On 6/24/2013 7:51 PM, James Propp wrote:
Mike Stay's argument seems sound; after all, if you had a mile-long rod sticking out of the front of your boat, and you called it part of the boat, the "front of the boat" (i.e., the tip of the rod) would travel farther than anything else if you steered a wiggly course. So, with enough asymmetry between how far the bow and stern protrude beyond the front and back edges of the keel, the effect Mike describes could be real.
On the other hand, Brent Meeker has some kind of vector physics argument in mind, and I suspect I'll find it convincing once I understand it! Does anyone else follow his reasoning, and if so, can they explain it to me?
As Fred Lunnon noted the function of the rudder is to change the direction the hull points. The change in direction that it moves is due to the lateral force on the hull and keel (which in fact is opposite the force on the rudder). This lateral force originates from the hull moving at an angle relative to its symmetry axis, which is called the "angle of attack" in hydrodynamics.
It's possible that there two different effects here, working in opposite directions, and that deciding which one dominates in the real world could be delicate.
But I think both Mike and Brent would agree that the point that travels farthest is either going to be the bow or the stern.
Actually not. If you're going to count protuberances, one could imagine a boom or a gangway extending out from the hull toward the outside of the turn so that ITs end travels further than either the bow or the stern. To make sense of the problem I think one should consider only the functional part of the hull, i.e. roughly the part along the water line.
I got this problem from a new book called "Paradoxes and Sophisms in Calculus", by Sergiy Klymchuk and Susan Staples. On page 14, the authors ask: "A yacht returns from a trip around the world. Different parts of the yacht have covered different distances. Which part of the yacht has covered the longest distance?" On page 59, they give the following answer: "The top of the yacht has covered the longest distance. The shape of the Earth is approximately spherical, so the top of the yacht has the longest radius compared to lower parts and therefore has the longest circumference." I found this unconvincing. Specifically, I think that this "altitude effect" is dwarfed by other effects, like the ones you guys have mentioned.
Jim Propp
On Mon, Jun 24, 2013 at 7:20 PM, meekerdb <meekerdb@verizon.net> wrote:
On 6/24/2013 3:47 PM, Cordwell, William R wrote:
Speaking of wheels turning, in many old movies, the stagecoach wheels seem to be turning backwards--is that simply an effect of the film frequency and the wheel angular frequency?
Yeah, that's just frequency aliasing as the film frame rate and the wheel spoke rate cross over. You also see it in movies of aircraft propellors as the engines start up.
Brent Meeker
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