# Online Calculation of the Pulling Force and Power / achievable Speed

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

• Suitable values for cars, bicycles and other trains you can find by "Make a choice".
• With the default values you are able to 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!

This calculator uses SI units!!

## Pulling Force and Power Calculator

 Make a choice:  Taurus 1116 with Railjet Taurus 1116 with freigth train 4020 (rapid transit railway) 4020 - goes downhill Garden railway 5 Zoll (Electric)car Cyclist (trekking bike) Select rail condition:  Dry Wet Slightly oily Select road condition:  Dry Wet Snowy Icy

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 m² 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

For these values set a minus in front of the number!

>> Here you will find additional information for the values to be entered.

## Instructions for this Calculator

• 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.
• Possible acceleration
• Mass of the railroad cars
• Coefficient of static friction required
• 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.
• 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:

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

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:

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

Curve resistanceLok

Resistance of acceleration

How to calculate the different resistances

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

### 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