With a view to optimizing the design of carbon-nanotube (CNT) windmills and to maximizing the internal magnetic field generated by chiral currents, we present analytical results for the group-velocity components of an electron flux through chiral carbon nanotubes. Chiral currents are shown to exhibit a rich behavior and can even change sign and oscillate as the energy of the electrons is increased. We find that the transverse velocity and associated angular momentum of electrons are a maximum for nonmetallic CNTs with a chiral angle of 18 degrees. Such CNTs are therefore the optimal choice for CNT windmills and also generate the largest internal magnetic field for a given longitudinal current. For a longitudinal current of order 10(-4) A, this field can be of order 10(-1) T, which is sufficient to produce interesting spintronic effects and a significant contribution to the self-inductance.