Calculation of the Pulling Force and Power / achievable Speed

One oft the following items can be calculated if all the other values are known:

  • Maximum speed. Normally the maximum speed is limited by the engine's running speed.
  • Power and traction force
  • Maximum tractive effort on starting as a result of the coefficient of static friction.
  • Gradient
  • Possible acceleration
  • Mass of the railroad cars
  • Coefficient of static friction required

The electrical current that is required can be calculated, too.

 

This calculator uses SI units!!

Table of Content

Pulling Force and Power Calculator

With the default settings the required power at a speed of 230 km/h and the necessary pulling force of a Railjet (locomotive "Taurus" 1116 and seven passenger cars) are calculated.

  • With the default values you can perform a calculation immediately by simply pressing the button "Calculate" or the enter key!
  • You can do the calculation several times, too. Just change the values in the white fields!

Calculator


 

  Please enter a number in seven of the following eight fields, the empty field will be calculated!

Driving/braking power  W Speed km/h
Mass of the loco
kg Coefficient of friction   
Mass of one car
kg  
Number of cars
 
Gradient % Acceleration/deceleration  m/s²

  Results and error messages (these values are computed by the calculator)

Required coefficient of friction   Total current consumption A
Required pulling force N    
Maximum traction of the loco
N
Error messages
Notes
 



All the following 16 fields must be filled out!
Make sure to have the correct cross sectional area!

 
Efficiency of the drive  % Efficiency of the engine  %
Cross sectional area  Supply voltage V
Head-/tailwind  km/h  Curve resistance  
Driven axles    Total number of axles 
Air density kg/m³  Factor of rotating masses   
Rolling resistance of the loco
 
Rolling resistance of the cars
 
Air resistance coefficient - loco
  Air resistance coeff. - first car  
Air resistance - intermediate car    Air resistance coeff. - last car   

Instructions for this Calculator

  • The listed coefficients of friction apply only at relatively low speeds.
  • As comma you have to use a point.
  • When calculating, engine and drive efficiency can be considered. As standard, an efficiency of 100% is assumed!
  • The calculation is only valid if the load on each axle is approximately the same.
  • When calculating the speed, there mustn't be any backwind!
  • If you want to use the name behind the slash (eg braking power), enter a negative number in the corresponding field.
  • The default values can be changed as desired.
  • All fields must be completed, only the field whose value you want to calculate must remain free.
  • Results are shown on a green background.
  • (Error) messages are displayed on a red background.
  • No guarantee can be given for the correct function - for corrections and suggestions for improvement, please use the contact form!

Background Knowledge and Formulas

Comparative Values for Maximum Traction, Hourly Power, Mass and µH

Please note: the maximum traction is given in kN, the hourly power in kW and the mass in t! K is the abbreviation for kilo and means 1000, so 1 kW = 1000 W, 1 kN = 1000 N.

 

Example (ÖBB)

Maximum Traction

in kN

Hourly Power

in kW

Mass

in t

µH *
Loco 1016/1116 300 6400 86 0.356
Loco 1044/1144 327 5400 84 0.397
Loco 2016 235 2000 80 0.299
Loco 2043 196 1104 68 0.294
Electrical multiple unit 4020 117 1200 129  
Railcar 5047 68 419 47  

Source: Wikipedia

* Necessary coefficient of friction when starting, calculated from the given values.

Calculation of the Maximum Pulling Force (Tractive Effort on Starting)

The maximum pulling force is calculated by the following formula:

 

Formula for calculating the maximum pulling force
Maximum pulling force due to coefficient of friction

FZ.max

mLok

g

α
Achsenangetrieben
Achsenalle

µH

Maximum pulling force in NLok

Mass of the locomotive in kga

Acceleration due to gravity in m/s²

Gradient angle in ° (for small angles cos α can be set to one)

Number of driven axlesa

Total number of axlesa

Coefficient of friction


 

For the acceleration of gravity 9.81 m/s² is used, for µH see my page coefficient of friction (in German). If all axles are driven, the term Achsenangetrieben/Achsenalle is dropped out. If not all the axles of the loco are driven, the formula applies only if each axle carries approximately the same load.

Traction Equation

The required pulling force during starting must always be less than the maximum available traction, otherwise the driving wheels will spin. The required pulling force can be calculated by the following formula:

 

Traction equation
Traction equation

FZ

mLok
mWagen

g
wR

wL

wS

wK

wB

Required pulling force in NLok

Mass of the locomotive in kgLok

Total mass of all the cars in kgLok

Acceleration due to gravity in m/s²

Rolling resistanceLok

Air resistanceLok

Gradient resistanceLok

Curve resistanceLok

Resistance of acceleration


 

How to calculate the different resistances

is described on a separate page (only in German available):

 

>> Ermittlung der Widerstände für die Zugkraftgleichung

Calculation of the Required Power

The power that is required can be calculated by the following way:

 

P = FZ⋅v

 

P

FZ

v

Required power in W

Pulling Force in NmLok

Speed in m/s