Crowning a barrel

Ok , I know of crowning a board for construction purposes. But I know jack doodley when it comes to barrels. So... 1- what is the intent when you crown a barrel? 2- how do you know when your barrel needs to be crowned? 3- how does crowning a barrel help with accuracy because to my mind a crowning effort in wood is to minimize the bend. If a barrel has a bend won’t that cause a pellet swirl / spiral in the direction of the bend? 
 
Someone here will have a better answer, but as I understand it, the crown is on the muzzle where the pellet exits. The muzzle must be square to the barrel so the gases escape around the pellet evenly. A crown can be straight across or recessed to protect the the area. Some muzzles use a specific angle on the crown and others are have arcs.
 
Agreed, the crown is the last part of the barrel touching the pellet before it goes out into the world so the idea is to ensure it has no burr left over from machining, and that it's perpendicular to the bore so the gases behind the pellet will release uniformly as the pellet emerges.

Here's a prior thread on the subject that may offer some more insight:
https://www.airgunnation.com/topic/anyone-using-an-11-degree-crown-on-a-pcp-barrel/

Sometimes a barrel will group well with a poor crown but gunsmiths and hobbyists alike will usually take great care to ensure it's done right.

It's possible to get good results with a handheld drill and brass screw. Here's one done that way:


Tips and tricks:
https://www.gatewaytoairguns.org/GTA/index.php?topic=130555