I think we can say a little more, without any contention. A reasonable model of a yacht is that it's a rigid object, and a reasonable model of "sailing in a circle" is that some point on that rigid object is moving tangent to some fixed circle. Only slightly less reasonable is that the yacht have a plane of symmetry passing from bow to stern. (I think we can relax this later.) Now consider the "tight turn" limit, where the length of the yacht is starting to get comparable to the radius of the turn. A point near the bow _may_ be traveling in a circle, but I'm quite willing to bet that the circle is not tangent to the plane of symmetry. The point that is (a) in the plane of symmetry, and (b) is traveling tangent to the plane of symmetry, is the key point on the yacht for this discussion. I suspect that the "key point" is mostly determined by the underwater geometry of the yacht, in particular the shape of the keel. There will be a center of thrust, or more pedantically a center of fluid resistance to moving sideways. That'd be my first candidate for the key point. On 06/24/2013 06:09 PM, Mike Stay wrote:
The bow of a yacht extends in front of the highest point on the hull that the water reaches, thus almost certainly travels on a circle of a larger radius.
On Mon, Jun 24, 2013 at 4:50 PM, James Propp <jamespropp@gmail.com> wrote:
I intended this to be an applied math question, not a pure math question. So I'm asking about real yachts, not models thereof, and the only assumption I'm making is that reasonable people can agree on what counts as a yacht and what doesn't.
Here's a question that I think is equivalent: If a yacht travels in a circle, do the front and back ends of the yacht travel on circles of the same radius?