en>Qwertyus: LogReg is not a regression method, it's a classifier

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LogReg is not a regression method, it's a classifier

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[[File:Einschienerp.jpg|thumb|upright|right|Brennan's Monorail]]

The '''gyro monorail''', '''gyroscopic monorail''', '''gyro-stabilized monorail''', or [[gyrocar]] are terms for a [[Rail profile|single rail]] [[land vehicle]] that uses the [[gyroscope|gyroscopic]] action of a [[Rotation|spinning]] wheel to overcome the inherent [[Mechanical equilibrium|instability]] of balancing on top of a single rail.

The monorail is associated with the names [[Louis Brennan]], [[August Scherl]] and [[Pyotr Shilovsky]], who each built full-scale working [[prototype]]s during the early part of the twentieth century. A version was developed by Ernest F. Swinney, Harry Ferreira and Louis E. Swinney in the USA in 1962.

The gyro monorail has never developed beyond the prototype stage.

The principal advantage of the monorail cited by Shilovsky is the suppression of [[hunting oscillation]], a speed limitation encountered by conventional railways at the time. Also, sharper turns are possible compared to the 7 km radius of turn typical of modern high-speed trains such as the [[TGV#Tracks|TGV]], because the vehicle will bank automatically on bends, like an aircraft,<ref>Graham R — Brennan, His Helicopter and other Inventions, Aeronautical Journal, Feb. 1973</ref> so that no lateral [[centrifugal acceleration]] is experienced on board.

A major drawback is that many cars - including passenger and freight cars, not just the locomotive - would require a constantly powered gyroscope to stay upright.

Unlike other means of maintaining balance, such as lateral shifting of the [[centre of gravity]] or the use of [[reaction wheels]], the gyroscopic balancing system is statically stable, so that the control system serves only to impart dynamic stability. The active part of the balancing system is therefore more accurately described as a [[Damped harmonic motion|roll damper]].

== Historical background ==
===Brennan's monorail===

The image in the leader section depicts the 22 [[tonne]] (unladen weight) prototype vehicle developed by [[Louis Brennan|Louis Philip Brennan CB]].<ref>Tomlinson, N - Louis Brennan, Inventor Extraordinaire. John Hallewell Publications. 1980. ISBN 0-905540-18-2</ref> Brennan filed his first monorail patent in 1903.

His first demonstration model was just a 2 ft 6in by 12 inch (762 mm by 300 mm) box containing the balancing system. However, this was sufficient for the Army Council to recommend a sum of £10,000 for the development of a full size vehicle. This was vetoed by their Financial Department. However, the Army found £2000 from various sources to fund Brennan's work.

Within this budget Brennan produced a larger model, 6 ft (1.83m) long by 1 ft 6in (0.46m) wide, kept in balance by two 5 inch (127 mm) diameter gyroscope rotors. This model is still in existence in the [[London Science Museum]]. The track for the vehicle was laid in the grounds of Brennan's house in [[Gillingham, Kent]]. It consisted of ordinary gas piping laid on wooden sleepers, with a fifty foot wire rope bridge, sharp corners and [[slope]]s up to one in five.

[[File:BrennanServo.png|thumb|400px|Brennan's 1909 Patent Pneumatic Servo]]

Brennan's reduced scale railway largely vindicated the [[War Department (UK)|War Department]]'s initial enthusiasm. However, the election in 1906 of a [[Liberal Party (UK)|Liberal]] government, with policies of financial retrenchment, effectively stopped the funding from the Army. However, the [[India Office]] voted an advance of £6000 in 1907 to develop the monorail for the [[North-West Frontier Province (1901–1955)|North West Frontier]] region, and a further £5000 was advanced by the [[Durbar (court)|Durbar]] of [[Kashmir region|Kashmir]] in 1908. This money was almost spent by January 1909, when the India Office advanced a further £2000.

On 15 October 1909, the [[railcar]] ran under its own power for the first time, carrying 32 people around the factory. The vehicle was 40 ft (12.2m) long and 10 ft (3m) wide, and with a 20 hp (15 kW) [[petrol engine]], had a [[speed]] of 22 mph (35 km/h). The [[transmission (mechanics)|transmission]] was [[electric]], with the petrol engine driving a [[Electrical generator|generator]], and [[electric motors]] located on both [[bogie]]s. This generator also supplied power to the gyro motors and the [[air compressor]]. The balancing system used a [[pneumatic]] [[Servomechanism|servo]], rather than the [[friction drive|friction wheel]]s used in the earlier model.

The gyros were located in the cab, although Brennan planned to re-site them under the floor of the vehicle before displaying the vehicle in public, but the unveiling of Scherl's machine forced him to bring forward the first public demonstration to 10 November 1909. There was insufficient time to re-position the gyros before the monorail's public debut.

