Help TD engineers.....roof spars question (six wide TTT)

Ok...I'm to the point in my build where I've got to figure in roof spars. Never having built anything like a small camper I'm basically clueless as to how wide/thick these will need to be.
This camper will be 6' wide. the roof will have 1/4"paneling inside, 1/4" luan outside. I'm using spruce lumber. Would 1 1/2"x 2" be strong enough for that span?
This camper will be 6' wide. the roof will have 1/4"paneling inside, 1/4" luan outside. I'm using spruce lumber. Would 1 1/2"x 2" be strong enough for that span?