This is a thread I have been meaning to start, but have shyed away because I don't have the time to do it properly right now, I am just slammed with work responsibilities and it's really cutting into my FTF time.
In short, you have to define what kind of AR application you are looking at doing the swap on.
If your weapon is a 16" barrelled, bare bones, SHTF, street to street shooter with 100 yard shots being "of distance"
AND you don't intend on putting thousands of rounds through it in a short period of time - than you probably don't need a free float tube, nor will you necessarily "benefit" from what it offers.
If on the other hand you have the same 16" barrel and you are going to shooting thousands of rounds, that plastic foreend is going to heat up quickly and become uncomfortable. Free floating allows for the heat to
dissipate quickly and keep it away from the shooter's front hand.
Okay, that takes care of the basic application models.
If you want to shoot at distance ( varmint hunting, target shooting at 400-500 yards, Tactical Support Weapon

) you need a free floated fore end for your weapon. And here is why.
As was indicated above, everytime a round is fired there are harmonics that are introduced to the barrel from where it is attached to the front of your receiver all way up to the point the round and gas pressure leave your barrel.
Harmonics are introduced on three axis (X, Y, & Z). You have torque from the bullet hitting the rifling and wanting to reverse twist the barrel as opposed to the bullet entering the rifling. You have back pressure from the gas explosion behind the round as it initially becomes "blocked" by the rifling and doesn't immediately want to start spinning ( an object in motion tends to stay in motion thing - in this case the bullet is not spinning and just wants to go forward ). And then you have "barrel waiver" as the round gets further down the rifling, develops it's spin, but is much further away from the lock down point of the front of your receiver ( much like you could use a crowbar on a man hole cover, but couldn't lift it with a pair of pliers = leverage ).
IF your barrel can react to those X, Y, & Z variables the same way everytime you pull the trigger, your group sizes will be more accurate and your overall accuracy will be better. That is why any competition boltgun has a FREE FLOATED barrel.
Now, if you have X, Y, or Z being influenced by adding tension from a sling, bracing the fore end across the roof of a car hood or the like, than the repeated harmonics that the barrel had shown you in previous shots will be altered.
Think about throwing a rock into a still puddle. The rings move outward at an even pace in 360 degrees from where the rock landed, right? Now, if throw the same rock into the same puddle, but on one side of the puddle is a barrier of some sort, the ripples are going to start the same, but when they encounter the barrier, they will change. Move the barrier slightly and the following set of ripples will also react differently. Remove the barrier all together and the ripples are back to reacting as they did the first time.
It's all about harmonics and physics of what is going on when you touch off that one round when it comes down to REAL accuracy.
I hope that helps, I just don't have the time to do this up right with pictures and examples. Sorry.
JD