One of the many recent discussions of flywheel physics sparked a realization about the design basis of a flywheel profile most elemental, and in hindsight, plainly obvious at least in theory. It involves concavity. So let's talk about concavity and ask the most basic question there is.
What the hell is the purpose of a concave flywheel profile, anyway?
(Be warned, theory ahead, but there are some cool things later on!)
Some would say it is to "support" the dart as it is deformed during contact.
Some would say it is to "get more contact area".
Others would note that a dart at rest is round, and if you smash it between cylindrical wheels, you don't get a uniform distribution of deformation, or normal force against the wheel, which is linearly related to deformation. You get a large spike in the centerline and a rapid decay toward the outside. Now this is the correct answer.
So can we go more basic than that? What is the purpose of flywheels? Well... To accelerate darts. With what force? Friction, dynamic friction. And whatever the coefficient of friction is in the system, the friction force is directly related to the total normal force on the contacting surfaces, and that is why we're deforming our darts with flywheels, to create a normal force against the flywheel surface. What do we want to get more friction? Well, we don't have the faintest idea on how to increase the coefficient of friction beyond what we have now in a practical system. That leaves the normal force. We want more normal force.
Now, concave flywheel profiles have so far proceeded in a rather "do it by feel" direction to my knowledge. It's pretty much a "Well, that oughtta fit the dart better than a flat one" type of deal. That the SSS format mounts the flywheel onto a motor shaft with a press fit, and flywheels must be a machined part which is not too easy to experiment with, does not help the matter at all. Profile geometry has lagged in its development IMO.
In particular there is a bit of philosophy I suspect of being misleading, and that is the focus on radial normal force. There are a lot of mild-concave profiles out there.
This is actually me CADoodling some large-diameter ideas prior to that spark, and what it is, is an excellent example of a mild-concave flywheel profile. You have probably heard me use that terminology, and specifically what I mean by "mild" is that the groove radius is greater than the root-to-root clearance when installed in a cage. As a result, the generating shape for the flywheel surface, which is also the shape of the resulting gap between them, is an intersection of two arcs that looks like an American football. Usually the endpoints of the "football" are off in the distance to the side of the cage and already get wiped out by the rim width of the flywheel. With SSS family parts based on compatibility with the old Hasbro 43.5mm center distance, there is further severe truncation imposed by the clearance in the cage or the blaster it is supposed to go inside. But you get the drift - with Artifact and Hooligan and especially BlasterParts and CC flywheels, you're forcing a round dart through a profoundly football-shaped hole. Seems right. Right? Isn't that what you want to do to a dart when there are two flywheels? We're applying a deformation in one direction. Right?
I'm gonna take a big leap and say that this is very wrong. We're not (necessarily) dealing with a deformation or a normal force in one axis. The normal force we are worried about is normal to what, exactly? Not some arbitrary axis going horizontally through the dart, ortho to it and the flywheel webs. No no no. Normal to the contact surface. Which can be and usually is curved.
So there's key element one, we shouldn't be throwing away the horizontal (parallel to the motor shaft) components of dart deformation and resulting force against the flywheel surface. Dealing only with the vertical component of the normal force is a relic of the cylindrical era, when the horizontal component was always zero.
Key element two is fairly obvious in my book. The whole reason to 