7 ms·

How Crossrail was affected by the curvature of the Earth (2018)

139 points by zeristor 5y ago

ninju 5y ago
> ...in three different coordinate systems (OSGB36, WGS84 and ED50) > Crossrail made use of a *customised projection* with a meridian that runs through central London https://xkcd.com/927/ https://xkcd.com/927/
- burnte 5y ago
  "... so I decided to use regex. Now I have two problems."
JackFr 5y ago
One of my favorite curvature-of-the-earth/engineering details is that the tops of the towers of the Verrazon Narrows Bridge are 1 5/8 inches farther apart at their tops than at their bases due to the curvature of the earth. https://en.wikipedia.org/wiki/Verrazzano-Narrows_Bridge https://en.wikipedia.org/wiki/Verrazzano-Narrows_Bridge
- adolph 5y ago
  I was thinking about this too from the perspective of potentially being easier to observe than ships at sea. On the other hand, the earth's curvature is imperfectly correlated to gravitational vector. Given a stable gravitational anomaly, would two towers such as that bridge be oriented to gravity or curvature? My guess the former, meaning that the change in distance between the base and top of two tall towers wouldn't add to understanding curvature.
TYPE_FASTER 5y ago
The first time I drove across the US, I wondered why the two lane roads we were driving on in the midwest (scenic route) did a quick dogleg every so often. https://kottke.org/18/01/us-road-grid-corrections-because-of-the-earths-curvature https://kottke.org/18/01/us-road-grid-corrections-because-of...
- rob74 5y ago
  Ok, the title "US road grid corrections because of the Earth’s curvature" is slightly misleading. The doglegs are not there because of the curvature of the earth, but because of the "Jefferson Grid", which divided a large portion of the US into plots which were each a square mile. But, due to the curvature of the earth, the north-south boundaries between these plots couldn't be exactly straight, and that led to these "misalignments".
  - helsinkiandrew 5y ago
    > Ok, the title "US road grid corrections because of the Earth’s curvature" is slightly misleading OK, but "US road grid corrections because of the north-south boundaries between Jefferson Grid plots that aren't straight due to the Earth's curvature" doesn't roll off the tongue quite as well.
- InCityDreams 5y ago
  I always figured it was to give drivers something to do to keep them awake.
  - drewzero1 5y ago
    I had heard of that idea in relation to the design of the US interstate highway system. I looked into it[0] and found that it may be a consideration, but not a requirement as I thought I remembered. https://www.fhwa.dot.gov/interstate/faq.cfm#question31a https://www.fhwa.dot.gov/interstate/faq.cfm#question31a
- Mountain_Skies 5y ago
  Though not the intended purpose, it probably also helps serve as a ground level windbreak.
triggercut 5y ago
Funny, I was just reminiscing about this very problem this afternoon. When you are working to specific locations at each end it is a really tricky problem, but local grids like the ones described here help. I've worked on rail projects for mines in remote areas that need a few hundred kms of new track and span across "zones". The problem is exacerbated (at least then, early 00s) by the way you represent these in various CAD products, especially when sharing data between them. There are two main 3D modeling kernels that most popular professional CAD products rely on, both from the 70's 80's with minor updates neither 64bit native. Why is this an issue? Well, you see, the standard for civil design is to model in "real world" coordinates. That means you could be dealing with a file at the resolutions of mm for engineering purposes, but thousands of kms away from the origin. Now we enter the world off floating point calculation errors and subsequent kernel issues. There are ways around it. Essentially offsets that move the origin of the file temporarily with a note to itself that everything must also account for the offset before displaying in the UI. But it can get confusing, fast, every product does it its own way and may not recognise this trickery. Working digitally with sparse real world reference data of varying qualities can be a big risk. I remember being in a large workshop with two surveying companies, our client and some civil engineers. I was horrified that I knew more about the various grids and their issues than any one else. I did one unit of surveying at uni, not long before and had to do a lot of research to get my head around the issues. These people were meant to be the experts. The good thing about linear projects is that on those scales you can usually get somewhere where you can "work it out" on site (i.e. fudge it to make it fit). But It potentially affects everything, like, how many meters of track are we ordering? What contingency do we need? What are our expected mass haul volumes and estimated fuel costs? How big should we make our margin of error? It'll all work itself out, it'll just cost. What happens when we start building beyond the planet and need to accomodate for curvatures in space time? Even ones that are brought about by the very thing you are building?
- ArchitectAnon 5y ago
  Back in the mid 2000's I tried to point out to the people writing the UK BIM standards why it was a bad idea to have all buildings drawn relative to the OS grid datum which is somewhere southwest of the Scilly Isles for exactly this reason. I even tried to explain that computers can't do accurate floating point calculations and they didn't believe me! And then CAD consultants are surprised when automatic 2D drawing generation from 3D models randomly fails to work properly (usually at 10pm the night before a big deadline) and then everyone wonders why architects are backwards and don't want to adopt 3D processes...
walnutclosefarm 5y ago
The article is kind of a tease, but doesn't really explain very well what's going on in these various coordinate systems that caused the need for the London area specific survey and model, and causes different coordinate systems to put the Greenwich "zero" point all over the map. Hard to tell whether the point of the article is that precise mapping is a hard problem with various solutions optimized for global applicability giving different lattitude/longitude results in specific locales (where it kinda leaves the impression some sort of error is involved, which is not the problem; the Greenwich zero point is not 102m East in GCS84 because of error, but because it approximates the shape of the earth globally differently than standard spherical coordinates), or, as the headline says, that the curvature of the earth figures into projects that cover city-scale distances (which is hardly a surprise to anyone who thinks ten seconds about it; you can see curvature effects on a calm sea at a distance of only a few miles).
