518 Train Headway Models and Carrying Capacity of Super-Speed Maglev System∗ Shiwei HE∗∗, Rui SONG∗∗ and Tony EASTHAM∗∗∗ Train headway models are established by analyzing the operation of the Transrapid Super-speed Maglev System (TSMS). The variation in the minimum allowable headway for trains of different speeds and consists is studied under various operational constraints. A potential Beijing – Shanghai Maglev line is used as an illustration to undertake capacity anal- yses with the model and methods. The example shows that the headway models for analyzing the carrying capacity of Maglev systems are very useful for the configurational design of this new transport system. Key Words: Maglev, Headway, Modeling, Line Capacity els of wheel-on-rail systems have been studied for dif- 1. Introduction ferent control schemes, such as fixed block and moving The super-speed maglev system Transrapid is a block(6). However, no detailed headway models for opera- guideway-bound transportation system for passengers and tional analysis of Maglev systems have yet been reported. high-value cargo traffic. It is one of the most significant in- The contents of this paper are as follows. First, TSMS novations in guided ground transport technology since the operation is analyzed and train following headway models construction of the first railroad. The non-contact tech- are set up. Second, the variation of minimum allowable nology of TSMS – controlled magnetics are used instead headway for trains of different consists is studied. Third, of mechanical components – overcomes for the first time carrying capacity of a Maglev system is calculated. The the limitations of wheel-on-rail technology. In operation, example of a Beijing – Shanghai Maglev line is used for Transrapid is faster and quieter than high speed rail sys- capacity analysis with the model and methods. Lastly, the tems. It is virtually impossible to derail and is comfort- main conclusions of this paper are presented. able at all speeds. The guideway of Transrapid requires 2. Dynamic Train Headway Models less space and can be flexibly aligned to accommodate lo- cal topographic variations. However, its cost-effectiveness 2. 1 Minimum headway criteria has yet to be proven. The first criterion for minimum headway of any The Transrapid system has been developed over 35 guided ground transportation system is that if a vehicle years(1) – (5). The first commercial Maglev line has been should stop suddenly for whatever reason, the following built at Pudong in Shanghai, China with German tech- vehicle must be able to come to a safe stop at an accept- nology. Also, the techno-economic attributes of Maglev able deceleration before reaching the location of the im- relative to high-speed wheel-on-rail technology are be- mobilized vehicle. For the case of a vehicle with a cruising ing evaluated for what is likely to be the first high-speed speed of 450 km/h, for example, the distance and time to inter-city line in China (Beijing – Shanghai). Train head- stop at a deceleration of 0.15 g are 5.2 km and 83 seconds, way is important both for safety and carrying capacity respectively. The minimum headway is, of course, speed when undertaking operational analysis. Headway mod- dependent, and other factors are likely to dictate a higher ∗ operational minimum headway. We now consider TSMS. Received 15th December, 2003 (No. 03-5152) 2. 2 Train following moving headway models for ∗∗ School of Traffic & Transportation, Northern Jiaotong TSMS University, Xizhimenwai, Beijing 100044, P.R. China. E-mail: [email protected] In the single-sided mode, one side of each power ∗∗∗ Department of Civil Engineering, Hong Kong University substation supplies energy to a section of the distributed of Science and Technology, Clear Water Bay, Kowloon, linear synchronous motor (LSM) armature in the guide- Hong Kong. E-mail: [email protected] way, while the adjacent sections are un-energised. The Series C, Vol. 47, No. 2, 2004 JSME International Journal 519 headway will be used as the dynamic separation of two trains in the following analysis. 2. 3 Departing, arrival headway models When the trains pass an off-line station and do not stop, the minimum headway is similar to the train follow- ing moving headway as determined by Eqs. (1) – (4). If at Fig. 1 Minimum train separation for a single-sided energy sup- least one train stops at the station, the minimum headway ply system must be increased. 2. 3. 