Maglev is a transport system that uses the magnetic levitation to move vehicles without contact to the guideway. The system uses magnetic forces for levitation, propulsion and guidance of the vehicle, thereby making practically negligible the friction forces and allowing very high speeds.

The technological evolution is making this transportation system competitive and gaining consideration as a viable option for high speed transport system.

Chūō Shinkansen is the holder of the highest operational speed – 505km/h – and of the land speed record for rail vehicles of 603 km/h  (21 April 2015).

Once overcome the issue of contact forces between the vehicle and the guiding system, the main constraint is the air friction. Hence, over time, a few options of pneumatic tube transportation systems ( low pressure or vacuum tube trains) have been proposed – the latest being Hyperloop, a linear induction motor application that uses magnetic levitation and air compressors for high speed transportation.  These systems are able to reach operational speeds of up to 1000 km/h; theoretically the maximum speed in vacuum tubes can be even more that this and is limited mainly by comfort and acceleration/deceleration considerations.

From design perspective, all the magnetic levitation systems are guided systems, similar (not only) from this perspective to roads and railways.

Together with the specifics of this modern system, the Maglev guideway requires also an alignment design. The principles of maglev guideway alignment design are similar to the ones used, for example, in railway track alignment design, with some subtle differences.

Below are summarised a few main differences between the design principles of Maglev Guideway Alignment compared to classical alignment design.

3D stationing

Most of the classical transport systems have such gradients that do not cause relevant difference between the real 3D alignment and its projection on the horizontal plane. Hence, for all these systems, there is a general convention to consider a projected alignment (called Horizontal Alignment) identical in length and stationing to the real 3D alignment.

Most of the Maglev systems are able to provide comfortable riding conditions for gradients up to 10%. The alignment definition of this system is required to be precise due mainly to the placement of the electromagnetic elements of the guideway. Because of this, the alignment stationing is defined in 3D, along the real path of the guideway and not on its horizontal projection as it happens for the other means of transport.

 Maglev transition curve

The clothoid is horizontal transition curve used by default for all transportation systems.

There are a few other types of transition curve, used mainly for high speed railway (not an exhaustive list):

• cosinusoidal transition (or the Japanese transition – half-sine) is the “veteran”, used since 1964 on Shinkansen high-speed railway. It is also the default transition curve for California High Speed.
• Bloss
• Bi-quadratic parabola (Helmert or Schramm transition) – is used on the German DB network together with the clothoid and Bloss.
• Hasslinger transition (Viennese curve) – experimentally used on the Austrian Railway Network. This transition is defined considering the trajectory of the centre of mass of the vehicle instead of considering the train as a material point moving along the track centreline, as it happens for all the other transition curves. This principle of design is reducing significantly the inherent inertial response of the vehicle.
• Klauder spirals – experimentally used on the American Amtrack Railway Network.

The Maglev system uses by default the sinusoidal transition. This curve is providing smooth variation for the vertical and lateral jerk, without the sudden changes found for most of the above transitions, including the clothoid. This smooth variation was seen as an essential requirement in defining the high speed alignment of the Maglev system and it imposed the sinusoidal curve as the default transition used by all the Maglev systems.

Maglev vertical curve

The vertical curve used for road and railway track is parabolic. This curve is providing a practically constant vertical acceleration over its entire length. This acceleration is dependant of speed and the equivalent radius of the vertical curve.

Due to the steep gradients used in the design of up to 10%, but also due to the desire to reduce the dynamic effects caused by the high speed of the Maglev system, the vertical curve used in the guideway design is not the parabola used for other transportation systems. The Maglev system requires the use of a vertical transition curve to allow gradual variation of the change in vertical acceleration. This curve is usually clothoid. The Transrapid Maglev vertical curve is comprised of a central circular curve, characterised by constant vertical acceleration, flanged by two vertical clothoidal transition curves.

Guideway banking angle

Due to the fact that there are no guiding rails nor a standard guideway width, the inclination of the guideway is not expressed in mm, as the railway cant, but it is defined as banking angle – similar to the road superelevation.

The maximum guideway banking angle is 12° for the Transrapid Maglev system which is equivalent to a 310 mm cant (for normal gauge). In some exceptional cases this can be increased to 16°, the equivalent of 410 mm cant.

This very steep inclination is providing an increased alignment flexibility to the Maglev system compared to the conventional High Speed Railway where, the cant is limited to half of these values, considering also that the non-compensated lateral accelerations of both systems are similar.

For example, the minimum radius is 5780 m for a 350 km/h high speed railway alignment defined for a maximum cant of 150 mm (6°) and a cant deficiency of 100 mm (non-compensated lateral acceleration 0.65 mm/s²).

The maglev alignment with a minimum radius of 5780 m is allowing 450 km/h for a guideway banking of 12° and 505 km/h for 16°, for the same non-compensated lateral acceleration of 0.65 mm/s² – this later value defines the maximum speed and design parameters for the Chūō Shinkansen maglev line. 

Alignment defined for the vehicle centre of mass

In road and railway track alignment design the vehicle is considered a material point, moving along the design centreline. The general section of the vehicle and the position of its centre of mass relative to the alignment centreline are ignored. This assumption is used to define easy to follow rules of design and to easily apply and maintain the cant transition on ballasted track – by keeping the inner rail at design level and lifting the outer rail by the full cant value. This principle, especially at low speed, makes no significant difference from riding perspective. Nevertheless, it is causing supplementary inertial forces, inherent to the design and not caused by installation irregularities. (AN: read my post on the orphan rule of cant design for more details).

In order to reduce these design inherent dynamic effects, some of the Maglev systems have their alignment defined for the vehicle section centre of mass – hence the vertical or horizontal transitions are defined considering a theoretical optimum trajectory of the vehicle.

Conclusion

The combination of all these differences, together with some particular elements defined for each specific maglev system, are making the maglev guideway alignment design a very complex and specialised discipline.

References

• BS EN 13848-1:2003 + A1:2008. Railway applications – Track – Track geometry quality – Part 1: Characterisation of track geometry.
• Lever, J. H. (1998). Technical Assessment of Maglev System Concepts: Final Report by the Government Maglev System Assessment Team. US DoT. National Transportation Library (online document)
• RR08-02 (2008). Improving Spiral Geometry for High Speed. US DoT. National Transportation Library (online document)