The real public debut for Brennan's monorail was the Japan-British Exhibition at the [[White City, London|White City]], London in 1910. The monorail car carried 50 passengers at a time around a circular track at 20 mph. Passengers included [[Winston Churchill]], who showed considerable enthusiasm. Interest was such that children's clockwork monorail toys, single-wheeled and gyro-stabilised, were produced in England and Germany.<ref >{{Cite book
|title=Mechanical Toys
|last=Spilhaus |first=Athelstan
|last2=Spilhaus |first2=Kathleen
|isbn=0-517-56966-3
|publisher=Crown Publishers |location=New York
|year=1989
|pages=45-46
|quote=Ely Cycle Co.
}}</ref><ref >{{Cite patent|GB|25732|year=1908}}</ref> Although a viable means of transport, the monorail failed to attract further investment. Of the two vehicles built, one was sold as scrap, and the other was used as a park shelter until 1930.
{{Commons category|Brennan monorail|position=left}}

===Scherl's car===

Just as Brennan completed testing his vehicle, [[August Scherl]], a German [[publisher]] and [[philanthropist]], announced a public demonstration of the gyro monorail which he had developed in [[Germany]]. The demonstration was to take place on Wednesday 10 November 1909 at the [[Zoologischer Garten Berlin|Berlin Zoological Gardens]].

[[File:ScherlCar.png|thumb|400px|Scherl's Monorail Car]]

Scherl's machine,<ref>Anon - The Scherl Gyroscopic Monorail Car. Scientific American. January 22, 1910</ref> also a full size vehicle, was somewhat smaller than Brennan's, with a length of only 17 ft (5.2m). It could accommodate four passengers on a pair of transverse bench seats. The gyros were located under the seats, and had vertical axes, while Brennan used a pair of horizontal axis gyros. The [[servomechanism]] was [[hydraulic]], and [[ground propulsion|propulsion]] electric. Strictly speaking, August Scherl merely provided the financial backing. The righting mechanism was invented by Paul Fröhlich, and the car designed by Emil Falcke.

Although well received and performing perfectly during its public demonstrations, the car failed to attract significant financial support, and Scherl wrote off his investment in it.

===Shilovsky's work===

Following the failure of Brennan and Scherl to attract the necessary investment, the practical development of the gyro-monorail after 1910 continued with the work of [[Pyotr Shilovsky]],<ref>Anon - The Schilowski Gyroscopic Monorail System. The Engineer, Jan 23, 1913.

</ref> a [[Russia]]n [[Aristocracy (class)|aristocrat]] residing in London. His balancing system was based on slightly different principles to those of Brennan and Scherl, and permitted the use of a smaller, more slowly spinning gyroscope. After developing a model gyro monorail in 1911, he designed a [[gyrocar]] which was built by [[Wolseley Motors|Wolseley Motors Limited]] and tested on the streets of London in 1913. Since it used a single gyro, rather than the counter-rotating pair favoured by Brennan and Scherl, it exhibited [[asymmetry]] in its behaviour, and became [[unstable]] during sharp left hand turns. It attracted interest but no serious funding.

===Post-World War I developments===

In 1922 the [[Soviet Union|Soviet]] government began construction of a Shilovsky monorail between [[Leningrad]] and [[Tsarskoe Selo]], but funds ran out shortly after the project was begun.

In 1929, at the age of 74, Brennan also developed a gyrocar. This was turned down by a consortium of [[Austin Motor Company|Austin]]/[[Morris Motors|Morris]]/[[Rover (car)|Rover]], on the basis that they could sell all the conventional cars they built.

== Principles of operation ==
=== Basic idea ===

The vehicle runs on a single conventional rail, so that without the balancing system it would topple over.

[[File:BasicPrinciple.png|thumb|300px|Basic principle]]

A spinning wheel is mounted in a [[gimbal]] frame whose axis of rotation (the precession axis) is [[perpendicular]] to the spin axis. The assembly is mounted on the vehicle [[chassis]] such that, at [[Mechanical equilibrium|equilibrium]], the spin axis, precession axis and vehicle [[Longitudinal axis|roll]] axis are mutually perpendicular.

Forcing the gimbal to rotate causes the wheel to precess resulting in gyroscopic [[torque]]s about the roll axis, so that the mechanism has the potential to right the vehicle when tilted from the [[vertical direction|vertical]]. The wheel shows a tendency to align its spin axis with the axis of rotation (the gimbal axis), and it is this action which rotates the entire vehicle about its roll axis.

