Design Principles High-speed Maglev System. Information (MSB, 2007)

High-speed maglev systems

Maglev Technical Committee

Design principles

Guideway

Annex II-B: Calculated vibration coefficients

General

(1)

The examples of the vibration coefficient diagrams given below include the global vibration coefficient

ϕ_Bg,z or ϕ_Bg,z,WSE for simple beams with spans L_St= 12.384 m and L_St= 24.768 m. This coefficient is not

dependent on the structural design or the construction method. In this regard, the vibration coefficients

indicate the dynamic camber as a result of the effects of the moved vehicle in the z direction.

(2)

Using the example of the loads E in the centre of the girder (e.g. deflection, internal forces, stresses),

the diagrams below show how the load develops over time in principle as a result of a vehicle passing

over and the associated assessment variables.

Fig. 161 - Passage of the vehicle along the simple beam with the assessment variable w in the midspan

E(t)

max E_dyn

∆E-

max ∆E

dyn

max E_stat

min E_dyn

Fig. 162 - Load development over time as a result of a vehicle passing along the simple beam

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(3)

Idealised mathematical models form the basis of the diagrams. These diagrams consider the dynamic

cambers as a result of period and harmonic stimulations (“Impact" and “Resonance”); cf. in this regard

R2, R3 and R4.

(4)

The following parameters form the basis of the diagrams:

• Span, simple beam, where:

L_St = 12.384 m and L_St = 24.768 m

• Vehicle lengths:

2; 4; 6; 10 sections

• Damping factor D:

0%; 0.3%; 0.6%; 1.6%

• Vehicle load scenarios:

as per Chapter 9

(5)

The following assessment variables are also covered by the diagrams:

• Deflection

max/min w_dyn

• Bending moment

max/min M_y,dyn

• Shearing load

max/min V_z,dyn

(6)

The diagrams were prepared in relation to furnishing the following proof:

• The vibration coefficient for furnishing proof of performance capability and loadbearing capacity

max E

dyn

Bg,z

max E

stat

• The vibration coefficient for furnishing proof of metal fatigue for determining the maximum load

amplitude:

(

max E

−min E

)

dyn

Bg,z,WSE

max E

stat

(7)

The vibration coefficients are read off using the non-dimensional value k in the diagrams. The value k

is established as follows depending on the span L_St, the speed of the vehicle v_Fzg and the first vertical

natural bending frequency f_z,1 of the support structure:

⋅

z,1

Fzg

Area of application

(1)

When using vibration coefficient diagrams (figs. 164 to 179), the following area of application must be

considered:

• a span which is approximately equal to the system length L_St ≈ L_Sys;

• girder-like, rigidly supported simple beams with an approximately constant weight per unit area µ

and flexural strength EI;

• with an approximately rigid connection (GA_V → ∞);

• specification of the damping (damping factor D = 0%; 0.3%; 0.6%; 1.6%);

(for values in-between, the next smallest damping factor should conservatively be specified.)

• vehicle load scenarios as per Chapter 9;

• magnet end poles of the levitation magnets shall carry at least 25% of the main magnet pole

loads;

• calculation only for vertical components of the effects arising from the vehicle, globally in the z di-

rection;

• application to deflection w, the bending moment M_y and the shearing load V_z;

• the diagrams do not generally apply to vehicle speeds where the vehicle - guideway interaction as

a result of magnet control must be considered (low vehicle speeds v_Fzg < 50 m/s), and especially

not to stationary vehicles v_Fzg = 0 m/s.

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(2)

The vibration coefficients for metal fatigue ϕ_Bg,z,WSE assist in determining the maximum load amplitude

max ∆E_dyn = ϕ_Bg,z,WSE ⋅ max E_stat = max E_dyn - min E_dyn, which shall only be specified once per vehicle

crossing.

When specifying a single-stage unit, it must be examined whether the existing double amplitudes of the load

progression are below the cut-off limit as a result of vibrations ∆E_dyn. This is satisfied as long as the following

applies to ∆E_dyn:

∆E

⋅γ

⋅

max E

⋅

(ϕ

−

< ∆E

dyn

stat

Bg,z

cut-off−limit

If this condition is not satisfied, and for materials or fatigue details without a “cut off limit” area, these oscilla-

tion amplitudes must also be considered in the metal fatigue proofs.

Examples of application

(1)

To illustrate the application of the vibration coefficient diagrams, examples are cited below of type I

support structures which are constructed in concrete or steel.

(2)

The following parameters form the basis of the examples:

• cross-sections in the panel area as per fig. 163;

• data concerning the rigidity EI and the weight per unit area µ from R1;

• simple beams with a span of L_St = 24.768 m;

• a damping factor of D = 0.6% for prestressed concrete girders;

• a damping factor of D = 0.3% for welded steel girders;

• a vehicle length consisting of 4 sections;

• max v_Fzg = 450 km/h = 125 m/s;

Type I, concrete construction

Type I, steel construction

EI_y = 18800 MNm²

EI_y = 23200 MNm²

µ = 3900 kg/m

µ = 2000 kg/m

Fig. 163 - Support structures for the example of application - cross-sections in the panel area

[Key to diagram:

Schott = bulkhead]

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(3)

Determining the k values for reading off the global vibration coefficients from the diagrams

• As regards the Type 1 concrete construction support structure:

1,88⋅10

⋅f

24,768⋅5,62

z,1

⋅

5,62 Hz

→

=1,11

z,1

2⋅24,768

3900

125

Fzg

⇒ from fig. 174:

Bg,z

=1,15

+1,0⋅(1,4

-k)=1,44

⇒ from fig. 175:

Bg,z,WSE

=1,8

• As regards the Type 1 steel construction support structure:

2,32⋅10

24,768⋅8,72

⋅

8,72 Hz

→

=1,73

z,1

2⋅24,768

2000

125

⇒ from fig. 174:

= 1,15

Bg,z

⇒ from fig. 175:

= 1,3

Bg,z,WSE

(4)

When choosing the damping factor, Chapter 7.4.3 must be taken into consideration.

(5)

The actual (measured) natural frequencies may deviate from the natural frequencies which have been

calculated. The other results shall then be adapted accordingly.

Examples of vibration coefficient diagrams

General

(1)

The following diagrams present examples of the vibration coefficients ϕ_Bg,z and ϕ_Bg,z,WSE in relation to

the spans and vehicle lengths listed in Table 116.

(2)

As a result of the investigations in R2, R3 and R4, vibration coefficient calculation lines were deter-

mined in relation to different areas of k and the damping values analysed which take into account the

dynamic cambers as a result of period and harmonic stimulation following a vehicle crossing.

Span

Vehicle length

Page

2 sections

Figs. 164 and 165

4 sections

Figs. 166 and 167

L_St = 12.384 m

6 sections

Figs. 168 and 169

10 sections

Figs. 170 and 171

2 sections

Figs. 172 and 173

4 sections

Figs. 174 and 175

L_St = 24.768 m

6 sections

Figs. 176 and 177

10 sections

Figs. 178 and 179

Table 116 - Spans and vehicle lengths of the vibration coefficient diagrams provided by way of example

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Vibration coefficient diagrams for simple beams where L_St = 12.384 m

Vibration coefficients for 2-section vehicles

D = 0 %; 0,3 %; 0,6 %

1.9

D = 1,6 %

1.8

ϕ_Bg,z

1.8

D = 0%; 0.3%; 0.6%

D = 1.6%

0.75 ≤ k ≤ 1.4

1.2 + 1.077 (1.4-k)

1.1 + 1.231 (1.4-k)

1.7

1.4 < k ≤ 4.5

1.2

1.1

1.7

4.5 < k < ∞

1.1

1.6

1.5

1.4

1.3

D = 0%; 0.3%; 0.6%

1.2

D = 1.6%

D = 0%; 0.3%; 0.6%; 1.6%

1.1

0.75

1.4

4.5

k [-]

Fig. 164 - ϕ_Bg,z for simple beams where L_St = 12.384 m - 2-section vehicle

2.5

D = 0%

D = 0 %

D = 0,3 %

2.4

D = 0.3%, 0.6%

2.4

D = 1,6 %

D = 1.6%

2.3

ϕ_Bg,z,WSE

2.2

D = 0%

D = 0.3%

D = 0.6%

D = 1.6%

0.75 ≤ k ≤ 1.0

2.5

2.4

2.3

1.0 ≤ k ≤ 1.4

1.3 + 3.0 (1.4-k)

1.3 + 2.75 (1.4-k)

1.2 + 2.75 (1.4-k)

1.4 < k ≤ 4.5

1.3

1.2

4.5 < k ≤ 8.5

1.2

1.1

8.5 < k < ∞

1.1

1.8

1.6

1.4

D = 0%, 0.3%, 0.6%

1.3

D = 1.6%

D = 0%, 0.3%

1.2

D = 0.6%, 1.6%

D =

0% - 1.6%

1.1

0.75 1

1.4

4.5

8.5

k [-]

Fig. 165 - ϕ_{Bg,z, WSE} for simple beams where L_St = 12.384 m - 2-section vehicle

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Vibration coefficients for 4-section vehicles

D = 0 %2

D = 0,3 %

D = 0,6 %

1.9

D = 1,61.9

ϕ_Bg,z

1.8

D = 0%

D = 0.3%; 0.6%

D = 1.6%

1.8

075 ≤ k ≤ 1.4

1.4 + 0.923 (1.4-k)

1.3 + 0.923 (1.4-k)

1.2 + 0.769 (1.4-k)

1.4 < k ≤ 4.5

1.4

1.3

1.2

1.7

4.5 < k ≤ 8.5

1.2

1.1

8.5 < k < ∞

1.1

1.6

D = 0%

1.4

D = 0.3%; 0.6%

1.3

D =1.6%

D = 0%

1.2

D = 0.3%; 0.6%; 1.6%

D =

0% - 1.6%

1.1

0.75

1.4

4.5

8.5

k [/]

Fig. 166 - ϕ_Bg,z for simple beams where L_St = 12.384 m - 4-section vehicle

D = 0 %

D = 0,3 %

D = 0,6 %

D = 1,6 %

2.8

ϕ_Bg,z,WSE

2.6

D = 0%

D = 0.3%

D = 0.6%

D = 1.6%

2.6

0.75 ≤ k ≤ 1.4

1.7 + 2.0 (1.4-k)

1.6 + 1.846 (1.4-k)

1.5 + 2.0 (1.4-k)

1.3 + 2.0 (1.4-k)

1.4 < k ≤ 4.5

1.7

1.6

1.5

1.3

2.4

4.5 < k ≤ 8.5

1.4

1.2

1.1

2.4

8.5 < k < ∞

1.2

1.1

2.2

1.8

D = 0%

1.7

D = 0.3%

1.6

D = 0.6%

1.5

1.4

D = 1.6%

1.3

D = 0.3%, 0.6%

D = 0%

1.2

D =

0.3% - 1.6%

1.1

0.75

1.4

4.5

8.5

k [-]

Fig. 167 - ϕ_{Bg,z, WSE} for simple beams where L_St = 12.384 m - 4-section vehicle

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Vibration coefficients for 6-section vehicles

2.2

D = 0 %2.2

D = 0,3 %

2.1

D = 0,6 %

2.1

D = 1,6 %

ϕ_Bg,z

D = 0%

D = 0.3%

D = 0.6%

D = 1.6%

1.9

0.75 ≤ k ≤ 1.4

1.6 + 0.923 (1.4-k)

1.4 + 1.077 (1.4-k)

1.3 + 1.077 (1.4-k)

1.2 + 0.769 (1.4-k)

1.9

1.4 < k ≤ 4.5

1.6

1.4

1.3

1.2

1.8

4.5 < k ≤ 8.5

1.3

1.2

1.1

1.8

8.5 < k < ∞

1.2

1.1

1.7

D = 0%

1.6

D = 0.3%

1.4

1.3

D = 0.6%

D = 0%

1.3

D = 1.6%

D = 0.3%

= 0%

1.2

D = 0.6%; 1.6%

D =

0.3% - 1.6%

1.1

0.75

1.4

4.5

8.5

k [/]

Fig. 168 - ϕ_Bg,z for simple beams where L_St = 12.384 m - 6-section vehicle

3.4

D = 0 %

D = 0,3 %

D = 0,6 %

3.2

D = 1,6 %

ϕ_Bg,z,WSE

D = 0%

D = 0.3%

D = 0.6%

D = 1.6%

2.8

0.75 ≤ k ≤ 1.4

2.0 + 2.154 (1.4-k)

1.7 + 2.308 (1.4-k)

1.5 + 2.308 (1.4-k)

1.3 + 2.0 (1.4-k)

2.8

1.4 < k ≤ 4.5

2.0

1.7

1.5

1.3

4.5 < k ≤ 8.5

1.6

1.3

1.2

1.1

2.6

8.5 < k < ∞

1.4

1.2

1.1

2.4

2.2

D = 0%

1.8

D = 0.3%

1.7

D = 0%

1.6

D = 0.6%

1.5

D = 0%

1.4

D = 1.6%

D = 0.3%

1.3

D = 0.6%

D = 0.3%

1.2

D = 1.6%

D = 0.6% - 1.6%

1.1

0.75

1.4

4.5

8.5

k [-]

Fig. 169 - ϕ_{Bg,z, WSE} for simple beams where L_St = 12.384 m - 6-section vehicle

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Vibration coefficients for 10-section vehicles

2.5

D = 0 %

D = 0,3 %

2.4

D = 0,62.4

D = 1,6 %

2.3

ϕ_Bg,z

2.2

D = 0%

D = 0.3%

D = 0.6%

D = 1.6%

2.2

0.75 ≤ k ≤ 1.4

1.9 + 0.923 (1.4-k)

1.5 + 1.231 (1.4-k)

1.4 + 1.231 (1.4-k)

1.2 + 0.769 (1.4-k)

1.4 < k ≤ 4.5

1.9

1.5

1.4

1.2

4.5 < k ≤ 8.5

1.5

1.2

1.1

8.5 < k < ∞

1.3

1.1

1.9

1.8

1.7

1.6

1.5

D = 0.3%

D = 0%

1.5

1.4

D = 0.6%

1.4

1.3

1.2

D =1.6%

D = 0.3%

1.2

1.1

D = 0.6%; 1.6%

D = 0.3% - 1.6%

1.1

0.75

1.4

4.5

8.5

k [/]

Fig. 170 - ϕ_Bg,z for simple beams where L_St = 12.384 m - 10-section vehicle

D = 0 %

D = 0,3 %

3.8

D = 0,63.

D = 1,6 %

3.6

ϕ_Bg,z,WSE

3.6

D = 0%

D = 0.3%

D = 0.6%

D = 1.6%

3.4

0.75 ≤ k ≤ 1.4

2.7 + 2.0 (1.4-k)

1.9 + 2.923 (1.4-k)

1.6 + 3.077 (1.4-k)

1.3 + 2.615 (1.4-k)

1.4 < k ≤ 4.5

2.7

1.9

1.6

1.3

3.2

4.5 < k ≤ 8.5

1.9

1.4

1.2

1.1

8.5 < k < ∞

1.6

1.2

1.1

2.8

2.7

2.6

2.4

2.2

D = 0.3%

D = 0%

1.9

1.8

D = 0.6%

1.6

D = 0.3%

1.4

D = 1.6%

1.3

D = 0.6%

D = 0.3%

1.2

1.1

D = 1.6%

D =

0.6% - 1.6%

1.1

0.75

1.4

4.5

8.5

k [-]

Fig. 171 - ϕ_{Bg,z, WSE} for simple beams where L_St = 12.384 m - 10-section vehicle

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Vibration coefficient diagrams for simple beams where L_St = 24.768 m

Vibration coefficients for 2-section vehicles

D = 0 %, 0,3 %, 0,6 %, 1,6 %

1.5

ϕ_Bg,z

1.45

D = 0%; 0.3%; 0.6%; 1.6%

1.45

1.05 ≤ k ≤ 1.4

1.2 + 0.857 (1.4-k)

1.4 < k ≤ 2.5

1.2

1.4

2.5 < k ≤ 4.5

1.1

4.5 < k < ∞

1.05

1.35

1.3

1.25

1.2

1.15

1.1

D = 0%; 0.3%; 0.6%; 1.6%

1.05

1.4

2.5

4.5

8.5

k [-]

Fig. 172 - ϕ_Bg,z for simple beams where L_St = 24.768 m - 2-section vehicle

D = 0 %, 0,3 %, 0,6 %, 1,1.7

1.7

ϕ_Bg,z,WSE

D = 0%; 0.3%; 0.6%; 1.6%

1.6

1.05 ≤ k ≤ 1.3

1.7

1.3 ≤ k ≤ 1.4

1.3 + 4.0 (1.4-k)

1.4 < k ≤ 2.5

1.3

1.5

2.5 < k ≤ 4.5

1.2

1.5

4.5 < k ≤ 8.5

1.1

8.5 < k < ∞

1.05

1.4

1.3

1.2

D = 0%; 0.3%; 0.6%; 1.6%

1.1

1.05

1.4

2.5

4.5

8.5

1.3

k [-]

Fig. 173 - ϕ_{Bg,z, WSE} for simple beams where L_St = 24.768 m - 2-section vehicle

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Vibration coefficients for 4-section vehicles

D = 0 %, 0,3 %, 0,6 %, 1,6 %

1.5

ϕ_Bg,z

1.45

D = 0%, 0.3%, 0.6% 1.6%

1.45

1.05 ≤ k ≤ 1.4

1.15 + 1.0 (1.4-k)

1.4 < k ≤ 2.5

1.15

1.4

2.5 < k ≤ 8.5

1.10

8.5 < k < ∞

1.05

1.35

1.3

1.25

1.2

1.15

D = 0%; 0.3%; 0.6%; 1.6%

1.1

1.05

1.4

2.5

4.5

8.5

k [-]

Fig. 174 - ϕ_Bg,z for simple beams where L_St = 24.768 m - 4-section vehicle

1.9

D = 0%; 0.3%

D = 0 %, 0,1.9

D = 0,6 %

D = 1,6 %

D = 0.6%

1.8

ϕ_Bg,z,WSE

1.8

D = 0%; 0.3%

D = 0.6%

D = 1.6%

1.05 ≤ k ≤ 1.3

1.9

1.8

1.7

1.3 ≤ k ≤ 1.4

1.3 + 6.0 (1.4-k)

1.3 + 5.0 (1.4-k)

1.3 + 4.0 (1.4-k)

1.7

1.4 < k ≤ 2.5

1.3

2.5 < k ≤ 8.5

1.2

1.1

1.6

8.5 < k < ∞

1.1

1.05

1.6

1.5

1.4

D = 0%; 0.3%; 0.6%; 1.6%

1.3

D = 0%; 0.3%; 0.6%

1.2

D = 1.6%

1.1

D =

1.6%

1.05

1.4

2.5

4.5

8.5

1,3

k [-]

