  We present Rossiter-McLaughlin observations of WASP-13b and WASP-32b and
determine the sky-projected angle between the normal of the planetary orbit and
the stellar rotation axis ($\lambda$). WASP-13b and WASP-32b both have prograde
orbits and are consistent with alignment with measured sky-projected angles of
$\lambda={8^{\circ}}^{+13}_{-12}$ and $\lambda={-2^{\circ}}^{+17}_{-19}$,
respectively.
  Both WASP-13 and WASP-32 have $T_{\mathrm{eff}}<6250$K and therefore these
systems support the general trend that aligned planetary systems are
preferentially found orbiting cool host stars. A Lomb-Scargle periodogram
analysis was carried out on archival SuperWASP data for both systems. A
statistically significant stellar rotation period detection (above 99.9\%
confidence) was identified for the WASP-32 system with $P_{\mathrm{rot}}=11.6
\pm 1.0 $ days. This rotation period is in agreement with the predicted stellar
rotation period calculated from the stellar radius, $R_{\star}$, and $v \sin i$
if a stellar inclination of $i_{\star}=90^{\circ}$ is assumed. With the
determined rotation period, the true 3D angle between the stellar rotation axis
and the planetary orbit, $\psi$, was found to be $\psi=11^{\circ} \pm 14$. We
conclude with a discussion on the alignment of systems around cool host stars
with $T_{\mathrm{eff}}<6150$K by calculating the tidal dissipation timescale.
We find that systems with short tidal dissipation timescales are preferentially
aligned and systems with long tidal dissipation timescales have a broad range
of obliquities.