Ideally, the mechanism applying control torques to the gimbal ought to be [[Passive component|passive]] (an arrangement of [[spring (device)|spring]]s, [[Dashpot|damper]]s and [[lever]]s), but the fundamental nature of the problem indicates that this would be impossible. The equilibrium position is with the vehicle upright, so that any disturbance from this position reduces the height of the [[centre of gravity]], lowering the [[potential energy]] of the system. Whatever returns the vehicle to equilibrium must be capable of restoring this potential energy, and hence cannot consist of passive elements alone. The system must contain an active [[servomechanism|servo]] of some kind.

[[File:Cgheight.png|thumb|300px|Disturbed cg height]]

=== Side loads ===

If constant side forces were resisted by gyroscopic action alone, the gimbal would rotate quickly on to the stops, and the vehicle would topple. In fact, the mechanism causes the vehicle to lean into the disturbance, resisting it with a component of weight, with the gyro near its undeflected position.

Inertial side forces, arising from cornering, cause the vehicle to lean into the corner. A single gyro introduces an [[asymmetry]] which will cause the vehicle to lean too far, or not far enough for the net force to remain in the plane of symmetry, so side forces will still be experienced on board.

In order to ensure that the vehicle [[flight dynamics|bank]]s correctly on corners, it is necessary to remove the gyroscopic [[torque]] arising from the vehicle rate of turn.

A free gyro keeps its orientation with respect to [[inertial space]], and gyroscopic moments are generated by rotating it about an axis perpendicular to the spin axis. But the [[control system]] deflects the gyro with respect to the [[chassis]], and not with respect to the fixed stars. It follows that the [[Pitch (flight)|pitch]] and [[yaw angle|yaw]] motion of the vehicle with respect to inertial space will introduce additional unwanted, gyroscopic torques. These give rise to unsatisfactory equilibria, but more seriously, cause a loss of static stability when turning in one direction, and an increase in static stability in the opposite direction. Shilovsky encountered this problem with his road vehicle, which consequently could not make sharp left hand turns.

Brennan and Scherl were aware of this problem, and implemented their balancing systems with pairs of counter rotating gyros, precessing in opposite directions. With this arrangement, all motion of the vehicle with respect to inertial space causes equal and opposite torques on the two gyros, and are consequently cancelled out. With the double gyro system, the instability on bends is eliminated and the vehicle will bank to the correct angle, so that no net side force is experienced on board.

[[File:Cornering.png|thumb|300px|Cornering]]

Shilovsky claimed to have difficulty ensuring stability with double-gyro systems, although the reason why this should be so is not clear. His solution was to vary the control loop parameters with turn rate, to maintain similar response in turns of either direction.

Offset loads similarly cause the vehicle to lean until the centre of gravity lies above the support point. Side winds cause the vehicle to tilt into them, to resist them with a component of weight. These contact forces are likely to cause more discomfort than cornering forces, because they will result in net side forces being experienced on board.

The contact side forces result in a gimbal deflection [[bias]] in a Shilovsky loop. This may be used as an input to a slower loop to shift the centre of gravity laterally, so that the vehicle remains upright in the presence of sustained non-inertial forces. This combination of gyro and lateral cg shift is the subject of a 1962 patent. A vehicle using a gyro/lateral [[Cargo|payload]] shift was built by Ernest F. Swinney, Harry Ferreira and Louis E. Swinney in the USA in 1962. This system is called the Gyro-Dynamics monorail.

== Potential advantages over two-track vehicles ==
{{Citations missing|date=February 2008}}
The advantages of the monorail over conventional railways were summarised by Shilovsky. The following have been claimed.

=== Universal gauge tracks ===

Different countries use different [[track gauge|gauges]] (widths) of tracks, so the logistics get rather problematic for trains that travel to different countries with different gauges, i.e. trains need to transfer cargo, change axles, or some similar time and money-consuming task must be performed. A single-rail track should eliminate these problems and hence simplify international rail transport.

=== Reduced right-of-way problem ===

The close association of the vehicle with its single rail, its inherent ability to bank on bends, and the reduced reliance on adhesion forces are all factors which are pertinent to the development of surface travel. In principle, steeper gradients and sharper corners may be negotiated compared with a conventional [[adhesion railway]]. Typical high speed train designs have radius of turn of 7 km, with consequently few options for new routes within developed countries, where almost all of the land is under individual or corporate ownership.

In his book, Shilovsky describes a form of on-track braking, which is feasible with a monorail, but would upset the directional stability of a conventional rail vehicle. This has the potential of much shorter stopping distances compared with conventional wheel on steel, with a corresponding reduction in safe separation between trains. The result is potentially higher occupancy of the track, and higher capacity.

=== Reduced total system cost ===

While the individual vehicles are likely to be expensive, the greatest cost arises from the construction and maintenance of the permanent way, which, for a single rail at ground level must be cheaper.

=== Benign failure modes ===

The angular momentum in the gyros is so high that loss of power will not present a hazard for a good half hour in a well designed system.

