In theory, the braking performance could be the same as the bicycle. In practice, the rider needs to guess the traction very precisely and to move their weight backwards to an angle just a smidge higher than arctan(static friction coefficient). Do you start to see a problem here?
While the bicycle rider only needs to move their weight so that the combined center of mass is projected between the contact patches of the wheels during the deceleration, the EUC rider absolutely needs this to be as close to the contact patch as possible. Shifting the weight too far back means an almost guaranteed wipeout, and you don’t know if the road is squeaky clean or has some trace amounts of sand that would reduce traction, so any sane rider would err on the side of caution and under-brake to avoid falling on their back.
>arctan(static friction coefficient)
>needs this to be as close to the contact patch as possible
That's not true, or perhaps you mean something other than how those words are directly interpreted? Static friction force isn't an arctan, it's just the normal force (which is you+wheel weight) x the friction coefficient. That's the force that's slowing your motion. And being close or far from the contact patch doesn't affect that at all. Elaborate what you're thinking?
Arctan(friction coefficient) gets you the "friction angle", which is a meaningful angle to know in a lot of physical systems. For example, it tells you how steep of an angled surface your object can rest on before it starts sliding downhill.
In this case, it sounds like the friction angle is important because it's the angle at which the reaction force is being applied to the unicycle by the road. (The normal force and friction force components make a right triangle with the resultant force, and their ratio - the friction coefficient - is by definition the tangent of that angle). I know nothing specific about unicycles, but it sounds like they're saying the rider needs to lean back so that the "shaft" between the seat and the axle is oriented along that line of force or else the system will become unstable.
Did you ever ride on one? They brake using the motor so it doesn't wipe you out. At worst you stand on the ground, but mostly you just start riding backwards.
I own one and I can assure you it’s very easy to fall on your back if you overestimate the friction when braking aggressively. Not even close to real life bike braking with disc brakes if you know how to transfer your weight properly (granted, a newbie would totally fly over the handlebars if they tried to brake to the limit without shifting their weight behind the seat..)
Odd - I ride EUC and bike mainly, and bike is easier to skid on accident. Opposite experience as you. It makes sense too, since on an EUC 100% of the normal force is utilized for friction force. On a bicycle you can only utilize 100% if you're extremely good at applying the front and back brake at the perfect ratio to each other.
While the bicycle rider only needs to move their weight so that the combined center of mass is projected between the contact patches of the wheels during the deceleration, the EUC rider absolutely needs this to be as close to the contact patch as possible. Shifting the weight too far back means an almost guaranteed wipeout, and you don’t know if the road is squeaky clean or has some trace amounts of sand that would reduce traction, so any sane rider would err on the side of caution and under-brake to avoid falling on their back.