Orthogonal subsets of root systems and the orbit method

Let $k$ be the algebraic closure of a finite field, $G$ a Chevalley group over $k$, $U$ the maximal unipotent subgroup of $G$. To each orthogonal subset $D$ of the root system of $G$ and each set $\xi$ of $|D|$ nonzero scalars in $k$ one can assign the coadjoint orbit of $U$. It is proved that the dimension of such an orbit does not depend on $\xi$. An upper bound for this dimension is also given in terms of the Weyl group.