View source for Gyro monorail

{{Short description|Single rail land vehicle}}
{{more footnotes|date=February 2015}}
{{Infobox machine
| image             = Einschienerp.jpg
| caption           = The {{convert|22|t|adj=on}} (unladen weight) prototype vehicle developed by [[Louis Brennan]]<ref>{{cite book| last=Tomlinson| first=N| title=Louis Brennan, Inventor Extraordinaire| publisher=John Hallewell Publications| year=1980| isbn=0-905540-18-2}}</ref>
| classification    = [[Monorail]]
| industry          = [[Rail transport]]
| application       = [[Transport|Transportation]]
| inventor          = [[Louis Brennan]]
| invented          = {{start date and years ago|1903|df=y|p=y}}
}}

A '''gyro monorail''', '''gyroscopic monorail''', or '''gyro-stabilized monorail''' is a [[Monorail|single-rail]] [[land vehicle]] that uses the [[gyroscope|gyroscopic]] action of one or more [[Rotation|spinning]] wheels to overcome the inherent [[Mechanical equilibrium|instability]] of balancing atop a single rail. For a similar steerable vehicle, see [[Gyrocar]].

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 US in 1962. 

The gyro monorail was 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 multi-kilometre 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>{{cite journal| last=Graham| first=R| title=Brennan, His Helicopter and other Inventions| journal=Aeronautical Journal| date=February 1973| volume=77| issue=746| pages=74–82| doi=10.1017/S0001924000040318| s2cid=117531165}}</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 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]].

== History ==
=== Brennan's monorail ===
[[File:Brennan monorail.png|thumb|left|[[Harmsworth Popular Science]] illustration showing the monorail mechanism, and (inset) Louis Brennan<ref>c.1913, Vol.3, p.1684</ref>]]

[[Louis Brennan]] developed a {{convert|22|t|adj=on}} (unladen weight) prototype vehicle.<ref>{{cite book| last=Tomlinson| first=N| title=Louis Brennan, Inventor Extraordinaire| publisher=John Hallewell Publications| year=1980| isbn=0-905540-18-2}}</ref> Brennan filed his first monorail patent in 1903.

His first demonstration model was just a {{convert|762|by|300|mm|in|adj=on|order=flip}} box containing the balancing system. However, this was sufficient for the Army Council to recommend a sum of {{GBP|10000|long=no|link=yes}} for the development of a full-size vehicle. This was vetoed by their Financial Department. However, the Army found {{GBP|2000|long=no|link=yes}} from various sources to fund Brennan's work.

Within this budget Brennan produced a larger model, {{convert|1.83|by|0.46|m|ft|order=flip}}, kept in balance by two {{convert|127|mm|in|adj=on|order=flip}} 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 {{convert|50|ft|m|adj=on}} wire rope bridge, sharp corners and [[slope]]s up to one in five. Brennan demonstrated his model in a lecture to the Royal Society in 1907 when it was shown running back and forth "on a taught and slender wire" "under the perfect control of the inventor".<ref>{{cite news |author=<!--Staff writer(s)/no by-line.--> |title=Revolution in Travel | work = [[Birmingham Gazette|Birmingham Daily Gazette]] | page = 8 |date=1907-05-09 | df=dmy-all}}</ref>

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 {{GBP|6000|1907|long=no|link=yes}} in 1907 to develop the monorail for the [[North-West Frontier Province (1901–1955)|North West Frontier]] region, and a further {{GBP|5000|1908|long=no|link=yes}} 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 {{GBP|2000|1909|long=no|link=yes}}.

On 15 October 1909, the [[railcar]] ran under its own power for the first time, carrying 32 people around the factory. The vehicle was {{convert|12.2|by|3|m|ft||order=flip}}, and with a {{convert|20|hp|kW|adj=on}} [[petrol engine]], had a [[speed]] of {{convert|22|mph}}. 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 {{convert|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
  |last1=Spilhaus
  |first1=Athelstan
  |last2=Spilhaus
  |first2=Kathleen
  |isbn=0-517-56966-3
  |publisher=Crown Publishers
  |location=New York
  |year=1989
  |pages=[https://archive.org/details/mechanicaltoysho00spil/page/45 45–46]
  |quote=Ely Cycle Co.
  |url-access=registration
  |url=https://archive.org/details/mechanicaltoysho00spil/page/45
  }}</ref><ref>{{Cite patent|country=GB|number=190811221|pubdate=1908-09-10|title=Improvements in or relating to Single Track Vehicles|inventor1-first=August|inventor1-last=Scherl}}</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.

