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Hace unas semanas intenté hacer en mi torno un recipiente aproximadamente cilíndrico, y me dio mucho trabajo ahuecarlo. Terminé rompiendo sin querer la pieza de madera, y aunque traté de recuperarla, no quedó bien.

Mientras trabajaba en ella, se me ocurrió que sería una buena idea partir de una pieza segmentada en vez de hacerlo de un solo trozo de madera. Es decir, armarla con una cierta cantidad de duelas idénticas encoladas entre sí, para formar la superficie lateral.

Pero la cuestión tiene sus bemoles, según uno desee hacer un cilindro, un disco o un cono.

Parto de la base de que trabajo con madera cepillada, es decir cuyas caras opuestas son paralelas. Las duelas irán pegadas entre sí por los bordes, o sea que las caras paralelas lo seguirán siendo hasta el momento del torneado, y apuntarán hacia la parte interna y externa de la pieza terminada.

A continuación analizo las diferentes alternativas que se presentan, y cómo se resuelven. No considero duelas curvas, pero la fórmula general deducida se aplica también a ellas, considerando que habrá que calcular nuevamente los ángulos en cada punto de la arista.

En la figura principal (dibujo lineal, segunda imagen), los ángulos B y C se toman en referencia a cada duela, no a la pieza terminada.  Esto se muestra con más claridad en la tercera imagen.

Lo aclaro porque alguien podría decir que tomando como modelo la imagen del disco, en la del cilindro estarían invertidos los ángulos B y C. 

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A few weeks ago I tried to do using my lathe an approximately cylindrical container, and it gave me a lot of work to hollow. I ended up accidentally breaking the piece, and though I tried to recover it, the result was not so good.

While working on it, I thought it would be a good idea to start from a segmented piece rather than a single piece of wood. It is to say assembled with a certain amount of identical planks glued together to form the side surface.

But the question is a bit tricky, as one wishes to make a cylinder, a disk or a cone.

I assume that I am working on planed wood,  whose opposite faces are parallel. The staves shall be glued together by the edges, meaning that the parallel faces will remain so until the time of turning, and will point to the inner and outer part of the finished piece.

Then I analyze the different
available alternatives, and how to undertake them. I am not considering curved staves, but deduced general formula also applies to them, considering that there will be necessary to recalculate the angles at each point of the edge.

In the main figure (linear draw, 2nd image), the angles B and C are related in reference to each stave, not to the finished part.
This is shown more clearly in the third image.

I clarify this because someone think that, taken as reference the disk image, in the cylinder the angles B and C would be inverted .

Step 1: Disk (disco)

Acá el cálculo es muy sencillo. Cada duela será un sector circular, de ángulo igual a 360 grados dividido por la cantidad de duelas. Ejemplo: si son 20 duelas, el ángulo debe ser de 360/20 = 18 grados.

La cosa terminaría acá si estuviéramos trabajando con chapa delgada, pero como se trata de madera con cierto espesor, hay que considerar el ángulo que forma cada lado de la duela con las superficies interna o externa. En este caso es obvio que ese ángulo es de 90 grados, dado que el conjunto es un disco plano.

En cuanto al largo de cada duela, evidentemente es igual al radio del disco.

Resumen: A = 90°; B = 0°; C = 18°

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Here the calculation is simple. Each stave is a circular sector of angle equal to 360 degrees divided by the number of staves. Example: If you are 20 staves, the angle should be 360​​/20 = 18 degrees.

The thing would end here if we were working with thin sheet, but as it comes with some thick wood, consider the angle between each side of the board with the internal or external surfaces. In this case it is obvious that this angle is 90 degrees, since the whole is a flat disc.

About the length of each board,
evidently equals the radius of the disk.

