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When I went to North U. they swore that running dead downwind was simply wrong no matter how it happened. And, after a long discussion about that, and two blown chutes (so all we could do was sit back and watch the fleet go away) we saw that the boats sailing way over there and there and taking the long way--were getting ahead of the boats going straight downwind.
So I got religion and swore off going dead downwind.
Then I met some folks with another boat of a different design, a smaller older boat. We were trying to work on boatspeed but they swore that boat went fastest dead downwind using the 150 and main, no chute available. Funny thing about that...I ran the polars, and they said the same thing! Then we ran some trial runs on the water...and reality agreed with the polars and experience!
Having seen both sides of "THE" answer, I can tell you that your best boat, for YOUR boat with YOUR sails, is to run the polars (if you can) and then get out on the water and actually do a test. There's no other "rule" that is going to give you the right answer, apparently a lot depends on the rig and the hull.
Now, maybe if you limit the question to whether using a chute is going to be faster dead downwind or gybing....There, I think if you are finding it faster to go dead downwind, there's something else wrong with the picture!
Again, there's nothing like sitting back and watching the fleet to see how the "slow" boats actually are the faster ones. Sometimes it pays to train, and skip a race, so you can do things like that and concentrate on getting things right instead of winning the day.