Fig. 175 - ϕ_{Bg,z, WSE} for simple beams where L_St = 24.768 m - 4-section vehicle

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Vibration coefficients for 6-section vehicles

D = 0 %

1.5

D = 0,3 %, 01.5

D = 1,6 %

1.45

ϕ_Bg,z

1.45

D = 0%

D = 0.3%; 0.6%

D = 1.6%

1.05 ≤ k ≤ 1.4

1.2 + 0.857 (1.4-k)

1.15 + 1.0 (1.4-k)

1.1 + 1.143 (1.4-k)

1.4

1.4 < k ≤ 8.5

1.2

1.15

1.1

8.5 < k < ∞

1.1

1.05

1.35

1.3

1.25

D = 0%

1.2

D = 0.3%; 0.6%

1.15

D = 1.6%

D =

1.1

D =

0.3% - 1.6%

1.05

1.4

2.5

4.5

8.5

k [-]

Fig. 176 - ϕ_Bg,z for simple beams where L_St = 24.768 m - 6-section vehicle

2.1

D = 0 %

2.1

D = 0,3 %

D = 0,6 %

D = 1,6 %

ϕ_Bg,z,WSE

1.9

D = 0%

D = 0.3%

D = 0.6%

D = 1.6%

1.9

1.05 ≤ k ≤ 1.3

2.1

2.0

1.9

1.8

1.3 ≤ k ≤ 1.4

1.4 + 7.0 (1.4-k)

1.35 + 6.5 (1.4-k)

1.3 + 6.0 (1.4-k)

1.25 + 5.5 (1.4-k)

1.8

1.4 < k ≤ 2.5

1.4

1.35

1.3

1.25

2.5 < k ≤ 8.5

1.4

1.25

1.2

1.1

1.7

8.5 < k < ∞

1.2

1.1

1.05

1.6

1.5

D = 0%

1.4

1.35

1.3

D = 0.3%

1.25

D = 0.6%

D = 0%

1.2

D = 1.6%

D =

0.3% - 0.6%

1.1

D = 1.6%

1.05

1.4

2.5

4.5

8.5

1.3

k [-]

Fig. 177 - ϕ_{Bg,z, WSE} for simple beams where L_St = 24.768 m - 6-section vehicle

Title

High-speed Maglev Systems - Design principles

Guideway - Part II: Design

Doc. no.:

57288

Version

White Paper Issue date

15.02.2007

Page 140

High-speed maglev systems

Maglev Technical Committee

Design principles

Guideway

Vibration coefficients for 10-section vehicles

D = 0 %

1.5

D = 0,3 %, 0,1.5

D = 1,6 %

1.45

ϕ_Bg,z

1.45

D = 0%

D = 0.3%; 0.6%

D = 1.6%

1.05 ≤ k ≤ 1.4

1.3 + 0.571 (1.4-k)

1.2 + 0.857 (1.4-k)

1.15 + 0.714 (1.4-k)

1.4

1.4 < k ≤ 2.5

1.3

1.2

1.15

2.5 < k ≤ 8.5

1.3

1.2

1.05

1.35

8.5 < k < ∞

1.1

1.05

1.35

D = 0%

1.3

1.25

D = 0.3%; 0.6%

1.2

1.15

D =

1.1

D = 1.6%

D = 0.3% - 1.6%

1.05

1.4

2.5

4.5

8.5

k [-]

Fig. 178 - ϕ_Bg,z for simple beams where L_St = 24.768 m - 10-section vehicle

D = 0 2

2.3

D = 0,3 %

D = 0,6 %

2.2

D = 1,6 %

2.1

ϕ_Bg,z,WSE

D = 0%

D = 0.3%

D = 0.6%

D = 1.6%

1.05 ≤ k ≤ 1.4

1.5 + 2.286 (1.4-k)

1.4 + 2.0 (1.4-k)

1.4 + 1.714 (1.4-k)

1.3 + 1.429 (1.4-k)

1.4 < k ≤ 2.5

1.5

1.4

1.3

1.9

2.5 < k ≤ 8.5

1.5

1.4

1.2

1.1

1.9

8.5 < k < ∞

1.2

1.1

1.05

1.8

1.7

1.6

1.5

D = 0%

1.5

= 0.3%; 0.6%

D = 0.3%

1.4

= 1.6%

1.3

D = 0.6%

D =

1.2

D = 1.6%

D = 0.3% - 0.6%

1.1

1.05

D = 1.6%

1.05

1.4

2.5

4.5

8.5

k [-]

Fig. 179 - ϕ_{Bg,z, WSE} for simple beams where L_St = 24.768 m - 10-section vehicle

Title

High-speed Maglev Systems - Design principles

Guideway - Part II: Design

Doc. no.:

57288

Version

White Paper Issue date

15.02.2007

Page 141

High-speed maglev systems

Maglev Technical Committee

Design principles

Guideway

Annex II-C: Limit values for routing elements

According to Chapter 4.1.7 of the Guideway design principles for high-speed maglev systems - Part IV:

Routing, the combination of the routing elements - horizontal radius R_H, vertical radius R_V and the lateral

incline of the guideway α - is limited by the R_x,zcriterion. In this regard, the limit value R_x,z is also dependent

on the guideway distortion ∆α. Table 117 gives examples of combination possibilities for routing parameter

limit values.

The longitudinal incline (slope, gradient) is set at s = 0% in Table 117.

R_x,z,min = 530 m where the distortion ∆α = 0°/m

Lateral incline α

Horizontal radius R_H

Vertical radius R_V,(K/W)

0°

350 m

R_V,W ≤ - 530 m

R_V,K≥ 530 m

12°

350 m

R_V,W ≤ - 756 m

R_V,K≥ 530 m

5050 m

R_V,W ≤ - 530 m

R_V,K≥ 554 m

R_x,z,min = 1100 m where the distortion ∆α = 0.1°/m

0°

350 m

R_V,W ≤ - 1100 m

R_V,K≥ 1100 m

12°

350 m

R_V,W ≤ - 3105 m

R_V,K≥ 651 m

Table 117 - Limit values for combinations of routing elements

Annex II-D: General limit values relating to de-

formation

The tables of general limit values relating to deformation are in the process of being drawn up. The deforma-

tion limit values to be specified shall be coordinated with the competent supervisory authority, where neces-

sary, until the report is complete.

Annex II-E: Tables of the magnetic forces as a

result of cross-winds (Q9a)

The following tables indicate the appurtenant guidance and levitation magnet forces of the advancing end

and middle sections for vehicle speeds of 0 km/h, 200 km/h, 300 km/h, 400 km/h and 500 km/h and cross-

Title

High-speed Maglev Systems - Design principles

Guideway - Part II: Design

Doc. no.:

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Version

White Paper Issue date

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High-speed maglev systems

Maglev Technical Committee

Design principles

Guideway

Guidance magnet forces p_y,W,FMTi in [kN/m]

[m/s]

37.1

13.6

19.5

14.1

13.6

13.8

11.0

8.1

7.5

6.1

4.9

1.8

1.3

35.5

13.1

18.9

13.6

13.0

13.3

10.5

7.8

7.2

5.9

4.7

1.8

1.2

33.9

12.7

18.2

13.0

12.5

12.7

10.1

7.5

6.9

5.7

4.5

1.7

1.2

32.4

12.2

17.6

12.5

12.0

12.2

9.7

7.2

6.7

5.4

4.3

1.6

1.1

30.9

11.7

16.9

12.0

11.5

11.6

9.2

6.9

6.4

5.2

4.2

1.6

1.1

29.4

11.3

16.3

11.4

11.0

11.1

8.8

6.6

6.1

5.0

4.0

1.5

1.0

27.9

10.8

15.6

10.9

10.5

10.6

8.4

6.3

5.8

4.7

3.8

1.5

1.0

26.5

10.4

15.0

10.4

10.0

10.1

8.0

6.0

5.6

4.5

3.6

1.4

0.9

25.1

9.9

14.4

9.9

9.5

9.6

7.6

5.7

5.3

4.3

3.4

1.3

0.9

23.8

9.5

13.8

9.4

9.0

9.1

7.2

5.4

5.1

4.1

3.3

1.3

0.9

22.5

9.1

13.2

9.0

8.6

6.8

5.1

4.8

3.9

3.1

1.2

0.8

21.2

8.6

12.6

8.5

8.1

8.2

6.4

4.9

4.6

3.7

2.9

1.2

0.8

19.9

8.2

12.0

8.0

7.7

6.1

4.6

4.3

3.5

2.8

1.1

0.7

18.7

7.8

11.4

7.6

7.3

5.7

4.3

4.1

3.3

2.6

1.0

0.7

17.5

7.4

10.8

7.1

6.8

5.4

4.1

3.9

3.1

2.5

1.0

0.7

16.3

7.0

10.3

6.7

6.4

5.0

3.8

3.6

2.9

2.3

0.9

0.6

Levitation magnet forces p_z,W,TMTi in [kN/m] (+/-)

[m/s]

(1)

7.4

5.6

6.8

4.7

8.3

2.0

5.6

3.2

3.8

4.2

4.8

2.6

5.0

1.4

3.7

7.1

5.4

6.5

4.5

8.0

1.9

5.4

3.1

3.6

4.0

4.6

2.5

4.8

1.4

3.6

6.8

5.2

6.3

4.4

7.7

1.8

5.2

3.0

3.5

3.9

4.4

2.4

4.6

1.3

3.4

6.5

5.0

6.0

4.2

7.4

1.8

5.0

2.8

3.3

3.7

4.2

2.3

4.4

1.3

3.3

6.3

4.8

5.7

4.0

7.1

1.7

4.7

2.7

3.2

3.5

4.0

2.2

4.2

1.2

3.1

6.0

4.6

5.5

3.8

6.7

1.6

4.5

2.6

3.1

3.4

3.9

2.1

4.1

1.2

3.0

5.7

4.4

5.2

3.7

6.4

1.5

4.3

2.5

2.9

3.2

3.7

2.0

3.9

1.1

2.9

5.4

4.2

5.0

3.5

6.1

1.5

4.1

2.3

2.8

3.1

3.5

1.9

3.7

1.1

2.7

5.2

4.0

4.7

3.3

5.8

1.4

3.9

2.2

2.6

2.9

3.3

1.8

3.5

1.0

2.6

4.9

3.8

4.5

3.2

5.6

1.3

3.7

2.1

2.5

2.8

3.2

1.7

3.3

1.0

2.5

4.7

3.6

4.2

3.0

5.3

1.2

3.6

2.0

2.4

2.7

3.0

1.6

3.2

0.9

2.3

4.4

3.5

4.0

2.9

5.0

1.2

3.4

1.9

2.2

2.5

2.8

1.5

3.0

0.9

2.2

4.2

3.3

3.8

2.7

4.7

1.1

3.2

1.8

2.1

2.4

2.7

1.4

2.8

0.8

2.1

3.9

3.1

3.6

2.5

4.5

1.0

3.0

1.7

2.0

2.2

2.5

1.4

2.7

0.8

2.0

3.7

2.9

3.4

2.4

4.2

1.0

2.8

1.6

1.9

2.1

2.4

1.3

2.5

0.7

1.9

3.5

2.8

3.1

2.3

3.9

0.9

2.7

1.5

1.8

2.0

2.2

1.2

2.4

0.7

1.7

Table 118 - Magnetic forces as a result of cross-winds: end section, v_Fzg = 500 km/h, v_W = 25 .. 40 m/s

Title

High-speed Maglev Systems - Design principles

Guideway - Part II: Design

Doc. no.:

57288

Version

White Paper Issue date

15.02.2007

Page 144

High-speed maglev systems

Maglev Technical Committee

Design principles

Guideway

Guidance magnet forces p_y,W,FMTi in [kN/m]

[m/s]

16.3

7.0

10.3

6.7

6.4

5.0

3.8

3.6

2.9

2.3

0.9

0.6

15.2

6.6

9.7

6.3

6.0

4.7

3.6

3.4

2.7

2.2

0.9

0.6

14.1

6.2

9.2

5.9

5.6

4.4

3.4

3.2

2.5

2.0

0.8

0.5

13.1

5.8

8.6

5.5

5.2

4.1

3.1

3.0

2.3

1.9

0.8

0.5

12.0

5.5

8.1

5.1

4.9

4.8

3.8

2.9

2.8

2.2

1.8

0.7

0.5

11.1

5.1

7.6

4.7

4.5

4.4

3.5

2.7

2.6

2.0

1.6

0.7

0.4

10.1

4.7

7.0

4.4

4.1

3.2

2.5

2.4

1.9

1.5

0.6

0.4

9.2

4.4

6.5

4.0

3.8

3.7

2.9

2.3

2.2

1.7

1.4

0.6

0.4

8.3

4.0

6.1

3.7

3.5

3.4

2.6

2.1

2.0

1.5

1.2

0.5

0.3

7.5

3.7

5.6

3.3

3.2

3.1

2.4

1.9

1.8

1.4

1.1

0.5

0.3

6.7

3.4

5.1

3.0

2.8

2.1

1.7

1.3

1.0

0.4

0.3

5.9

3.1

4.6

2.7

2.5

1.9

1.5

1.1

0.9

0.4

0.3

5.2

2.8

4.2

2.4

2.3

2.2

1.7

1.4

1.3

1.0

0.8

0.4

0.2

4.5

2.5

3.8

2.1

2.0

1.9

1.5

1.2

0.9

0.7

0.3

0.2

3.9

2.2

3.3

1.8

1.7

1.3

1.0

0.8

0.6

0.3

0.2

3.3

1.9

2.9

1.6

1.5

1.4

1.1

0.9

0.7

0.5

0.2

Levitation magnet forces p_z,W,TMTi in [kN/m] (+/-)

[m/s]

(1)

3.5

2.8

3.1

2.3

3.9

0.9

2.7

1.5

1.8

2.0

2.2

1.2

2.4

0.7

1.7

3.3

2.6

2.9

2.1

3.7

0.9

2.5

1.4

1.6

1.9

2.1

1.1

2.2

0.6

1.6

3.0

2.4

2.7

2.0

3.5

0.8

2.3

1.3

1.5

1.7

2.0

1.1

2.1

0.6

1.5

2.8

2.3

2.5

1.8

3.2

0.7

2.2

1.2

1.4

1.6

1.8

1.0

1.9

0.6

1.4

2.6

2.1

2.4

1.7

3.0

0.7

2.0

1.1

1.3

1.5

1.7

0.9

1.8

0.5

1.3

2.4

2.0

2.2

1.6

2.8

0.6

1.9

1.0

1.2

1.4

1.6

0.8

1.6

0.5

1.2

2.2

1.8

2.0

1.5

2.5

0.6

1.7

0.9

1.1

1.3

1.4

0.8

1.5

0.4

1.1

2.0

1.7

1.8

1.3

2.3

0.5

1.6

0.9

1.0

1.2

1.3

0.7

1.4

0.4

1.0

1.9

1.5

1.7

1.2

2.1

0.5

1.4

0.8

0.9

1.1

1.2

0.6

1.3

0.4

0.9

1.7

1.4

1.5

1.1

1.9

0.4

1.3

0.7

0.8

1.0

1.1

0.6

1.1

0.3

0.9

1.5

1.3

1.4

1.0

1.7

0.4

1.2

0.6

0.8

0.9

1.0

0.5

1.0

0.3

0.8

1.4

1.2

0.9

1.6

0.4

1.1

0.6

0.7

0.8

0.9

0.5

0.9

0.3

0.7

1.2

1.0

1.1

0.8

1.4

0.3

0.9

0.5

0.6

0.7

0.8

0.4

0.8

0.2

0.6

1.1

0.9

0.7

1.2

0.3

0.8

0.4

0.5

0.6

0.7

0.4

0.7

0.2

0.5

0.9

0.8

0.6

1.1

0.2

0.7

0.4

0.5

0.6

0.3

0.6

0.2

0.5

0.8

0.7

0.5

0.9

0.2

0.6

0.3

0.4

0.5

0.3

0.5

0.2

0.4

Table 119 - Magnetic forces as a result of cross-winds: end section, v_Fzg = 500 km/h, v_W = 10 .. 25 m/s

Title

High-speed Maglev Systems - Design principles

Guideway - Part II: Design

Doc. no.:

57288

Version

White Paper Issue date

15.02.2007

Page 145

High-speed maglev systems

Maglev Technical Committee

Design principles

Guideway

Guidance magnet forces p_y,W,FMTi in [kN/m]

[m/s]

2.4

1.8

4.4

6.0

6.2

6.4

8.1

9.6

9.5

9.8

12.6

10.7

6.1

2.6

2.3

1.7

4.3

5.7

5.9

6.2

7.8

9.1

9.4

12.1

10.3

5.9

2.5

2.2

1.7

4.1

5.5

5.7

5.9

7.5

8.7

9.0

11.6

9.9

5.6

2.4

2.1

1.6

4.0

5.3

5.5

5.7

7.2

8.3

8.7

11.1

9.5

5.4

2.3

2.0

1.6

3.8

5.1

5.2

5.5

6.9

7.9

8.3

10.7

9.1

5.2

2.2

1.9

1.5

3.6

4.8

5.0

5.2

6.6

7.5

7.9

10.2

8.7

5.0

2.2

1.8

1.5

3.5

4.6

4.8

5.0

6.3

7.1

7.2

7.6

9.7

8.3

4.8

2.1

1.7

1.4

3.3

4.4

4.6

4.8

6.0

6.7

6.8

7.2

9.3

8.0

4.6

2.0

1.6

1.3

3.2

4.2

4.4

4.5

5.7

6.3

6.5

6.9

8.9

7.6

4.3

1.9

1.5

1.3

3.0

4.0

4.2

4.3

5.4

6.0

6.1

6.5

8.4

7.2

4.1

1.8

1.5

1.2

2.9

3.8

4.0

4.1

5.2

5.6

5.8

6.2

8.0

6.9

3.9

1.8

1.4

1.2

2.7

3.6

3.8

3.9

4.9

5.3

5.5

5.9

7.6

6.5

3.7

1.7

1.3

1.1

2.6

3.4

3.6

3.7

4.6

4.9

5.2

5.6

7.2

6.2

3.5

1.6

1.2

1.1

2.5

3.2

3.4

3.5

4.4

4.6

4.8

5.2

6.8

5.8

3.4

1.5

1.1

1.0

2.3

3.0

3.2

3.3

4.1

4.3

4.5

4.9

6.4

5.5

3.2

1.5

1.1

1.0

2.2

2.8

3.0

3.1

3.9

4.0

4.3

4.6

6.0

5.2

3.0

1.4

Levitation magnet forces p_z,W,TMTi in [kN/m] (+/-)

[m/s]