Summary: A = 90°, B = 0° C = 18°
<p>Спасибо!</p>
<p>Estimado Osvaldo, muchas gracias por haber subido las tablas y planillas. Amo la geometr&iacute;a pero... la trigonometr&iacute;a es a&uacute;n a mi edad una materia pendiente. Saludos cordiales desde el sur del sur.</p>
<p>&iquest;De d&oacute;nde sos/eres? </p><p>La trigonometr&iacute;a es MUY &Uacute;TIL, y te simplifica enormemente un mont&oacute;n de tareas. Por ejemplo, para hacer o construir &aacute;ngulos es mucho m&aacute;s f&aacute;cil medir senos, cosenos y tangentes que &aacute;ngulos. Te sugiero que estudies un poco el tema, en la web hay material de sobra. No se necesita mucho tiempo, en una hora pod&eacute;s entender y aprender lo b&aacute;sico. </p>
Vivo en Ushuaia-Tierra del fuego &iquest;&iquest;?? Argentina. El sur del sur.<br>Yo no tengo dudas de que es muy &uacute;til, especialmente para quienes como yo, somos locos por los poliedros. Seguir&eacute; tu consejo y tratar&eacute; de &quot;amigarme&quot; con la trigonometr&iacute;a. Saludos cordiales
<p>Hi there. Very interesting work. I appreciate your publication. It will be possible to obtain the table?</p><p>Muy interesante trabajo, muchas gracias. Ser&aacute; posible obtener la tabla ? Saludos</p>
<p>I uploaded again the charts and worksheets in PDF and ODS format, now they appear.</p>
<p>&iquest;Qu&eacute; funci&oacute;n tiene pintar con clara de huevo?</p>
<p>Fue una prueba que hice, llevado por lo que le&iacute; en la web. Al principio parec&iacute;a todo un logro, pero a los pocos d&iacute;as me di cuenta de que algo no funcionaba y tuve que sacarla. </p>
Qu&eacute; dise&ntilde;os m&aacute;s chulos! pero eso s&iacute;, el trabajazo que te pegas con la trigonometria es todo un logro! mi m&aacute;s sincera enhorabuena desde Espa&ntilde;a! hay que fomentar m&aacute;s artesan&iacute;a de este tipo..yo aun soy joven y estudiante pero persigo mucho estos proyectos para poder alg&uacute;n d&iacute;a vivir de lo que me gusta...gracias Osvaldo!
<p>Gracias, lcaruncho, por tu amable comentario. Pero te advierto que si piensas vivir de la artesan&iacute;a tendr&aacute;s que desarrollar habilidades art&iacute;sticas sobresalientes, y si no, resignarte como yo a ganar menos que la se&ntilde;ora que viene a lavar los platos. </p><p>Intent&eacute; hacer estos bols en una hora o algo as&iacute;, pero no pude bajar de varias horas. Tal vez es cuesti&oacute;n de insistir, pero me pregunto si valdr&aacute; la pena, habiendo tantas otras cosas interesantes para hacer. </p>
Yet again, nicely done. A good explanation of how to find the angles.
Thanks kleinjahr, glad you find useful my formulas.
I have used this technique to make wooden hand drums (african style ashiko and Djembe), and I agree there was always some trial and error to fit the last piece. <br> <br>In order to save time and decrease errors I switched from using equal angles on each side of each stave, to a 90 degree (as the material was supplied) on one side, and the calculated angle on the other side. The result of this approach was less material waste, and fewer errors. The top and bottom edges of the rough assembly end up uneven, (sawtoothed) due to the uneven angles on each stave. Correcting this still took much less time than making double cuts on each stave. <br> <br>As a bonus, in making a drum with this method, I used the scrap pieces to make a mini drum (as each cut off had essentially mirrored angles from the original piece. I suppose if one starts with the right size rough stock, 2 matching assemblies could be made with this approach with no waste.
I have almost zero waste of wood: I set the angles of the blade (vertical) and the sled (horizontal). Do the first cut (less than half stave of waste), turn longitudinally 180&deg; the wood and cut the first stave. Measure its angles, if they are good, I follow rotating 180&deg; and cutting each stave. So until end. I do 3 or 4 additional staves, just in case. After I sand them with my <a href="http://www.instructables.com/id/Table-belt-sander-lijadora-de-banda-de-mesa/" rel="nofollow">homemade table sander</a> (I added it a tilting guide), put all staves with their greater side upwards, join them with painter tape and glue them. The last is always a problem, as you says.<br> <br> Thanks for comment!
