[math-fun] yacht question
Do the front and back of a yacht travel the same distance? (Let's assume that the earth is flat for purposes of this problem.) 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? Jim Propp
What assumptions are you making? --Dan On 2013-06-24, at 1:55 PM, James Propp wrote:
Do the front and back of a yacht travel the same distance?
(Let's assume that the earth is flat for purposes of this problem.)
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?
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. Jim Propp On Monday, June 24, 2013, Dan Asimov <dasimov@earthlink.net> wrote:
What assumptions are you making?
--Dan
On 2013-06-24, at 1:55 PM, James Propp wrote:
Do the front and back of a yacht travel the same distance?
(Let's assume that the earth is flat for purposes of this problem.)
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?
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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.
Jim Propp
On Monday, June 24, 2013, Dan Asimov <dasimov@earthlink.net> wrote:
What assumptions are you making?
--Dan
On 2013-06-24, at 1:55 PM, James Propp wrote:
Do the front and back of a yacht travel the same distance?
(Let's assume that the earth is flat for purposes of this problem.)
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?
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-- Mike Stay - metaweta@gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com
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?
To travel in a circle requires acceleration toward the center, which requires a force in that direction. A ship or yacht generates lateral force on the hull/keel by having an angle between the direction the vessel is pointing and its veolcity vector. It points inward relative to the circle, so the bow travels a smaller radius and less far than the stern. Brent Meeker On 6/24/2013 2:50 PM, James Propp 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.
Jim Propp
On Monday, June 24, 2013, Dan Asimov <dasimov@earthlink.net> wrote:
What assumptions are you making?
--Dan
On 2013-06-24, at 1:55 PM, James Propp wrote:
Do the front and back of a yacht travel the same distance?
(Let's assume that the earth is flat for purposes of this problem.)
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?
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Henry Baker: << The real question is why boats stear from the rear (other than the fact that it is more comfortable for the captain to be there (not crashing up & down in the front), and perhaps it is the case that even with more modern technology, no one bothered to re-think where the best place to put the rudder would be. >> On a small motor vessel driven by a single screw propeller, a considerable amount of steering force is generated by the action of the propeller stream on the rudder, which therefore has to be in line with and adjacent to the propeller. Given an inboard engine and the necessity for the thrust to lie along the axis, the only alternative would be to mount both at the bow, where they constitute a menace to themselves and everything else in the vicinity, and are lifted clear of the water at speed by the bow wave. WFL On 6/24/13, meekerdb <meekerdb@verizon.net> wrote:
To travel in a circle requires acceleration toward the center, which requires a force in that direction. A ship or yacht generates lateral force on the hull/keel by having an angle between the direction the vessel is pointing and its veolcity vector. It points inward relative to the circle, so the bow travels a smaller radius and less far than the stern.
Brent Meeker
On 6/24/2013 2:50 PM, James Propp 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.
Jim Propp
On Monday, June 24, 2013, Dan Asimov <dasimov@earthlink.net> wrote:
What assumptions are you making?
--Dan
On 2013-06-24, at 1:55 PM, James Propp wrote:
Do the front and back of a yacht travel the same distance?
(Let's assume that the earth is flat for purposes of this problem.)
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?
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So, a rocket, if it has the speed and acceleration just right, can go in a circle with its exhaust (stern) outside of the circle and the bow inside of the circle--so the bow would traverse a smaller distance. Alternately, if the rocket is in a circular orbit and its spin is phase locked (like the moon), one could pick either the stern or the bow to be continually facing inward. One could fiddle with the center of mass and the shape of all these things to magnify the difference. One could envision a yacht whose CM is equidistant from the bow and the stern, heading straight out, coasting to a stop, then twisting about the CM 180 deg, then heading back straight, so that the distance travelled is the same for the bow and the stern. I suppose that, like most objects, if the CM is towards the bow, the motion might be somewhat more stable; if that is true for yachts, then I would guess that the stern travels a slightly longer path. There is something called the center of pressure (if I recall correctly), which might affect the estimates. -----Original Message----- From: math-fun-bounces@mailman.xmission.com [mailto:math-fun-bounces@mailman.xmission.com] On Behalf Of James Propp Sent: Monday, June 24, 2013 2:55 PM To: math-fun Subject: [EXTERNAL] [math-fun] yacht question Do the front and back of a yacht travel the same distance? (Let's assume that the earth is flat for purposes of this problem.) 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? Jim Propp _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com http://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
participants (7)
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Cordwell, William R -
Dan Asimov -
Fred lunnon -
James Propp -
John Aspinall -
meekerdb -
Mike Stay