Flying only a genny should give you lee helm, not weather helm as a general rule. Of course, losing the rudder moves the center of lateral resistance forward, since the rudder is a large portion of the underwater lateral plane on a fin keeled boat.
Towing a drogue, with more resistance than plain warps, from a bridle would have probably allowed you to keep the boat on a relatively straight course.
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You know what the first rule of sailing is? ...Love. You can learn all the math in the 'verse, but you take
a boat to the sea you don't love, she'll shake you off just as sure as the turning of the worlds. Love keeps
her going when she oughta fall down, tells you she's hurting 'fore she keens. Makes her a home.
—Cpt. Mal Reynolds, Serenity (edited)
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Still—DON'T READ THAT POST AGAIN.