1.5

1.6

2.7

1.8

2.5

2.6

1.9

2.1

2.7

1.3

3.9

2.6

3.0

3.9

1.8

1.5

1.4

1.6

2.6

1.8

2.4

2.5

1.8

2.0

2.6

1.3

3.8

2.5

2.8

3.8

1.8

1.4

1.3

1.5

2.5

1.7

2.3

2.4

1.8

2.5

1.2

3.6

2.4

2.7

3.6

1.7

1.3

1.4

2.3

1.6

2.2

2.3

1.7

2.4

1.1

3.5

2.3

2.6

3.5

1.6

1.3

1.2

1.4

2.2

1.5

2.1

2.2

1.6

2.3

1.1

3.3

2.2

2.5

3.3

1.5

1.2

1.3

2.1

1.5

2.0

2.1

1.5

2.2

1.0

3.2

2.1

2.4

3.2

1.5

1.2

1.1

1.3

2.1

1.4

1.9

2.0

1.5

1.4

2.1

1.0

3.0

2.0

2.3

3.0

1.4

1.1

1.2

2.0

1.3

1.8

1.9

1.4

1.3

2.0

1.0

2.9

1.9

2.2

2.9

1.3

1.1

1.0

1.1

1.9

1.3

1.7

1.8

1.3

1.2

2.0

0.9

2.8

1.8

2.1

2.7

1.3

1.0

1.1

1.8

1.2

1.7

1.3

1.1

1.9

0.9

2.6

1.7

2.0

2.6

1.2

1.0

0.9

1.0

1.7

1.2

1.6

1.2

1.1

1.8

0.8

2.5

1.6

1.9

2.5

1.2

0.9

1.0

1.6

1.1

1.5

1.1

1.0

1.7

0.8

2.4

1.5

1.8

2.3

1.1

0.9

0.8

0.9

1.5

1.0

1.4

1.5

1.1

0.9

1.6

0.7

2.3

1.4

1.7

2.2

1.0

0.8

0.9

1.4

1.0

1.3

1.4

1.0

0.8

1.5

0.7

2.1

1.4

1.6

2.1

1.0

0.8

0.7

0.8

1.3

0.9

1.2

1.3

0.9

0.8

1.4

0.6

2.0

1.3

1.5

2.0

0.9

0.7

0.8

1.3

0.9

1.2

0.9

0.7

1.4

0.6

1.9

1.2

1.4

1.8

0.9

0.7

Table 120 - Magnetic forces as a result of cross-winds: middle section, v_Fzg = 500 km/h, v_W = 25 .. 40 m/s

Title

High-speed Maglev Systems - Design principles

Guideway - Part II: Design

Doc. no.:

57288

Version

White Paper Issue date

15.02.2007

Page 146

High-speed maglev systems

Maglev Technical Committee

Design principles

Guideway

Guidance magnet forces p_y,W,FMTi in [kN/m]

[m/s]

1.1

1.0

2.2

2.8

3.0

3.1

3.9

4.0

4.3

4.6

6.0

5.2

3.0

1.4

1.0

0.9

2.1

2.7

2.8

2.9

3.6

3.7

4.0

4.3

5.7

4.9

2.8

1.3

0.9

1.9

2.5

2.6

2.7

3.4

3.7

4.1

5.3

4.5

2.6

1.2

0.9

0.8

1.8

2.3

2.5

3.1

3.2

3.4

3.8

4.9

4.2

2.5

1.2

0.8

1.7

2.2

2.3

2.4

2.9

3.2

3.5

4.6

3.9

2.3

1.1

0.7

1.6

2.0

2.1

2.2

2.7

2.9

3.3

4.3

3.7

2.1

1.0

0.7

1.5

1.8

2.0

2.5

2.4

2.7

3.0

3.9

3.4

2.0

1.0

0.6

1.3

1.7

1.8

1.9

2.3

2.2

2.4

2.8

3.6

3.1

1.8

0.9

0.6

1.2

1.5

1.7

2.1

2.0

2.2

2.5

3.3

2.8

1.7

0.8

0.5

0.6

1.1

1.4

1.5

1.9

1.8

2.0

2.3

3.0

2.6

1.5

0.8

0.4

0.5

1.0

1.3

1.4

1.7

1.6

1.8

2.1

2.7

2.3

1.4

0.7

0.4

0.5

0.9

1.1

1.2

1.3

1.5

1.4

1.6

1.8

2.4

2.1

1.2

0.6

0.4

0.8

1.0

1.1

1.4

1.2

1.4

1.6

2.2

1.9

1.1

0.6

0.3

0.4

0.7

0.9

1.0

1.2

1.0

1.2

1.4

1.9

1.7

1.0

0.5

0.3

0.6

0.8

0.9

1.0

0.9

1.0

1.3

1.7

1.4

0.9

0.5

0.2

0.3

0.6

0.7

0.9

0.7

0.9

1.1

1.4

1.2

0.7

0.4

Levitation magnet forces p_z,W,TMTi in [kN/m] (+/-)

[m/s]

0.7

0.8

1.3

0.9

1.2

0.9

0.7

1.4

0.6

1.9

1.2

1.4

1.8

0.9

0.7

0.6

0.7

1.2

0.8

1.1

0.8

0.6

1.3

0.6

1.8

1.1

1.3

1.7

0.8

0.6

0.7

1.1

0.8

1.0

1.1

0.8

0.6

1.2

0.5

1.7

1.0

1.2

1.6

0.8

0.6

1.0

0.7

1.0

0.7

0.5

1.1

0.5

1.5

1.0

1.2

1.5

0.7

0.6

0.5

0.6

1.0

0.7

0.9

0.7

0.5

1.1

0.5

1.4

0.9

1.1

1.4

0.7

0.5

0.9

0.6

0.8

0.9

0.6

0.4

1.0

0.4

1.3

0.8

1.0

1.3

0.6

0.5

0.4

0.5

0.8

0.6

0.8

0.6

0.4

0.9

0.4

1.2

0.8

0.9

1.2

0.6

0.4

0.5

0.7

0.5

0.7

0.5

0.3

0.8

0.4

1.1

0.7

0.8

1.1

0.5

0.4

0.7

0.5

0.6

0.7

0.5

0.3

0.8

0.3

1.0

0.6

0.8

1.0

0.5

0.4

0.3

0.4

0.6

0.4

0.6

0.4

0.2

0.7

0.3

0.9

0.6

0.7

0.9

0.4

0.3

0.6

0.4

0.5

0.4

0.2

0.6

0.3

0.8

0.5

0.6

0.8

0.4

0.3

0.5

0.3

0.5

0.3

0.2

0.6

0.2

0.8

0.5

0.6

0.7

0.3

0.2

0.3

0.4

0.3

0.4

0.3

0.1

0.5

0.2

0.7

0.4

0.5

0.6

0.3

0.2

0.4

0.3

0.4

0.3

0.1

0.5

0.2

0.6

0.4

0.6

0.3

0.2

0.3

0.2

0.3

0.2

0.1

0.4

0.2

0.5

0.3

0.4

0.5

0.2

0.3

0.2

0.3

0.2

0.1

0.4

0.1

0.4

0.3

0.4

0.2

Table 121 - Magnetic forces as a result of cross-winds: middle section, v_Fzg = 500 km/h, v_W = 10 .. 25 m/s

Title

High-speed Maglev Systems - Design principles

Guideway - Part II: Design

Doc. no.:

57288

Version

White Paper Issue date

15.02.2007

Page 147

High-speed maglev systems

Maglev Technical Committee

Design principles

Guideway

Guidance magnet forces p_y,W,FMTi in [kN/m]

[m/s]

27.9

13.4

18.6

13.2

12.7

12.9

10.2

7.6

7.1

5.6

4.6

1.9

1.0

26.7

12.9

18.0

12.7

12.2

12.4

9.8

7.3

6.8

5.4

4.4

1.8

0.9

25.5

12.4

17.4

12.2

11.7

11.9

9.4

7.0

6.5

5.2

4.2

1.8

0.9

24.4

11.9

16.7

11.7

11.2

11.4

9.0

6.7

6.3

5.0

4.0

1.7

0.9

23.3

11.4

16.1

11.2

10.7

10.9

8.6

6.4

6.0

4.7

3.9

1.6

0.8

22.2

11.0

15.5

10.7

10.3

10.4

8.2

6.1

5.7

4.5

3.7

1.6

0.8

21.1

10.5

14.9

10.2

9.8

9.9

7.8

5.9

5.5

4.3

3.5

1.5

0.8

20.0

10.0

14.3

9.7

9.3

9.4

7.4

5.6

5.3

4.1

3.3

1.4

0.7

19.0

9.6

13.7

9.3

8.9

9.0

7.0

5.3

5.0

3.9

3.2

1.4

0.7

18.0

9.2

13.1

8.8

8.5

6.7

5.1

4.8

3.7

3.0

1.3

0.7

17.0

8.7

12.6

8.4

8.0

8.1

6.3

4.8

4.5

3.5

2.9

1.3

0.6

16.1

8.3

12.0

7.9

7.6

6.0

4.6

4.3

3.3

2.7

1.2

0.6

15.1

7.9

11.4

7.5

7.2

5.6

4.3

4.1

3.2

2.6

1.1

0.6

14.2

7.5

10.9

7.1

6.8

5.3

4.1

3.9

3.0

2.4

1.1

0.5

13.3

7.0

10.3

6.7

6.4

5.0

3.8

3.6

2.8

2.3

1.0

0.5

12.5

6.6

9.8

6.3

6.0

4.7

3.6

3.4

2.6

2.1

1.0

0.5

Levitation magnet forces p_z,W,TMTi in [kN/m] (+/-)

[m/s]

(1)

6.6

5.4

6.4

4.4

7.9

1.8

5.3

3.0

3.5

3.9

4.5

2.4

4.7

1.3

3.5

6.3

5.2

6.1

4.2

7.6

1.7

5.1

2.9

3.4

3.7

4.3

2.3

4.5

1.2

3.3

6.1

5.0

5.8

4.0

7.2

1.7

4.8

2.7

3.2

3.6

4.1

2.2

4.3

1.2

3.2

5.8

4.8

5.6

3.9

6.9

1.6

4.6

2.6

3.1

3.4

3.9

2.1

4.1

1.1

3.1

5.6

4.6

5.4

3.7

6.7

1.5

4.4

2.5

3.0

3.3

3.8

2.0

4.0

1.1

2.9

5.3

4.4

5.1

3.5

6.4

1.5

4.3

2.4

2.8

3.2

3.6

1.9

3.8

1.0

2.8

5.1

4.2

4.9

3.4

6.1

1.4

4.1

2.3

2.7

3.0

3.4

1.8

3.6

1.0

2.7

4.8

4.0

4.6

3.2

5.8

1.3

3.9

2.2

2.6

2.9

3.3

1.7

3.4

1.0

2.5

4.6

3.8

4.4

3.1

5.5

1.3

3.7

2.1

2.4

2.7

3.1

1.7

3.3

0.9

2.4

4.4

3.6

4.2

2.9

5.2

1.2

3.5

2.0

2.3

2.6

3.0

1.6

3.1

0.9

2.3

4.2

3.5

4.0

2.8

5.0

1.1

3.3

1.9

2.2

2.5

2.8

1.5

2.9

0.8

2.2

3.9

3.3

3.7

2.6

4.7

1.1

3.1

1.8

2.1

2.3

2.7

1.4

2.8

0.8

2.1

3.7

3.1

3.5

2.5

4.5

1.0

3.0

1.7

2.0

2.2

2.5

1.3

2.6

0.7

2.0

3.5

3.0

3.3

2.4

4.2

0.9

2.8

1.6

1.9

2.1

2.4

1.3

2.5

0.7

1.8

3.3

2.8

3.1

2.2

4.0

0.9

2.6

1.5

1.7

2.0

2.2

1.2

2.3

0.7

1.7

3.1

2.6

2.9

2.1

3.7

0.8

2.5

1.4

1.6

1.9

2.1

1.1

2.2

0.6

1.6

Table 122 - Magnetic forces as a result of cross-winds: end section, v_Fzg = 400 km/h, v_W = 25 .. 40 m/s

Title

High-speed Maglev Systems - Design principles

Guideway - Part II: Design

Doc. no.:

57288

Version

White Paper Issue date

15.02.2007

Page 148

High-speed maglev systems

Maglev Technical Committee

Design principles

Guideway

Guidance magnet forces p_y,W,FMTi in [kN/m]

[m/s]

12.5

6.6

9.8

6.3

6.0

4.7

3.6

3.4

2.6

2.1

1.0

0.5

11.6

6.3

9.2

5.9

5.6

4.3

3.4

3.2

2.5

2.0

0.9

0.4

10.8

5.9

8.7

5.5

5.3

5.2

4.0

3.2

3.0

2.3

1.9

0.9

0.4

10.0

5.5

8.2

5.1

4.9

4.8

3.8

2.9

2.8

2.1

1.7

0.8

0.4

9.2

5.1

7.7

4.8

4.6

4.5

3.5

2.7

2.6

2.0

1.6

0.7

0.4

8.5

4.8

7.2

4.4

4.2

4.1

3.2

2.5

2.4

1.8

1.5

0.7

0.3

7.8

4.4

6.7

4.1

3.9

3.8

2.9

2.3

2.2

1.7

1.4

0.6

0.3

7.1

4.1

6.2

3.7

3.6

3.5

2.7

2.1

1.6

1.3

0.6

0.3

6.4

3.7

5.8

3.4

3.3

3.2

2.4

1.9

1.4

1.2

0.6

0.3

5.8

3.4

5.3

3.1

3.0

2.9

2.2

1.8

1.7

1.3

1.0

0.5

0.2

5.2

3.1

4.9

2.8

2.7

2.6

2.0

1.6

1.2

0.9

0.5

0.2

4.6

2.8

4.4

2.5

2.4

2.3

1.8

1.4

1.0

0.8

0.4

0.2

4.1

2.5

4.0

2.2

2.1

2.0

1.6

1.3

1.2

0.9

0.8

0.4

0.2

3.5

2.2

3.6

2.0

1.9

1.8

1.4

1.1

0.8

0.7

0.3

0.2

3.1

2.0

3.2

1.7

1.6

1.2

1.0

0.7

0.6

0.3

0.1

2.6

1.7

2.8

1.5

1.4

1.3

1.0

0.8

0.6

0.5

0.3

0.1

Levitation magnet forces p_z,W,TMTi in [kN/m] (+/-)

[m/s]

(1)

3.1

2.6

2.9

2.1

3.7

0.8

2.5

1.4

1.6

1.9

2.1

1.1

2.2

0.6

1.6

2.9

2.5

2.7

2.0

3.5

0.8

2.3

1.3

1.5

1.7

2.0

1.0

2.1

0.6

1.5

2.7

2.3

2.6

1.8

3.3

0.7

2.2

1.2

1.4

1.6

1.8

1.0

1.9

0.5

1.4

2.5

2.2

2.4

1.7

3.0

0.7

2.0

1.1

1.3

1.5

1.7

0.9

1.8

0.5

1.3

2.3

2.0

2.2

1.6

2.8

0.6

1.9

1.0

1.2

1.4

1.6

0.8

1.7

0.5

1.2

2.2

1.9

2.0

1.5

2.6

0.6

1.7

1.0

1.1

1.3

1.5

0.8

1.5

0.4

1.1

2.0

1.7

1.9

1.4

2.4

0.5

1.6

0.9

1.0

1.2

1.3

0.7

1.4

0.4

1.0

1.8

1.6

1.7

1.2

2.2

0.5

1.5

0.8

1.0

1.1

1.2

0.7

1.3

0.4

1.0

1.7

1.5

1.6

1.1

2.0

0.4

1.3

0.7

0.9

1.0

1.1

0.6

1.2

0.3

0.9

1.5

1.3

1.4

1.0

1.8

0.4

1.2

0.7

0.8

0.9

1.0

0.5

1.1

0.3

0.8

1.4

1.2

1.3

0.9

1.6

0.4

1.1

0.6

0.7

0.8

0.9

0.5

1.0

0.3

0.7

1.2

1.1

0.8

1.5

0.3

1.0

0.5

0.6

0.7

0.8

0.4

0.9

0.2

0.6

1.1

1.0

0.7

1.3

0.3

0.9

0.5

0.6

0.7

0.4

0.8

0.2

0.6

0.9

0.7

1.2

0.2

0.8

0.4

0.5

0.6

0.3

0.7

0.2

0.5

0.8

0.6

1.0

0.2

0.7

0.4

0.5

0.6

0.3

0.6

0.2

0.4

0.7

0.5

0.9

0.2

0.6

0.3

0.4

0.5

0.3

0.5

0.1

0.4

Table 123 - Magnetic forces as a result of cross-winds: end section, v_Fzg = 400 km/h, v_W = 10 .. 25 m/s

Title

High-speed Maglev Systems - Design principles

Guideway - Part II: Design

Doc. no.:

57288

Version

White Paper Issue date

15.02.2007

Page 149

High-speed maglev systems

Maglev Technical Committee

Design principles

Guideway

Guidance magnet forces p_y,W,FMTi in [kN/m]

[m/s]

1.4

2.1

4.2

5.0

5.7

5.9

7.4

8.7

8.8

9.2

10.8

8.6

4.4

2.3

1.4

2.0

4.1

4.8

5.4

5.7

7.1

8.3

8.5

8.8

10.3

8.2

4.3

2.2

1.3

2.0

3.9

4.6

5.2

5.4

6.8

7.9

8.1

8.5

9.9

7.9

4.1

2.1

1.3

1.9

3.8

4.4

5.0

5.2

6.5

7.5

7.7

8.1

9.5

7.6

3.9

2.1

1.2

1.8

3.6

4.2

4.8

5.0

6.2

7.2

7.4

7.8

9.1

7.3

3.8

2.0

1.2

1.8

3.5

4.1

4.6

4.8

6.0

6.8

7.0

7.4

8.7

7.0

3.6

1.9

1.1

1.7

3.3

3.9

4.4

4.6

5.7

6.4

6.7

7.1

8.3

6.7

3.5

1.8

1.0

1.7

3.2

3.7

4.2

4.4

5.4

6.1

6.4

6.8

8.0

6.4

3.3

1.8

1.0

1.6

3.0

3.5

4.0

4.2

5.2

5.8

6.0

6.4

7.6

6.1

3.2

1.7

0.9

1.5

2.9

3.3

3.8

4.0

4.9

5.4

5.7

6.1

7.2

5.8

3.0

1.6

0.9

1.5

2.8

3.2

3.6

3.8

4.7

5.1

5.4

5.8

6.9

5.5

2.9

1.6

0.8

1.4

2.6

3.0

3.4

3.6

4.4

4.8

5.1

5.5

6.5

5.2

2.7

1.5

0.8

1.3

2.5

2.9

3.3

3.4

4.2

4.5

4.8

5.2

6.2

4.9

2.6

1.4

0.7

1.3

2.4

2.7

3.1

3.2

3.9

4.2

4.5

4.9

5.8

4.7

2.4

1.4

0.7

1.2

2.2

2.5

2.9

3.0

3.7

3.9

4.2

4.6

5.5

4.4

2.3

1.3

0.7

1.2

2.1

2.4

2.7

2.8

3.5

3.6

4.0

4.4

5.2

4.1

2.2

1.2

Levitation magnet forces p_z,W,TMTi in [kN/m] (+/-)

