Street grid pattern
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From: Ron Peterson on 19 May 2010 10:44 Some cities have a rectangular grid pattern for their streets and in the worst case, trips can be 40% longer than a straight line trip. Other cities, have streets that follow the geography because of mountains, streams, and lakes with some trips being several times as long as a straight line trip. Is there a non-Cartesian grid pattern for a flat community that does better for the worst case than the Cartesian grid pattern? Am I asking the right question? -- Ron
From: Gordon Sande on 19 May 2010 10:58 On 2010-05-19 11:44:13 -0300, Ron Peterson <ron(a)shell.core.com> said: > Some cities have a rectangular grid pattern for their streets and in > the worst case, trips can be 40% longer than a straight line trip. > Other cities, have streets that follow the geography because of > mountains, streams, and lakes with some trips being several times as > long as a straight line trip. > > Is there a non-Cartesian grid pattern for a flat community that does > better for the worst case than the Cartesian grid pattern? > > Am I asking the right question? The trivial solution is to pave everything and just go! No very useful so try specifying some constraints on how much area you are willing to give to streets and how small the other pieces can be. Will some roads need to be bigger than others? Etc? Etc?
From: alexy on 19 May 2010 11:57 Ron Peterson <ron(a)shell.core.com> wrote: >Some cities have a rectangular grid pattern for their streets and in >the worst case, trips can be 40% longer than a straight line trip. Actually, that is true only for a long trip. Worst case is a trip from x street, midway between y avenue and y+1 avenue to the same place on x+1 street. As the crow flies, it is 1 block, but by road it is 2 blocks, a 100% longer trip. >Other cities, have streets that follow the geography because of >mountains, streams, and lakes with some trips being several times as >long as a straight line trip. > >Is there a non-Cartesian grid pattern for a flat community that does >better for the worst case than the Cartesian grid pattern? With streets laid out in equilateral triangles, the worst case is a 75% longer (actually sqrt(3)-1) trip, but unlike the square blocks, the potential inefficiency doesn't decrease with distance. So the triangles are better for short trips, but worse for long ones. >Am I asking the right question? Hard to know -- it's your question! :) -- Alex -- Replace "nospam" with "mail" to reply by email. Checked infrequently.
From: Mike Terry on 19 May 2010 12:48 "alexy" <nospam(a)asbry.net> wrote in message news:ht11oe$l3t$1(a)news.eternal-september.org... > Ron Peterson <ron(a)shell.core.com> wrote: > > >Some cities have a rectangular grid pattern for their streets and in > >the worst case, trips can be 40% longer than a straight line trip. > Actually, that is true only for a long trip. Worst case is a trip from > x street, midway between y avenue and y+1 avenue to the same place on > x+1 street. As the crow flies, it is 1 block, but by road it is 2 > blocks, a 100% longer trip. > > >Other cities, have streets that follow the geography because of > >mountains, streams, and lakes with some trips being several times as > >long as a straight line trip. > > > >Is there a non-Cartesian grid pattern for a flat community that does > >better for the worst case than the Cartesian grid pattern? > > With streets laid out in equilateral triangles, the worst case is a > 75% longer (actually sqrt(3)-1) trip, but unlike the square blocks, > the potential inefficiency doesn't decrease with distance. So the > triangles are better for short trips, but worse for long ones. This seems the wrong way round to me. Also the 75% seems wrong... For a triangular grid: - max inefficiency for short trip is 100% - max inefficiency for long trip is about 15% For a square grid, both are about 41% So the triangles are better for LONG trips, but worse for SHORT ones?? If we assumed that there were a fixed number of terminal points rather than journeys being able to start/end anywhere on a road, then we could just join up all terminals with direct roads. (So this doesn't make much sense as a problem. Needs more restrictions on valid solutions etc.) Mike.
From: alexy on 19 May 2010 13:35
"Mike Terry" <news.dead.person.stones(a)darjeeling.plus.com> wrote: >"alexy" <nospam(a)asbry.net> wrote in message >news:ht11oe$l3t$1(a)news.eternal-september.org... >> Ron Peterson <ron(a)shell.core.com> wrote: >> >> >Some cities have a rectangular grid pattern for their streets and in >> >the worst case, trips can be 40% longer than a straight line trip. >> Actually, that is true only for a long trip. Worst case is a trip from >> x street, midway between y avenue and y+1 avenue to the same place on >> x+1 street. As the crow flies, it is 1 block, but by road it is 2 >> blocks, a 100% longer trip. >> >> >Other cities, have streets that follow the geography because of >> >mountains, streams, and lakes with some trips being several times as >> >long as a straight line trip. >> > >> >Is there a non-Cartesian grid pattern for a flat community that does >> >better for the worst case than the Cartesian grid pattern? >> >> With streets laid out in equilateral triangles, the worst case is a >> 75% longer (actually sqrt(3)-1) trip, but unlike the square blocks, >> the potential inefficiency doesn't decrease with distance. So the >> triangles are better for short trips, but worse for long ones. > >This seems the wrong way round to me. Also the 75% seems wrong... > >For a triangular grid: >- max inefficiency for short trip is 100% You are correct. I was thinking from the midpoint of one side to the opposite apex. But the greater inefficiency is from points on two sides, equidistant from the junction of their two sides (and not too close to the other end of the street). >- max inefficiency for long trip is about 15% I don't get this. Assume the streets are laid out (using compass points) 0-180, 60-240, and 120-300. If you want to go due east, you are forced to take roads heading either 60 or 120 to make eastward progress, and N-S roads to bring you back to the intended due east course. How can you do that with only 15% inefficiency? > >For a square grid, both are about 41% How do you get from 13th street, half-way between 1st and 2nd avenues, to 14th street, half-way between 1st and 2nd avenues while walking only 1.41 blocks? > >So the triangles are better for LONG trips, but worse for SHORT ones?? No, with your correction of my shart-trip inefficiency for the triangle, I believe the triangular layout is worse for both. > >If we assumed that there were a fixed number of terminal points rather than >journeys being able to start/end anywhere on a road, then we could just join >up all terminals with direct roads. (So this doesn't make much sense as a >problem. Needs more restrictions on valid solutions etc.) > >Mike. > > > > -- Alex -- Replace "nospam" with "mail" to reply by email. Checked infrequently. |