocking to understand. Thanks guys. |
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| Author: | Jim Watts [ Wed Oct 31, 2007 2:24 pm ] |
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No, not strength , stiffness. There's a difference. Other than that you got it. |
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| Author: | Kent Chasson [ Wed Oct 31, 2007 2:34 pm ] |
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First, this is a guitar forum. I thought I could assume that people would understand that with a 1/4" x 1/2" brace, the 1/4" would be the width. It gets pretty time consuming and wordy to assume nothing when posting. And, as I said, it could have been clearer. I was hurrying trying to get out for a bike ride before dark. But if I'm unclear, I have no problem with someone asking for clarification. If I make a mistake, by all means, correct me. But after 3 topics have been closed in a couple of days and after all the other needless arguments on this and other forums, I would think it would become obvious that the editorializing is unproductive. |
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| Author: | Andy Zimmerman [ Wed Oct 31, 2007 3:51 pm ] |
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Exactly Todd I use a dial indicator to measure each top since I don't have the dexterity skills to do it by hand reliably. |
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| Author: | grumpy [ Wed Oct 31, 2007 4:03 pm ] |
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Dude, you take yourself WAY too seriously. Really. It was a joke. a little jab in the ribs. Since you rarely mind your own business, and make no apologies for it(and you shouldn't, because you are who you are), I poked at you a bit. Lighten up... Look at yourself from another's perspective for a second <bg> The MIMF is doing fine, and I posted more there today than I did here, including helping out a OLF-er with a serious enough issue... I also stopped by the mandolin cafe for a while, as well as a small handful of jazz guitar and jazz mandolin sites/forums that I frequent. There's more to life than jus making the instruments; I also play them. Here, I teach and share; there, I learn(and mostly lurk) I'm here because I love to help, and part of that is to clarify things that are wrong, wrongly worded, or misrepresented. As was the case here. I also love to teach and share. But y'all put WAY TOO MUCH EMOTION into this forum. A simple little "sigh" and the thread has more posts on -that- than the facts pertaining to the question asked by the thread's starter. And understanding what was asked is very important. From what I gather, all of Ervin's teachings on brace functions relies on it, and it should. Yet, all it is is simple, first semester engineering. But we must get it right. In the end, if every little emotion will be called to the floor, screw it, y'all can have your little forum. Ya did fine without me, and trust me, I did fine without the emotional antics of this place. May I suggest everyone check their emotions at the door, please? And learn to take a joke and/or a jab, fercryingoutloud. How old ARE each of you? |
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| Author: | James Ringelspaugh [ Wed Oct 31, 2007 4:14 pm ] |
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| Author: | JohnAbercrombie [ Wed Oct 31, 2007 4:26 pm ] |
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[QUOTE=Bruce Dickey] Okay, let me restate this so I'm sure I've got it. double the width of a given brace, double the strength double the height of a given brace, cube the strength [/QUOTE] Since everybody is being so 'picky' to get the details right on this....... double the width of a given brace, double the strength double the height of a given brace, cube the strength should be: double the width of a given brace, double the stiffness double the height of a given brace, 8 times the stiffness But- you obviously understand the idea: a scallop which halves the height of a brace will reduce its stiffness in that area by 8 times. And, as Al Carruth pointed out to somebody recently, if you are comparing tops for stiffness, you have to get the thickness values quite accurately- small differences in thickness produce big stiffness changes. Most folks find this out when they first get a thickness sander..just one more pass, and.... 
Cheers John |
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| Author: | Andy Zimmerman [ Wed Oct 31, 2007 5:07 pm ] |
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So true John Just a bit thinner on a top make such a difference...That cube rule. Since I measure top deflections you really see it numerically with the dial indicator. This was never that clear until I started measureing. Just one more pass, and ......WOOOOPS!!!!!!!!! Here is some data from my collection on one of my guitars Lutz L-OO 64 0.153 Lutz L-OO 75 0.143 Lutz L-OO 120 0.127 Lutz L-OO 169 0.11 Lutz L-OO 241 0.096 Lutz L-OO 275 0.091 Lutz L-OO 290 0.087 Lutz L-OO 330 0.083 The 1st number is the degree of deflection and the 2nd is top thickness. See how quickly the top loses stiffness with slight changes is thickenss. BTW The numbers above are meaningless to all of you because everyone measures deflection differently with different weights different setups, different lengths etc..etc but they show numerically what is hard to grasp conceptually. You all know I took Ervins class and praise it frequently so LET ME BE CLEAR ON THIS POINT. The data above are NOT super secret confidential data that are the holy grail to building a guitar!!! It is not secret Somogyi data. It is just numbers from my collection that I am using to show a point!!! |
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| Author: | Andy Zimmerman [ Wed Oct 31, 2007 5:42 pm ] |