1 Departing headway models The headway for a train leaving an off-line station should at least meet Eqs. (5) and (6). f L +0.5L + L + L f 1 j l,q a s Iz = tu +t f + (5) v¯q f 1 f = + + + + + Lz Lu L f L j 0.5Ll,q La Ls (6) f 1 f 1 where Iz and Lz are headway and distance interval of the departing train relative to the leading train when the lead- Fig. 2 Minimum train separation for a double-sided energy ing train needs to leave at least one energy supply section supply system and the merging switch must be changed to allow the de- parting train to join the mainline; t f , tu, L f and Lu are times minimum separation of two Maglev trains is thus two of changing and confirming the integrity of the switch and LSM sections (see Fig. 1). For the double-sided mode, the corresponding distances advanced by the leading train; each power-substation can energise two sequential sec- and La is a safety distance. Also, Lg is length of switch; tions, and the minimum separation of two Maglev trains Lb is redundancy distance when a train stops;v ¯q is the av- becomes just one section of the propulsion system (see erage velocity of the leading train when passing through Fig. 2). Note that each section of the propulsion system f the switch in its mainline position; and L j is the distance may be subdivided and each sub-section switched sequen- between the center of the station and the furthest switch ffi tially to increase motor e ciency. in the departure direction. Suppose one station (together In order to assure safety with the two configurations with its deceleration and acceleration lanes) corresponds of energy supplying system, the minimum separation (Lz) to an energy supply section with length Ls,wehave: between Transrapid trains should meet Eqs. (1) and (3), f L = max(0.5Ls,Lg +0.5Ll,h + Lb)(7) respectively. The time interval (headway) (Iz) should meet j Eqs. (2) and (4). After passing through the merging switch, the leading and following trains are on the same route. Thus, train depart- Lz = Lc + Lz,h + La +0.5Ll,q +0.5Ll,h +2Ls (1) + + + + ing headway should also meet Eqs. (1) – (4). Departing Lz,h La 0.5l,h 0.5Ll,q 2Ls f Iz = tc + (2) headway (I ) is the greater of the headway of Eqs. ((2) or v z h (4)) and (6). We have : Lz = Lc + Lz,h + La +0.5Ll,q +0.5Ll,h + Ls (3) I f = max{I ,I f 1} (8) Lz,h + La +0.5l,q +0.5Ll,h + Ls z z z Iz = tc + (4) vh The calculation method for train departing headway from where Lc and tc are the distance and time advanced by the a station yard is similar to that for intermediate stations. following train when the leading train transmits informa- When trains depart from yards of different lengths, safe tion to the following train, via the central control system. train headway is assured by considering switch activation f Lz,h is the dynamic braking distance of the following train. time and braking time before the mainline switch. L j is Ll,q and Ll,h are the lengths of the leading and following then calculated as: f trains, respectively. vh is the average velocity of the fol- = + + + L j max(0.5Ls,Lg 0.5Ll,h La lz,h)(9) lowing train in Lz. La is a safety distance, and Ls is the separation of adjacent power sub-stations. The result can be put into Eqs. (5) and (6) to obtain the The train dynamic headway models of Eqs. (1) – (4) appropriate minimum train departing headway. are basic conditions for assuring safe train operation. In 2. 3. 2 Arrival headway models The headway ff order to maximize line capacity, the following train should for a train stopping at an o -line station should meet maintain minimum dynamic headway. If headway is in- Eqs. (10) and (11). d creased, the leading train will not influence the follow- L +0.5Ll,h + La + Lz,h d1 = + + j ing train in normal operational conditions. This minimum Iz tu td (10) v¯h JSME International Journal Series C, Vol. 47, No. 2, 2004 520 d1 = + + d + + + Lz Lu Ld L j 0.5Ll,h La Lz,h (11) d1 d1 where Iz and Lz are the headway and distance interval of the arriving train when the leading train does not stop and the divergent switch position is changed to allow the arriving train onto the deceleration lane into the station; td, tu, Ld and Lu are times of changing and confirming the integrity of the divergent switch, and the corresponding distances advanced by the following train;v ¯h is the average d velocity when the following train passes the switch; L j is the distance between the furthest switch in the arrival direction and the center of the station. Suppose again that Fig. 3 Transrapid vehicle headway the station lane corresponds to one energy supply section with length Ls,wehave: of a leading train departing from a station and the follow- Ld = max(0.5L ,L +0.5L + L ) (12) j s g l,q b ing train passing that station will be discussed in 3.2.2.