Manual methods to compact base for concrete?
When I was younger and worked in foundation construction we made our own effective manual soil compactors. They consisted of two parts, a pipe handle and a round base. The handle was a five or six foot long piece of 1" galvanized pipe. The base was a cast iron wheel hub from junk yard similar to that pictured below. The hubs were about six or seven inches in diameter and weighed enough that they easily absorbed the shock when tamped to the ground. 



The pipe handle was threaded into a pipe fitting that was welded into the center hole of the hub. (Obviously the grease cover of the hub was discarded). If I recall there was no issue of the bottom side of the hub having a small diameter center hole. Use of the compactor was a good amount of exercise and always seemed to be assigned to us young folks at the time by my father who was the foreman.