Symmetry

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KAM

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Should the mast be symmetrical to boat geometry or perpendicular with the water assuming the boat is evenly loaded.
 
I think not necessarily either!

Few masts are in a central position fore-and-aft.
Most seem to be central port-starboard - but mine isn't; the mast is offset to port.

A lot of masts look vertical with respect to the water, but I suspect many will have a slight rake to them. Some masts are quite steeply raked, either backwards (think American schooners) or forwards (think foremast on a junk rigged schooner or ketch)

Assuming I've correctly interpreted what you mean by symmetrical...
 
Athwartships, most boats have the mast in the middle, but not all. Mine, as I said, is offset to port though not by a lot. Of course it's a different game again with catamarans.
And if you do place a mast anything other than centrally athwartships, be prepared for comments!
The issues with an off centre mast will be weight distribution, lateral position of the centre of effort, and (if it's a stayed mast), the positioning of the standing rigging.
In my case, the mast is unstayed. The rig is a junk sail, so it lies to one side of the mast. I've put my mast offcentre by half a mast diameter. This means that the sail is on the centreline. It also means that the keel-stepped mast doesn't lie on the centreline, so it's easier to fit inside the accommodation.
 
I don't think it matters when sailing. However as intimated it might look odd when viewed from shore. I had a friend tell me my little boat needed rake on the mast. In fact it did havwe rake but at the mooring at the time I hauled the mooring buoy up onto deck so weight of the chain was on the bow giving a bow down pitch to the boat. When sailing however with 4 people in cockpit it was decidedly stern down so lots of mast rake. For OP I would tend to set mast vertical by adjusting cap shrouds to equal length. That should bring close to vertical to hull. Then adjust balance to make it look right on mooring. When sailing it will never be vertical. ol'will
 
I don't think it matters when sailing. However as intimated it might look odd when viewed from shore. I had a friend tell me my little boat needed rake on the mast. In fact it did havwe rake but at the mooring at the time I hauled the mooring buoy up onto deck so weight of the chain was on the bow giving a bow down pitch to the boat. When sailing however with 4 people in cockpit it was decidedly stern down so lots of mast rake. For OP I would tend to set mast vertical by adjusting cap shrouds to equal length. That should bring close to vertical to hull. Then adjust balance to make it look right on mooring. When sailing it will never be vertical. ol'will
The fact that serious racers spend a great deal of time and effort to ensure their mast is perfectly symmettrical should tall you it matters. Your boat will sail differently on port and starboard tack if it’s not. In fact that’s one of the telling signs that something is amiss up there. Rake, do what feels right to you, but athwart, exactly upright, no compromise. I treat my cruiser the same as my racer in that respect.
 
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