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!
Furthermore, you will find on this page:
This calculator uses SI units!!
Pulling Force and Power Calculator
* For these values set a minus in front of the number!
>> Here you will find additional information for the values to be entered.
Table of Content
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.
- Gradient
- 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
Gradient 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