Re: [math-fun] yacht question
The front wheel of a bicycle travels more than the rear wheel, because it is the steering wheel. (The rear wheel track always points at the direction of tangent contact of the front wheel, more-or-less.) I would imagine that since the rudder in a (prototypical) yacht is in the rear, that the rear end of a yacht travels further than the front end. On submarines & some very large ships, they have front rudder-like steering apparatuses, as well, so perhaps they are more balanced. 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. A little-known 'turning point' in history took place right around the turn of the century 1900, when the rudder wheels started turning in the direction of the turn, instead of the reverse, which had been standard up until then. This change may have been done to make it consistent with those new-fangled automobiles. Many movies get this wheel direction/turning direction relationship of these older ships wrong. http://en.wikipedia.org/wiki/Ship's_wheel At 01:55 PM 6/24/2013, 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?
Jim Propp
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? -----Original Message----- From: math-fun-bounces@mailman.xmission.com [mailto:math-fun-bounces@mailman.xmission.com] On Behalf Of Henry Baker Sent: Monday, June 24, 2013 4:42 PM To: math-fun Subject: [EXTERNAL] Re: [math-fun] yacht question The front wheel of a bicycle travels more than the rear wheel, because it is the steering wheel. (The rear wheel track always points at the direction of tangent contact of the front wheel, more-or-less.) I would imagine that since the rudder in a (prototypical) yacht is in the rear, that the rear end of a yacht travels further than the front end. On submarines & some very large ships, they have front rudder-like steering apparatuses, as well, so perhaps they are more balanced. 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. A little-known 'turning point' in history took place right around the turn of the century 1900, when the rudder wheels started turning in the direction of the turn, instead of the reverse, which had been standard up until then. This change may have been done to make it consistent with those new-fangled automobiles. Many movies get this wheel direction/turning direction relationship of these older ships wrong. http://en.wikipedia.org/wiki/Ship's_wheel At 01:55 PM 6/24/2013, 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?
Jim Propp
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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
At frame rates of 24fps (the current US movie standard -- very close to the European 25fps TV standard), many 'fast' motions produce 'aliasing'/'strobing', including wagon wheels, airplane propellors, etc. Fast 'pans' of the camera will also produce unpleasant strobing/stuttering effects if a surface has a repetitive pattern. I once did an analysis to try to figure out what the 'maximum non-aliased pan rate' for a still image should be. I concluded that the pan couldn't move more than 1/2 a wavelength per frame for the highest spatial frequency (in the panning direction) in the image. That's an extremely slow pan for an image of any significant resolution. Of course, this slow a pan, or this fuzzy of an image is completely impractical, so you will always see artifacts. Hollywood people know how to minimize these artifacts, but amateurs violate these rules most of the time. Modern computer graphics cards can now render photorealistic 3D 1920x1080 at 60fps _in real time_, and some movies this past year are available in frame rates higher than 24fps. Many Hollywood people hate this non-film 'look', as it eliminates most of the last vestiges of the viewer not being in the scene along with the actors. Animated graphics can generate the correct frames for any frame rate you want, so they are 'frame-rate independent'. Movies can also be made 'frame-rate independent' by using sophisticated computer vision algorithms to figure out which objects are moving relative to other objects; once this is done, the 'in-between' positions can be simulated. In fact, the basic 'motion prediction' elements of the various MPEG standard video compression algorithms do a crude version of this analysis simply to reduce the number of bits that are required to be coded. At 04:20 PM 6/24/2013, meekerdb 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
On Mon, 24 Jun 2013, Henry Baker wrote:
Many Hollywood people hate this non-film 'look', as it eliminates most of the last vestiges of the viewer not being in the scene along with the actors.
Reference? I'd be really interested in knowing who says this.
Movies can also be made 'frame-rate independent' by using sophisticated computer vision algorithms to figure out which objects are moving relative to other objects; once this is done, the 'in-between' positions can be simulated.
Again: reference? In this case, I don't believe it (in general, though you can certainly fake it in some easy cases.) Aliases, once introduced, cannot reliably be removed. -- Tom Duff. Nothing's Beatleproof!
On 6/24/2013 5:16 PM, Tom Duff wrote:
On Mon, 24 Jun 2013, Henry Baker wrote:
Many Hollywood people hate this non-film 'look', as it eliminates most of the last vestiges of the viewer not being in the scene along with the actors.
Reference? I'd be really interested in knowing who says this.
My son, who works in CGI for movies and games, says there is a lot of discussion over such topics and preserving "the movie look" both in terms of frame rate and also lighting and color saturation.
Movies can also be made 'frame-rate independent' by using sophisticated computer vision algorithms to figure out which objects are moving relative to other objects; once this is done, the 'in-between' positions can be simulated.
Again: reference? In this case, I don't believe it (in general, though you can certainly fake it in some easy cases.) Aliases, once introduced, cannot reliably be removed.
That's right. But I think what was meant is that in creating a computer animation you can make it to be shown at any specified frame rate and not show aliasing at that rate. Of course this is one of the things that Hollywood types object to and CGI sequences will deliberately introduce the aliasing so "it looks like a movie", depending on the ambiance to be created. Brent
At 05:16 PM 6/24/2013, Tom Duff wrote:
On Mon, 24 Jun 2013, Henry Baker wrote:
Many Hollywood people hate this non-film 'look', as it eliminates most of the last vestiges of the viewer not being in the scene along with the actors.