=== 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.svg|thumb|400px|Scherl's monorail car]]

Scherl's machine,<ref>{{cite journal| title=The Scherl Gyroscopic Monorail Car| journal=Scientific American| date=January 22, 1910| volume=102| issue=4| page=84| doi=10.1038/scientificamerican01221910-84| bibcode=1910SciAm.102...84.}}</ref> also a full-size vehicle, was somewhat smaller than Brennan's, with a length of only {{convert|17|ft}}. 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 ===
[[file:Машина незадолго до испытаний.jpg|thumb|[[Pyotr Shilovsky]]'s gyrocar]]

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>{{cite journal| title=The Schilowski Gyroscopic Monorail System| journal=The Engineer| date=January 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.

=== 21st century: Monocab ===
In October 2022 the [[Technische Hochschule OWL]], the [[Bielefeld University of Applied Sciences]], the [[Fraunhofer society|Fraunhofer-Institut für Optronik, Systemtechnik und Bildauswertung]] and the Landeseisenbahn Lippe e. V. presented a gyro-stabilized monorail based on Brennan's system on a section of the Extertal railway in Germany.<ref>{{cite web |url=https://www.monocab-owl.de/das-projekt/ |title=Monocab – das Projekt |work=monocab-owl.de |access-date=2022-11-17}}</ref>

The system called ''Monocab'' is meant to permit bi-directional service on a single track since the vehicles use only one rail. The cabins that shall operate autonomously on-demand are designed accordingly narrow.

In September 2020 Monocab was funded from the [[European Regional Development Fund]] and by the state of [[North Rhine-Westphalia]] with 3.6 million euros combined.<ref>{{cite web |url=https://www.ostwestfalenlippe.de/owl-gmbh/regionale-2022/3,6-millionen-förderung-für-mobilitätsprojekt-monocab/|title=3.6 Millionen Förderung für Mobilitätsprojekt Monocab |publisher=Ostwestfalen Lippe GmbH Gesellschaft zur Förderung der Region |date=2020-09-09 |access-date=2022-11-18}}</ref>

== 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|Basic principle of operation: rotation about the vertical axis causes movement about the horizontal axis.]]

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 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 [[Passivity (engineering)|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|Disturbed cg height.{{huh?|date=January 2016}} (The difference in height shown is exaggerated.) The balancing system must do work against gravity to right the vehicle when disturbed. ]]

=== 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|left|When cornering, the counter-rotating gyros avoid instability on corners.]]

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 US in 1962. This system is called the Gyro-Dynamics monorail.

== Comparison to two-rail vehicles ==
{{more citations needed|section|date=February 2008}}
[[File:Toppling.png|thumb|300px|Monorail v two-rail response]]

Shilovsky gave a number of claimed benefits including reduced right-of-way problems because steeper gradients and sharper corners may be negotiated in theory. 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.

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.

[[file:TurningInstability.png|thumb|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.<ref>{{cite journal| last=Hamill| first=P.A.| others=et al.| title=Comments on a Gyro-Stabilised Monorail Proposal| location=Canada| publisher=Control Systems Laboratory| journal=LTR-Cs-77| date=December 1972}}</ref> Their analysis  was correct, but restricted in scope to single vertical axis gyro systems, and not universal.{{or|date=September 2024}}

[[Gas turbine engine]]s are designed with peripheral speeds as high as {{convert|400|m/s}},<ref>{{cite book| last1=Rogers| first1=G.F.C.| first2=Y.R.| last2=Mayhew| title=Engineering Thermodynamics, Work and Heat Transfer| edition=third| publisher=[[Longman]]| year=1972| page=433}}</ref> and have operated reliably on thousands of aircraft over the past 50 years. Hence, an estimate of the gyro mass for a {{convert|10|t}}, with a center-of-gravity height of {{convert|2|m}}, assuming a peripheral speed of half what is used in jet engine design, is a mere {{convert|140|kg}}. Brennan's recommendation of 3–5% of the vehicle mass was therefore highly conservative.{{or|date=September 2024}}

