above ground pole support for sail cloth
It will be very hard to give guidance as to if a particular size of base will be adequate for your application. Here are some of the variables to consider:


Length of the metal pipe that holds the sail cloth. The longer (and presumed higher) this pole the more lateral leverage it can apply to the base.
Span of the sail cloth overhead. The longer span you have for the sail cloth the more tension it will place on the metal poles and in turn on the base. 
Placing the base into the ground. I know that you desire a mobile application but be aware that putting the base assembly into the ground will give it a lot more stability that just letting it sit at ground level. It would also look a lot better than having a huge block of concrete sitting there. I can easily imagine a buried base that would only project enough from the ground level so that the dirt and debris does not easily get into the slide in hole for the metal poles.


Do also consider that even at the size you asked about that these bases would not be so "mobile". Concrete weighs approximately 150 pounds per cubic foot. A 16" (i.e. 1.333 feet) diameter concrete pillar 4 feet high is going to be:



V = 3.1415 x 0.666 feet x 0.666 feet x 4 feet

V = 5.57 cubic feet

Weight = 5.57 x 150 pounds

Weight = 836 pounds

That does not seem particularly mobile to me.