Reference? I'd be really interested in knowing who says this.
Luckily, "The Hobbit" just came out in wide release at 48fps in December, 2012, so there's lots of articles online about this. Google "the hobbit" "frame rate". For example: http://gizmodo.com/5969817/the-hobbit-an-unexpected-masterclass-in-why-48-fp... "The Hobbit: An Unexpected Masterclass in Why 48 FPS Fails" "Therefore Peter Jackson decided to shoot the Hobbit in 48 fps to try to counter this effect, and to render a more realistic or what he deems "immersive" 3D experience if you will." "And he has indeed accomplished thatÂbut in doing so, he's killed a lot of the magic of what makes a film entrance an audience if you will, at least in my opinion. I did find myself become more "immersed" in the 3 dimensional environment and all of these details-Âbut to the detriment of the film and the narrative itself."
Movies can also be made 'frame-rate independent' by using sophisticated computer vision algorithms to figure out which objects are moving relative to other objects; once this is done, the 'in-between' positions can be simulated.
Again: reference? In this case, I don't believe it (in general, though you can certainly fake it in some easy cases.) Aliases, once introduced, cannot reliably be removed.
You are correct. The 'motion aliasing' isn't removed -- e.g., the backwards wagon wheels -- but some of the stuttering goes away. However, once again, critics hate the loss of the lower frame rate "film look", which Wikipedia dubs the "soap opera effect": http://en.wikipedia.org/wiki/Motion_interpolation 'The "video" look is a byproduct of the perceived increase in framerate due to the interpolation and is commonly referred to as the "soap opera effect", a reference to the distinctive appearance of most broadcast television soap operas, which were typically shot using less expensive 60i video rather than film. Some complain that the effect ruins the theatrical look of cinematic movies. For this reason, almost all manufacturers have built in an option to turn the feature off.'
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? 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. 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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Obviously this was a theoretical yacht, therefore totally pitch-, yaw- and roll-free --- and none of the crew ever gets sea-sick. But if it was a motor-yacht, the pistons in its engines reciprocated through at least twice the distance covered by any part of the keel. WFL Jim Propp: << 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. >> On 6/25/13, James Propp <jamespropp@gmail.com> 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?
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.
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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Then give three cheers, and one cheer more! On Mon, Jun 24, 2013 at 11:31 PM, Dan Asimov <dasimov@earthlink.net> wrote:
Well, hardly ever.
--Dan
On 2013-06-24, at 8:56 PM, Fred lunnon wrote:
and none of the crew ever gets sea-sick.
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-- Mike Stay - metaweta@gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com
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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Just like your problem, this one failed to state its assumptions. Maybe it's just me, but I could not be less interested in problems that fail to state their assumptions. We can debate what the assumptions should be till kingdom come, but each set of assumptions generally defines a different problem. Megayawn. --Dan Jim Propp wrote:
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.
On 6/24/2013 3:42 PM, Henry Baker wrote:
The front wheel of a bicycle travels more than the rear wheel, because it is the steering wheel. (The rear wheel track always points at the direction of tangent contact of the front wheel, more-or-less.)
I would imagine that since the rudder in a (prototypical) yacht is in the rear, that the rear end of a yacht travels further than the front end.
On submarines & some very large ships, they have front rudder-like steering apparatuses, as well, so perhaps they are more balanced.
If you look at air-to-air missiles, which also maneuver by fluid dynamic forces, you see all three placements. Some have the smaller movable fins at the front and then large fixed fins at the rear to keep stability. Some have the movable fins at the rear and fixed wings or narrow strakes just ahead along the after part of the body. And some had movable wings at the middle, near the center of gravity, with smaller fins at the rear for stability. Of course modern air-to-air missiles may have only marginal aerodynamic stability and rely on active controls for stable flight. Racing yachts are also designed to have only slight positive stability so that they will turn well. Normal yachts and ships probably have a large stability margin. But in almost any design the front is going to point inside the tangent to the turning circle because that's the way to be lateral force from the whole body, not just the movable fins. The only exception I know of were the older SPARROW air-to-air missiles which got all their lift from the movable wings located near the center of mass. They were designed this way so the radar wouldn't have to gimbal back and forth a lot as the wings moved; the body always just pointed along the velocity vector because of the fixed tail fins.
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.
Of course originally boats were steered with one of the oars (as you may still steer a canoe). It's hard to do this from the bow since you want the steering oar to trail behind the its pivot point; otherwise it's unstable. The reason the captain and the quarterdeck were at the rear was so he and the helmsman could easily see the sails and sailors while also being able to see the ship and it's relation to docks and buoys etc. On modern ships the quarterdeck is often well forward since the helmsman doesn't need to see the sails. Brent Meeker
A little-known 'turning point' in history took place right around the turn of the century 1900, when the rudder wheels started turning in the direction of the turn, instead of the reverse, which had been standard up until then. This change may have been done to make it consistent with those new-fangled automobiles. Many movies get this wheel direction/turning direction relationship of these older ships wrong.
http://en.wikipedia.org/wiki/Ship's_wheel
At 01:55 PM 6/24/2013, 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?
Jim Propp
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participants (8)
-
Cordwell, William R -
Dan Asimov -
Fred lunnon -
Henry Baker -
James Propp -
meekerdb -
Mike Stay -
Tom Duff