Three-wheeled bandsaws suck, wheel size matters
Why bigger wheels are better
More elbow roomA bandsaw has a post on the left side, which is as far from the blade as the wheels are in diameter. So a 14" bandsaw will have 14" of space between the blade and the post where the blade goes back up (minus a few millimeters for the blade guard). This means the maximum width piece I could cut through the middle is twice that wide. When cutting out complicated shapes in larger pieces of wood, hitting the post, even with smaller pieces is not unusual. You can often work around it by flipping the piece over or strategising over which order to make the cuts, but having the post further away always makes it easier. Bigger is better.
Longer blade life, less metal fatigueIf you take a typical bandsaw blade, you can bend it to a fairly tight radius and it will spring back to its original shape. So having fairly small wheels, say 8" (20 cm) in diameter, would seem adequate for most bandsaw blades. I could bend the blade to an 8" diameter hundreds of times and not run into problems. But if I bend it to that radius hundreds of thousands of times, It will break from a problem known as "metal fatigue". The smaller the wheels, the tighter the bend that the blade needs to make. Generally speaking, most general purpose bandsaw blades are about 0.026" thick (.65 mm), so a 14" (35 cm) diameter is large enough to avoid this problem. 9" bench top bandsaws have to use thinner (flimsier) blades. For thicker blades, such as used on Wood-Mizer saw mills, 14" would be too small. My friend Kurt, who runs a Wood-Mizer sawmill, says that blades cracking (from metal fatigue) limits blade life to about 10 hours run time before they break. The blades could be re-welded, but after 10 hours, it will soon break somewhere else, so no point in welding it. Wood-Mizer's wheels are just under 50 cm in diameter.
More elbow roomA way to get extra "elbow room" without making a very large bandsaw is to make a bandsaw with three wheels. The third wheel pulls the blade way off to the side, making for a "throat depth" that is larger than the wheel diameter. This would allow you to build a bandsaw with a 20-inch (50 cm) throat depth that could still be used on a bench top.
Moving it aroundBut you also need a lot of room around a bandsaw. I keep my bandsaw pushed against the wall, but it's on wheels. When I run out of room around the saw, I just pull it out from the wall to make the cut. Now imagine a bench top 3-wheeled bandsaw. If you run out of room, you have to pick it up and move it somewhere else to get the extra space.
Less space efficientOf course, you could always put the 3-wheeled bandsaw on its own stand on the floor, so you could pull it out. But if the saw is floor standing, then you have lots of vertical room, so you could just have two larger wheels. But worse yet, the three-wheeled bandsaw typically needs at least the width of the wheel of additional room on the left for the third wheel. So a 20" three-wheeled bandsaw will be wider than a 20" two-wheeled bandsaw, even though the 20" two-wheeler will be much taller. So in terms of footprint, a conventional large 2-wheeled bandsaw makes better use of space. Granted, the 3-wheeler may have a smaller table and save room that way, but you could always put a too-small table on a larger bandsaw and achieve the same effect.
More complicatedThree wheels instead of two means more wheels need to be built. And the three wheels need to be aligned with each other. If the blade doesn't track right, it's much harder to figure out what's wrong on a 3-wheeler than a 2-wheeled bandsaw.
The forces will be all vertical on two-wheeled machine, which, for a homemade machine, makes the shafts much easier to support than the diagonal forces on a three-wheeler.
Hard to find 3-wheelersI did a quick Google search for three-wheeled bandsaw , and two of the images that came up were for Mikionos' bandsaw and for Pekka's bandsaw. I guess there isn't much on three wheeled bandsaws on the web.
Three-wheeled bandsaws were popular in the 1970s. It seemed like a good idea at the time. But, I imagine manufacturers got fed up with unhappy customers from 3-wheeled machines. They break blades far more often, are more finicky, and more complicated to produce. Blade changes are also harder. So I don't know of any general purposes 3-wheeled bandsaws for sale anymore.
More bad bandsaw ideasAnswering some further suggestions that keep coming up....
Use bicycle wheels: See here
Four-wheeled bandsaw:A four wheeled bandsaw would eliminate the extra width needed for the third wheel, because the blade would no longer have to move at a diagonal. But now you have four wheels instead of three, introducing even more complexity. That said, this is perhaps the least dumb idea that keeps popping up. At least this type of saw would only be about as bad as a three wheeled bandsaw.
How about adding some small idlers to deflect the bladeYou could add two small idler wheels to deflect the blade further left, giving extra throat depth without making the wheels bigger. Except, when you add small wheels, the blade has to bend to the radius of the small wheels. Small wheels are a problem. any small wheel is a problem, even if it deflects the blade by just 10 degrees, the blade still has to bend to the radius of the blade. The only exception is wheels as blade guides - because these generally don't deflect the blade.
How about a Teflon guide in the shape of an arc or semi-circle to deflect the bladeThis would eliminate a third wheel, or the wheels altogether. But with the amount of tension on a blade, Teflon would not be slippery enough. In addition, the teeth would dig into the Teflon. Also, the Teflon would get hot. There's a reason Teflon isn't used for bandsaw guide blocks.
How about a semicircle of small wheels?Maybe an arc of 20 small wheels to gently deflect the blade instead of a big wheel? That might work if the blade was very thick and there were a LOT of rollers, and blade tension relatively low, so that the blade never actually bends to the curvature of the rollers. But to actually use a saw, the blade tension needs to be high enough that any regular saw blade would bend to the rollers. In addition, all those rollers would be very difficult to align, would have to turn very fast (and wear out quickly), and would be very noisy. The fallacy this idea tends to be based on is that if the wheel only deflects the blade by a small angle, it won't cause as much wear. But the blade needs to bend to each wheel and unbend again. Whether it goes around the roller 180 degrees or 10 degrees doesn't matter much. If it did matter, wrapping the blade in a coil and spinning the coil (without unwrapping the blade) would also cause it to wear out! At any rate, the semicircle of small wheels is an incredibly dumb idea. Don't agree with me? Do the experiment, like John Heisz did.
What it comes down to...There are reasons that bandsaws are built the way they are, and those reasons are based on physical limitations and not the lack of imagination of bandsaw builders. So if you have a brilliant idea for how to build a better bandsaw (and I haven't shot it down here yet), don't try to prove your idea by arguing with me. Just try it out by building it. Don't have the ability to build it? You might want to consider the possibility that those who do have the ability to build it might have a better understanding of the problem than you do.
More about bandsaws.