  We present measurements of the spin-orbit alignment angle, lambda, for the
hot Jupiter systems WASP-32, WASP-38, and HAT-P-27/WASP-40, based on data
obtained using the HARPS spectrograph. We analyse the Rossiter-McLaughlin
effect for all three systems, and also carry out Doppler tomography for WASP-32
and WASP-38. We find that WASP-32 (T_eff = 6140 +90 -100 K) is aligned, with an
alignment angle of lambda = 10.5 +6.4 -6.5 degrees obtained through tomography,
and that WASP-38 (T_eff = 6180 +40 -60 K) is also aligned, with tomographic
analysis yielding lambda = 7.5 +4.7 -6.1 degrees. This latter result provides
an order of magnitude improvement in the uncertainty in lambda compared to the
previous analysis of Simpson et al. (2011). We are only able to loosely
constrain the angle for HAT-P-27/WASP-40 (T_eff = 5190 +160 -170 K) to lambda =
24.2 +76.0 -44.5 degrees, owing to the poor signal-to-noise of our data. We
consider this result a non-detection under a slightly updated version of the
alignment test of Brown et al. (2012). We place our results in the context of
the full sample of spin-orbit alignment measurements, finding that they provide
further support for previously established trends.
