Modification of the Relation Between Grade and Curvature — Purpose, Reasons, and Advantages

In cases where grades and horizontal curves are combined, the current relation between the grade and the degree of curve, D, is defined as follows:

G + c D = r

in which

G = The maximum allowable compensated grade in %,

D = Degree of curve,

c = 0.04, compensation factor in % grade per degree of curve,

r = The maximum grade achievable by the train in %.

The above relation is a design tool to combine grade and curvature. The author intends to modify the above relation for two purposes —

• to make the relation more rational for combining grade and curve for LRT design, and

• to make the relation useful in computing the installation slope of special trackwork.

A modified formula is suggested as under:

G + c D = k r

in which

c = compensation factor in % grade per degree of curve determined on the basis of curvature,

k = grade reduction factor arbitrarily chosen between 0.2 ∼ 1 depending on curvature and type of rail.

The justification of the proposed modification and the advantages of the modified formula are discussed in details.

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