Re: Problem Turning Windward
I think DavidPM answered the questions you had for me...but I'll repeat.
1 - why does fighting with the tiller slow you down? Anytime the rudder is more than 2-3 degrees away from straight fore and aft, it's creating drag. If your arm gets tired from working against rudder pressure, you're creating drag - guaranteed.
2 - be careful about generalizing - sail trim CAN help you turn a boat...but not the way you tried to do it. Imagine the sail is a flat plywood board. (I know it has shape - but this simplifies it in my mind) If the board is at 45 degrees to the wind, the wind is creating movement in 2 directions - leeward and forward. In a zero-energy-loss environment, a 10kn wind would create 5kn of leeward force, and 5kn of forward force. This is what makes the boat move forward. the 5kn of leeward force is countered by the keel. Additionally, this is the force that causes the boat to heel.
Back to the board. Imagine now, that it is 90 degrees to the wind (if you could sheet the sail in tight, straight back on the centerline. All 10kn of force are now leeward. Because the sail (board) area is ahead of the pivot point of the boat, all of that leeward force is pushing your bow downwind, while providing zero forward forces. In this case, you're better off leaving the sail looser, and steering up into the wind, until the sail luffs, then trim a bit, then steer up a bit, etc....
I'm sorry to those who know much more about this than I do - I know I'm over-simplifying. These are just simple images that make sense to me.