Slope of track

Calculate the average slope (in permille and even in degrees) of the rail tracks between Prievidza (309 m AMSL) and Nitrianske Pravno (354 m AMSL), if the track is 11 km long.

Result

s1 =  4.09
s2 =  0.234 °

Solution:

s=11 km=11 1000 m=11000 m y=309354=45 m  x=s2y2=110002452=235 2191 m10999.908 m  s1=1000 yx=1000 4510999.9084.0909=4.09 ‰s = 11 \ km = 11 \cdot \ 1000 \ m = 11000 \ m \ \\ y = |309 - 354| = 45 \ m \ \\ \ \\ x = \sqrt{ s^2-y^2 } = \sqrt{ 11000^2-45^2 } = 235 \ \sqrt{ 2191 } \ m \doteq 10999.908 \ m \ \\ \ \\ s_{ 1 } = 1000 \cdot \ \dfrac{ y }{ x } = 1000 \cdot \ \dfrac{ 45 }{ 10999.908 } \doteq 4.0909 = 4.09 \ ‰
s2=180πarctan(yx)=180πarctan(4510999.908)0.2344=0.234=0144"s_{ 2 } = \dfrac{ 180^\circ }{ \pi } \cdot \arctan(\dfrac{ y }{ x } ) = \dfrac{ 180^\circ }{ \pi } \cdot \arctan(\dfrac{ 45 }{ 10999.908 } ) \doteq 0.2344 = 0.234 ^\circ = 0^\circ 14'4"







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Our permille calculator will help you quickly calculate various typical tasks with permilles. Do you want to convert length units? See also our right triangle calculator. See also our trigonometric triangle calculator. Try conversion angle units angle degrees, minutes, seconds, radians, grads.

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