== See also ==
* [[Advanced Passenger Train]]
* [[Adhesion railway]]
* [[Bicycle and motorcycle dynamics]]
* [[Gyrobus]]
* [[Gyrocar]]
* [[Segway HT]]
* [[Lit Motors]]

== References ==
{{reflist}}

== Bibliography ==
* {{cite book| last=Schilovsky| first=Petr Petrovich| title=The Gyroscope, Its construction and Practical Application| publisher=E Spon Publications| year=1922}}
* {{cite journal| last=Cousins| first=H| title=The Stability of Gyroscopic Single Track Vehicles| journal=Engineering 2|pages=678–681 |date=1913}}
* {{cite journal| last=Graham| first=R| title=Brennan, His Helicopter and other Inventions| journal=Aeronautical Journal| date=February 1973|pages=74–82 |volume=77 |issue=746 | doi=10.1017/S0001924000040318| s2cid=117531165}}
* {{cite journal| last=Mee| first=A| title=Harmsworth| journal=Popular Science| volume=3| pages=1680–1693| year=1912}}
* {{cite journal| last=Eddy| first=H.T.| title=The Mechanical Principles of Brennan's Mono-Rail Car| journal=Journal of the Franklin Institute |date=1910 |volume=169 |issue=6 | pages=467–485| doi=10.1016/s0016-0032(10)90004-5| url=https://zenodo.org/record/1428514}}
* {{cite book| last=Tomlinson| first=N| title=Louis Brennan, Inventor Extraordinaire| publisher=John Hallewell Publications| year=1980| isbn=0-905540-18-2}}
* {{cite journal| title=The Scherl Gyroscopic Monorail Car| journal=Scientific American| date=January 22, 1910| volume=102| issue=4| page=84| doi=10.1038/scientificamerican01221910-84| bibcode=1910SciAm.102...84.}}
* {{cite journal| title=The Brennan Mono-Track Vehicle| journal=The Commercial Motor| date=November 18, 1909}}
* {{cite journal| title=The Schilowski Gyroscopic Monorail System| journal=The Engineer| date=January 23, 1913}}
* {{cite journal| last=Hamill| first=P.A.| others=et al.| title=Comments on a Gyro-Stabilised Monorail Proposal| location=Canada| publisher=Control Systems Laboratory| journal=LTR-Cs-77| date=December 1972}}
* {{cite journal| title=Monorail Vehicles| journal=Engineering| date=June 14, 1907| page=794}}
* {{cite book| last1=Rogers| first1=G.F.C.| first2=Y.R.| last2=Mayhew| title=Engineering Thermodynamics, Work and Heat Transfer| edition=third| publisher=Longman| year=1972| page=433}}
* {{cite book| last=Mori| first=Hiroshi| title=Theories and Experiments fro Gyro Monorail| publisher=| year=2017 |url=https://thebbb.net/free/theories-and-experiments-for-gyro-monorails.pdf}}
* {{cite book| last=Mori| first=Hiroshi| title=How to Build a Simple Gyro Monorail| publisher=| year=2017 |url=https://thebbb.net/free/how-to-build-a-simple-gyro-monorail.pdf}}

== External links ==
{{commonscat-inline|Gyro monorail}}
* [http://www.monorails.org/tMspages/Gyro-Dynamics.html Monorail Society Special Feature on Swinney's monorail]
* [http://www.catskillarchive.com/rrextra/odgyro.Html Gyroscope Railroad]
* [https://www.youtube.com/watch?v=kUYzuAJeg3M The Self Balancing Monorail]

{{DEFAULTSORT:Gyro Monorail}}
[[Category:Monorails]]
[[Category:Experimental and prototype gyroscopic vehicles]]
[[Category:Irish inventions]]
[[Category:Australian inventions]]