  In this paper, we study on the characterizations of loxodromes on the
rotational surfaces satisfying some special geometric properties such as having
constant Gaussian curvature, flat and minimality in Euclidean 3-space. First,
we give the parametrizations of loxodromes parametrized by arc-length parameter
on any rotational surfaces in $\mathbb{E}^{3}$ and then, we calculate the
curvature and the torsion of such loxodromes. Then, we give the
parametrizations of loxodromes on rotational surfaces with constant Gaussian
curvature. In particular, we prove that the loxodrome on the flat rotational
surface is a general helix. Also, we investigate the loxodromes on the
rotational surfaces with a constant ratio of principal curvatures (CRPC
rotational surfaces). Moreover, we give the parametrizations of loxodromes on
the minimal rotational surface which is a special case of CRPC rotational
surfaces. Then, we show that the loxodrome intersects the meridians of minimal
rotational surface by the angle $\pi/{4}$ becomes an asymptotic curve. Finally,
we give some visual examples to strengthen our main results via Wolfram
Mathematica.