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The key to the above data that can be so hard to grasp, is that with thinner plates, which we use with our tops, slight changes can make dramatic changes in stiffness or deflection. This can be more dramatic than with braces!!! As you thin a plate, the same amount removed causes a greater change in stiffness!!!! Example If you take a plate that is 0.100 inches thick and remove 0.010 you get a much greater change is stiffness than if the plate started at 0.120 and you removed the same 0.010. I will let the engineers and math guys give you the exact difference in stiffness. I would just screw that up You can sort of see that in my data above When the plate went from 0.153 to 0.143 (0.01 thinner) my deflection increased by 9 units. But when I went from 0.096 to 0.087 the deflection increased by 49 units. DRAMATIC!!!!! It may not follow the exact engineering formula but this is real data on my top!!!!! |
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| Author: | JohnAbercrombie [ Wed Oct 31, 2007 5:50 pm ] |
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Andy- Thanks for that data- it makes it much clearer than just stating the theory. Did you actually use that top, or was it a 'Whoops!'? I keep reminding myself that with smaller-body guitars (OO, parlor), the decreased span means that everything can be lightened up a bit. Cheers John |
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| Author: | Andy Zimmerman [ Wed Oct 31, 2007 6:15 pm ] |
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Sorry Bruce but I am on a roll...I don't want to hijack but this is a critical teaching topic that many don't grasp and it is related to your post. For the veterans sorry if this is too basic, but this is great for the newbies. So what do I do with all that data. Keep track of it. Lots of it. I certainly cannot remember what I top felt like during construction after the guitar is done!!! Can you tell the difference in the stiffness of a top 3 months later??? Well with the above data, I LOVED!!!! the sound of that L-OO so you can bet your last dollar, that when I build another one I will thickness it to the same degree of deflection as that one. Who knows, the next piece of spruce might be stiffer and it will need to be taken down to 0.080 inches to be the same or it might be flimsier and only be 0.100. That is why in my opinion you cannot just thickness all of your tops the same like Taylor guitars etc. Each piece of wood is different. Also it is different for different size guitars. The same stiffness top on parlor will be quite different on a jumbo!!! My opinion is that you need a thicker top on a larger bodied guitar to keep things relatively equal. (Bigger drum head) In that controversial thread with photos of my tops, that piece of redwood was WAY different than that piece of spruce. I just looked up my data and I thicknessed the redwood to 0.113 but the spruce was only 0.088. AND the spruce was on the LARGER body guitar where I want a stiffer top!!!! Measuring and keeping data is so revealing and priceless. It has help me in trying to be consistent. |
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| Author: | Andy Zimmerman [ Wed Oct 31, 2007 6:19 pm ] |
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John That top was no wooops. I love that little guitar. Its top is 0.083. Now that number is somewhat meaningless since each piece is different and bracing plays a large part!!!!! You might get to the same relative point with a stiffer top and smaller braces |
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| Author: | Jim Kirby [ Wed Oct 31, 2007 10:43 pm ] |
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[QUOTE=azimmer1] BTW The numbers above are meaningless to all of you because everyone measures deflection differently with different weights different setups, different lengths etc..etc but they show numerically what is hard to grasp conceptually. [/QUOTE] Therein lies my pet peave as an engineer - why can't we standardize a deflection test so that Andy's numbers (or anyone else's) actually mean something to someone else? This process of testing and obtaining non-transferable data would be laughable out in the real mechanical testing world. And yet, people tend to blow off the idea when it comes up. Why? |
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| Author: | Parser [ Thu Nov 01, 2007 12:18 am ] |
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I think that another question that we should be asking is whether or not we want all of our guitars to sound the same? Personally, I don't mind if they are unique sounding as long as the construction is good. If I wanted something consistent I'd use something other than wood...! 
[QUOTE=jtkirby] [QUOTE=azimmer1] BTW The numbers above are meaningless to all of you because everyone measures deflection differently with different weights different setups, different lengths etc..etc but they show numerically what is hard to grasp conceptually. [/QUOTE] Therein lies my pet peave as an engineer - why can't we standardize a deflection test so that Andy's numbers (or anyone else's) actually mean something to someone else? This process of testing and obtaining non-transferable data would be laughable out in the real mechanical testing world. And yet, people tend to blow off the idea when it comes up. Why? [/QUOTE] |
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| Author: | Jim Kirby [ Thu Nov 01, 2007 12:42 am ] |
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Heh, there's nothing saying that any one of us wouldn't take the info about a soundboard and go a completely different direction with it. That's not what testing is about. Consistent testing would allow me to ask someone whose work I appreciate what longitudinal stiffness they are looking for in their thicknessed top plates, for example. If we had standardized testing methods, their answer to me would be meaningful to me. Now, as Andy points out, the numbers are not transferable in an absolute sense. |
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| Author: | Andy Zimmerman [ Thu Nov 01, 2007 1:14 am ] |
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The numbers are meaningful in the sense it show how the cube rule works and as you thin a top you get exponential changes. There is no magic bullet, but by keeping track of things, it is much easier to make guitars that have the voice you want. In my example above, some might not like the sound of that guitar. If a customer said that he wanted more highs and more sustain, then I would have some idea how to change it. I would probably thin the top a bit less and got with less deflection. |
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