- bloak 5y ago
  > you can see curvature effects on a calm sea at a distance of only a few miles Open sea is rarely calm. But lakes are sometimes calm. I've sometimes thought it would be fun to set up some kind of permanent markers, something like giant clapper boards along a straight line at the same height above the water, so that people walking around a lake could easily observe the curvature of the Earth. Has this been done anywhere?
  - Nzen 5y ago
    Dan Olsen published a video [0], last year, outlining his experiment on Minnewanka Curve and the ideology driving people who deny his, and similar results, demonstrating the curvature of the earth. While there is no artificial structure, he observes that trees on the opposite side of the lake are obscured by the water surface. He also published raw footage of the multiple recordings he took as a separate 28 minute video. [0] https://www.youtube.com/watch?v=JTfhYyTuT44 https://www.youtube.com/watch?v=JTfhYyTuT44 90 minutes
    - momojo 5y ago
      Great video by itself
ArchitectAnon 5y ago
Also Kansai airport [0] had to cope with this issue, complicated by the fact that it's built on reclaimed land and the whole thing is (or was) on software controlled hydraulic jacks which control differential settlement. [0] http://www.rpbw.com/project/kansai-international-airport-terminal http://www.rpbw.com/project/kansai-international-airport-ter... [1] http://engineering-timelines.com/scripts/engineeringItem.asp?id=1280 http://engineering-timelines.com/scripts/engineeringItem.asp...
- boredumb 5y ago
  Extremely interesting and an amazing feat of engineering. "The terminal was completed in less than 36 months." Blows me away the most I think.
londons_explore 5y ago
A good chunk of this problem is because they don't just use the global WGS-84 standard, and instead decide to try to use locally-flat custom coordinate systems. It's like trying to design your own car from scratch to travel somewhere rather than just using one from Ford. Lots of extra effort with little gain. If WGS-84 had been used throughout (and all old measurements converted), everything would have been far simpler and cheaper, both now and for future modifications.
- pacaro 5y ago
  I worked for a small British GIS company in the mid-nineties. Having an entire country on a single rectilinear coordinate system really makes life easier. The OS grid makes sense for mapping a country the shape, size and location of the UK. And on 16-bit windows machines, not having to deal with WGS-84 or UTM, was a reasonable call
  - londons_explore 5y ago
    But now all the complex math is hidden away behind abstractions, and the extra computation to do everything in WGS-84 space is insignificant. Yet the benefits are huge in that every engineer who works on the design won't need all this extra knowledge of many custom coordinate systems and the way conversions and interactions between them work. Not to mention the huge possible costs when someone messes up and uses the wrong coordinate system for something and a beam ends up only half the thickness it should have been because the top was constrained by something in one coordinate system and the bottom by something in another... I think a close parallel is the complexity of UTF-8 is now worth it over encoding things using codepages.
    - lmc 5y ago
      > the extra computation to do everything in WGS-84 space is insignificant There is still significant overhead involved in conversion - arbitrary trig functions, even optimised, are still really expensive compared to planar geometry. Remember these folks will be working at super high resolutions too.
avs733 5y ago
a number of years ago when I traveled frequently for work I was very focused on optimizing my airline miles and points. At some point as part of a computer system cutover, United Airlines suddenly started shorting people miles on airport to airport differences. Not a lot, but a few here and there. A group of folks on flyertalk slowly realized that the change was perfectly explained by the difference between treating the globe as a perfect sphere and treating it as an oblate spheroid. The previous model had been technically correct and precise. Whoever built the new model had simplified the code for some reason. After much kvetching United fixed it.
- aidenn0 5y ago
  I propose that to simplify geographic calculations, we should all pack up and move to venus.
  - avs733 5y ago
    I'd sooner breathe sulpheric acid than...something something oblate spheroids?
- simonh 5y ago
  Or the Earth could be shrinking.
  - burnte 5y ago
    This is the truth no one wants to admit. In ten years we'll be orbiting the moon!
chx 5y ago
What the article mentions in passing was called "threading the needle" where an earth pressure balance tunnel-boring machine mined the section of tunnel directly above the operational Northern line platform tunnels at Tottenham Court Road, directly below the London Underground station structures, with less than 800mm clearance to each. Read more at https://www.theengineer.co.uk/content/in-depth/your-questions-answered-crossrail https://www.theengineer.co.uk/content/in-depth/your-question...
- lifeisstillgood 5y ago
  Wait what? There are three tunnels under London separated by a two feet of earth?! I doubt we even need a Bond villain to break through that ! I am not sure I trust engineering that much?
  - timthorn 5y ago
    They posted an engineer (and a film crew[1]) to stand on the relevant platform at Tottenham Court Road while the TBM was boring through, to watch for anything going wrong. That's trust :) 1. For this documentary. The title hasn't aged well... : https://www.bbc.co.uk/programmes/b08ry6fy https://www.bbc.co.uk/programmes/b08ry6fy I wonder if the Bond villain is responsible for the late opening of the eponymous Station?
    - lifeisstillgood 5y ago
      It's more, is that going to hold for a hundred years? I mean it's just ... clay under London. Then again what do I know. I look up at Jumbo Jets flying past and think, "no way can that stay up there" If we turn out to live in the Matrix and heavier than air flight is done with a continuous loop in a Perl script, I will not be surprised.
  - avs733 5y ago
    make the project engineers who signed the plans stand there.
  - chx 5y ago

