  We study the dependence of the exposure required to directly detect a WIMP
directional recoil signal on the capabilities of a directional detector.
Specifically we consider variations in the nuclear recoil energy threshold, the
background rate, whether the detector measures the recoil momentum vector in 2
or 3 dimensions and whether or not the sense of the momentum vector can be
determined. We find that the property with the biggest effect on the required
exposure is the measurement of the momentum vector sense. If the detector
cannot determine the recoil sense, the exposure required is increased by an
order of magnitude for 3-d read-out and two orders of magnitude for 2-d
read-out. For 2-d read-out the required exposure, in particular if the senses
can not be measured, can be significantly reduced by analyzing the reduced
angles with the, time dependent, projected direction of solar motion
subtracted. The background rate effectively places a lower limit on the WIMP
cross-section to which the detector is sensitive; it will be very difficult to
detect WIMPs with a signal rate more than an order of magnitude below the
background rate. Lowering the energy threshold also reduces the required
exposure, but only for thresholds above 20 keV.