[m/s]

1.3

1.5

2.4

1.7

2.3

1.8

1.9

2.5

1.2

3.6

2.4

2.7

3.7

1.8

1.3

1.4

2.3

1.6

2.2

2.3

1.7

1.8

2.4

1.2

3.5

2.3

2.6

3.5

1.7

1.3

1.2

1.4

2.2

1.6

2.1

2.2

1.6

1.7

2.3

1.1

3.3

2.2

2.5

3.4

1.6

1.2

1.3

2.1

1.5

2.0

2.1

1.6

2.2

1.1

3.2

2.1

2.4

3.2

1.6

1.2

1.1

1.3

2.0

1.4

1.9

2.0

1.5

2.2

1.0

3.1

2.0

2.3

3.1

1.5

1.1

1.2

2.0

1.4

1.9

1.4

2.1

1.0

2.9

1.9

2.2

2.9

1.4

1.1

1.0

1.2

1.9

1.3

1.8

1.4

1.3

2.0

0.9

2.8

1.8

2.1

2.8

1.4

1.0

1.1

1.8

1.2

1.7

1.3

1.2

1.9

0.9

2.7

1.8

2.0

2.7

1.3

1.0

0.9

1.1

1.7

1.2

1.6

1.2

1.1

1.8

0.8

2.5

1.7

1.9

2.6

1.2

0.9

1.0

1.6

1.1

1.5

1.6

1.2

1.0

1.7

0.8

2.4

1.6

1.8

2.4

1.2

0.9

0.8

0.9

1.5

1.1

1.4

1.5

1.1

1.0

1.6

0.8

2.3

1.5

1.7

2.3

1.1

0.8

0.9

1.5

1.0

1.4

1.0

0.9

1.6

0.7

2.2

1.4

1.6

2.2

1.1

0.8

0.7

0.8

1.4

1.0

1.3

1.0

0.8

1.5

0.7

2.1

1.3

1.6

2.1

1.0

0.7

0.8

1.3

0.9

1.2

1.3

0.9

0.8

1.4

0.6

1.9

1.3

1.5

1.9

0.9

0.7

0.8

1.2

0.9

1.1

1.2

0.9

0.7

1.3

0.6

1.8

1.2

1.4

1.8

0.9

0.7

0.6

0.7

1.1

0.8

1.1

0.8

0.6

1.3

0.6

1.7

1.1

1.3

1.7

0.8

0.6

Table 124 - Magnetic forces as a result of cross-winds: middle section, v_Fzg = 400 km/h, v_W = 25 .. 40 m/s

Title

High-speed Maglev Systems - Design principles

Guideway - Part II: Design

Doc. no.:

57288

Version

White Paper Issue date

15.02.2007

Page 150

High-speed maglev systems

Maglev Technical Committee

Design principles

Guideway

Guidance magnet forces p_y,W,FMTi in [kN/m]

[m/s]

0.7

1.2

2.1

2.4

2.7

2.8

3.5

3.6

4.0

4.4

5.2

4.1

2.2

1.2

0.6

1.1

2.0

2.2

2.6

3.3

3.4

3.7

4.1

4.8

3.9

2.0

1.2

0.6

1.0

1.9

2.1

2.4

2.5

3.1

3.4

3.8

4.5

3.6

1.9

1.1

0.5

1.0

1.7

1.9

2.3

2.8

2.9

3.2

3.6

4.2

3.4

1.8

1.0

0.5

0.9

1.6

1.8

2.1

2.2

2.6

2.9

3.3

3.9

3.2

1.7

1.0

0.4

0.9

1.5

1.7

1.9

2.0

2.4

2.7

3.1

3.6

2.9

1.5

0.9

0.4

0.8

1.4

1.5

1.8

2.3

2.2

2.5

2.8

3.4

2.7

1.4

0.8

0.4

0.8

1.3

1.4

1.7

2.1

2.0

2.3

2.6

3.1

2.5

1.3

0.8

0.3

0.7

1.2

1.3

1.5

1.9

1.8

2.1

2.4

2.8

2.3

1.2

0.7

0.3

0.7

1.1

1.2

1.4

1.7

1.6

1.9

2.1

2.6

2.1

1.1

0.7

0.3

0.6

1.0

1.1

1.2

1.3

1.6

1.4

1.7

1.9

2.3

1.9

1.0

0.6

0.2

0.5

0.9

1.0

1.1

1.4

1.2

1.5

1.7

2.1

1.7

0.9

0.6

0.2

0.5

0.8

1.0

1.2

1.1

1.3

1.5

1.9

1.5

0.8

0.5

0.2

0.5

0.7

0.9

1.1

0.9

1.1

1.4

1.6

1.3

0.7

0.5

0.2

0.4

0.6

0.7

0.8

0.9

0.8

1.0

1.2

1.4

1.2

0.6

0.4

0.1

0.4

0.5

0.6

0.7

0.8

0.7

0.8

1.0

1.2

1.0

0.5

0.4

Levitation magnet forces p_z,W,TMTi in [kN/m] (+/-)

[m/s]

0.6

0.7

1.1

0.8

1.1

0.8

0.6

1.3

0.6

1.7

1.1

1.3

1.7

0.8

0.6

0.7

1.1

0.8

1.0

0.8

0.6

1.2

0.5

1.6

1.0

1.2

1.6

0.8

0.6

0.5

0.6

1.0

0.7

0.9

1.0

0.7

0.5

1.1

0.5

1.5

1.0

1.1

1.5

0.7

0.5

0.6

0.9

0.7

0.9

0.7

0.5

1.0

0.5

1.4

0.9

1.1

1.4

0.7

0.5

0.9

0.6

0.8

0.6

0.4

1.0

0.4

1.3

0.8

1.0

1.3

0.6

0.5

0.4

0.5

0.8

0.6

0.8

0.6

0.4

0.9

0.4

1.2

0.8

0.9

1.2

0.6

0.4

0.5

0.7

0.5

0.7

0.5

0.3

0.8

0.4

1.1

0.7

0.8

1.1

0.5

0.4

0.7

0.5

0.6

0.7

0.5

0.3

0.8

0.3

1.0

0.7

0.8

1.0

0.5

0.4

0.3

0.4

0.6

0.4

0.6

0.4

0.3

0.7

0.3

0.9

0.6

0.7

0.9

0.4

0.3

0.6

0.4

0.5

0.6

0.4

0.2

0.7

0.3

0.9

0.5

0.6

0.8

0.4

0.3

0.5

0.4

0.5

0.3

0.2

0.6

0.2

0.8

0.5

0.6

0.8

0.4

0.3

0.2

0.3

0.5

0.3

0.4

0.3

0.2

0.5

0.2

0.7

0.4

0.5

0.7

0.3

0.2

0.4

0.3

0.4

0.3

0.1

0.5

0.2

0.6

0.4

0.5

0.6

0.3

0.2

0.4

0.3

0.2

0.1

0.4

0.2

0.5

0.3

0.4

0.5

0.3

0.2

0.3

0.2

0.3

0.2

0.1

0.4

0.1

0.5

0.3

0.4

0.5

0.2

0.1

0.2

0.3

0.2

0.3

0.2

0.1

0.3

0.1

0.4

0.3

0.4

0.2

0.1

Table 125 - Magnetic forces as a result of cross-winds: middle section, v_Fzg = 400 km/h, v_W = 10 .. 25 m/s

Title

High-speed Maglev Systems - Design principles

Guideway - Part II: Design

Doc. no.:

57288

Version

White Paper Issue date

15.02.2007

Page 151

High-speed maglev systems

Maglev Technical Committee

Design principles

Guideway

Guidance magnet forces p_y,W,FMTi in [kN/m]

[m/s]

15.1

9.6

15.7

12.1

11.7

9.2

6.9

6.5

5.0

4.1

1.8

0.6

14.5

9.2

15.2

11.6

11.2

8.8

6.6

6.2

4.8

3.9

1.8

0.6

13.8

8.9

14.7

11.2

10.7

8.4

6.4

6.0

4.6

3.8

1.7

0.6

13.2

8.5

14.1

10.7

10.3

8.0

6.1

5.7

4.4

3.6

1.6

0.6

12.6

8.2

13.6

10.2

9.9

9.8

7.7

5.8

5.5

4.2

3.5

1.6

0.5

12.0

7.8

13.1

9.8

9.4

7.3

5.6

5.3

4.0

3.3

1.5

0.5

11.4

7.5

12.6

9.4

9.0

8.9

7.0

5.3

5.0

3.8

3.2

1.5

0.5

10.9

7.2

12.1

8.9

8.6

8.5

6.6

5.1

4.8

3.7

3.0

1.4

0.5

10.3

6.8

11.6

8.5

8.2

8.1

6.3

4.8

4.6

3.5

2.9

1.3

0.5

9.8

6.5

11.1

8.1

7.8

7.7

6.0

4.6

4.4

3.3

2.7

1.3

0.4

9.2

6.2

10.6

7.7

7.4

7.3

5.7

4.4

4.1

3.1

2.6

1.2

0.4

8.7

5.9

10.1

7.3

7.0

6.9

5.4

4.1

3.9

3.0

2.4

1.2

0.4

8.2

5.6

9.7

6.9

6.6

6.5

5.1

3.9

3.7

2.8

2.3

1.1

0.4

7.7

5.3

9.2

6.5

6.2

6.1

4.8

3.7

3.5

2.7

2.2

1.0

0.3

7.2

5.0

8.7

6.1

5.9

5.8

4.5

3.5

3.3

2.5

2.1

1.0

0.3

6.7

4.7

8.3

5.8

5.5

5.4

4.2

3.3

3.1

2.3

1.9

0.9

0.3

Levitation magnet forces p_z,W,TMTi in [kN/m] (+/-)

[m/s]

(1)

5.7

4.9

5.8

3.9

7.2

1.6

4.8

2.7

3.2

3.5

4.0

2.1

4.2

1.2

3.1

5.5

4.8

5.5

3.8

6.9

1.5

4.6

2.6

3.1

3.4

3.9

2.0

4.1

1.1

3.0

5.3

4.6

5.3

3.6

6.7

1.5

4.4

2.5

2.9

3.3

3.7

2.0

3.9

1.1

2.9

5.0

4.4

5.1

3.5

6.4

1.4

4.2

2.4

2.8

3.1

3.6

1.9

3.7

1.0

2.8

4.8

4.2

4.9

3.3

6.1

1.3

4.1

2.3

2.7

3.0

3.4

1.8

3.6

1.0

2.6

4.6

4.0

4.6

3.2

5.8

1.3

3.9

2.2

2.6

2.9

3.3

1.7

3.4

0.9

2.5

4.4

3.9

4.4

3.0

5.6

1.2

3.7

2.1

2.4

2.7

3.1

1.6

3.3

0.9

2.4

4.2

3.7

4.2

2.9

5.3

1.2

3.5

2.0

2.3

2.6

3.0

1.6

3.1

0.9

2.3

4.0

3.5

4.0

2.7

5.1

1.1

3.4

1.9

2.2

2.5

2.8

1.5

3.0

0.8

2.2

3.8

3.4

3.8

2.6

4.8

1.0

3.2

1.8

2.1

2.4

2.7

1.4

2.8

0.8

2.1

3.6

3.2

3.6

2.5

4.6

1.0

3.0

1.7

2.0

2.2

2.5

1.3

2.7

0.7

2.0

3.4

3.1

3.4

2.4

4.3

0.9

2.9

1.6

1.9

2.1

2.4

1.3

2.5

0.7

1.9

3.2

2.9

3.2

2.2

4.1

0.9

2.7

1.5

1.8

2.0

2.3

1.2

2.4

0.7

1.8

3.0

2.7

3.0

2.1

3.9

0.8

2.6

1.4

1.7

1.9

2.1

1.1

2.2

0.6

1.7

2.9

2.6

2.8

2.0

3.6

0.8

2.4

1.3

1.6

1.8

2.0

1.1

2.1

0.6

1.6

2.7

2.4

2.7

1.9

3.4

0.7

2.3

1.2

1.5

1.7

1.9

1.0

2.0

0.6

1.5

Table 126 - Magnetic forces as a result of cross-winds: end section, v_Fzg = 300 km/h, v_W = 25 .. 40 m/s

Title

High-speed Maglev Systems - Design principles

Guideway - Part II: Design

Doc. no.:

57288

Version

White Paper Issue date

15.02.2007

Page 152

High-speed maglev systems

Maglev Technical Committee

Design principles

Guideway

Guidance magnet forces p_y,W,FMTi in [kN/m]

[m/s]

6.7

4.7

8.3

5.8

5.5

5.4

4.2

3.3

3.1

2.3

1.9

0.9

0.3

6.3

4.5

7.8

5.4

5.2

5.0

3.9

3.1

2.9

2.2

1.8

0.9

0.3

5.8

4.2

7.4

5.0

4.8

4.7

3.6

2.9

2.8

2.1

1.7

0.8

0.3

5.4

3.9

6.9

4.7

4.5

4.4

3.4

2.7

2.6

1.9

1.6

0.8

0.3

5.0

3.6

6.5

4.4

4.2

4.1

3.1

2.5

2.4

1.8

1.5

0.7

0.2

4.6

3.4

6.1

4.0

3.9

3.7

2.9

2.3

2.2

1.6

1.3

0.7

0.2

4.2

3.1

5.7

3.7

3.6

3.4

2.6

2.1

2.0

1.5

1.2

0.6

0.2

3.8

2.9

5.3

3.4

3.3

3.1

2.4

1.9

1.4

1.1

0.6

0.2

3.5

2.7

4.9

3.1

3.0

2.9

2.2

1.8

1.7

1.3

1.0

0.5

0.2

3.1

2.4

4.5

2.8

2.7

2.6

2.0

1.6

1.1

0.9

0.5

0.2

2.8

2.2

4.1

2.6

2.4

2.3

1.8

1.5

1.4

1.0

0.9

0.4

0.1

2.5

2.0

3.7

2.3

2.2

2.1

1.6

1.3

0.9

0.8

0.4

0.1

2.2

1.8

3.4

2.0

1.9

1.8

1.4

1.2

1.1

0.8

0.7

0.4

0.1

1.9

1.6

3.0

1.8

1.7

1.6

1.2

1.0

0.7

0.6

0.3

0.1

1.6

1.4

2.7

1.6

1.5

1.4

1.1

0.9

0.6

0.5

0.3

0.1

1.4

1.2

2.4

1.3

1.2

0.9

0.8

0.5

0.4

0.2

0.1

Levitation magnet forces p_z,W,TMTi in [kN/m] (+/-)

[m/s]

(1)

2.7

2.4

2.7

1.9

3.4

0.7

2.3

1.2

1.5

1.7

1.9

1.0

2.0

0.6

1.5

2.5

2.3

2.5

1.7

3.2

0.7

2.1

1.2

1.4

1.6

1.8

0.9

1.9

0.5

1.4

2.3

2.2

2.3

1.6

3.0

0.6

2.0

1.1

1.3

1.5

1.7

0.9

1.7

0.5

1.3

2.2

2.0

2.2

1.5

2.8

0.6

1.8

1.0

1.2

1.4

1.5

0.8

1.6

0.5

1.2

2.0

1.9

2.0

1.4

2.6

0.5

1.7

0.9

1.1

1.3

1.4

0.8

1.5

0.4

1.1

1.9

1.7

1.8

1.3

2.4

0.5

1.6

0.9

1.0

1.2

1.3

0.7

1.4

0.4

1.0

1.7

1.6

1.7

1.2

2.2

0.5

1.5

0.8

0.9

1.1

1.2

0.6

1.3

0.4

0.9

1.6

1.5

1.6

1.1

2.0

0.4

1.3

0.7

0.9

1.0

1.1

0.6

1.2

0.3

0.9

1.4

1.0

1.8

0.4

1.2

0.7

0.8

0.9

1.0

0.5

1.1

0.3

0.8

1.3

1.2

1.3

0.9

1.7

0.4

1.1

0.6

0.7

0.8

0.9

0.5

1.0

0.3

0.7

1.2

1.1

0.8

1.5

0.3

1.0

0.5

0.6

0.8

0.4

0.9

0.2

0.6

1.1

1.0

0.7

1.4

0.3

0.9

0.5

0.6

0.7

0.4

0.8

0.2

0.6

0.9

0.7

1.2

0.2

0.8

0.4

0.5

0.6

0.7

0.4

0.7

0.2

0.5

0.8

0.6

1.1

0.2

0.7

0.4

0.5

0.6

0.3

0.6

0.2

0.4

0.7

0.5

0.9

0.2

0.6

0.3

0.4

0.5

0.3

0.5

0.2

0.4

0.6

0.4

0.8

0.2

0.5

0.3

0.4

0.2

0.5

0.1

0.3

Table 127 - Magnetic forces as a result of cross-winds: end section, v_Fzg = 300 km/h, v_W = 10 .. 25 m/s

Title

High-speed Maglev Systems - Design principles

Guideway - Part II: Design

Doc. no.:

57288

Version

White Paper Issue date

15.02.2007

Page 153

High-speed maglev systems

Maglev Technical Committee

Design principles

Guideway

Guidance magnet forces p_y,W,FMTi in [kN/m]

[m/s]

1.8

1.7

3.3

4.9

5.0

5.2

6.6

7.8

8.0

8.3

10.2

8.7

4.6

2.6

1.8

1.6

3.2

4.7

4.8

5.0

6.3

7.4

7.6

8.0

9.8

8.3

4.4

2.6

1.7

1.6

3.0

4.5

4.6

4.8

6.1

7.1

7.3

7.7

9.4

8.0

4.2

2.5

1.6

1.5

2.9

4.3

4.4

4.6

5.8

6.7

7.0

7.4

9.1

7.7

4.0

2.4

1.5

2.8

4.1

4.2

4.4

5.6

6.4

6.7

7.0

8.7

7.4

3.9

2.3

1.5

1.4

2.7

4.0

4.1

4.2

5.3

6.1

6.3

6.7

8.3

7.0

3.7

2.2

1.4

2.6

3.8

3.9

4.0

5.1

5.8

6.0

6.4

7.9

6.7

3.6

2.1

1.3

2.5

3.6

3.7

3.9

4.9

5.4

5.7

6.1

7.6

6.4

3.4

2.0

1.3

2.4

3.4

3.5

3.7

4.6

5.1

5.4

5.8

7.2

6.1

3.2

2.0

1.2

2.2

3.3

3.4

3.5

4.4

4.8

5.2

5.6

6.9

5.8

3.1

1.9

1.1

1.2

2.1

3.1

3.2

3.3

4.2

4.6

4.9

5.3

6.5

5.5

2.9

1.8

1.1

2.0

2.9

3.0

3.2

4.0

4.3

4.6

5.0

6.2

5.3

2.8

1.7

1.0

1.1

1.9

2.8

2.9

3.0

3.7

4.0

4.3

4.7

5.9

5.0

2.7

1.6

0.9

1.0

1.8

2.6

2.7

2.8

3.5

3.8

4.1

4.5

5.5

4.7

2.5

1.6

0.9

1.0

1.7

2.5

2.6

2.7

3.3

3.5

3.8

4.2

5.2

4.4

2.4

1.5

0.8

0.9

1.6

2.3

2.4

2.5

3.1

3.3

3.6

3.9

4.9

4.2

2.2

1.4

Levitation magnet forces p_z,W,TMTi in [kN/m] (+/-)

