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Dead reckoning needed probably because they lost vacuum and gyro power to instruments, which then spin down and float randomly if there’s no battery backup

Inertial Navigation System... a mechanical system which maintains position by double integrating acceleration, which means infinitesimal errors grow to dominate over time, and so need to be recalibrated often.

    a, v0 maybe vectors; x maybe a point insead of a number
    x(t) = a(t)*t^2 + v0*t + x0

Modern human-portable INSes for adventuring/surveying use laser ring gyros, and GPS when available.


Your formula only works for constant acceleration.




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