To survive an arid environment, desert cacti are capable of harvesting water from fog by transporting condensed water drops using their spines. Cactus spines have a conical shape. In this work, on the basis of the difference of liquid pressure, a new theoretical model has been developed for a barrel-shaped liquid drop on a conical wire. This model is further simplified to interpret the effects of contact angles, conical angle, surface microgrooves, and gravity on the drop movement along a cactus spine.