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Schuler tuning is a modification to the electronic control system used in inertial navigation systems that accounts for the curvature of the Earth. An inertial navigation system, used in submarines, ships, aircraft, and other vehicles to keep track of position, determines directions with respect to three axes pointing "north", "east", and "down". To detect the vehicle's orientation, the system contains an "inertial platform" mounted on gimbals, with gyroscopes that keep it pointing in a fixed orientation in space. However, the directions "north", "east" and "down" change as the vehicle moves on the curved surface of the Earth. Schuler tuning describes the modifications necessary to an inertial navigation system to keep the inertial platform always pointing "north", "east" and "down", so it gives correct directions on Earth.

Principle

As first explained by German engineer Maximilian Schuler in a 1923 paper,^[1] a pendulum whose period exactly equals the orbital period of a hypothetical satellite orbiting just above the surface of the Earth (about 84 minutes) will tend to remain pointing at the center of the Earth when its support is suddenly displaced. Such a pendulum would have a length equal to the radius of the Earth. Consider a simple gravity pendulum, whose length equals the radius of the Earth, suspended in a uniform gravitational field of the same strength as that experienced at the Earth's surface. If suspended from the surface of the Earth, the bob of the pendulum would be at the center of the Earth. If it is hanging motionless and its support is moved sideways, the bob tends to remain motionless, so the pendulum always points at the center of the Earth. If such a pendulum were attached to the inertial platform of an inertial navigation system, the platform would remain level, facing "north", "east" and "down", as it was moved about on the surface of the Earth.

A rigid pendulum may also be made to have the required period, with a pivot near its center of gravity.^[2]

The Schuler period can be derived from the classic formula for the period of a pendulum:

T = 2 π \sqrt{\frac{L}{g}} \approx 2 π \sqrt{\frac{6378100}{9.81}} \approx 5066 seconds \approx 84.4 minutes

where L is the radius of the earth in meters and g is the local acceleration of gravity in metres per second per second.

Application

A pendulum the length of the Earth's radius is impractical, so Schuler tuning doesn't use physical pendulums. Instead, the electronic control system of the inertial navigation system is modified to make the platform behave as if it were attached to a pendulum. The inertial platform is mounted on gimbals, and an electronic control system keeps it pointed in a constant direction with respect to the three axes. As the vehicle moves, the gyroscopes detect changes in orientation, and a feedback loop applies signals to torquers to rotate the platform on its gimbals to keep it pointed along the axes.

To implement Schuler tuning, the feedback loop is modified to tilt the platform as the vehicle moves in the north-south and east-west directions, to keep the platform facing "down".^[3] To do this, the torquers that rotate the platform are fed a signal proportional to the vehicle's north-south and east-west velocity. The turning rate of the torquers is equal to the velocity divided by the radius of the Earth R:

\dot{θ} = v / R

So:

\ddot{θ} = a / R

The acceleration a is a combination of the actual vehicle acceleration and the acceleration due to gravity acting on the tilting inertial platform. So this equation can be seen as a version of the equation for a simple gravity pendulum with a length equal to the radius of the Earth. The inertial platform acts as if it were attached to such a pendulum.

Schuler's time constant has other applications. Suppose a tunnel is dug from one end of the Earth to the other end straight through its center, a stone dropped in such a tunnel oscillates with Schuler's time constant. It can also be proved that the time is the same constant for a tunnel that is not through the center of Earth also.

References

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A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang
↑ Schuler Pendulum by Robert H. Cannon, Accessscience.com
↑ One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang

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In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang

[2] Schuler Pendulum by Robert H. Cannon, Accessscience.com

[3] One of the biggest reasons investing in a Singapore new launch is an effective things is as a result of it is doable to be lent massive quantities of money at very low interest rates that you should utilize to purchase it. Then, if property values continue to go up, then you'll get a really high return on funding (ROI). Simply make sure you purchase one of the higher properties, reminiscent of the ones at Fernvale the Riverbank or any Singapore landed property Get Earnings by means of Renting

