Vertical Curve ~ GB Maps ギビマップ Project

Vertical curve is the curve in vertical layout to connect two track gradients together whether it is for changing from an upgrade to a downgrade (summit), changing from a downgrade to an upgrade (sag or valley), changing in two levels of upgrades or changing in two levels of downgrades.

(縦断曲線)

勾配が変化する地点において、一点で突然勾配を変化させると路線に「折れ」が生じてしまい、走行性を阻害したり、路面に車両の底が接触したりするなど好ましくない。そこで、勾配の変化点では縦断方向に曲線を挿入し、徐々に勾配を変化させる。この曲線を縦断曲線、または英語表記からバーチカル・カーブ(vertical curve)と呼び、とくに鉄道においては縦曲線と呼ぶ^[2]。縦断曲線は二次曲線（放物線）が用いられるが、円弧で近似できるため、半径を用いてその大きさを表す。

less sharp grade

smooth grade transition with vertical curve

Equations to use

There are several methods and standards used in the calculation of the vertical curve. In BVE5 Trainsim, circular curve formula is used with standard radius value.

Distance calculation

Scenario 1

Total Distance = D

Scenario 2

note:

Technical Standard for Japanese Railway (by Railway Bureau Ministry of Standard)

III-7 Related to Article 18 (Gradient)
The maximum gradient of the track in traveling areas and stopping areas (including parking
areas and areas for coupling and decoupling the rolling stock) shall be determined in
consideration of the performance of motive device, braking device, operation speed and other such
factors of the rolling stock.
(1) The maximum gradient of ordinary railways (excluding Shinkansen railways) shall be according
to the following standards.
[1] The maximum gradient in the traveling areas for trains shall be as follows.
(A) 25/1000 on tracks traveled by trains pulled by locomotive (limited to the line sections where
freight trains travel). (Including where the equivalent assessed gradient is 25/1000)
(B) 35/1000 on tracks other than [1].
(C) Notwithstanding the provisions of [1] and [2] above, the maximum gradient of the track used
only by trains powered by linear induction motor trains shall be 60/1000.
[4] Notwithstanding the provisions of [1]～(C) above, the maximum gradient in turnout areas
shall be 25/1000.
[2] The maximum gradient in the stopping areas shall be 5/1000. However, it may be 10/1000 in
the areas not used for parking or coupling/decoupling of the rolling stock, but only if there is no
possibility of interference with train departure and arrival.
(2) The maximum gradient of Shinkansen railways shall be according to the following standards.
[1] The maximum gradient in the traveling areas for trains shall be as follows.
(A) 25/1000.
(B) Where the above standard cannot be applied for topographic or other reason, it may be
35/1000, taking the performance of the motive device, power transmission device, running
gear and braking device into consideration.
[2] The maximum gradient in the stopping areas for trains shall be 3/1000.

III-8 Related to Article 19 (Vertical Curve)
1 The radius of a vertical curve shall not be less than the following values. However, this does not
apply if it has been verified that safe operation of the rolling stock can be ensured based upon
operation speed and other factors.
(1) 2,000m (where the horizontal curve radius is not greater than 600m, it shall be 3,000m) for
ordinary railways (except Shinkansen railways). However, where the change of gradient is
smaller than 10/1000, insertion of vertical curves may be omitted.
(2) 10,000m (5,000m for the sections where the traveling speed is not greater than 250km/h) for
Shinkansen railways.

therefore, suggested default value,

r = 3,000 m for ordinary railways OR 4000m on horizontal curve with radius less than 600m.

r = 1,0000 m for Shinkansen railways or high speed railway

Vertical Curve in BVE5 Trainsim

Vertical curve example from http://bvets.net/en/edit/tutorial/. Track start at 0‰(level), then gradient up 25‰, gradient down 35‰ and then back to 0‰ (level).

BVE code

in this example, R=2000 m. therefore, vertical curve length for each gradient

Note

The vertical curve will be included in the next version of GBMAPS. We still programmed this feature, make revisions and corrections of errors. However, application development progress might a bit slow. Really sorry!

thankyou

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