[m/s]

1.2

1.4

2.2

1.5

2.1

1.6

1.7

2.3

1.1

3.3

2.2

2.5

3.3

1.6

1.2

1.3

2.1

1.4

2.0

1.5

1.6

2.2

1.0

3.2

2.1

2.4

3.1

1.5

1.2

1.1

1.3

2.0

1.4

1.9

2.0

1.5

2.1

1.0

3.1

2.0

2.3

3.0

1.5

1.1

1.2

1.9

1.3

1.8

1.9

1.4

2.0

0.9

2.9

1.9

2.2

2.9

1.4

1.1

1.0

1.2

1.8

1.3

1.7

1.8

1.3

2.0

0.9

2.8

1.8

2.1

2.8

1.4

1.0

1.1

1.8

1.2

1.7

1.3

1.9

0.9

2.7

1.7

2.0

2.6

1.3

1.0

0.9

1.1

1.7

1.2

1.6

1.2

1.8

0.8

2.6

1.7

1.9

2.5

1.2

0.9

1.0

1.6

1.1

1.5

1.6

1.2

1.1

1.7

0.8

2.4

1.6

1.8

2.4

1.2

0.9

0.8

1.0

1.5

1.1

1.4

1.5

1.1

1.0

1.6

0.7

2.3

1.5

1.7

2.3

1.1

0.8

0.9

1.5

1.0

1.4

1.1

0.9

1.6

0.7

2.2

1.4

1.7

2.2

1.1

0.8

0.9

1.4

1.0

1.3

1.0

0.9

1.5

0.7

2.1

1.4

1.6

2.1

1.0

0.8

0.7

0.8

1.3

0.9

1.2

1.3

0.9

0.8

1.4

0.6

2.0

1.3

1.5

1.9

1.0

0.7

0.8

1.2

0.9

1.2

0.9

0.7

1.4

0.6

1.9

1.2

1.4

1.8

0.9

0.7

0.6

0.7

1.2

0.8

1.1

0.8

0.7

1.3

0.6

1.8

1.1

1.3

1.7

0.9

0.6

0.7

1.1

0.8

1.0

1.1

0.8

0.6

1.2

0.5

1.7

1.1

1.3

1.6

0.8

0.6

1.0

0.7

1.0

0.7

0.6

1.1

0.5

1.6

1.0

1.2

1.5

0.8

0.6

Table 128 - Magnetic forces as a result of cross-winds: middle section, v_Fzg = 300 km/h, v_W = 25 .. 40 m/s

Title

High-speed Maglev Systems - Design principles

Guideway - Part II: Design

Doc. no.:

57288

Version

White Paper Issue date

15.02.2007

Page 154

High-speed maglev systems

Maglev Technical Committee

Design principles

Guideway

Guidance magnet forces p_y,W,FMTi in [kN/m]

[m/s]

0.8

0.9

1.6

2.3

2.4

2.5

3.1

3.3

3.6

3.9

4.9

4.2

2.2

1.4

0.8

0.9

1.5

2.2

2.3

2.9

3.0

3.3

3.7

4.6

3.9

2.1

1.3

0.7

0.8

1.4

2.0

2.1

2.2

2.7

2.8

3.1

3.5

4.3

3.7

2.0

1.3

0.7

0.8

1.3

1.9

2.0

2.6

2.9

3.2

4.0

3.4

1.8

1.2

0.6

0.7

1.3

1.8

1.9

2.4

2.7

3.0

3.7

3.2

1.7

1.1

0.6

0.7

1.2

1.6

1.7

1.8

2.2

2.4

2.8

3.5

3.0

1.6

1.0

0.5

0.7

1.1

1.5

1.6

2.0

2.2

2.5

3.2

2.7

1.5

1.0

0.5

0.6

1.0

1.4

1.5

1.9

1.8

2.0

2.3

2.9

2.5

1.4

0.9

0.4

0.6

0.9

1.3

1.4

1.7

1.6

1.9

2.1

2.7

2.3

1.2

0.8

0.4

0.5

0.8

1.2

1.5

1.4

1.7

1.9

2.4

2.1

1.1

0.8

0.3

0.5

0.8

1.0

1.1

1.4

1.3

1.5

1.8

2.2

1.9

1.0

0.7

0.3

0.4

0.7

0.9

1.0

1.2

1.1

1.3

1.6

2.0

1.7

0.9

0.7

0.3

0.4

0.6

0.8

0.9

1.1

1.0

1.2

1.4

1.8

1.5

0.8

0.6

0.2

0.4

0.5

0.7

0.8

1.0

0.8

1.0

1.2

1.6

1.3

0.7

0.5

0.2

0.3

0.5

0.6

0.7

0.8

0.7

0.9

1.1

1.4

1.2

0.6

0.5

0.2

0.3

0.4

0.5

0.6

0.7

0.6

0.8

0.9

1.2

1.0

0.6

0.4

Levitation magnet forces p_z,W,TMTi in [kN/m] (+/-)

[m/s]

0.6

1.0

0.7

1.0

0.7

0.6

1.1

0.5

1.6

1.0

1.2

1.5

0.8

0.6

0.5

0.6

1.0

0.7

0.9

0.7

0.5

1.1

0.5

1.5

0.9

1.1

1.4

0.7

0.5

0.6

0.9

0.6

0.8

0.9

0.6

0.5

1.0

0.4

1.4

0.9

1.0

1.3

0.7

0.5

0.8

0.6

0.8

0.6

0.4

0.9

0.4

1.3

0.8

1.0

1.2

0.6

0.5

0.4

0.5

0.8

0.5

0.7

0.8

0.6

0.4

0.9

0.4

1.2

0.8

0.9

1.2

0.6

0.4

0.7

0.5

0.7

0.5

0.3

0.8

0.3

1.1

0.7

0.8

1.1

0.5

0.4

0.7

0.5

0.6

0.7

0.5

0.3

0.8

0.3

1.0

0.6

0.8

1.0

0.5

0.4

0.3

0.4

0.6

0.4

0.6

0.4

0.3

0.7

0.3

0.9

0.6

0.7

0.9

0.4

0.3

0.6

0.4

0.5

0.4

0.2

0.6

0.3

0.9

0.5

0.6

0.8

0.4

0.3

0.5

0.4

0.5

0.4

0.2

0.6

0.2

0.8

0.5

0.6

0.7

0.4

0.3

0.5

0.3

0.4

0.3

0.2

0.5

0.2

0.7

0.4

0.5

0.7

0.3

0.2

0.3

0.4

0.3

0.4

0.3

0.1

0.5

0.2

0.6

0.4

0.5

0.6

0.3

0.2

0.4

0.3

0.4

0.2

0.1

0.4

0.2

0.6

0.3

0.4

0.5

0.3

0.2

0.3

0.2

0.3

0.2

0.1

0.4

0.1

0.5

0.3

0.4

0.5

0.2

0.3

0.2

0.3

0.2

0.1

0.3

0.1

0.4

0.3

0.4

0.2

0.1

0.2

0.1

0.3

0.1

0.4

0.2

0.3

0.4

0.2

0.1

Table 129 - Magnetic forces as a result of cross-winds: middle section, v_Fzg = 300 km/h, v_W = 10 .. 25 m/s

Title

High-speed Maglev Systems - Design principles

Guideway - Part II: Design

Doc. no.:

57288

Version

White Paper Issue date

15.02.2007

Page 155

High-speed maglev systems

Maglev Technical Committee

Design principles

Guideway

Guidance magnet forces p_y,W,FMTi in [kN/m]

[m/s]

11.7

8.3

12.2

10.3

10.0

9.9

11.0

8.1

7.5

6.1

4.9

1.8

1.3

11.3

8.0

11.8

9.9

9.6

9.5

10.5

7.8

7.2

5.9

4.7

1.8

1.2

10.8

7.7

11.4

9.5

9.2

9.1

10.1

7.5

6.9

5.7

4.5

1.7

1.2

10.4

7.4

11.0

9.1

8.9

8.7

9.7

7.2

6.7

5.4

4.3

1.6

1.1

10.0

7.1

10.6

8.7

8.5

8.3

9.2

6.9

6.4

5.2

4.2

1.6

1.1

9.6

6.8

10.2

8.4

8.1

7.9

8.8

6.6

6.1

5.0

4.0

1.5

1.0

9.1

6.5

9.8

8.0

7.7

7.6

8.4

6.3

5.8

4.7

3.8

1.5

1.0

8.7

6.2

9.4

7.6

7.4

7.2

8.0

6.0

5.6

4.5

3.6

1.4

0.9

8.3

5.9

9.0

7.3

7.0

6.8

7.6

5.7

5.3

4.3

3.4

1.3

0.9

7.9

5.6

8.6

6.9

6.7

6.5

7.2

5.4

5.1

4.1

3.3

1.3

0.9

7.5

5.4

8.2

6.6

6.3

6.2

6.8

5.1

4.8

3.9

3.1

1.2

0.8

7.2

5.1

7.9

6.2

6.0

5.8

6.4

4.9

4.6

3.7

2.9

1.2

0.8

6.8

4.8

7.5

5.9

5.7

5.5

6.1

4.6

4.3

3.5

2.8

1.1

0.7

6.4

4.6

7.1

5.5

5.4

5.2

5.7

4.3

4.1

3.3

2.6

1.0

0.7

6.1

4.3

6.8

5.2

5.1

4.9

5.4

4.1

3.9

3.1

2.5

1.0

0.7

5.7

4.1

6.4

4.9

4.7

4.6

5.0

3.8

3.6

2.9

2.3

0.9

0.6

Levitation magnet forces p_z,W,TMTi in [kN/m] (+/-)

[m/s]

(1)

5.0

4.3

5.0

3.5

6.1

1.4

4.1

2.3

2.7

3.1

3.5

1.8

3.7

1.0

2.7

4.8

4.1

4.8

3.3

5.9

1.4

3.9

2.2

2.6

3.0

3.4

1.8

3.5

1.0

2.6

4.6

3.9

4.6

3.2

5.6

1.3

3.8

2.2

2.5

2.8

3.2

1.7

3.4

0.9

2.5

4.4

3.8

4.4

3.1

5.4

1.3

3.6

2.1

2.4

2.7

3.1

1.6

3.2

0.9

2.4

4.2

3.6

4.2

2.9

5.2

1.2

3.5

2.0

2.3

2.6

2.9

1.5

3.1

0.8

2.3

4.0

3.5

4.0

2.8

4.9

1.2

3.3

1.9

2.2

2.5

2.8

1.5

3.0

0.8

2.2

3.8

3.3

3.8

2.7

4.7

1.1

3.2

1.8

2.1

2.4

2.7

1.4

2.8

0.8

2.1

3.6

3.2

3.6

2.6

4.5

1.0

3.0

1.7

2.0

2.3

2.6

1.3

2.7

0.7

2.0

3.5

3.0

3.5

2.4

4.3

1.0

2.9

1.6

1.9

2.2

2.4

1.3

2.6

0.7

1.9

3.3

2.9

3.3

2.3

4.1

0.9

2.7

1.5

1.8

2.1

2.3

1.2

2.4

0.7

1.8

3.1

2.8

3.1

2.2

3.9

0.9

2.6

1.5

1.7

2.0

2.2

1.2

2.3

0.6

1.7

3.0

2.6

2.9

2.1

3.7

0.8

2.5

1.4

1.6

1.9

2.1

1.1

2.2

0.6

1.6

2.8

2.5

2.8

2.0

3.5

0.8

2.3

1.3

1.5

1.8

2.0

1.0

2.1

0.6

1.5

2.6

2.4

2.6

1.9

3.3

0.8

2.2

1.2

1.4

1.7

1.8

1.0

1.9

0.5

1.4

2.5

2.2

2.5

1.8

3.1

0.7

2.1

1.2

1.3

1.6

1.7

0.9

1.8

0.5

1.3

2.3

2.1

2.3

1.7

2.9

0.7

1.9

1.1

1.3

1.5

1.6

0.9

1.7

0.5

1.3

Table 130 - Magnetic forces as a result of cross-winds: end section, v_Fzg = 200 km/h, v_W = 25 .. 40 m/s

Title

High-speed Maglev Systems - Design principles

Guideway - Part II: Design

Doc. no.:

57288

Version

White Paper Issue date

15.02.2007

Page 156

High-speed maglev systems

Maglev Technical Committee

Design principles

Guideway

Guidance magnet forces p_y,W,FMTi in [kN/m]

[m/s]

5.7

4.1

6.4

4.9

4.7

4.6

5.0

3.8

3.6

2.9

2.3

0.9

0.6

5.4

3.8

6.1

4.6

4.4

4.3

4.7

3.6

3.4

2.7

2.2

0.9

0.6

5.0

3.6

5.7

4.3

4.2

4.0

4.4

3.4

3.2

2.5

2.0

0.8

0.5

4.7

3.3

5.4

4.0

3.9

3.7

4.1

3.1

3.0

2.3

1.9

0.8

0.5

4.4

3.1

5.0

3.7

3.6

3.4

3.8

2.9

2.8

2.2

1.8

0.7

0.5

4.1

2.9

4.7

3.5

3.3

3.2

3.5

2.7

2.6

2.0

1.6

0.7

0.4

3.7

2.7

4.4

3.2

3.1

2.9

3.2

2.5

2.4

1.9

1.5

0.6

0.4

3.4

2.5

4.1

2.9

2.8

2.7

2.9

2.3

2.2

1.7

1.4

0.6

0.4

3.2

2.2

3.8

2.7

2.6

2.4

2.6

2.1

2.0

1.5

1.2

0.5

0.3

2.9

2.1

3.5

2.4

2.3

2.2

2.4

1.9

1.8

1.4

1.1

0.5

0.3

2.6

1.9

3.2

2.2

2.1

2.0

2.1

1.7

1.3

1.0

0.4

0.3

2.3

1.7

2.9

2.0

1.9

1.8

1.9

1.5

1.1

0.9

0.4

0.3

2.1

1.5

2.6

1.7

1.6

1.7

1.4

1.3

1.0

0.8

0.4

0.2

1.9

1.3

2.3

1.5

1.4

1.5

1.2

0.9

0.7

0.3

0.2

1.6

1.2

2.1

1.3

1.2

1.3

1.0

0.8

0.6

0.3

0.2

1.4

1.0

1.8

1.2

1.1

1.0

1.1

0.9

0.7

0.5

0.2

Levitation magnet forces p_z,W,TMTi in [kN/m] (+/-)

[m/s]

(1)

2.3

2.1

2.3

1.7

2.9

0.7

1.9

1.1

1.3

1.5

1.6

0.9

1.7

0.5

1.3

2.2

2.0

2.2

1.5

2.7

0.6

1.8

1.0

1.2

1.4

1.5

0.8

1.6

0.4

1.2

2.0

1.9

2.0

1.4

2.5

0.6

1.7

0.9

1.1

1.3

1.4

0.8

1.5

0.4

1.1

1.9

1.7

1.9

1.3

2.4

0.5

1.6

0.9

1.0

1.2

1.3

0.7

1.4

0.4

1.0

1.8

1.6

1.7

1.3

2.2

0.5

1.5

0.8

0.9

1.1

1.2

0.7

1.3

0.4

1.0

1.6

1.5

1.6

1.2

2.0

0.5

1.4

0.7

0.9

1.0

1.1

0.6

1.2

0.3

0.9

1.5

1.4

1.5

1.1

1.9

0.4

1.2

0.7

0.8

0.9

1.0

0.6

1.1

0.3

0.8

1.4

1.3

1.0

1.7

0.4

1.1

0.6

0.7

0.9

1.0

0.5

1.0

0.3

0.7

1.3

1.2

0.9

1.6

0.4

1.0

0.6

0.7

0.8

0.9

0.5

0.9

0.3

0.7

1.1

0.8

1.4

0.3

0.9

0.5

0.6

0.7

0.8

0.4

0.8

0.2

0.6

1.0

0.7

1.3

0.3

0.9

0.5

0.7

0.4

0.8

0.2

0.6

0.9

0.7

1.1

0.3

0.8

0.4

0.5

0.6

0.3

0.7

0.2

0.5

0.8

0.6

1.0

0.2

0.7

0.4

0.5

0.6

0.3

0.6

0.2

0.4

0.7

0.5

0.9

0.2

0.6

0.3

0.4

0.5

0.3

0.5

0.1

0.4

0.6

0.5

0.8

0.2

0.5

0.3

0.4

0.2

0.5

0.1

0.3

0.5

0.4

0.7

0.1

0.4

0.2

0.3

0.4

0.2

0.4

0.1

0.3

Table 131 - Magnetic forces as a result of cross-winds: end section, v_Fzg = 200 km/h, v_W = 10 .. 25 m/s

Title

High-speed Maglev Systems - Design principles

Guideway - Part II: Design

Doc. no.:

57288

Version

White Paper Issue date

15.02.2007

Page 157

High-speed maglev systems

Maglev Technical Committee

Design principles

Guideway

Guidance magnet forces p_y,W,FMTi in [kN/m]

[m/s]

1.1

1.6

3.2

3.8

4.3

4.5

5.6

6.6

6.9

7.2

8.9

7.8

4.8

2.5

1.0

1.5

3.1

3.7

4.2

4.3

5.4

6.3

6.6

6.9

8.6

7.5

4.6

2.5

1.0

1.5

3.0

3.5

4.0

4.2

5.1

6.0

6.3

6.7

8.2

7.2

4.4

2.4

0.9

1.4

2.9

3.4

3.8

4.0

4.9

5.7

6.0

6.4

7.9

6.9

4.2

2.3

0.9

1.4

2.8

3.2

3.7

3.8

4.7

5.4

5.7

6.1

7.6

6.6

4.1

2.2

0.9

1.3

2.6

3.1

3.5

3.7

4.5

5.1

5.5

5.8

7.3

6.4

3.9

2.1

0.8

1.3

2.5

3.0

3.4

3.5

4.3

4.9

5.2

5.6

6.9

6.1

3.7

2.0

0.8

1.2

2.4

2.8

3.2

3.3

4.1

4.6

5.0

5.3

6.6

5.8

3.6

2.0

0.7

1.2

2.3

2.7

3.1

3.2

3.9

4.4

4.7

5.1

6.3

5.5

3.4

1.9

0.7

1.1

2.2

2.6

2.9

3.0

3.7

4.1

4.5

4.8

6.0

5.3

3.2

1.8

0.7

1.1

2.1

2.4

2.8

2.9

3.5

3.9

4.2

4.6

5.7

5.0

3.1

1.7

0.6

1.0

2.0

2.3

2.6

2.7

3.3

3.6

4.0

4.3

5.4

4.7

2.9

1.7

0.6

1.0

1.9

2.2

2.5

2.6

3.2

3.4

3.7

4.1

5.1

4.5

2.8

1.6

0.6

1.0

1.8

2.1

2.4

3.0

3.2

3.5

3.9

4.8

4.2

2.6

1.5

0.5

0.9

1.7

1.9

2.2

2.3

2.8

3.0

3.3

3.6

4.6

4.0

2.5

1.4

0.5

0.9

1.6

1.8

2.1

2.2

2.6

2.8

3.1

3.4

4.3

3.8

2.3

1.4

Levitation magnet forces p_z,W,TMTi in [kN/m] (+/-)