139 points by zeristor 5y ago

> ...in three different coordinate systems (OSGB36, WGS84 and ED50) > Crossrail made use of a *customised projection* with a meridian that runs through central London https://xkcd.com/927/ https://xkcd.com/927/

burnte 5y ago
"... so I decided to use regex. Now I have two problems."

JackFr 5y ago

One of my favorite curvature-of-the-earth/engineering details is that the tops of the towers of the Verrazon Narrows Bridge are 1 5/8 inches farther apart at their tops than at their bases due to the curvature of the earth. https://en.wikipedia.org/wiki/Verrazzano-Narrows_Bridge https://en.wikipedia.org/wiki/Verrazzano-Narrows_Bridge

adolph 5y ago
I was thinking about this too from the perspective of potentially being easier to observe than ships at sea. On the other hand, the earth's curvature is imperfectly correlated to gravitational vector. Given a stable gravitational anomaly, would two towers such as that bridge be oriented to gravity or curvature? My guess the former, meaning that the change in distance between the base and top of two tall towers wouldn't add to understanding curvature.

TYPE_FASTER 5y ago

The first time I drove across the US, I wondered why the two lane roads we were driving on in the midwest (scenic route) did a quick dogleg every so often. https://kottke.org/18/01/us-road-grid-corrections-because-of-the-earths-curvature https://kottke.org/18/01/us-road-grid-corrections-because-of...

rob74 5y ago
Ok, the title "US road grid corrections because of the Earth’s curvature" is slightly misleading. The doglegs are not there because of the curvature of the earth, but because of the "Jefferson Grid", which divided a large portion of the US into plots which were each a square mile. But, due to the curvature of the earth, the north-south boundaries between these plots couldn't be exactly straight, and that led to these "misalignments".
- helsinkiandrew 5y ago
  > Ok, the title "US road grid corrections because of the Earth’s curvature" is slightly misleading OK, but "US road grid corrections because of the north-south boundaries between Jefferson Grid plots that aren't straight due to the Earth's curvature" doesn't roll off the tongue quite as well.
InCityDreams 5y ago
I always figured it was to give drivers something to do to keep them awake.
- drewzero1 5y ago
  I had heard of that idea in relation to the design of the US interstate highway system. I looked into it[0] and found that it may be a consideration, but not a requirement as I thought I remembered. https://www.fhwa.dot.gov/interstate/faq.cfm#question31a https://www.fhwa.dot.gov/interstate/faq.cfm#question31a
Mountain_Skies 5y ago
Though not the intended purpose, it probably also helps serve as a ground level windbreak.

