Curve Resistance Calculator

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Design of Transition Curves and Setback Distances

✖Tractive force is the force needed to overcome the resistance caused by friction when two bodies slide or roll on each other.ⓘ Tractive Force [T]			+10% -10%
✖Angle subtended by Radius of Curve for Single Lane is the angle formed by radius of curve where Ls is less than Lc.ⓘ Angle subtended by Radius of Curve for Single Lane [α₁]			+10% -10%

✖Curve resistance is the added resistance or “drag” on a train that must be overcome by the tractive effort in rounding a curve. Resistance is usually measured in newtons per ton of train weight.ⓘ Curve Resistance [CR]

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Formula

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Curve Resistance

Formula

`"CR" = "T"-"T"*cos("α"_{"1"})`

Example

`"321.8688mi⁻¹"="0.2N"-"0.2N"*cos("90°")`

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Curve Resistance Solution

STEP 0: Pre-Calculation Summary

Formula Used

Curve Resistance = Tractive Force-Tractive Force*cos(Angle subtended by Radius of Curve for Single Lane)
CR = T-T*cos(α₁)
This formula uses 1 Functions, 3 Variables

Functions Used

cos - Cosine of an angle is the ratio of the side adjacent to the angle to the hypotenuse of the triangle., cos(Angle)

Variables Used

Curve Resistance - (Measured in 1 per Meter) - Curve resistance is the added resistance or “drag” on a train that must be overcome by the tractive effort in rounding a curve. Resistance is usually measured in newtons per ton of train weight.
Tractive Force - (Measured in Newton) - Tractive force is the force needed to overcome the resistance caused by friction when two bodies slide or roll on each other.
Angle subtended by Radius of Curve for Single Lane - (Measured in Radian) - Angle subtended by Radius of Curve for Single Lane is the angle formed by radius of curve where Ls is less than Lc.

STEP 1: Convert Input(s) to Base Unit

Tractive Force: 0.2 Newton --> 0.2 Newton No Conversion Required
Angle subtended by Radius of Curve for Single Lane: 90 Degree --> 1.5707963267946 Radian (Check conversion here)

STEP 2: Evaluate Formula

Substituting Input Values in Formula

CR = T-T*cos(α₁) --> 0.2-0.2*cos(1.5707963267946)

Evaluating ... ...

CR = 0.199999999999941

STEP 3: Convert Result to Output's Unit

0.199999999999941 1 per Meter -->321.868799999905 1 per Mile (Check conversion here)

FINAL ANSWER

321.868799999905 ≈ 321.8688 1 per Mile <-- Curve Resistance

(Calculation completed in 00.004 seconds)

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Home » Physics » Transportation System » Design of Transition Curves and Setback Distances » Curve Resistance

Credits

Created by Avayjit Das

University of Engineering and Management,Kolkata (UEMK), Kolkata

Avayjit Das has created this Calculator and 25+ more calculators!

Verified by Kartikay Pandit

National Institute Of Technology (NIT), Hamirpur

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< 13 Design of Transition Curves and Setback Distances Calculators

Setback Distance for Multi Lane Road where Ls is greater than Lc

Go Setback Distance = Radius for Transition Curve-(Radius for Transition Curve-Center Distance between Road and Inner Lane)*cos(Angle subtended by Radius of Curve for Single Lane/2)+((Sight Distance-Length of Transition Curve)/2)*sin(Angle subtended by Radius of Curve for Single Lane/2)

Setback Distance for Single Lane Road where Ls is greater than Lc

Go Setback Distance = Radius for Transition Curve-Radius for Transition Curve*cos(Angle subtended by Radius of Curve for Single Lane/2)+((Sight Distance-Length of Transition Curve)/2)*sin(Angle subtended by Radius of Curve for Single Lane/2)

Angle Subtended by Radius of Curve for Multi Lane Road

Go Angle subtended by Radius of Curve for Multi Lane = (180*Length of Transition Curve)/(pi*(Radius for Transition Curve-Center Distance between Road and Inner Lane))