[m/s]

1.0

1.2

1.9

1.3

1.8

1.4

1.5

2.0

0.9

2.9

1.8

2.2

2.8

1.4

1.0

1.1

1.8

1.3

1.7

1.8

1.3

1.4

1.9

0.9

2.8

1.8

2.1

2.7

1.3

1.0

0.9

1.1

1.7

1.2

1.6

1.7

1.3

1.8

0.8

2.7

1.7

2.0

2.6

1.3

0.9

1.0

1.7

1.2

1.6

1.2

1.8

0.8

2.6

1.6

1.9

2.5

1.2

0.9

1.0

1.6

1.1

1.5

1.2

1.7

0.8

2.4

1.5

1.9

2.3

1.2

0.9

0.8

1.0

1.5

1.1

1.4

1.5

1.1

1.6

0.7

2.3

1.5

1.8

2.2

1.1

0.8

0.9

1.5

1.0

1.4

1.1

1.0

1.6

0.7

2.2

1.4

1.7

2.1

1.1

0.8

0.9

1.4

1.0

1.3

1.0

0.9

1.5

0.7

2.1

1.3

1.6

2.0

1.0

0.8

0.7

0.8

1.3

0.9

1.2

1.3

1.0

0.9

1.4

0.6

2.0

1.3

1.5

1.9

1.0

0.7

0.8

1.3

0.9

1.2

0.9

0.8

1.4

0.6

1.9

1.2

1.5

1.8

0.9

0.7

0.6

0.7

1.2

0.8

1.1

1.2

0.9

0.8

1.3

0.6

1.8

1.2

1.4

1.7

0.9

0.6

0.7

1.1

0.8

1.1

0.8

0.7

1.2

0.5

1.7

1.1

1.3

1.7

0.8

0.6

0.7

1.1

0.8

1.0

0.8

0.6

1.2

0.5

1.7

1.0

1.3

1.6

0.8

0.6

0.5

0.6

1.0

0.7

0.9

1.0

0.7

0.6

1.1

0.5

1.6

1.0

1.2

1.5

0.7

0.5

0.6

0.9

0.7

0.9

0.7

0.5

1.0

0.4

1.5

0.9

1.1

1.4

0.7

0.5

0.6

0.9

0.6

0.8

0.9

0.6

0.5

1.0

0.4

1.4

0.9

1.0

1.3

0.6

0.5

Table 132 - Magnetic forces as a result of cross-winds: middle section, v_Fzg = 200 km/h, v_W = 25 .. 40 m/s

Title

High-speed Maglev Systems - Design principles

Guideway - Part II: Design

Doc. no.:

57288

Version

White Paper Issue date

15.02.2007

Page 158

High-speed maglev systems

Maglev Technical Committee

Design principles

Guideway

Guidance magnet forces p_y,W,FMTi in [kN/m]

[m/s]

0.5

0.9

1.6

1.8

2.1

2.2

2.6

2.8

3.1

3.4

4.3

3.8

2.3

1.4

0.5

0.8

1.5

1.7

2.0

2.5

2.6

2.9

3.2

4.0

3.5

2.2

1.3

0.4

0.8

1.4

1.6

1.9

2.3

2.4

2.7

3.0

3.8

3.3

2.1

1.2

0.4

0.7

1.3

1.5

1.7

1.8

2.2

2.5

2.8

3.5

3.1

1.9

1.1

0.4

0.7

1.2

1.4

1.6

2.0

2.3

2.6

3.3

2.9

1.8

1.1

0.3

0.7

1.1

1.3

1.5

1.9

1.8

2.1

2.4

3.0

2.7

1.7

1.0

0.3

0.6

1.1

1.2

1.4

1.7

1.9

2.2

2.8

2.5

1.5

0.9

0.3

0.6

1.0

1.1

1.3

1.6

1.5

1.8

2.0

2.6

2.3

1.4

0.9

0.3

0.5

0.9

1.0

1.2

1.4

1.6

1.9

2.3

2.1

1.3

0.8

0.2

0.5

0.8

0.9

1.1

1.3

1.2

1.4

1.7

2.1

1.9

1.2

0.7

0.2

0.4

0.7

0.8

1.0

1.2

1.1

1.3

1.5

1.9

1.7

1.1

0.7

0.2

0.4

0.7

0.9

1.1

0.9

1.1

1.4

1.7

1.5

1.0

0.6

0.2

0.4

0.6

0.8

0.9

0.8

1.0

1.2

1.5

1.4

0.9

0.6

0.1

0.3

0.5

0.6

0.7

0.8

0.7

0.9

1.1

1.4

1.2

0.8

0.5

0.1

0.3

0.5

0.6

0.7

0.6

0.8

0.9

1.2

1.1

0.7

0.5

0.1

0.3

0.4

0.5

0.6

0.5

0.6

0.8

1.0

0.9

0.6

0.4

Levitation magnet forces p_z,W,TMTi in [kN/m] (+/-)

[m/s]

0.5

0.6

0.9

0.6

0.8

0.9

0.6

0.5

1.0

0.4

1.4

0.9

1.0

1.3

0.6

0.5

0.8

0.6

0.8

0.6

0.4

0.9

0.4

1.3

0.8

1.0

1.2

0.6

0.5

0.4

0.5

0.8

0.6

0.7

0.8

0.6

0.4

0.9

0.4

1.2

0.7

0.9

1.1

0.6

0.4

0.5

0.7

0.5

0.7

0.5

0.4

0.8

0.3

1.1

0.7

0.9

1.1

0.5

0.4

0.7

0.5

0.6

0.7

0.5

0.3

0.8

0.3

1.1

0.6

0.8

1.0

0.5

0.4

0.3

0.4

0.6

0.4

0.6

0.4

0.3

0.7

0.3

1.0

0.6

0.7

0.9

0.5

0.3

0.4

0.6

0.4

0.5

0.6

0.4

0.3

0.7

0.3

0.9

0.5

0.7

0.8

0.4

0.3

0.5

0.4

0.5

0.4

0.2

0.6

0.2

0.8

0.5

0.6

0.8

0.4

0.3

0.5

0.3

0.5

0.3

0.2

0.6

0.2

0.8

0.5

0.6

0.7

0.3

0.2

0.3

0.4

0.3

0.4

0.3

0.2

0.5

0.2

0.7

0.4

0.5

0.6

0.3

0.2

0.4

0.3

0.4

0.3

0.1

0.5

0.2

0.6

0.4

0.5

0.6

0.3

0.2

0.4

0.3

0.2

0.1

0.4

0.2

0.6

0.3

0.4

0.5

0.3

0.2

0.3

0.2

0.3

0.2

0.1

0.4

0.1

0.5

0.3

0.4

0.5

0.2

0.3

0.2

0.3

0.2

0.1

0.3

0.1

0.4

0.3

0.4

0.2

0.1

0.2

0.1

0.3

0.1

0.4

0.2

0.3

0.2

0.1

0.2

0.1

0.2

0.1

0.3

0.1

0.3

0.2

0.3

0.1

Table 133 - Magnetic forces as a result of cross-winds: middle section, v_Fzg = 200 km/h, v_W = 10 .. 25 m/s

Title

High-speed Maglev Systems - Design principles

Guideway - Part II: Design

Doc. no.:

57288

Version

White Paper Issue date

15.02.2007

Page 159

High-speed maglev systems

Maglev Technical Committee

Design principles

Guideway

Guidance magnet forces p_y,W,FMTi in [kN/m]

[m/s]

3.2

3.6

3.2

3.6

5.0

3.6

3.2

4.1

3.6

2.2

1.9

3.0

3.4

3.0

3.4

4.8

3.4

3.0

3.9

3.4

2.1

1.8

2.8

3.3

2.8

3.3

4.5

3.3

2.8

3.7

3.3

2.0

1.7

2.7

3.1

2.7

3.1

4.3

3.1

2.7

3.5

3.1

1.9

1.6

2.6

2.9

2.6

2.9

4.1

2.9

2.6

3.3

2.9

1.8

1.5

2.4

2.8

2.4

2.8

3.8

2.8

2.4

3.1

2.8

1.7

1.4

2.3

2.6

2.3

2.6

3.6

2.6

2.3

3.0

2.6

1.6

1.4

2.1

2.5

2.1

2.5

3.4

2.5

2.1

2.8

2.5

1.5

1.3

2.0

2.3

2.0

2.3

3.2

2.3

2.0

2.6

2.3

1.4

1.2

1.9

2.2

1.9

2.2

3.0

2.2

1.9

2.5

2.2

1.3

1.1

1.8

2.0

1.8

2.0

2.8

2.0

1.8

2.3

2.0

1.2

1.1

1.7

1.9

1.7

1.9

2.6

1.9

1.7

2.2

1.9

1.2

1.0

1.5

1.8

1.5

1.8

2.5

1.8

1.5

2.0

1.8

1.1

0.9

1.4

1.7

1.4

1.7

2.3

1.7

1.4

1.9

1.7

1.0

0.9

1.3

1.5

1.3

1.5

2.1

1.5

1.3

1.7

1.5

0.9

0.8

1.2

1.4

1.2

1.4

2.0

1.4

1.2

1.6

1.4

0.9

0.7

Levitation magnet forces p_z,W,TMTi in [kN/m] (+/-)

[m/s]

(1)

0.8

1.7

1.0

1.1

1.5

1.4

1.0

0.8

1.1

0.8

1.6

1.0

1.1

1.4

1.3

1.0

0.8

1.1

0.7

1.6

0.9

1.0

1.4

1.3

0.9

0.7

1.0

0.7

1.5

0.9

1.0

1.3

1.2

0.9

0.7

1.0

0.7

1.4

0.9

1.0

1.2

1.1

0.9

0.7

1.0

0.6

1.4

0.8

0.9

1.2

1.1

0.8

0.6

0.9

0.6

1.3

0.8

0.9

1.1

1.0

0.8

0.6

0.9

0.6

1.3

0.7

0.8

0.7

0.8

1.1

1.0

0.7

0.8

0.7

0.6

0.8

0.6

1.2

0.7

0.8

1.0

0.9

0.7

0.6

0.8

0.5

1.1

0.7

1.0

0.9

0.7

0.5

0.8

0.5

1.1

0.6

0.7

0.9

0.8

0.6

0.5

0.7

0.5

1.0

0.6

0.7

0.9

0.8

0.6

0.5

0.7

0.4

1.0

0.6

0.8

0.6

0.4

0.6

0.4

0.9

0.5

0.6

0.8

0.7

0.5

0.4

0.6

0.4

0.9

0.5

0.6

0.7

0.5

0.4

0.6

0.4

0.8

0.5

0.7

0.6

0.5

0.4

0.5

Table 134 - Magnetic forces as a result of cross-winds: end section, v_Fzg = 0 km/h, v_W = 25 .. 40 m/s

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Design principles

Guideway

Guidance magnet forces p_y,W,FMTi in [kN/m]

[m/s]

1.2

1.4

1.2

1.4

2.0

1.4

1.2

1.6

1.4

0.9

0.7

1.1

1.3

1.1

1.3

1.8

1.3

1.1

1.5

1.3

0.8

0.7

1.0

1.2

1.0

1.2

1.7

1.2

1.0

1.4

1.2

0.7

0.6

1.0

1.1

1.0

1.1

1.5

1.1

1.0

1.2

1.1

0.7

0.6

0.9

1.0

0.9

1.0

1.4

1.0

0.9

1.1

1.0

0.6

0.5

0.8

0.9

0.8

0.9

1.3

0.9

0.8

1.0

0.9

0.6

0.5

0.7

0.8

0.7

0.8

1.1

0.8

0.7

0.9

0.8

0.5

0.4

0.6

0.7

0.6

0.7

1.0

0.7

0.6

0.8

0.7

0.4

0.6

0.7

0.6

0.7

0.9

0.7

0.6

0.7

0.4

0.3

0.5

0.6

0.5

0.6

0.8

0.6

0.5

0.7

0.6

0.4

0.3

0.4

0.5

0.4

0.5

0.7

0.5

0.4

0.6

0.5

0.3

0.4

0.6

0.4

0.5

0.4

0.3

0.2

0.3

0.4

0.3

0.4

0.5

0.4

0.3

0.4

0.2

0.3

0.5

0.3

0.4

0.3

0.2

0.3

0.2

0.3

0.4

0.3

0.2

0.3

0.2

0.1

0.2

0.3

0.2

0.3

0.2

0.1

Levitation magnet forces p_z,W,TMTi in [kN/m] (+/-)

[m/s]

(1)

0.4

0.8

0.5

0.7

0.6

0.5

0.4

0.5

0.3

0.8

0.4

0.5

0.7

0.6

0.4

0.5

0.4

0.3

0.5

0.3

0.7

0.4

0.5

0.6

0.5

0.4

0.3

0.5

0.3

0.7

0.4

0.6

0.5

0.4

0.3

0.4

0.3

0.6

0.4

0.5

0.4

0.3

0.4

0.3

0.6

0.3

0.4

0.5

0.4

0.3

0.4

0.2

0.6

0.3

0.4

0.3

0.2

0.3

0.2

0.5

0.3

0.4

0.3

0.2

0.3

0.2

0.5

0.3

0.4

0.3

0.2

0.3

0.2

0.4

0.2

0.3

0.2

0.3

0.2

0.4

0.2

0.3

0.2

0.1

0.3

0.2

0.3

0.2

0.1

0.2

0.1

0.3

0.2

0.1

0.2

0.1

0.3

0.1

0.2

0.1

0.2

0.1

0.2

0.1

0.2

0.1

0.2

0.1

0.2

0.1

0.2

0.1

0.2

0.1

Table 135 - Magnetic forces as a result of cross-winds: end section, v_Fzg = 0 km/h, v_W = 10 .. 25 m/s

Title

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Design principles

Guideway

Guidance magnet forces p_y,W,FMTi in [kN/m]

[m/s]

1.9

2.2

3.2

3.6

3.2

3.6

5.0

3.6

3.2

3.6

3.2

2.2

1.9

1.8

2.1

3.0

3.4

3.0

3.4

4.8

3.4

3.0

3.4

3.0

2.1

1.8

1.7

2.0

2.8

3.3

2.8

3.3

4.5

3.3

2.8

3.3

2.8

2.0

1.7

1.6

1.9

2.7

3.1

2.7

3.1

4.3

3.1

2.7

3.1

2.7

1.9

1.6

1.5

1.8

2.6

2.9

2.6

2.9

4.1

2.9

2.6

2.9

2.6

1.8

1.5

1.4

1.7

2.4

2.8

2.4

2.8

3.8

2.8

2.4

2.8

2.4

1.7

1.4

1.6

2.3

2.6

2.3

2.6

3.6

2.6

2.3

2.6

2.3

1.6

1.4

1.3

1.5

2.1

2.5

2.1

2.5

3.4

2.5

2.1

2.5

2.1

1.5

1.3

1.2

1.4

2.0

2.3

2.0

2.3

3.2

2.3

2.0

2.3

2.0

1.4

1.2

1.1

1.3

1.9

2.2

1.9

2.2

3.0

2.2

1.9

2.2

1.9

1.3

1.1

1.2

1.8

2.0

1.8

2.0

2.8

2.0

1.8

2.0

1.8

1.2

1.1

1.0

1.2

1.7

1.9

1.7

1.9

2.6

1.9

1.7

1.9

1.7

1.2

1.0

0.9

1.1

1.5

1.8

1.5

1.8

2.5

1.8

1.5

1.8

1.5

1.1

0.9

1.0

1.4

1.7

1.4

1.7

2.3

1.7

1.4

1.7

1.4

1.0

0.9

0.8

0.9

1.3

1.5

1.3

1.5

2.1

1.5

1.3

1.5

1.3

0.9

0.8

0.7

0.9

1.2

1.4

1.2

1.4

2.0

1.4

1.2

1.4

1.2

0.9

0.7

Levitation magnet forces p_z,W,TMTi in [kN/m] (+/-)

[m/s]

1.1

0.8

1.0

0.8

1.1

1.4

1.3

1.1

0.8

1.0

0.8

1.1

0.8

1.0

0.8

1.1

1.4

1.3

1.1

0.8

1.0

0.8

1.1

1.0

0.7

0.9

0.7

1.0

1.3

1.2

1.0

0.7

0.9

0.7

1.0

0.7

0.9

0.7

1.0

1.2

1.0

0.7

0.9

0.7

1.0

0.7

0.9

0.7

1.0

1.1

1.2

1.0

0.7

0.9

0.7

1.0

0.9

0.6

0.8

0.6

0.9

1.1

0.9

0.6

0.8

0.6

0.9

0.6

0.8

0.6

0.9

1.0

1.1

0.9

0.6

0.8

0.6

0.9

0.8

0.6

0.8

0.6

0.8

0.9

1.0

0.8

0.6

0.8

0.6

0.8

0.6

0.7

0.6

0.8

0.9

1.0

0.8

0.6

0.7

0.6

0.8

0.5

0.7

0.5

0.7

0.8

0.9

0.7

0.5

0.7

0.5

0.8

0.7

0.5

0.6

0.5

0.7

0.9

0.7

0.5

0.6

0.5

0.7

0.5

0.6

0.5

0.7

0.8

0.7

0.5

0.6

0.5

0.7

0.6

0.4

0.6

0.4

0.5

0.6

0.8

0.6

0.5

0.4

0.6

0.4

0.6

0.4

0.5

0.4

0.6

0.8

0.6

0.4

0.5

0.4

0.6

0.4

0.5

0.4

0.6

0.5

0.7

0.6

0.4

0.5

0.4

0.6

0.5

0.4

0.5

0.4

0.5

0.7

0.5

0.4

0.5

0.4

0.5

Table 136 - Magnetic forces as a result of cross-winds: middle section, v_Fzg = 0 km/h, v_W = 25 .. 40 m/s

Title

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Guidance magnet forces p_y,W,FMTi in [kN/m]

[m/s]