In its statement, the singapore property listing - website link, government claimed that the majority citizens buying their first residence won't be hurt by the new measures. Some concessions can even be prolonged to chose teams of consumers, similar to married couples with a minimum of one Singaporean partner who are purchasing their second property so long as they intend to promote their first residential property. Lower the LTV limit on housing loans granted by monetary establishments regulated by MAS from 70% to 60% for property purchasers who are individuals with a number of outstanding housing loans on the time of the brand new housing purchase. Singapore Property Measures - 30 August 2010 The most popular seek for the number of bedrooms in Singapore is 4, followed by 2 and three. Lush Acres EC @ Sengkang

Discover out more about real estate funding in the area, together with info on international funding incentives and property possession. Many Singaporeans have been investing in property across the causeway in recent years, attracted by comparatively low prices. However, those who need to exit their investments quickly are likely to face significant challenges when trying to sell their property – and could finally be stuck with a property they can't sell. Career improvement programmes, in-house valuation, auctions and administrative help, venture advertising and marketing, skilled talks and traisning are continuously planned for the sales associates to help them obtain better outcomes for his or her shoppers while at Knight Frank Singapore. No change Present Rules

Extending the tax exemption would help. The exemption, which may be as a lot as $2 million per family, covers individuals who negotiate a principal reduction on their existing mortgage, sell their house short (i.e., for lower than the excellent loans), or take part in a foreclosure course of. An extension of theexemption would seem like a common-sense means to assist stabilize the housing market, but the political turmoil around the fiscal-cliff negotiations means widespread sense could not win out. Home Minority Chief Nancy Pelosi (D-Calif.) believes that the mortgage relief provision will be on the table during the grand-cut price talks, in response to communications director Nadeam Elshami. Buying or promoting of blue mild bulbs is unlawful.

A vendor's stamp duty has been launched on industrial property for the primary time, at rates ranging from 5 per cent to 15 per cent. The Authorities might be trying to reassure the market that they aren't in opposition to foreigners and PRs investing in Singapore's property market. They imposed these measures because of extenuating components available in the market." The sale of new dual-key EC models will even be restricted to multi-generational households only. The models have two separate entrances, permitting grandparents, for example, to dwell separately. The vendor's stamp obligation takes effect right this moment and applies to industrial property and plots which might be offered inside three years of the date of buy. JLL named Best Performing Property Brand for second year running

The data offered is for normal info purposes only and isn't supposed to be personalised investment or monetary advice. Motley Fool Singapore contributor Stanley Lim would not personal shares in any corporations talked about. Singapore private home costs increased by 1.eight% within the fourth quarter of 2012, up from 0.6% within the earlier quarter. Resale prices of government-built HDB residences which are usually bought by Singaporeans, elevated by 2.5%, quarter on quarter, the quickest acquire in five quarters. And industrial property, prices are actually double the levels of three years ago. No withholding tax in the event you sell your property. All your local information regarding vital HDB policies, condominium launches, land growth, commercial property and more

There are various methods to go about discovering the precise property. Some local newspapers (together with the Straits Instances ) have categorised property sections and many local property brokers have websites. Now there are some specifics to consider when buying a 'new launch' rental. Intended use of the unit Every sale begins with 10 p.c low cost for finish of season sale; changes to 20 % discount storewide; follows by additional reduction of fiftyand ends with last discount of 70 % or extra. Typically there is even a warehouse sale or transferring out sale with huge mark-down of costs for stock clearance. Deborah Regulation from Expat Realtor shares her property market update, plus prime rental residences and houses at the moment available to lease Esparina EC @ Sengkang

