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Railroad track spirit level in place indicating 5 in (130 mm) of superelevation between the inside and outside rails of a curve along the Keystone Corridor near Narberth, Pennsylvania In curved track, it is usually designed to raise the outer rail, providing a banked turn , thus allowing trains to maneuver through the curve at higher speeds ...
To compensate for this, the gradient should be a little less steep the sharper the curve is; the necessary grade reduction is assumed to be given by a simple formula such as 0.04 per cent per "degree of curve", the latter being a measure of curve sharpness used in the United States. On a 10-degree curve (radius 573.7 feet) the grade would thus ...
For the United States, with a standard maximum unbalanced superelevation of 75 mm (3 in), the formula is this: v m a x = E a + 3 0.00066 d {\displaystyle v_{max}={\sqrt {\frac {E_{a}+3}{0.00066d}}}} where E a {\displaystyle E_{a}} is the superelevation in inches, d {\displaystyle d} is the curvature of the track in degrees per 100 feet, and v m ...
l = slope length α = angle of inclination. The grade (US) or gradient (UK) (also called stepth, slope, incline, mainfall, pitch or rise) of a physical feature, landform or constructed line refers to the tangent of the angle of that surface to the horizontal. It is a special case of the slope, where zero indicates horizontality. A larger number ...
Астахов proposed the use of a formula which when plotted [15] is in substantial disagreement with the experimental results curves previously mentioned. His formula for curve resistance (in kgf/tonne) is the sum of two terms, the first term being a conventional k/R term (R is the curve radius in meters) with k=200
The actual equation given in Rankine is that of a cubic curve, which is a polynomial curve of degree 3, at the time also known as a cubic parabola. In the UK, only from 1845, when legislation and land costs began to constrain the laying out of rail routes and tighter curves were necessary, were the principles beginning to be applied in practice.
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Balsam Mountain, home of highest railroad station east of the Rockies; average grade about 4.0%, max 4.5%. 1 of 2 grades on southern railways former Murphy branch that are +4% grade. Balsam Mountain has seen many runaways. It is still in service operated by the Blue Ridge Southern Railroad . 1 in 22 (4.5%) Darjeeling Himalayan Railway, India