0.7

0.9

1.2

1.4

1.2

1.4

2.0

1.4

1.2

1.4

1.2

0.9

0.7

0.8

1.1

1.3

1.1

1.3

1.8

1.3

1.1

1.3

1.1

0.8

0.7

0.6

0.7

1.0

1.2

1.0

1.2

1.7

1.2

1.0

1.2

1.0

0.7

0.6

0.7

1.0

1.1

1.0

1.1

1.5

1.1

1.0

1.1

1.0

0.7

0.6

0.5

0.6

0.9

1.0

0.9

1.0

1.4

1.0

0.9

1.0

0.9

0.6

0.5

0.6

0.8

0.9

0.8

0.9

1.3

0.9

0.8

0.9

0.8

0.6

0.5

0.4

0.5

0.7

0.8

0.7

0.8

1.1

0.8

0.7

0.8

0.7

0.5

0.4

0.6

0.7

0.6

0.7

1.0

0.7

0.6

0.7

0.6

0.4

0.3

0.4

0.6

0.7

0.6

0.7

0.9

0.7

0.6

0.7

0.6

0.4

0.3

0.4

0.5

0.6

0.5

0.6

0.8

0.6

0.5

0.6

0.5

0.4

0.3

0.4

0.5

0.4

0.5

0.7

0.5

0.4

0.5

0.4

0.3

0.2

0.3

0.4

0.6

0.4

0.3

0.2

0.3

0.4

0.3

0.4

0.5

0.4

0.3

0.4

0.3

0.2

0.3

0.5

0.3

0.2

0.1

0.2

0.3

0.2

0.3

0.4

0.3

0.2

0.3

0.2

0.1

0.2

0.3

0.2

0.1

Levitation magnet forces p_z,W,TMTi in [kN/m] (+/-)

[m/s]

0.5

0.4

0.5

0.4

0.5

0.7

0.5

0.4

0.5

0.4

0.5

0.4

0.5

0.3

0.4

0.5

0.4

0.6

0.5

0.4

0.3

0.5

0.3

0.5

0.3

0.4

0.3

0.5

0.4

0.6

0.5

0.3

0.4

0.3

0.5

0.4

0.3

0.4

0.3

0.4

0.6

0.4

0.3

0.4

0.3

0.4

0.3

0.4

0.3

0.4

0.3

0.5

0.4

0.3

0.4

0.3

0.4

0.3

0.4

0.3

0.5

0.4

0.3

0.4

0.3

0.2

0.3

0.2

0.3

0.2

0.5

0.3

0.2

0.3

0.2

0.3

0.2

0.3

0.2

0.3

0.2

0.4

0.3

0.2

0.3

0.2

0.3

0.2

0.3

0.2

0.3

0.2

0.4

0.3

0.2

0.3

0.2

0.3

0.2

0.3

0.2

0.3

0.2

0.1

0.3

0.2

0.1

0.2

0.1

0.2

0.1

0.3

0.2

0.1

0.2

0.1

0.2

0.1

0.2

0.1

0.2

0.1

0.3

0.2

0.1

0.2

0.1

0.2

0.1

0.2

0.1

0.2

0.1

0.2

0.1

0.2

0.1

0.2

0.1

0.2

0.1

0.2

0.1

Table 137 - Magnetic forces as a result of cross-winds: middle section, v_Fzg = 0 km/h, v_W = 10 .. 25 m/s

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Design principles

Guideway

Annex II-F: Calculating the levitation magnet

pole forces

Without rearrangement for standard and front and rear-mounted levitation magnets (see

Example

figs. 180 and 181)

Line load, part

z,az,EG/MG/ZG/HG,TMT

from equation 15

kN/m

magnets i, i+1

z,az,EG/MG/ZG/HG,TMT

i+1

0.5⋅p_{z,az,EG/MG/ZG/HG,TMT(i/i+1)} ⋅L_{sys,TMT(i/i+1)} / 5.5

Levitation

1.41;

magnet termi-

P_z,EP,i/i+1

0.70

nal pole forces

0.5⋅p_{z,az,EG/MG/ZG/HG,TMT(i/i+1)} ⋅L_{sys,TMT(i/i+1)} / 7.5 *

1.39 *

p_{z,az,EG/MG/ZG/HG,TMT(i/i+1)} ⋅L_{sys,TMT(i/i+1)} / 5.5

Levitation

2.82;

magnet main

P_z,HP,i/i+1

1.40

pole forces

p_{z,az,EG/MG/ZG/HG,TMT(i/i+1)} ⋅L_{sys,TMT(i/i+1)} / 7.5 *

2.77 *

* with a front and rear-mounted levitation magnet

Table 138 - Levitation magnet pole forces without rearrangement

With 30% rearrangement for standard levitation magnets (see fig. 180)

Example

z,az,EG/MG/ZG/HG,TMT

Line load, part

≥

from equation 15

kN/m

magnets i, i+1

z,az,EG/MG/ZG/HG,TMT

i+1

Result of the

uneven distribu-

R_TMTi,30%

z,az,EG/MG/ZG/HG,TMT

⋅30% ⋅ L

sys,TMT

/ 2

2.32

tion TMT_i

Levitation mag-

net terminal pole

P_z,EP,30,i

Pz,EP,i + RTMTi,30% · 3 / 18

1.79

force i

Levitation mag-

net main pole

P_z,HP1,30,i

P_z,HP,i + R_TMTi,30% · 5 / 18

3.46

force 1,i

Levitation mag-

net main pole

P_z,HP2,30,i

P_z,HP,i + R_TMTi,30% · 4 / 18

3.33

force 2,i

Levitation mag-

net main pole

P_z,HP3,30,i

P_z,HP,i + R_TMTi,30% · 3 / 18

3.20

force 3,i

Levitation mag-

net main pole

P_z,HP4,30,i

P_z,HP,i + R_TMTi,30% · 2 / 18

3.07

force 4,i

Levitation mag-

net main pole

P_z,HP5,30,i

P_z,HP,i + R_TMTi,30% · 1 / 18

2.94

force 5,i

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Levitation mag-

net main pole

P_z,HP6,30,i+1

P_z,HP,i+1 - R_TMTi,30% · 1 / 18

1.27

force 6,i+1

Levitation mag-

net main pole

P_z,HP7,30,i+1

P_z,HP,i+1 - R_TMTi,30% · 2 / 18

1.14

force 7,i+1

Levitation mag-

net main pole

P_z,HP8,30,i+1

P_z,HP,i+1 - R_TMTi,30% · 3 / 18

1.02

force 8,i+1

Levitation mag-

net main pole

P_z,HP9,30,i+1

P_z,HP,i+1 - R_TMTi,30% · 4 / 18

0.89

force 9,i+1

Levitation mag-

net main pole

P_{z,HP10,30,i+1}

P_z,HP,i+1 - R_TMTi,30% · 5 / 18

0.76

force 10,i+1

Levitation mag-

net terminal pole

P_z,EP,30,i+1

P_z,EP,i+1 - R_TMTi,30% · 3 / 18

0.31

force i+1

Table 139 - Levitation magnet pole forces with 30% rearrangement (standard levitation magnet)

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With 30% rearrangement for front and rear-mounted levitation magnets (see fig. 181)

Example

z,az,EG/MG/ZG/HG,TMT

Line load, part

≥

kN/

from equation 15

magnets i, i+1

i+1

z,az,EG/MG/ZG/HG,TMT

Result of the

⋅30% ⋅ L

/ 2

z,az,EG/MG/ZG/HG,TMT

sys,TMT,Bug / Heck

uneven distribu-

R_TMTi,30%

3.12

tion TMT_i

Levitation mag-

net terminal pole

P_z,EP,30,i

Pz,EP,i + RTMTi,30% · 4 / 32

1.77

force i

Levitation mag-

net main pole

P_z,HP1,30,i

P_z,HP,i + R_TMTi,30% · 7 / 32

3.45

force 1,i

Levitation mag-

net main pole

P_z,HP2,30,i

P_z,HP,i + R_TMTi,30% · 6 / 32

3.36

force 2,i

Levitation mag-

net main pole

P_z,HP3,30,i

P_z,HP,i + R_TMTi,30% · 5 / 32

3.26

force 3,i

Levitation mag-

net main pole

P_z,HP4,30,i

P_z,HP,i + R_TMTi,30% · 4 / 32

3.16

force 4,i

Levitation mag-

net main pole

P_z,HP5,30,i

P_z,HP,i + R_TMTi,30% · 3 / 32

3.06

force 5,i

Levitation mag-

net main pole

P_z,HP6,30,i

P_z,HP,i + R_TMTi,30% · 2 / 32

2.97

force 6,i

Levitation mag-

net main pole

P_z,HP7,30,i

P_z,HP,i + R_TMTi,30% · 1 / 32

2.87

force 7,i

Levitation mag-

net main pole

P_z,HP8,30,i+1

P_z,HP,i+1 - R_TMTi,30% · 1 / 18

1.23

force 8,i+1

Levitation mag-

net main pole

P_z,HP9,30,i+1

P_z,HP,i+1 - R_TMTi,30% · 2 / 18

1.06

force 9,i+1

Levitation mag-

net main pole

P_{z,HP10,30,i+1}

P_z,HP,i+1 - R_TMTi,30% · 3 / 18

0.88

force 10,i+1

Levitation mag-

net main pole

P_{z,HP11,30,i+1}

P_z,HP,i+1 - R_TMTi,30% · 4 / 18

0.71

force 11,i+1

Levitation mag-

P_{z,HP12,30,i+1}

P_z,HP,i+1 - R_TMTi,30% · 5 / 18

0.54

net main pole

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Regel-Tragmagnete

4.0

3.5

3.0

ohne 30 %

mit 30 %

2.5

2.0

1.5

1.0

0.5

0.0

HP1

HP2

HP3

HP4

HP5

HP6

HP7

HP8

HP9

HP10

Tragmagnetpole

Fig. 180 - Levitation magnet pole forces; example of standard levitation magnets

[Key to diagram:

Regel-Tragmagnete = standard levitation magnets

ohne 30% = less 30%

mit 30% = plus 30%

Polkraft = pole force

Tragmagnetpole = levitation magnet poles]

Bug-/Heck-Tragmagnete

4,0

3,5

3,0

ohne 30 %

mit 30 %

2,5

2,0

1,5

1,0

0,5

0,0

HP1

HP2

HP3

HP4

HP5

HP6

HP7

HP8

HP9

HP10

HP11

HP12

Tragmagnetpole

Fig. 181 - Levitation magnet pole forces; example of front and rear-mounted levitation magnets

Title

High-speed Maglev Systems - Design principles

Guideway - Part II: Design

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Design principles

Guideway

General

Object and area of application

This document sets out in detail the generally applicable technical requirements concerning the

guideway geometry of the maglev train system.

These design principles apply to a maglev train in accordance with the General Maglev Systems’

Act.

Document structure

These design principles set out in detail the geometric requirements pertaining to the functional

levels of maglev train support structures.

Requirements concerning the precise positioning of the girders are set out in the Guideway design

principles for high-speed maglev systems - Part IV: Surveying.

The explanatory notes concerning positional deviations, specifications and tolerances assist in a

basic understanding of the construction of a maglev train guideway.

Based on the correlation between the individually stipulated limit values, taking into account the

system as a whole, the limit values may be shifted in either direction. The requirements as per the

Principles concerning the overall system design of high-speed maglev systems are included in the

overall assessment in this regard.

The limit values indicated assist in observing the travel comfort offered by the system as a whole

as well as its technical requirements.

Explanatory note concerning application

The document defines the permitted variations and positional deviations in the functional levels of

the support structures which are to be observed in the equipped and precisely positioned states,

without a live load, the only load coming from the girder’s own weight.

In a further step, taking into account the envisaged manufacturing process, the manufacturing tol-

erances concerning guideway manufacture (the raw materials used in the guideway, its equipment

and assembly) and maintenance shall be derived from this.

Unless expressly noted to the contrary, all data relates to a guideway under a project-specific refe-

rence temperature.

All data relates to the functional levels in the placed, coated state.

The stipulation of requirements in terms of guideway dimensions (e.g. limit values in terms of the

permissible deviation, in combination with the guideway’s deformation) is essentially based on ex-

periences with guideways which have been tested previously and their interaction with magnetic

trains which are driven under test and operational conditions.

The individual permitted variations partly produce overlaps during an overall tolerance assessment.

With additional tolerance stipulations or those which are independent from one another, care must

be taken that the respective individual tolerance is observed or that those stipulations with smaller

tolerance values have priority.

If the document does not list permissible deviations of individual functional levels in terms of form

and position, from the point of view of the system as a whole, there is no inducement to this end.

This case presupposes a manufacturing tolerance as per DIN ISO 2768-1 and DIN ISO 2768-2.

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Design principles

Guideway

Principles for the design of high-speed maglev systems

This document is part of the documentation relating to high-speed maglev systems con-

sisting of several design principles. The document tree is presented in fig. 1 of the Prin-

ciples concerning the overall system design of high-speed maglev systems.

The primary overall system design documentation and its annexes apply in a uniform manner to

the documentation as a whole:

• Principles concerning the overall system design of high-speed maglev systems, do-

cument number 50630, and its annexes:

• Annex 1: Abbreviations and definitions, document number 67536 [Principles for

the design of high-speed maglev systems - Abbreviations and definitions]

• Annex 2: Acts, Orders, Standards and Guidelines, document number 67539

[Principles for the design of high-speed maglev systems - Standards and guide-

lines]

• Annex 3: Environmental conditions, document number 67285 [Principles for the

design of high-speed maglev systems - The environment]

• Annex 4: Rules for operation (driving and maintenance), document number

69061 [Principles for the design of high-speed maglev systems - Driving and

maintenance]

• Annex 5: Sound, document number 72963 [Principles for the design of high-

speed maglev systems - Sound]

Abbreviations and definitions

The abbreviations and definitions specified in the Principles for the design of high-speed maglev

systems - Abbreviations and definitions - apply.

Acts, Orders, Standards and Guidelines

The normative documents listed in the Principles for the design of high-speed maglev systems -

Standards and guidelines, contain stipulations which, by reference to the Principles for the design

of high-speed maglev systems, become part of the same. Later amendments or revisions to these

publications do not apply to dated, normative documents found in the Principles for the design of

high-speed maglev systems - Standards and guidelines. Where references are not dated, the most

recent version of the normative document referred to applies.

The status of the standards and guidelines to be taken into consideration in a maglev train project

must be laid down in a binding manner specific to the project.

Indicating requirements and their binding nature

The provisions pursuant to DIN 820 were essentially applied when preparing this document.

In the chapters following and the annexes to this document,

• requirements are set out in standard type and

• explanatory notes, standard values and examples are set out in italics

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Clearances for built-in guideway fixtures

The placement clearances for guideway equipment which is specific to high-speed maglev sys-

tems are laid down below in figs. 182, 183 and 184 based on the Principles concerning the overall

system design of high-speed maglev systems. In addition, the dimensions specified in the Annex of

the Guideway design principles for high-speed maglev systems - Part I: Principle requirements, in

relation to standard guideway types must be observed as standard gauges.

A definition of “clearance” is to be found in the Guideway design principles for high-speed maglev

systems - Part IV: Alignment.

Spurweite 2800

1400

1110

Seitenführschiene SFS

Raumkurve

250

min. 30

Gleitebene GE

285

Gleitleiste GL

Statorpaketbefestigung

305

240

max. 240

StatorebeneSE

185

240

842.5

715

885

Fahrwegumgrenzung

1102

Freiraum für externe

Freiraum für

Bordenergieversorgung

Ortungsbaugruppen

Freiraum für

LSW Zu- und Ableitung

Motorwicklung

( ) Werte in Klammern sind bauartspezifisch

Fig. 182:

Clearances for the guideway equipment which is specific to high-speed maglev systems and the support

structures

[Key to diagram:

Spurweite = guideway gauge

Seitenführebene = lateral guide level

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Seitenführschiene = lateral guide rail

Raumkurve = space curve

Gleitebene = slider level

Gleitleiste = slider strip

Statorpaketbefestigung = stator plate attachment

Fahrwegachse = guideway axis

Zangenmaß = hover clearance

Statorebene = stator level

Fahrwegumgrenzung = guideway boundary

Freiraum für externe Bordenergieversorgung = clearance for external inductive power supply

Freiraum für Ortungsbaugruppen = clearance for location-finding assemblies

Freiraum für LSW Zu- und Ableitung = clearance for LSW supply lines and offtakes

Freiraum für Motorwicklung = clearance for motor winding

Werte in Klammern sind bauartspezifisch = the values in brackets are specific to the design]

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Explanatory notes to fig. 182:

1) The guideway boundary line describes the maximum feasible wrap-around of the support

structure, including its tolerances.

2) Design-specific deviations from the guideway boundary line are only permitted once they

have been tested for compatibility with the system as a whole.

3) Provision is made for a clearance for securing the guideway equipment between that e-

quipment which is specific to high-speed maglev systems and the support structures. The si-

ze of this clearance depends on the choice of mounting structure and requires a check con-

firming its compatibility with the system as a whole.

Langstatormittachse

Raumkurve

Seitenführschiene SFS

Gleitebene GE

Befestigung

Abstand UK Kragarm

Seitenführschiene-

von GE ist

Trägerkragarm ³⁾

bauartspezifisch ¹⁾

Statorebene

1110 zur Raumkurve

1400 halbe Spurweite zur Raumkurve

Fig. 183:

Guide span position

[Key to diagram:

Langstatormittachse = centre axis of the longitudinal stator

Raumkurve = space curve

Seitenführschiene = lateral guide rail

Gleitebene = slider level

Führspaltmessbereich = guide span

Befestigung Seitenführschiene-Trägerkragarm = lateral guide rail girder jib boom attachment

Abstand UK Kragarm von GE ist bauartspezifisch = the distance between the bottom side of the jib boom

and the slider level is specific to the design

Seitenführebene = lateral guide level

Statorebene = stator level

zur Raumkurve = in relation to the space curve

halbe Spurweite zur Raumkurve = half the guideway gauge in relation to the space curve]

Explanatory notes to fig. 183:

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1) The distance between the bottom side of the jib boom and the slider level is specific to the

design and is established by the type of stator plate mounting and the motor winding hou-

sing.

2) The guide sensor areas depicted correspond to the position when the vehicle is hovering

with a reference loadbearing gap of 10 mm.

3) The mounting for the lateral guide rails and the clearance which is required shall be stipu-

lated in accordance with the particular design.

4) Centre point of the guidance magnets of the hovering vehicle with a reference loadbearing

gap of 10 mm;

Seitenführschiene SFS

Freiraum zur Befestigung

der Statorpakete und für

Freiraum

Erdungsbauteile

Motorwicklung

Statorpaket

R15

45°

R15

Statorebene SE

147.5

185

147.5

480

Fig. 184:

Long stator winding housing

[Key to diagram:

Seitenführschiene = lateral guide rail

Freiraum zur Befestigung der Statorpakete und für Erdungsbauteile = clearance for attaching the stator pla-

tes and for earthing elements

Statorpaket = stator plate

Freiraum Motorwicklung = clearance for motor winding

Statorebene = stator level]

Explanatory notes to fig. 184:

The motor winding housing depicted also takes into account the space required by the

motor winding cable for the assembly process. The clearances required by the mounting

device lie within the vehicle’s gauge.