My rough stock was not ever a single large piece of wood, but pre cut planks (in one instance reclaimed hardwood flooring), so cutting many pieces in series would not have worked. <br> <br>I like your method though (flipping 180 degrees). It will work great with larger stock. I'll have to try it next time.
In order to have the grain of the staves longitudinal, I cut many short pieces from a long timber, and then glue them adjacent. This worked very well, shortening the cutting time and mainly the waste. If you want transversal grain, you only should have a long timber, or glue two by their ends.
&iquest; Es este m&eacute;todo de tu invenci&oacute;n?
No, Bill, It is my <strong>deduction</strong>. I love trigonometry, in cases as this, it is imprescindible.<br> -----------------------------<br> No<strong>, </strong>Bill, es mi <strong>deducci&oacute;n</strong>. Amo la trigonometr&iacute;a, en casos como este es imprescindible.
an excellent job as always. keep up the good work.
Thanks, LordDrake!
Tengo que pensar en esto por un tiempo. <br> <br>Muchas gracias amigo. <br> <br>
Me alegro que te intereses en el tema, Bill. Cuando hice la cocina solar descubr&iacute; el c&aacute;lculo del &aacute;ngulo C, necesario para aprovechar con espejos planos la mayor superficie posible. Y cuando fui a aplicarlo al trabajo en madera descubr&iacute; el &aacute;ngulo C. <br>------- <br>Glad you interest in the subject, Bill. When I made solar cooker discovered angle C, calculation necessary for fully cover as possible the surface with planes mirrors. And when I went to apply it to woodworking, discovered the angle C. <br>
We thank you in Spanish also posting form. Just use google translator least. :) <br>Se agradece que lo postees tambi&eacute;n en espa&ntilde;ol. As&iacute; uso menos el traductor de google. <br> <br>Sobre el post, muy interesante. Dentro de poco empezar&eacute; a hacer cosas en madera y todo esto ya me lo guardo.
Automatic translators will never be perfect, because languages ​​are difficult or impossible to systematize. I must fix the translation almost always, otherwise it would be ununderstandable. <br> <br>Glad you find useful my instructable.
Hi Rimar : <br>How are you ? We are OK. Some time back, I passed on the concept of using a copper backing strip, when welding thin metal, to minimize &quot;blow through&quot;. Recently saw some USA Mfg'd copper heat sinks, incorporating powerful magnets, for thin mild steel, etc. Not cheap ! If I need any, in the future, I would make from flat copper, using neo dymium powerful magnets, secured in tight fitting cut outs, secured by careful center popping, to secure them on the same plane as the surface of the copper, in contact with the parts to be welded. <br>Cheers, <br>Dennis.
Hello Dennis. Never heard about those heat sinks, the idea seems clever. <br> <br>In those cases I have used pieces of ceramic tiles in order to decrease the drip of melted iron, successfully.
Osvaldo, This is also similar to making a hopper joint, but with more pieces and more joints. One possibility is simply to clamp the tapered pieces into something that holds them at the proper angle and then run a handsaw between them two or three times until the pieces fit tightly. In any event, bucket and barrel staves are not easy for those of us who seldom do it.
Yes, Phil, I considered that possibility. But I discarded it to try this method, and it was successful. With some enhancements to my cutting table (I will post an instructable) now it is very easy and fast to do these staves. In less than 10 minutes I can set the blade and slider at angle, and then cut around 50 staves in a minute, with almost zero waste. The precision is good enough for my needs. <br> <br>Today I am turning the bowl, and I am surprised with the precision of the joints.
This is seems like traditional Turkish tub &quot;yayık&quot;, it uses for to make butter and ayran, Your Project reminded to me :)
Yes, it is the same technic. There are also pails made with this system. <br> <br>Thanks for comment.

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