[[File:Toppling.png|thumb|300px|Monorail v two track response]]

=== Reduced weight ===

Shilovsky claimed his designs were actually lighter than the equivalent duo-rail vehicles. The gyro mass, according to Brennan, accounts for 3-5% of the vehicle weight, which is comparable to the bogie weight saved in using a single track design.

=== Potential for high speed ===

High speed conventionally requires straight track, introducing a right of way problem in developed countries. Wheel profiles which permit sharp cornering tend to encounter the classical [[hunting oscillation]] at low speeds. Running on a single rail is an effective means to suppress hunting.

===Turning corners===
[[File:TurningInstability.png|thumb|300px|Contribution of body rotation]]

Considering a vehicle negotiating a horizontal curve, the most serious problems arise if the gyro axis is vertical. There is a component of turn rate <math>\Omega</math> acting about the gimbal pivot, so that an additional gyroscopic moment is introduced into the roll equation:
:::<math>A\frac{d^2\phi}{dt^2}+H(\frac{d\theta}{dt}+\Omega \phi)=Wh \phi </math>
This displaces the roll from the correct bank angle for the turn, but more seriously, changes the constant term in the characteristic equation to:
:::<math>\frac{(Wh-H\Omega)k}{AJ}</math>
Evidently, if the turn rate exceeds a critical value:
::<math>\Omega=\frac{Wh}{H}</math>
The balancing loop will become unstable.
However, an identical gyro spinning in the opposite sense will cancel the roll torque which is causing the instability, and if it is forced to precess in the opposite direction to the first gyro will produce a control torque in the same direction.

In 1972, the Canadian Government's Division of Mechanical Engineering rejected a monorail proposal largely on the basis of this problem. Their analysis <ref>Hamill, P.A. et al. - Comments on a Gyro-Stabilised Monorail Proposal. Canada. Control Systems Laboratory. LTR-CS-77. December 1972</ref> was correct, but restricted in scope to single vertical axis gyro systems, and not universal.

====Maximum spin rate====

[[Gas turbine engine]]s are designed with peripheral speeds as high as 400 m/s,<ref>Rogers G.F.C. and Y.R.Mayhew - Engineering Thermodynamics, Work and Heat Transfer. Third Edition. Longman 1972, p433</ref> and have operated reliably on thousands of aircraft over the past 50 years. Hence, an estimate of the gyro mass for a 10 tonne vehicle, with cg height at 2m, assuming a peripheral speed of half what is used in jet engine design, is a mere 140 kg. Brennan's recommendation of 3-5% of the vehicle mass was therefore highly conservative.

== See also ==
* [[Adhesion railway]]
* [[Bicycle and motorcycle dynamics]]
* [[Gyrocar]]
* [[Segway HT]]

== References ==
{{reflist}}

== Bibliography ==
* Schilovsky P P — The Gyroscope, Its construction and Practical Application, E Spon Publications 1922

* Cousins H — The Stability of Gyroscopic Single Track Vehicles, Engineer Nov 21, Nov 28, Dec. 12 1913

* Graham R — Brennan, His Helicopter and other Inventions, Aeronautical Journal, Feb. 1973

* Mee A — Harmsworth Popular Science, Volume 3, Pages 1680 to 1693, 1912

* Eddy, H.T. - The Mechanical Principles of Brennan's Mono-Rail Car. Journal of the Franklin Institute, Vol CLXIX p467

* Tomlinson, N - Louis Brennan, Inventor Extraordinaire. John Hallewell Publications. 1980. ISBN 0-905540-18-2

* Anon - The Scherl Gyroscopic Monorail Car. Scientific American. January 22, 1910

* Anon - The Brennan Mono-Track Vehicle. The Commercial Motor. 18 November 1909.

* Anon - The Schilowski Gyroscopic Monorail System. The Engineer, Jan 23, 1913.

* Hamill, P.A. et al. - Comments on a Gyro-Stabilised Monorail Proposal. Canada. Control Systems Laboratory. LTR-CS-77. December 1972
* Anon - Monorail Vehicles, Engineering. June 14, 1907. p794.

* Rogers G.F.C. and Y.R.Mayhew - Engineering Thermodynamics, Work and Heat Transfer. Third Edition. Longman 1972, p433

== External links ==
* [http://www.monorails.org/tMspages/Gyro-Dynamics.html Monorail Society Special Feature on Swinney's monorail]
* [http://azby.videosearch.nifty.com/video/watch/299f2a9a24d68974?chartype= Model Gyro monorail]
* [http://www.catskillarchive.com/rrextra/odgyro.Html Gyroscope Railroad]

{{DEFAULTSORT:Gyro Monorail}}
[[Category:Monorails]]

Multinomial logistic regression - Revision history

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