I am trying to figure out how to declare a plane angle to be dimensionless. In the code I have so far I am using:

typedef boost::units::make_system

boost::units::angle::radian_base_unit >::type myproject_system_t;

I have one velocity in radii^1.5/min and a second velocity in radian/min. When I divide the radii^1.5/min by radian/min I am expecting to see radii to be the final dimension. What I am seeing is the denominator has radians in it. Here is my equation

ke = radii^1.5/min

n = radian/min

a1 = ( ke / n ) ^ (2/3)

The 'min' dimension cancel out so I am left with radii^1.5/radian before applying the power of 2/3. Applying the power of 2 I see the units are radii^3/radian^2 and then the 1/3 to get a final of radii/radian^(2/3).

This is clearly not dimensionally correct, so the library is doing what is promises... Your quantity in radian/min is not a velocity, it is an angular velocity. Somewhere your equations are implicitly assuming that the object is moving on (probably) a circular trajectory of known radius. In that case, the velocity is n * x where x is the radius in question (which has units meters/radian.

According to the almighty Wikipedia the radian angle is a dimensionless term. I am wondering what is the recommended course of action I should be taking here?

Either deal correctly with radians as units or just use a bare value_type for them. Matthias