Stopping (Braking) Distance, Acceleration / Deceleration, Speed and Time

For different road or rail conditions, this braking distance calculator computes:

  • starting/final velocity
  • acceleration/deceleration
  • (overall) stopping distance
  • braking time.

Input of reaction time is also possible. After the calculators one finds the table of content, some examples for the use of these calculators and finally some background knowledge and formulas which this program uses.

Stopping (Braking) Distance Calculator

      Enter a reaction time:   s

There has to be one number in three out of five lines - the empty fields will be calculated!

stopping distance  m   overall stopping distance  m
time s
acceleration/deceleration*  m/s²
starting velocity  km/h
final velocity km/h


 

 

 

* For a deceleration, set a minus in front of the number!

For Experts: Calculation of the maximum possible Deceleration*

Please enter a number in the top four fields!

gradient***  % length l (centre of gravity)** m
coefficient of friction    hight h (centre of gravity)** m  
Absolute braking (stiction)  m/s²   Absolute braking (overturn)  m/s²  


 

 

 

Change the rail or road condition in the first calculator; assumption: all wheels are braked.

** The meaning of the two abbreviations l and h can be found here: General Information.

*** Negative values are possible, too!

Short Info:

  • Minimum braking distance, overall stopping distance and the time which is needed therefore, are calculated for the following conditions with the default settings: starting velocity of the vehicle is 100 km/h, the roadway has to be dry, clean, flat, straight and sealed. Reaction time is one second.
  • With the default values you can perform a calculation 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!

Table of Content:

Functions of the calcuators

Depending on the road conditions, the two calculators compute the following, assuming an uniform acceleration (or deceleration):

  • The first calculator is able to calculate the following, whereby three of the six variables must be known:
    • Stopping (Braking) distance or acceleration distance
    • Overall stopping distance
    • Acceleration or deceleration
    • Time
    • Starting velocity
    • Final velocity
  • The second calculator computes the absolute braking that is possible, depending on road condition (coefficient of friction) and centre of gravity (overturn of a vehicle).

Manual

  • As comma you have to use a point.
  • The calculation is only valid for uniform acceleration or constant deceleration.
  • In curves, there is less acceleration or deceleration possible.
  • It is assued that all the wheels are braked or driven.
  • If you want to enter a deceleration in the corresponding field you have to use a negative number.
  • For braking, of course, you must choose a higher initial velocity than the final speed.
  • The default values can be changed as desired.
  • You have to enter one number in three out of five lines, i.e.: in the first line there should always be one number only!
  • When accelerating from 0 km/h, the initial velocity must be set to zero.
  • Results are displayed on a green background.
  • Accuracy can not be guaranteed - for corrections or additions please use my contact form!

Background Knowledge and Formulas

General Information

Overall stopping distance is the sum of braking distance and thinking distance. The total time for braking is made up of reaction time and braking time.

In the following diagram you can find the distances h and l which are required for the calculation of the overturn of a vehicle.

Figure 1: Centre of gravity of a vehicle
Figure 1: Centre of gravity of a vehicle
h: Distance centre of gravity of the vehicle - road surface
l:

Distance centre of gravity of the vehicle - front wheel (= tipping point)

β:    Slope angle of the road
Schwerpunkt: centre of gravity
Fahrtrichtung:   direction of travel

 

Reference Values for Acceleration or Deceleration

 Example

Acceleration/Deceleration

in m/s²

car - mean acceleration 0 - 100 km/h 3

car - average deceleration at full braking on a dry,

clean, flat and sealed road

-7.8 to -11.8

car - average deceleration at full braking on a wet,

flat and sealed road

-3.9 to -5.9
bicycle - deceleration necessary by law in Austria -4 *
bicycle - absolute braking for an average driver -5.5
Tram Vienna (ULF) - starting acceleration 1.3
Tram Vienna (ULF) - service braking -1.8

Rapid braking of trams, with magnetic track brake

-3
ÖBB 4020 (Wiener Schnellbahn) - starting acceleration 0.7
Siemens Desiro ML, ÖBB 5022 - starting acceleration 1.1
acceleration of gravity 9.81

Source: Wikipedia, manufacturer sites

* Source: Bundeskanzleramt - RIS

Uniform Acceleration - with Starting Velocity

The following formulas are valid for uniform acceleration only:

Figure 2: Formulas for calculating braking distance, acceleration, velocity and time; Starting velocity is not 0.
Figure 2: Formulas for calculating braking distance, acceleration, velocity and time; Starting velocity is not 0.
v: final velocity in m/s
v0:     starting velocity in m/s
a: acceleration in m/s²
s: way in m
t: time in s

 

Uniform Acceleration - without Starting Velocity

The following formulas are valid for uniform acceleration only:

Figure 3: Starting velocity is 0.
Figure 3: Starting velocity is 0.