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Dimensional relationships, principal measuring points, reference planes

and influencing variables

Functional levels and principal measuring point

locations

The locations of the functional levels and the associated measuring points in the x, y and z directi-

ons are depicted in figs. 185, 186, 187 and 188.

Spurweite 2800

1400

1110

Gleitebene GE

y-Achse

StatorebeneSE

Spurweite: Messpunkt 5, 6

Zangenmaß: Messpunkt 1, 3 bzw. 2, 4

Fig. 185:

Functional levels and principle measuring points in the y and z directions

[Key to diagram:

Spurweite = guideway gauge

Seitenführebene = lateral guide level

Gleitebene = slider level

Zangenmaß = hover clearance

y-Achse = y-axis

Statorebene = stator level

Langstatormittenachse = centre axis of the longitudinal stator

Fahrwegachse (z-Achse) = guideway axis (z-axis)

Spurweite: Messpunkt 5, 6 = guideway gauge: measuring points 5, 6

Zangenmaß: Messpunkt 1, 3 bzw. 2, 4 = hover clearance: measuring points 1, 3 or 2, 4]

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Guideway

1032 (Raumkurve)

100

170

Gleitebene GE

Zangenmaß 398

Seitenführebene SFE

StatorebeneSE

Messpunkte

1.Statorpaket

2.Statorpaket

3.Statorpaket

(n-2).Statorpaket

(n-1).Statorpaket

n.Statorpaket

Bei gekürzten Trägerlängen sind Endmaße entsprechend anzupassen.

Messpunkt

Fig. 186:

Principal measuring points in the x and z directions

[Key to diagram:

Systemachse = system axis

Raumkurve = space curve

Zangenmaß = hover clearance

Gleitebene = slider level

Seitenführebene = lateral guide level

Statorebene = stator level

letzter Vollzahn = last full-depth tooth

erster Vollzahn = first full-depth tooth

Messpunkte = measuring points

Statorpaket = stator plate

Bei gekürzten Trägerlängen sind Endmaße entsprechend anzupassen = with shorter girder lengths, the final

dimensions shall be adapted accordingly

Messpunkt = measuring point]

The principal measuring point locations in the x direction (refer to fig. 186 for the longitudinal di-

rection) shall be selected such that a measured value for evaluation purposes is at least established

within the system grid dimension of 1032 mm.

Where functional levels which have already been divided up are present, the gap dividing grid must

be observed. In this instance, a measuring point shall be arranged on both sides of the gap.

The first measuring point at the beginning or end of the support structure shall be placed at a uni-

form distance of 100 mm from the system axis and should be durably marked.

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Seitenführebene SFE

Gleitebene GE

1400

x * 1032

1110

Gleitebene GE

1110

1400

Seitenführebene SFE

Fig. 187:

Principal lateral guide and slider level measuring points

[Key to diagram:

Seitenführebene = lateral guide level

Gleitebene = slider level

Bogenaußen = outer side of the curve

Raumkurve = space curve

Bogeninnen = inner side of the curve

Messprofil = measuring profile]

StatorebeneSE

x * 1032

1110

StatorebeneSE

1110

Fig. 188:

Principal stator level measuring points

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[Key to diagram:

Bogenaußen = outer side of the curve

Statorpaket = stator plate

Statorebene = stator level

Raumkurve = space curve

Bogeninnen = inner side of the curve

1. Vollzahn = first full-depth tooth

letzter Vollzahn = last full-depth tooth

Messprofil = measuring profile]

Requirements pertaining to principal measur-

ing points and measured values

The measured values determined for the principal measuring points must allow a representative

statement on the location of the functional level.

This means that measurement procedures and methods which are suitable for determining the

measured value shall be applied which eliminate one-off influences on the measuring result (e.g.

graduated edges, flaws in the material, local surface finishings, anomalies in the coating).

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Coordinate systems

The tolerances given in the document relate to the coordinate axis designations

• y, x, z relate to the space curve coordinate system

(girder-related sector of the space curve with a redefined zero point, see also Chapter 6.6),

and

• Y, X, Z relate to the girder production coordinate system

(machine-related production coordinate system taken into consideration in the design pre-

curvature and production corrections which may be required).

Fig. 189 presents the correlations.

As regards work on the building site (staking out, constructing foundations, precise positioning of

the guideway), the coordinates of the maglev train coordinate system are used.

(refer to the Guideway design principles for high-speed maglev systems - Part IV: Surveying re-

garding the x, y and z coordinates in the maglev train coordinate system)

The beginning and end coordinates of the support structures from the space curve coordinate sys-

tem are transformed into the maglev train coordinate system at the same time via reference points.

Fig. 189:

Geometric correlation between the coordinate systems (girder production coordinate system and local

guideway coordinates)

[Key to diagram:

Querneigungsdifferenz = lateral incline differential

Längsneigungsdifferenz = longitudinal gradient differential

Ursprung TFK im Trägerraster liegt auf Raumkurve = the zero point of the girder fabrication coordinates in

the girder grid lies on the space curve

globale Trägerfertigungskoordinaten (TFK)

X, Y, Z Achsen rechtwinkelig zueinander, fahrwegträgerbezogen =

global girder production coordinates

X, Y, Z axes at right angles to one another, relative to the guideway

lokale Fahrwegkoordinaten (RKK)

x-Achse mit U β mitdrehend

y- u. z-Achse mit U α mitdrehend =

local guideway coordinates

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System and building component lengths

All measurements along the space curve which represent a multiple of 86 mm (this corresponds to a

groove/tooth period according to the Principles concerning the overall system design of high-speed

maglev systems) can be designated system lengths. Support structure lengths are specified when

converting the route into system lengths.

Their actual length (building component length) depends on the design of the functional levels at

the beginning and end of the support structure, as well as the horizontal and vertical radii (see fig.

190).

Bauteillänge (L)

Systemachse

Statorachse (bogenaußen)

Systemlänge des

Fahrwegträgers

)

Sys

Raumkurve

Statorachse (bogeninnen)

Spalt am Trägerstoß

Fig. 190:

Correlation between building component length and system length

[Key to diagram:

Bauteilänge = building component length

Systemachse = system axis

Statorachse (bogenaußen) = stator axis (outer side of the curve)

Systemlänge des Fahrwegträgers = system length of the support structure

Raumkurve = space curve

Statorachse (bogeninnen) = stator axis (inner side of the curve)

Spalt am Trägerstoß = opening in the girder joint]

Sign stipulations

The sign conventions facilitate a clear interpretation of the maglev train / guideway interface on the

following basis:

When considered from the point of view of increasing chainage (positive x direction), a negative

sign always indicates a deviation towards the space curve, while a positive sign points to a deviati-

on away from the same curve or towards the outside. Regarding the guideway gauge, a negative

sign therefore indicates a reduction, and a positive sign an increase, in the guideway gauge.

When applying the following equations, a clear direction of the deviation from the theoretical posi-

tion is possible by means of the result sign. In the case of vibrations in elements, the displacement

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shall be calculated by extrapolating measuring lines (each time from 2 measuring points) with the

axes of intersection.

• Refer to fig. 191 for the sign convention for lateral guide level displacement:

right side:

∆y

=-y

Equation 7

i+1

left side:

∆y

Equation 8

i+1

Maßbezugslinie SFE

(linke Seite)

x-Achse

Maßbezugslinie SFE

(rechte Seite)

z-Achse

Fig. 191:

Lateral guide level displacement, tolerance zone with sign allocation as per equations 7 and 8

[Key to diagram:

Maßbezugslinie SFE (linke Seite) = zero-datum line, lateral guide level (left side)

Maßbezugslinie SFE (rechte Seite) = zero-datum line, lateral guide level (right side)

x-Achse = x-axis

z-Achse = z-axis]

• Refer to fig. 192 for the sign convention for stator level displacement:

∆z

=-z

Equation 9

i+1

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x-Achse

Maßbezugslinie SE

(linke Seite)

Maßbezugslinie SE

(rechte Seite)

z-Achse

Fig. 192:

Stator level displacement, tolerance zone with sign allocation as per equation 3

[Key to diagram:

Maßbezugslinie SE (linke Seite) = zero-datum line, stator level (left side)

Maßbezugslinie SE (rechte Seite) = zero-datum line, stator level (right side)

x-Achse = x-axis

z-Achse = z-axis]

• Refer to fig. 193 for the sign convention for slider level displacement:

∆z

Equation 10

i+1

Maßbezugslinie GE

(linke Seite)

x-Achse

Maßbezugslinie GE

(rechte Seite)

z-Achse

Fig. 193:

Slider level displacement, tolerance zone with sign stipulation as per equation 4

[Key to diagram:

Maßbezugslinie GE (linke Seite) = zero-datum line, slider level (left side)

Maßbezugslinie GE (rechte Seite) = zero-datum line, slider level (right side)

x-Achse = x-axis

z-Achse = z-axis]

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• Refer to fig. 194 for the sign convention for altering the guideway gauge (S):

Equation 11

∆y

=-S

;

i+1

Maßbezugslinie SFE

(linke Seite)

x-Achse

Maßbezugslinie SFE

(rechte Seite)

z-Achse

Fig. 194:

Altering the guideway gauge, tolerance zones with sign stipulation as per equation 11

[Key to diagram:

Maßbezugslinie SFE (linke Seite) = zero-datum line, lateral guide level (left side)

Maßbezugslinie SFE (rechte Seite) = zero-datum line, lateral guide level (right side)

x-Achse = x-axis

z-Achse = z-axis]

• The sign convention for the gradient-altering criterion of the lateral guide level within the

girder, and at the girder joint and element transition, is extrapolated in accordance with

equation 14 while observing the intervals between measuring points. Refer to fig. 195 for

the graphic representation of the sign convention:

right side:

⎡

⎛

⎞⎤

i-1

Equation 12

NGK

2*⎢-y

SFE

⎜

⎟

⎥

⎣

⎝

⎠

⎦

left side:

⎡

⎛

⎞⎤

i-1 i+1

Equation 13

NGK

2*⎢y

−

SFE

⎜

⎟

⎥

⎣

⎝

⎠

⎦

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Maßbezugslinie SFE

(linke Seite)

x-Achse

Maßbezugslinie SFE

(rechte Seite)

z-Achse

Fig. 195:

Gradient-altering criterion of the lateral guide level, tolerance zones and sign stipulation as per equations

12 and 13

[Key to diagram:

Maßbezugslinie SFE (linke Seite) = zero-datum line, lateral guide level (left side)

Maßbezugslinie SFE (rechte Seite) = zero-datum line, lateral guide level (right side)

x-Achse = x-axis

z-Achse = z-axis]

• The sign convention for the gradient-altering criterion of the stator level over four measu-

ring points (first and last full-depth tooth of the stator plate numbered continuously (z₁, z₂, z₃

and z₄)). Refer to fig. 196 for the graphic representation of the sign:

1000

Equation 14

NGK

=⎣(z

(

−

)

⎦

860

x-Achs

Maßbezugslinie SE

(linke Seite)

Maßbezugslinie SE

(rechte Seite)

z-Achse

Fig. 196:

Gradient-altering criterion of the stator level, tolerance zones with sign allocation as per equation 14

[Key to diagram:

Maßbezugslinie SE (linke Seite) = zero-datum line, stator level (left side)

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Maßbezugslinie SE (rechte Seite) = zero-datum line, stator level (right side)

x-Achse = x-axis

z-Achse = z-axis]

• Refer to fig. 197 for the sign convention for the gradient-altering criterion of the slider le-

vel:

⎡

⎛

⎞⎤

i-1 i+1

Equation 15

NGK

GLE

⎢

⎜

⎟⎥

⎣

⎝

⎠⎦

Maßbezugslinie GE

(linke Seite)

x-Achse

+ Maßbezugslinie GE

(rechte Seite)

z-Achse

Fig. 197:

Gradient-altering criterion of the slider level, tolerance zones with sign allocation as per equation 15

[Key to diagram:

Maßbezugslinie GE (linke Seite) = zero-datum line, slider level (left side)

Maßbezugslinie GE (rechte Seite) = zero-datum line, slider level (right side)

x-Achse = x-axis

z-Achse = z-axis]

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High-speed maglev systems

Maglev Technical Committee

Design principles

Guideway

Definitions and stipulations for tolerances and

positional deviations

The tolerances and positional deviations described below relate exclusively to the girder production

coordinate system.

Assuming a bearing arrangement, a distinction is drawn between simple beams, two-span beams

and multiple span girders as well as gauge change devices.

When stipulating the tolerance zones, guideway plates are treated as simple beams.

In the diagrams which follow, the x-axis of the coordinate system mirrors the layout of the

space curve.

Design precurvature

The design precurvature is designed to compensate the deflection of the support structure in the z

direction as a result of the live load (mean vehicle weight under normal load conditions as per the

Guideway design principles for high-speed maglev systems - Part II: Dimensioning) and also taking

into account the project-specific prevailing temperature differentials in the guideway cross-section

(change in temperature between the top and bottom booms) under operating conditions. In the case

of concrete girders, where necessary, consideration must be given to the creep and shrinkage cha-

racteristics over the first 25-30 years (refer to the Guideway design principles for high-speed

maglev systems - Part II: Dimensioning).

The aim as regards the guideway functional levels arranged in the z direction is that the reference

surface is as flat as possible during operation. In this connection, the progression of the design

precurvature generally relates to the position of the stator level under operating conditions (the

theoretical position in the operating state corresponds in this connection to the progression of the

space curve).

For determining the share of deformation to be taken into consideration as a result of the guideway

temperature differential, a project-specific temperature change shall be stipulated (taking into ac-

count, inter alia, the design of the girder and the material used in its construction, the typical day-

time temperature distribution within the girder and the gradient).

In the load-free theoretical position, for instance, during production (no live load, uniform building

component temperature [∆ T = 0 K], the building component temperature = the project-specific

reference temperature), the functional levels arranged in the z direction (stator, slider levels) are

therefore deflected upwards (see fig. 198, exception: refer to fig. 203 for stipulating the gauge

change devices).

Title

High-speed Maglev Systems - Design principles

Guideway - Part III: Geometry

Doc. no.:

41727

Version White Paper Issue date

15.02.2007

Page 24

High-speed maglev systems

Maglev Technical Committee

Design principles

Guideway

Soll-Vorkrümmung (z _{i, Soll});

entspr. Soll-Lage der Funktionsebene,

bei ∆T= 0 K im unbelasteten Zustand

f_{z, Fzg}

Soll-Lage

x-Achse

der Statorebene im Betriebszustand

(entspr. Verlauf der Raumkurve)

z, ∆T 0

LSt/ 2

LSt

Fig. 198:

Design precurvature and its proportions (the diagram does not take account of creep and shrinkage charac-

teristics)

[Key to diagram:

Soll-Vorkrümmung (z_{i / soll}); entspr. Soll-Lage der Funktionsebene, bei UT= 0 K im unbelasteten Zustand =

design precurvature (z_{i / soll}); corresponding to the theoretical position of the functional level, where UT = 0 K

in the load-free state

Soll-Lage der Statorebene im Betriebszustand (entspr. Verlauf der Raumkurve) = theoretical position of the

stator level in the operating state (corresponding to the progression of the space curve)

x-Achse = x-axis

z-Achse = z-axis]

Design precurvature in the case of simple beams

Between the girder supports, the progression of the design precurvature can be determined in the

case of simple beams as per equation 16 (see also fig. 201).

To stipulate the progression of the design precurvature in the support structure areas from the sup-

port axes up to the beginning or end of the girder, tangents are laid at the design precurvature curve

determined using support axis x values.

The progression of the design precurvature in relation to the z coordinates, by way of example:

384

⎛

2*x

⎞

Equation 16

[mm]

i,Soll

max

⎜

⎟

120

⎝

⎠

Limit values for z_max = f_{z, Fzg} - fz, ∆T o as per the Guideway design principles for high-speed

maglev systems - Part II: Dimensioning

Title

High-speed Maglev Systems - Design principles

Guideway - Part III: Geometry

Doc. no.:

41727

Version White Paper Issue date

15.02.2007

Page 25

High-speed maglev systems

Maglev Technical Committee

Design principles

Guideway

Design precurvature in the case of two-span beams

In the case of two-span beams with the same spans, the progression of the design precurvature can

be determined for each span from the existing, calculated maximum deflection of the beam where

both spans are subjected to loads depending on the length of the beam and its rigidity as per equati-

on 17 (see also fig. 202).

The maximum deflection each time is 0.421* L _St viewed from the section support axis.

To stipulate the progression of the design precurvature in the areas of the guideway from the section

support axes up to the beginning or end of the girder, tangents are laid at the design precurvature

curve determined using support axis x values.

The progression of the design precurvature of two-span beams with unequal spans or different gir-

der section rigidities shall be determined in the same way for every L_i.

The progression of the design precurvature in relation to the z coordinates, by way of example:

⎛

⎞

185

3*x

2*x

Equation 17

*⎜

⎟

[mm]

i,Soll

max

⎜

⎟

⎝ Sti

⎠

Limit values for z_max = f_{z, Fzg} - fz, ∆T o as per the Guideway design principles for high-speed maglev

systems - Part II: Dimensioning

Design precurvature in the case of multiple span girders and gauge change devices

In the case of multiple span girders, a decision shall be reached on taking into account the design

precurvature depending on the elastic line which is adjusted and the resulting deflections in the z

direction and the end tangent angle at the beginning and end of the girder.

In the case of gauge change devices, as a rule, no design precurvature is taken into consideration.

Long-wave deviation

The definition of long-wave deviation is based, in principle, on the elastic line characteristic of the

support structure to which a maximum permitted excursion (“deflection”) is assigned in both direc-

tions (+/-) for each section under consideration.

The following stipulations are laid down as regards the upper and lower tolerance zone limits in

terms of the long-wave deviation from the theoretical position (see also figs. 201, 202 and 203):

• In the case of simple and two-span beams, the x value of the maximum long-wave deviation

is consistent with the x value of the maximum theoretical guideway deformation as a result

of the impact of loads.

• In the case of simple and two-span beams, the progression from the maximum point to the

beginning or end of the support structure may be described by equations 18 and 19 respecti-

vely.²⁸

As regards a design precurvature in the functional level which is to be taken into considera-

tion, the limits can be determined in a simplified manner according to equation 20.

• In the case of simple and two-span beams, the functions of the theoretical elastic lines bet-

ween the support locations are used as a basis for determining the tolerance band for long-

Title

High-speed Maglev Systems - Design principles

Guideway - Part III: Geometry

Doc. no.:

41727

Version White Paper Issue date

15.02.2007

Page 26

Design Principles High-speed Maglev System. Information (MSB, 2007) - page 12