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IRS can't be aligned at higher lattitudes ( above 70 deg) , but if once aligned near equator, can we fly till higher lattitudes with IRS in that flight?

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Yes this would be possible. The limitation is for gyro-compassing only (alignment).

However being technically possible is only one aspect, there are associated regulations. Going into polar regions is not allowed without authorization for commercial aviation. For the US the requirements are described in FAR 135.98 and AC 135-42.

Navigating the polar regions

Aircraft IRS sense true heading, but also provide the magnetic heading. As magnetic heading cannot be determined accurately in polar regions, magnetic heading use is prohibited in polar regions.

  • Navigating in polar regions prior to FMS wide use required the crews to use a specific navigation grid.

  • On a FMS equipped aircraft this is transparent, heading is changed automatically from magnetic to true when entering a polar region. Similarly the system uses only one of the IRS instead of 3. More about these details in this Boeing document.

Inertial navigation for polar navigation has been common

This is inertial navigation which allowed the Nautilus submarine to travel under the north pole ice in 1958. This system, a N6A designed for aircraft, was borrowed to USAF. The periodic realignment had to be done using astronavigation and hyperbolic positioning. INS can also be gyro-compassed at high latitude by transfer alignment, like it is done for torpedoes.

INS were used (and are still common) in all missile navigation systems. Most of them had high latitudes routes to either nuke Washington or Leningrad.

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    $\begingroup$ So a modern airliner if aligned on equator, would normally be able to fly in polar regions? $\endgroup$ Nov 21, 2021 at 21:08
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    $\begingroup$ On the equator or anywhere south of about 70N or north of about 70S $\endgroup$
    – Nic
    Nov 21, 2021 at 21:20
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    $\begingroup$ One detail to add - you not only have to consider normal operations - but also if the INS has some failure and needs to be put into attitude mode - and this realignment might have issues too close to the poles. $\endgroup$
    – tsg
    Mar 30, 2023 at 14:50
  • $\begingroup$ @tsg: I covered this a bit in the last paragraph but one, mentioning possible realignment methods. None is available for civil aircraft. INS position could be easily transferred from the GPS receiver, but instantaneous GPS-determined north azimuth is by several orders not precise enough for INS operation. $\endgroup$
    – mins
    Mar 30, 2023 at 15:22

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