I have been thinking of putting a sail on my canoe with will probably require the use of an outrigger. (related: Outrigger and/or leeboard when sailing a canoe?) I was thinking about using a section of PVC pipe as an outrigger, this reference indicates a 4 inch pipe will hold 0.653 gallons of water per foot weighing 5.44 pounds, a 5 inch pipe will hold 1.02 gallons at 8.50 pounds. Every pound of water displaced is a pound of lift. The farther out you place the outrigger the more leverage is applied, but at the same time it applies more strain to the arm that connects the outrigger to your vessel
The first image below could be considered two outriggers with a sail between them. At this point my mind spirals out of control with all the variables. If the base was wide enough they would not tip, but then it would require stronger cross bars, which would add more weight...
Many of the off the shelf out riggers for canoes, only have a couple feet long arms with volume of a couple of gallons, but if you see professional sea going outriggers they have much larger volumes with much longer arms (second image).
What are the basic things I need to consider and how do I calculate how much lift I need from an outrigger? I am planning on inland water (river, lake) sailing, so will not be at the extremes in the images, but I want to understand the principles required to keep the canoe from tipping over, and keep away from putting to much pressure on the outrigger.