triggercut 5y ago

Funny, I was just reminiscing about this very problem this afternoon. When you are working to specific locations at each end it is a really tricky problem, but local grids like the ones described here help. I've worked on rail projects for mines in remote areas that need a few hundred kms of new track and span across "zones". The problem is exacerbated (at least then, early 00s) by the way you represent these in various CAD products, especially when sharing data between them. There are two main 3D modeling kernels that most popular professional CAD products rely on, both from the 70's 80's with minor updates neither 64bit native. Why is this an issue? Well, you see, the standard for civil design is to model in "real world" coordinates. That means you could be dealing with a file at the resolutions of mm for engineering purposes, but thousands of kms away from the origin. Now we enter the world off floating point calculation errors and subsequent kernel issues. There are ways around it. Essentially offsets that move the origin of the file temporarily with a note to itself that everything must also account for the offset before displaying in the UI. But it can get confusing, fast, every product does it its own way and may not recognise this trickery. Working digitally with sparse real world reference data of varying qualities can be a big risk. I remember being in a large workshop with two surveying companies, our client and some civil engineers. I was horrified that I knew more about the various grids and their issues than any one else. I did one unit of surveying at uni, not long before and had to do a lot of research to get my head around the issues. These people were meant to be the experts. The good thing about linear projects is that on those scales you can usually get somewhere where you can "work it out" on site (i.e. fudge it to make it fit). But It potentially affects everything, like, how many meters of track are we ordering? What contingency do we need? What are our expected mass haul volumes and estimated fuel costs? How big should we make our margin of error? It'll all work itself out, it'll just cost. What happens when we start building beyond the planet and need to accomodate for curvatures in space time? Even ones that are brought about by the very thing you are building?

ArchitectAnon 5y ago
Back in the mid 2000's I tried to point out to the people writing the UK BIM standards why it was a bad idea to have all buildings drawn relative to the OS grid datum which is somewhere southwest of the Scilly Isles for exactly this reason. I even tried to explain that computers can't do accurate floating point calculations and they didn't believe me! And then CAD consultants are surprised when automatic 2D drawing generation from 3D models randomly fails to work properly (usually at 10pm the night before a big deadline) and then everyone wonders why architects are backwards and don't want to adopt 3D processes...

walnutclosefarm 5y ago

The article is kind of a tease, but doesn't really explain very well what's going on in these various coordinate systems that caused the need for the London area specific survey and model, and causes different coordinate systems to put the Greenwich "zero" point all over the map. Hard to tell whether the point of the article is that precise mapping is a hard problem with various solutions optimized for global applicability giving different lattitude/longitude results in specific locales (where it kinda leaves the impression some sort of error is involved, which is not the problem; the Greenwich zero point is not 102m East in GCS84 because of error, but because it approximates the shape of the earth globally differently than standard spherical coordinates), or, as the headline says, that the curvature of the earth figures into projects that cover city-scale distances (which is hardly a surprise to anyone who thinks ten seconds about it; you can see curvature effects on a calm sea at a distance of only a few miles).

bloak 5y ago
> you can see curvature effects on a calm sea at a distance of only a few miles Open sea is rarely calm. But lakes are sometimes calm. I've sometimes thought it would be fun to set up some kind of permanent markers, something like giant clapper boards along a straight line at the same height above the water, so that people walking around a lake could easily observe the curvature of the Earth. Has this been done anywhere?
- Nzen 5y ago
  Dan Olsen published a video [0], last year, outlining his experiment on Minnewanka Curve and the ideology driving people who deny his, and similar results, demonstrating the curvature of the earth. While there is no artificial structure, he observes that trees on the opposite side of the lake are obscured by the water surface. He also published raw footage of the multiple recordings he took as a separate 28 minute video. [0] https://www.youtube.com/watch?v=JTfhYyTuT44 https://www.youtube.com/watch?v=JTfhYyTuT44 90 minutes
  - momojo 5y ago
    Great video by itself

