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Motivated by Federico's answer to Can a great circle be drawn between any two points on Earth?

Earth is not a perfect sphere, and it can be argued that the degree of oblateness is negligible. So is the ICAO/aviation adoption of WGS-84 really necessary? Or in other words: when was the need for a truer Earth shape for aeronautical navigation realized?

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    Note: WGS84 is not the true shape of earth, and we have better models. Just US decided that keeping WGS84 for GPS is much better then updating the shape from time to time. And WGS84 is well known and well defined, so it can be converted to other coordinates (this is often not true with old coordinates). PS: "great circle" implies a spherical shape (else one call it just "geodetic"). WGS84 is just the first (and only) wide used (standard for share (and coordinates). – Giacomo Catenazzi Apr 14 '22 at 10:12
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    @GiacomoCatenazzi note that the WGS84 datum is constantly maintained/updated. Last retouch was a few months ago. – Federico Apr 14 '22 at 15:21
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    @Federico: right some parts are updated (mostly about continental shifts: reducing global changes, instead of having fix Greenwich), but no major changes (as in this question: the length of the two semi-axes). It is explicitly described on GPS official documentation. – Giacomo Catenazzi Apr 19 '22 at 07:55

1 Answers1

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The mid-70s was of the earliest mentions of the problem:

In the mid-1970's, during trajectography experiments with the French SAVVAN System (Système Automatique de Vérification en Vol des Aides a la Navigation, i.e. Automatic In-flight Navigation Aids Checking System) positional 'jumps' were noticed when switching between Distance Measurement Equipment (DME) transponders located in different countries. Once more, the errors could only be attributed to incompatibility of the coordinates of ground aids.[1]

This "incompatibility of the coordinates" does not bode well for international cross-border/region navigation. But is it a big jump for a worst-case spherical scenario? It is my understanding that calculating the difference was a mathematical challenge that was solved by computers doing iterative calculations, but the rule of thumb is ±0.3%.[2]

That means when flying at 450 knots ground speed (B737, A320), it will take only around 40 minutes of flying to get an Unable RNP message in RNP-1 airspace, or in other words an uncertainty of 1 NM—that is if the plane's and published datums differ by Earth's oblateness.

There was a time when the lateral separation over the Atlantic was 120 NM, and it wasn't unheard of for 1–2% of the planes to show up after the crossing +40 NM off track.[3] With the continuous rise in air travel, and thus the need for reduced separation, both in oceanic and continental airspace, came the need for more accurate navigation. It's unthinkable to have the ATC nudge every single plane back on track by giving minute vectors when the airspaces are running near capacity.

Notable mentions:

  • GPS If GPS, augmented or not, didn't use a truer shape, applications that need geometric altitude wouldn't be feasible, e.g. LPV approaches and EGPWS. Related: Does altimeter setting affect the vertical guidance in a LPV approach?

  • INS Inertial navigation already must account for a spheroid shape for the purposes of finding the local vertical (example Sperry patent), without which, a built-in error of ~12 NM would be unavoidable.[4]

    • Accelerometers, like bubble levels, can measure either acceleration, or level, but not both at the same time. So the basic principle is fixing the accelerometers in space, and accounting for the gravitation (via e.g. torque motors based on Earth's local radius, or computationally);[5] any simple erecting mechanism will be subject to acceleration (affecting the measurements), like a glass of water for attitude indication.

  • RNAV Even pre-WGS-84 adoption, in RNAV systems the patents already show the engineers accounting for the spheroid shape, as in this Honeywell patent from the 80s.

  • ATC For air traffic control/management, it was in the 80s with the more stringent specifications that more accurate surveillance was needed—the issue also affects the projection of moving targets.[6]

1. European Organization for the Safety of Air Navigation (EUROCONTROL) and Institute of Geodesy and Navigation (IfEN). "WGS 84 Implementation Manual." (1998). (PDF)
2. Geyer, Michael. Earth-referenced aircraft navigation and surveillance analysis. No. DOT-VNTSC-FAA-16-12. John A. Volpe National Transportation Systems Center (US), 2016. (PDF)
3. White, A. "Air Traffic Control Separation Minima and Navigational Capability." The Journal of Navigation 24.4 (1971): 443-456.
4. Pitman, George R., and J. D. Trimmer. "Inertial guidance." American Journal of Physics 30.12 (1962): 937-937.
5. King, A. D. "Inertial navigation-forty years of evolution." GEC review 13.3 (1998): 140-149. (PDF)
6. Mulholland, Robert G. On the Application of Stereographic Projection to the Representation of Moving Targets in Air Traffic Control Systems. Federal Aviation Administration Technical Center, 1985. (PDF)

