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Ideal body width

Hello everyone, for some time now I have decided that I was going to build an instrument on my own. I don't have a very strict plan in my head as I am still in the early stages of designing and the biggest restriction for me right now is my budget. While searching for the wood I was going to use for the body I stumbled upon a local seller that is offering a piece of elm which is 500x250x40mm (62€). It seemed like a nice piece of wood but I was worried that the width and the thickness may be too limiting while working or even the thickness not being able to withstand the string tension. I am asking you to tell me your opinion on this subject and please let me know if you believe the wood is fairly priced. Thanks.
 
I have no idea about "reasonable wood prices in your local area."

40mm (slightly more than 1.5 inches) is plenty thick enough for basswood to "resist string tension" and elm is considerably stronger/harder, so no issue there.

Width is personal taste once you get past enough of it for the strings, bridge, and pickups, everything else is optional. It's also easily altered by gluing more wood on (as is thickness, but that's a little more effort.) With adequate planning that can be wood from the same plank you cut off as waste in one spot and glue back on another (mostly for width. Thickness would be trickier.)
 
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Is the board(s) surfaced? 40mm is indeed just over 1 1/2” but if that’s rough cut you will loose some thickness planing / surfacing the wood. I believe a few of the folks on here have built bodies down to 1 1/4” (31.75mm) and possibly, if I’m remembering correctly, 1” or just over (25.4mm). However, once you get much below 40mm it may require additional planning as things like push pull pots and even thicker pickups may not fit.

The other dimensions are to your taste. Some players like the “boat paddle” Steinbergers and similar instruments, others like explorers. I like both :D. Most likely an interesting and functional body can be designed within the limits of your wood dimensions but it may not be Fender or even Gibson looking.
 
I have no idea about "reasonable wood prices in your local area."

40mm (slightly more than 1.5 inches) is plenty thick enough for basswood to "resist string tension" and elm is considerably stronger/harder, so no issue there.

Width is personal taste once you get past enough of it for the strings, bridge, and pickups, everything else is optional. It's also easily altered by gluing more wood on (as is thickness, but that's a little more effort.) With adequate planning that can be wood from the same plank you cut off as waste in one spot and glue back on another (mostly for width. Thickness would be trickier.)
Is the board(s) surfaced? 40mm is indeed just over 1 1/2” but if that’s rough cut you will loose some thickness planing / surfacing the wood. I believe a few of the folks on here have built bodies down to 1 1/4” (31.75mm) and possibly, if I’m remembering correctly, 1” or just over (25.4mm). However, once you get much below 40mm it may require additional planning as things like push pull pots and even thicker pickups may not fit.

The other dimensions are to your taste. Some players like the “boat paddle” Steinbergers and similar instruments, others like explorers. I like both :D. Most likely an interesting and functional body can be designed within the limits of your wood dimensions but it may not be Fender or even Gibson looking.

Thank you everyone for your help. As I was searching some more I found a piece of limba which is considerably cheaper (32€) and bigger than the other wood and I believe it would be more suitable to buy it for my first project as it wouldn't require such detailed plans and would immediately make my life easier. It comes surfaced and consists of two glued together pieces.
 
Detailed planning will save trouble when it comes to actually cutting wood, regardless of the size of the piece of wood you have.

Far better to find a mistake or miscalculation when it's just pencil and paper (or pixels and screen) than after you've cut the wood.
 
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What kind of construction do you have in mind? A neck-through-body design means the neck's wood contributes between 65-90mm to the body width, possibly more if you're making a very wide neck. Even with a set neck or bolt-on design you can use different wood to make a center beam, and use the elm wood to make the body wings.

As far as ideal body width, that also depends. I personally like a smaller body, but then again I play sitting down and a large body can force my picking arm into an uncomfortable position. Standing up it might be a question of how much mass the body contributes rather than the width itself.
 
I've made bodies that are 270mm in width. They can look long and narrow at that size. I think 300 to 330mm is more usual.

Fender make bodies that are 44 or 45 mm thick, from memory. That's just a 50mm raw slab that is planed on both sides. It is thicker than you need and a bit heavy as a result. I tend to use wood that is planed to 32mm thickness. That's fine if you're not using push/pull pots. Thinner can be done but takes more thought.