Length of Transition Curve given Super-Elevation

Go Length of Transition Curve = Allowable Rate of Super Elevation*Rate of Super Elevation*(Total Widening Needed at Horizontal Curve+Normal Width of Pavement)

Setback Distance where Ls is Smaller than Lc

Go Setback Distance = Radius for Transition Curve-Radius for Transition Curve*cos(Angle subtended by Radius of Curve for Single Lane/2)

Curve Resistance

Go Curve Resistance = Tractive Force-Tractive Force*cos(Angle subtended by Radius of Curve for Single Lane)

Length of Transition Curve given Centrifugal Acceleration

Go Length of Transition Curve = Velocity^3/(Rate of Change of Centrifugal Acceleration*Radius for Transition Curve)

Rate of Change of Centrifugal Acceleration

Go Rate of Change of Centrifugal Acceleration = Velocity^3/(Length of Transition Curve*Radius for Transition Curve)

Angle Subtended by Radius of Curve for Single Lane Road

Go Angle subtended by Radius of Curve for Single Lane = (180*Shift)/(pi*Radius for Transition Curve)

Length of Transition Curve for Steep and Hilly Terrains

Go Length of Transition Curve = (12.96*Velocity^2)/Radius for Transition Curve

Length of Transition for Curve Plain and Rolling Terrain

Go Length of Transition Curve = (35*Velocity^2)/Radius for Transition Curve

Shift given Length of Transition Curve

Go Shift = Length of Transition Curve^2/(24*Radius of Curve)

Rate of Change of Centrifugal Acceleration given Empirical Formula

Go Rate of Change of Centrifugal Acceleration = 80/(75+3.6*Velocity)

Curve Resistance Formula

Curve Resistance = Tractive Force-Tractive Force*cos(Angle subtended by Radius of Curve for Single Lane)
CR = T-T*cos(α₁)

How is Curve Resistance measured?

Curve resistance is typically measured in per mille, with the correct physical unit being Newton per kilo-Newton (N/kN). Older texts still use the wrong unit of kilogram-force per tonne (kgf/t).

How to Calculate Curve Resistance?

Curve Resistance calculator uses Curve Resistance = Tractive Force-Tractive Force*cos(Angle subtended by Radius of Curve for Single Lane) to calculate the Curve Resistance, The Curve Resistance formula is defined as the added resistance or “drag” on a train that must be overcome by the tractive effort in rounding a curve. Resistance is usually measured in newtons per ton of train weight. Curve Resistance is denoted by CR symbol.

How to calculate Curve Resistance using this online calculator? To use this online calculator for Curve Resistance, enter Tractive Force (T) & Angle subtended by Radius of Curve for Single Lane (α₁) and hit the calculate button. Here is how the Curve Resistance calculation can be explained with given input values -> 517997.6 = 0.2-0.2*cos(1.5707963267946).

FAQ

What is Curve Resistance?

The Curve Resistance formula is defined as the added resistance or “drag” on a train that must be overcome by the tractive effort in rounding a curve. Resistance is usually measured in newtons per ton of train weight and is represented as CR = T-T*cos(α₁) or Curve Resistance = Tractive Force-Tractive Force*cos(Angle subtended by Radius of Curve for Single Lane). Tractive force is the force needed to overcome the resistance caused by friction when two bodies slide or roll on each other & Angle subtended by Radius of Curve for Single Lane is the angle formed by radius of curve where Ls is less than Lc.

How to calculate Curve Resistance?

The Curve Resistance formula is defined as the added resistance or “drag” on a train that must be overcome by the tractive effort in rounding a curve. Resistance is usually measured in newtons per ton of train weight is calculated using Curve Resistance = Tractive Force-Tractive Force*cos(Angle subtended by Radius of Curve for Single Lane). To calculate Curve Resistance, you need Tractive Force (T) & Angle subtended by Radius of Curve for Single Lane (α₁). With our tool, you need to enter the respective value for Tractive Force & Angle subtended by Radius of Curve for Single Lane and hit the calculate button. You can also select the units (if any) for Input(s) and the Output as well.

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