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In many situations, we will be interested only in the length grading, in which case we use the notation (T V ) n = ⊕ k = 0 n (T V ) k, (T V ) > n = ⊕ k > n (T V ) k,.
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Model results for uniformly distributed season length indicate that with more realistic distribution functions and observed variability of season length graded control is rather improbable.
The mechanical behaviors can be affected by the through-length grading of the FG material and therefore may be controlled by choosing appropriate values of the power-law index.
The work of profile design includes determining the maximum gradient of grade, length of grade section, connection of point of gradient change, etc.
Tracks have different lengths, grades, shapes and layouts; in the past, large teams had about 20 cars that were used for varying conditions.
In their 1988 paper, Lavender and Malmgren quantified root resorption with an index in which grade 1 is an irregular root contour; grade 2 is apical root resorption of less than 2 mm; grade 3 is apical root resorption greater than 2 mm to one third of the original root length; and grade 4 is root resorption exceeding one third of the original root length [4].
They are classified by length, steepness grade, type of scenery (coastal, moorland, riverside etc).
The length of grade section is one of the main technical parameters of railway line.
Therefore, our task is to design production cycles that contains all required products by minimizing the total length of grade transitions.
From the point of view of engineering quantity, the use of a shorter length of grade section can be better adapted to the terrain, to reduce the number of subgrade, bridge, and tunnel projects.
So the determination of length of grade section should not only satisfy the stability requirements of the train operation but also save engineering investment as much as possible so that the two achieve the best unity.
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