There is another method that you may want to look at: a "long compass". It's easier than the method I demonstrated and at least as accurate if not more. there are some useful videos on their use here on KZfaq. Thanks for watching.

Thank you. I appreciate your comment.

Thanks for your very encouraging comment. I enjoy making these videos and look toward more and better presentations.

I sincerely appreciate your comment. It's very encouraging.

Thank you! If you can get the Math workable, the fabrication becomes straight forward.

Thank you so much for your comment. It is very encouraging.

Absolutely! And I'm afraid of heights. Tying that rope off way up in the barn rafters is a killer:)

Thank you for the laugh…definitely needed these days…!😂

Thank you for sharing that information! I remember Open Math and other subjects early in my career. You're absolutely correct: it was a TOTAL FAILURE.

Kinda gives the adage, "hind sight is 20/20", new meaning doesn't it? On the other hand, if math was taught from a real as opposed to a theoretical perspective, it would have been helpful to all of us.

@@thepragmaticluthier Absolutely.

Im' very glad that you found this useful or at least entertaining.

Thank you. It is both useful and entertaining. I do a lot of the same things that you are showing, but I would like to say that your methods and workmanship is much better than mine. So your videos are helping me refine my work quite a bit.@@thepragmaticluthier

That piece of wood is "Yellow Wood", Cladrastis kentukea. It is rare in my region of the country but quite prevalent in the southern region. My research made me aware that it had value in Colonial times, being prized as a gunstock wood. It makes a great guitar if you get large enough pieces of it.

I'll check it out!

Little geometry goes a long way and trigonometry goes even further.

I cannot give you an authoritative history of doming guitar tops and I've heard and read so many ridiculous rumors that it makes things even more confusing. I dome my tops to increase stiffness and to provide for some shrinkage room during dry months. Generally, determine the amount of doming based on my perceived flexibility of a top and the desired result that I'm working toward, i.e., enhancement of low or high frequencies, or balance. I do this intuitively and keep notes which help objectify my experience so that more intelligent or predictable choices can be made going forward.

Sounds very encouraging. Did your spreadsheet reveal how much deflection from a perfect arc there is?

@@thepragmaticluthier I oopened up my spreadsheet and added a sheet using the deflected beam approximation you used. for starters, I discovered that I estimate the central deflection should be .1499" not .16" for a 40' radius dish. The maximum error from a circle with a deflected beam (method you demonstrated) is .011" a bit less than 10 %. I am not sure how accurate you can cut your lines in the template but 0.01" is not an insignificant error.

This deflection method creates a catenary - the profile of the droop of a rope between two poles. Not an arc. It’s a pretty shape but is not a segment of a circle. I’m sure at this scale there is no measurable difference. But please be clear, I can argue with your method as it doesn’t achieve what your math correctly calculates.

You're correct. If you read the comments above, you'll se that another contributor has calculated the disparity to be .011". The purpose of the entire procedure is to create an even, consistent curve to work with. The calculations provide a quantifiable goal and the method demonstrated provides a technique to reach it at a level of precision that is beyond actual necessity and one that can be performed by nearly anyone. "To be clear", I pointed out the likely imprecision in this technique and also pointed out that departure from the mathematic precision was to be expected and is acceptable. If you demand mathematical precision in your dish, buy one or produce one with CNC equipment, then demonstrate how it makes a marked difference in the mechanical or tonal quality of a guitar made today and or before such precision was within the reach of even the best producers of them.

@@thepragmaticluthier I don’t demand excessive precision in the woodworking involved building an instrument, rather request that we be clear that this technique creates an useful approximation of an arc. Thank you for your demonstration of a method to produce a fixture broadening the accessibility of your craft.

I'm more similar to you in that regard than you may think. The upside is that when you arrive at a problem that is important to you, you will amaze yourself with the power you have to learn what you need to know. It's all a matter of relevance.

Excellent question and suggestion for a video. I may try to present that in the future. In the meantime, I believe the short answer is; given a cord of the proposed radius, equal in length to the diameter of the dish you're creating, you will need to first calculate distance from the bisector to the arc as shown in this video. When that distance is plotted, you now have three points to work from. Draw a straight pin from each end of the cord to the calculated point. The resultant angle is the angle needed to construct the long compass.

The entire top is domed. The area where the fingerboard will cross the top can be flattened . At a 25 foot radius, for example, the high point of the chord of the dome of the chord representing a 3 inch wide fingerboard would be .00376", not much to sand away:)

@@thepragmaticluthier thank you!