ArchitectAnon 5y ago

Also Kansai airport [0] had to cope with this issue, complicated by the fact that it's built on reclaimed land and the whole thing is (or was) on software controlled hydraulic jacks which control differential settlement. [0] http://www.rpbw.com/project/kansai-international-airport-terminal http://www.rpbw.com/project/kansai-international-airport-ter... [1] http://engineering-timelines.com/scripts/engineeringItem.asp?id=1280 http://engineering-timelines.com/scripts/engineeringItem.asp...

boredumb 5y ago
Extremely interesting and an amazing feat of engineering. "The terminal was completed in less than 36 months." Blows me away the most I think.

londons_explore 5y ago

A good chunk of this problem is because they don't just use the global WGS-84 standard, and instead decide to try to use locally-flat custom coordinate systems. It's like trying to design your own car from scratch to travel somewhere rather than just using one from Ford. Lots of extra effort with little gain. If WGS-84 had been used throughout (and all old measurements converted), everything would have been far simpler and cheaper, both now and for future modifications.

pacaro 5y ago
I worked for a small British GIS company in the mid-nineties. Having an entire country on a single rectilinear coordinate system really makes life easier. The OS grid makes sense for mapping a country the shape, size and location of the UK. And on 16-bit windows machines, not having to deal with WGS-84 or UTM, was a reasonable call
- londons_explore 5y ago
  But now all the complex math is hidden away behind abstractions, and the extra computation to do everything in WGS-84 space is insignificant. Yet the benefits are huge in that every engineer who works on the design won't need all this extra knowledge of many custom coordinate systems and the way conversions and interactions between them work. Not to mention the huge possible costs when someone messes up and uses the wrong coordinate system for something and a beam ends up only half the thickness it should have been because the top was constrained by something in one coordinate system and the bottom by something in another... I think a close parallel is the complexity of UTF-8 is now worth it over encoding things using codepages.
  - lmc 5y ago
    > the extra computation to do everything in WGS-84 space is insignificant There is still significant overhead involved in conversion - arbitrary trig functions, even optimised, are still really expensive compared to planar geometry. Remember these folks will be working at super high resolutions too.

avs733 5y ago

a number of years ago when I traveled frequently for work I was very focused on optimizing my airline miles and points. At some point as part of a computer system cutover, United Airlines suddenly started shorting people miles on airport to airport differences. Not a lot, but a few here and there. A group of folks on flyertalk slowly realized that the change was perfectly explained by the difference between treating the globe as a perfect sphere and treating it as an oblate spheroid. The previous model had been technically correct and precise. Whoever built the new model had simplified the code for some reason. After much kvetching United fixed it.

aidenn0 5y ago
I propose that to simplify geographic calculations, we should all pack up and move to venus.
- avs733 5y ago
  I'd sooner breathe sulpheric acid than...something something oblate spheroids?
simonh 5y ago
Or the Earth could be shrinking.
- burnte 5y ago
  This is the truth no one wants to admit. In ten years we'll be orbiting the moon!

chx 5y ago

What the article mentions in passing was called "threading the needle" where an earth pressure balance tunnel-boring machine mined the section of tunnel directly above the operational Northern line platform tunnels at Tottenham Court Road, directly below the London Underground station structures, with less than 800mm clearance to each. Read more at https://www.theengineer.co.uk/content/in-depth/your-questions-answered-crossrail https://www.theengineer.co.uk/content/in-depth/your-question...

lifeisstillgood 5y ago
Wait what? There are three tunnels under London separated by a two feet of earth?! I doubt we even need a Bond villain to break through that ! I am not sure I trust engineering that much?
- timthorn 5y ago
  They posted an engineer (and a film crew[1]) to stand on the relevant platform at Tottenham Court Road while the TBM was boring through, to watch for anything going wrong. That's trust :) 1. For this documentary. The title hasn't aged well... : https://www.bbc.co.uk/programmes/b08ry6fy https://www.bbc.co.uk/programmes/b08ry6fy I wonder if the Bond villain is responsible for the late opening of the eponymous Station?
  - lifeisstillgood 5y ago
    It's more, is that going to hold for a hundred years? I mean it's just ... clay under London. Then again what do I know. I look up at Jumbo Jets flying past and think, "no way can that stay up there" If we turn out to live in the Matrix and heavier than air flight is done with a continuous loop in a Perl script, I will not be surprised.
- avs733 5y ago
  make the project engineers who signed the plans stand there.
- chx 5y ago