  • Good question and answer! Just a comment and question on your first two notable mentions: First, regardless of the accuracy of your non-spherical earth model, without augmentation from ground based stations you can't obtain the vertical accuracy required to shoot an LPV approach. Second, why would an INS need a spheroid shape to find local vertical? A vacuum driven gyro can find local vertical. (Heck, a rock on a string can find it too...) In fact, couldn't an INS theoretically function on a flat earth? – Michael Hall Apr 14 '22 at 00:54
  • "Errors could only be attributed to incompatibility of the coordinates of ground aids" - this doesn't necessarily relate to oblateness or 'truer' shape of the Earth. Incompatibility could relate to the differences in the reference meridian or other parameters. Also, prior to adoption of WGS, systems were mostly locally-optimised; for example, Pulkovo-42 was more accurate for Eastern Europe than the much later WGS 60 (both use the same flattening), and much more accurate than the contemporary international standard. – Zeus Apr 14 '22 at 01:14
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    @MichaelHall An already aligned INS could function on a flat Earth, but how would the alignment work? INS alignment senses the Earth's rotation and can accurately determine your orientation from that alone. But that requires knowing about the non-spherical shape to determine local vertical. The erection system of a vacuum gyro uses gravity for local vertical, but the INS doesn't. Even after alignment, the non-spherical shape is important to keep local vertical perpendicular to the Earth's surface when moving to a different location. – Bianfable Apr 14 '22 at 06:05
  • @Zeus: Very informative insight as usual. I've added a sentence to get my point across clearer. –  Apr 14 '22 at 08:25
  • @MichaelHall: Thanks for the compliment. I added remarks to both points. –  Apr 14 '22 at 12:58
  • @Bianfable, to the extent that alignment is the process of breaking down earth's rotation to determine local vertical and true north, it would be neither necessary nor possible on a flat (non-rotating) earth. Just give the system a starting position on your 2D grid and tell it what direction it is pointing. I do have a couple other related questions and comments though, that I will need to defer until later... – Michael Hall Apr 14 '22 at 15:21
  • @MichaelHall: I thought it was a jest or for effect :D An INS theoretically would *not* work on a flat Earth; Earth's curvature is baked into it since its inception 99 years ago (Schuler tuning). –  Apr 14 '22 at 20:53
  • I presumed that a flat earth with vertical being uniformly down, (which functionally is how it works on smaller scales) that accelerometers would measure magnitude and duration of any horizontal acceleration to compute a vector along the surface. I am not understanding why that wouldn't work, Schuler pendulums aside... – Michael Hall Apr 15 '22 at 00:46
  • @MichaelHall: In aircraft (and any near-Earth vehicle), there's a Schuler feedback loop (see fig. 4 ref. 5) in the INS that will tilt the platform in your scenario; without this loop an INS is useless near-Earth. –  Apr 15 '22 at 01:05
  • I don’t have enough knowledge to argue either way, but it’s worth noting that there’s a difference between a design feature that enables a device to function under certain conditions, and those same conditions being at the core of base functionality. My gut tells me that a level platform on a flat earth, equipped with inertial sensors, would be capable of sensing movement, thereby performing simple inertial based electronic dead reckoning. Is there a plain language explanation of why it wouldn’t that lies somewhere between the single word “Schuler” and poring over reams of research papers? – Michael Hall Apr 15 '22 at 15:58
  • @MichaelHall: Sorry in advance for having to post consecutive replies, because if I suggested asking a separate question, it may be taken the wrong way or argued against, even though it's the best/correct course of action in such cases (expanding scope). 1) You could make a platform to function as you want (e.g. in a simulated flat environment), sure, but it wouldn't be an aircraft INS. So my question (or confusion) is: what is the point of this thought experiment, if not to probe how an aircraft INS works? –  Apr 15 '22 at 17:24
  • 2) The simple explanation: a core functionality of the INS is to tilt the platform as it moves to account for Earth's curvature, without having to sense it, because in a self-contained unit, either acceleration or level can be measured, and we want the former here. (I had already added that to the answer.) 3) The point of the references isn't to complicate matters, rather providing citations to the facts. –  Apr 15 '22 at 17:24