Schuler period
- 2π√(R/g)
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Inertial navigation
The Schuler period is 2π√(R/g). R is the GRS80 mean radius, …, and g is the stated standard gravity. An uncorrected accelerometer bias walks the position. The curve is that walk. Earth-rate compensation depends on latitude the same way as the Foucault page: the sidereal rate times the sine of the latitude. This page has no waypoints, and it does not claim to align a real system.
The curve is ½ b t² for two hours. It is the open-loop walk, not a Schuler oscillation and not a flight.
- Position error
- The value at two hours
Uncorrected bias
- Position after one hour
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Earth rate
- sin(latitude)
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What this page shows
A pendulum as long as the Earth’s radius, or an inertial navigator tuned the same way, has the period 2π√(R/g). The card is that period. R is the shared mean radius. g is 9.80665 m/s², the conventional standard gravity, not a gravity measured at the latitude you type.
Without that tuning, a constant accelerometer bias b is integrated twice. The position error is ½ b t². The curve is that parabola for two hours, and the card is the error after one hour. A negative bias walks the other way. This is not a flight path.
Compensating for the Earth’s rotation depends on latitude the same way as the Foucault page. The vertical component is the sidereal rate times sin(latitude). North of the equator the sense is clockwise, as on that page. South of the equator it is anticlockwise. At the equator there is none of that rate. The sidereal day is the one the Foucault page uses. Saying so is not a claim that the page aligns a real system.
Assumptions
- The period uses one radius and one g. It does not vary g with latitude, and it does not use a local plumb line.
- The walk is the open-loop double integral. A Schuler-tuned loop oscillates instead of walking off without bound. The curve is the walk, not that oscillation.
- The bias is whatever you type. The opening value 0.001 m/s² is an example, not a specification of an instrument.
- There are no waypoints, no gyrocompass, and no stored alignment. The Earth-rate card is only the sine.
Sources
- Schuler, M. (1923). Die Störung von Pendel- und Kreiselapparaten durch die Beschleunigung des Fahrzeuges. Physikalische Zeitschrift, 24.
- 3rd General Conference on Weights and Measures (1901). Standard gravity 9.80665 m/s².
- Moritz, H. (1980). Geodetic Reference System 1980. R is the mean radius from the shared geometry module.
- The sidereal rate is the one derived on the Foucault page from the mean solar day and the ratio 1.002737909350795. This page uses that rate. It does not copy a second Earth radius.