This is an older post, but one thing seemed missing to me for a round or barrel shape, and that's that the staves for a straight side need to be cut at a slight angle. Count the number of pieces you will need to surround the entire tub, divide 360 by the number of staves, then divide that by two. This will give you the angle you need to cut each side, and the angle to set the blade you'll use to cut the grooves. Each groove should be just a noogie deeper than the half the width of the splines. Waterproof glue to hold them together during assembly. Over time the seal will be made by the wet staves swelling tightly together. In fact, most wood hot tubs are unusable if they dry out. .
You will need to construct the bottom in a similar way, but cut the grooves 90 degrees, not at an angle. Cut to the size of the bottom, plus another inch or so. Use a router to cut all round so it can fit into a dado you cut near the bottom of each stave. The bottom will fit in this groove.
You will need straps around the bottom and top of the tub, and possibly in the middle. While assembling this, build it in two halves, carefully fit the bottom, then join the two halves. Be prepared to do a little final fitting with a hand plane. Get some help assembling this, it will be quite awkward.
I would use motorcycle tie downs for assembly, but I'd get some steel straps (hoops) to go around the barrel. You will need a way to tighten the hoops. Although you're using a water proof glue, the hoops will be holding back both water and the weight of users laying back against the sides. In a barrel with tapered staves, the hoops are made separately and jammed down onto the barrel, but you're using straight sides, so you will need some kind of nut and bolt on the hoop so you can tighten it in place. You can use some tacks to hold it in place as you tighten it.
You will have to find hardware to let hot water pumped in from a heater, plus a drain for the cooler water to recirculate.
This thing is likely to leak like mad, depending on how tight you build it, but it will also absorb a lot of water and swell so there are few to zero leaks left. if it continues leaking, retighten the hoops or use a calk as a last resort. The hot water and chemicals are likely to eat away at that seal over time, so be prepared for a certain amount of maintenance.
One of my wives was into mother nature and we used to go to a nudist place that had redwood hot tubs just like this. It was a very pleasant and relaxing experience. Once you get a project like this done, you will need it to deal with your sore back from making it.
If you want to make this without splines, using T&G, you still need to cut the staves sides at the computed angle, and then leaving the blade at that angle, make the groove so it fits the tongue at the required angle.
"A square or rectangular tub might be easier to make, but you will have to replace the hoops with something stiff, like a set of 2x4s overlapped to keep the water pressure from collapsing the sides. You might have a thousand or more gallons of water, each weighing 8 lbs and more pressure at the bottom. Add six people leaning back on the staves and, well, you get the idea. I guess you could use some L shaped angle iron to reinforce the corners of the 2x4 bracing. I'd want to use stainless steel nuts and bolts with fender washers to hold the brace, and I'd also consider adding four braces to a 42 inch high tub with a 36 inch water level.
I realize that this is pretty much a dead string, but since it reappeared, I thought I'd cover this territory in a little detail. Building something like this is not something I'd under take.
