No need for tarps if you are in a big tent already, Arnoud.
Looks like you'll need to make turtle-type stands. Two hammocks could share one tower so you'd need one tower more than the number of hammocks, where A=tower and ~=hammock: A~A~A~A
There are several versions of them discussed and pictured on this site.
I'd like to have one made of bamboo. It's a strong and light natural material.
But Jesus often withdrew to lonely places and prayed. (Luke 5:16 NIV)
He said to them, “But now let the one who has a moneybag take it, and likewise a knapsack. And let the one who has no sword sell his cloak and buy one." (Luke 22:36 ESV)
While people are saying, “There is peace and security,” then sudden destruction will come upon them as labor pains come upon a pregnant woman, and they will not escape. (1 Thessalonians 5:3 ESV)