  For high energy processes ($M\gg \Lambda_{QCD}$) there are infrared safe
hadronic shape variables that have a calculable perturbative expansion in
$\alpha_s(M^2)$. However, nonperturbative power suppressed corrections to these
variables are not well understood. We use the behavior of large orders of the
perturbation expansion to gain insight into the nonperturbative corrections.
Our results suggest that certain shape variables have nonperturbative
corrections suppressed by fractional powers of $\Lambda_{QCD}^2/M^2$.