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+'''Schuler tuning''' is a modification to the electronic control system used in [[inertial navigation system]]s that accounts for the curvature of the Earth.  An inertial navigation system, used in submarines, ships, aircraft, and other vehicles to keep track of position, determines directions with respect to three [[Coordinate axis|axes]] pointing "north", "east", and "down".  To detect the vehicle's orientation, the system contains an "[[inertial platform]]" mounted on [[gimbal]]s, with [[gyroscope]]s that keep it pointing in a fixed orientation in space.  However, the directions "north", "east" and "down" change as the vehicle moves on the curved surface of the Earth.  Schuler tuning describes the modifications necessary to an inertial navigation system to keep the inertial platform always pointing "north", "east" and "down", so it gives correct directions on Earth.
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+==Principle==
+As first explained by German engineer [[Maximilian Schuler]] in a 1923 paper,<ref>{{cite journal
+| last = Schuler
+| first = M.
+| authorlink =
+| coauthors =
+| title = Die Störung von Pendel und Kreiselapparaten durch die Beschleunigung des Fahrzeuges
+| journal = Physikalische
+Zeitschrift
+| volume = 24
+| issue = 16
+| pages =
+| publisher =
+| location =
+| year = 1923
+| url = http://www.webcitation.org/6JBR8WNRq
+| doi =
+| id =
+| accessdate = 2008-12-02}}</ref> a [[pendulum]] whose period exactly equals the [[orbit]]al period of a hypothetical [[satellite]] orbiting just above the surface of the [[Earth]] (about 84 minutes) will tend to remain pointing at the center of the Earth when its support is suddenly displaced.  Such a pendulum would have a length equal to the radius of the Earth.  Consider a [[simple gravity pendulum]], whose length equals the [[radius]] of the Earth, suspended in a uniform gravitational field of the same strength as that experienced at the Earth's surface.  If suspended from the surface of the Earth, the bob of the pendulum would be at the center of the Earth.  If it is hanging motionless and its support is moved sideways, the bob tends to remain motionless, so the pendulum always points at the center of the Earth.  If such a pendulum were attached to the inertial platform of an inertial navigation system, the platform would remain level, facing "north", "east" and "down", as it was moved about on the surface of the Earth.
+A rigid pendulum may also be made to have the required period, with a pivot near its [[center of gravity]].<ref>[http://accessscience.com/content/Schuler-pendulum/606900 Schuler Pendulum] by Robert H. Cannon, Accessscience.com</ref>
+The '''Schuler period''' can be derived from the classic formula for the period of a [[pendulum]]:
+:<math>T = 2\pi \sqrt\frac{L}{g} \approx 2\pi \sqrt\frac{6378100}{9.81} \approx 5066 \ \text{seconds} \approx 84.4 \ \text{minutes}</math>
+where '''''L''''' is the radius of the earth in meters and '''''g''''' is the local [[acceleration of gravity]] in [[metres per second per second]].
+==Application==
+A pendulum the length of the Earth's radius is impractical, so Schuler tuning doesn't use physical pendulums. Instead, the electronic control system of the [[inertial navigation system]] is modified to make the platform behave as if it were attached to a pendulum.   The inertial platform is mounted on [[gimbal]]s, and an [[Electronics|electronic]] [[control system]] keeps it pointed in a constant direction with respect to the three axes.  As the vehicle moves, the gyroscopes detect changes in orientation, and a [[feedback loop]] applies signals to torquers to rotate the platform on its gimbals to keep it pointed along the axes.
+To implement Schuler tuning, the feedback loop is modified to tilt the platform as the vehicle moves in the north-south and east-west directions, to keep the platform facing "down".<ref>{{cite journal
+| last = King
+| first = A.D.
+| authorlink =
+| coauthors =
+| title = Inertial Navigation - Forty Years of Evolution
+| journal = GEC Review
+| volume = 13
+| issue = 3
+| pages = p.141
+| publisher =
+| location =
+| year = 1998
+| url = http://www.imar-navigation.de/downloads/papers/inertial_navigation_introduction.pdf
+| doi =
+| id =
+| accessdate = 2010-09-27}}</ref>   To do this, the torquers that rotate the platform are fed a signal proportional to the vehicle's north-south and east-west [[velocity]].  The turning rate of the torquers is equal to the velocity divided by the radius of the Earth ''R'':
+:<math>\dot{\theta} = v/R</math>
+So:
+:<math>\ddot{\theta} = a/R</math>
+The acceleration ''a'' is a combination of the actual vehicle acceleration and the acceleration due to gravity acting on the tilting inertial platform.  So this equation can be seen as a version of the equation for a simple gravity [[pendulum]] with a length equal to the radius of the Earth.  The inertial platform acts as if it were attached to such a pendulum.
+Schuler's time constant has other applications. Suppose a tunnel is dug from one end of the Earth to the other end straight through its center, a stone dropped in such a tunnel oscillates with Schuler's time constant. It can also be proved that the time is the same constant for a tunnel that is not through the center of Earth also.
+==References==
+{{reflist}}
+[[Category:Navigational equipment]]

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