Overview of stopping & Reaction distance
Our brains are fast, but there is a short delay between our brain and our body muscles. You will feel this when there is a dangerouse situation and everything is feeling very "slow". The result of this delay can cause a serious car accidents if we do not give ourselfs enough space and time to accomodate our delay.
Definitions
- Reaction distance: Reaction distance is the distance you travel during the time it takes from noticing the obstruction until you start braking.
- Braking distance: The distance you travel from when you start applying the brakes until the car is completely stopped
- Stopping distance: Stopping distance combines reaction distance and braking distance together.
Stopping distance = reaction distance + braking distance
Reaction time and distance overview
- Typical reaction time is between 0.5 secs to 1.5 secs ~= 1 sec
- 45–54 year olds have the best reaction time in traffic. 18–24 year-olds and those over 60 have the worst reaction time. (Reason 18-24 year olds look straight in front of them and don't see object all around the car, 60+ is slow to react due to age)
- If vehicle speed proportionally increase by X2: The reaction distance increase x2 higher
- If vehicle speed proportionally increase by X3: The reaction distance increase x3 times higher
Speed increase from 30km/h to 60km/h (X2) Reaction distance increase from 9ms to 18ms (X2) Speed increase from 30km/h to 90km/h (X3) Reaction distance increase from 9ms to 27ms (X3) See calculation below on how to calculate reaction distance
Calculate the reaction distance
Simple Calculation without calculator: Formula: D = (S "delete the 0" x R ) x 3 3 = approximate constant for converting km/h to m/s. Example: Car speed (S) = 30km/h Reaction time (R) = 1 sec Delete the "0" = 30 km/h = 3m/s Reaction distance (D) = (3 x 1) x 3 = 9 ms You react in 1 second thus you will travel 9m If you react in 0.5 seconds you will travel 4.5m
Percise calculation with calculator: Formula: D = (S * R) / 3.6 3.6 = fixed constant for converting km/h to m/s. Example: Car speed (S) = 30km/h Reaction time (R) = 1 sec Reaction distance (D) = (30 x 1) / 3.6 = 8.3 ms You react in 1 second thus you will travel 8.3 ms If you react in 0.5 seconds you will travel 4.125 ms
Factors that can increase reaction distance
- Anticipation hazards in front of you. Example if you see children next to the road, anticipate that they might run across the street.
- Preparedness. Example prepare to break or reduce your speed in advance to accommodate for the situation
Factors that can decrease reaction distance
- Alcohol, medication, drugs. Being under the influence of any narcotic can severely reduce your reaction time
- Tiredness. Not enough sleep is a serious cause of accidents
Braking time and distance overview
The braking distance is the distance traveled by the car from the time it begins to brake until it comes to a complete stop. The braking distance depends on many factors. The vehicles speed, brakes, the conditions of the tyres, the state of the road
Braking distance increases quadratically as the speed of the car increase Formula: speed ^{2} x braking distance Speed increase from 30km/h to 90km/h (speed increased by x3 ) Assume the braking distance was 4m then = (3 ^{2} m) x braking distance = 9 x 4 = 36 meter breaking distance increases See calculation below on how to calculate braking distance
Calculate the braking distance
Different road conditions will calculate different braking distance. Example if a car apply the same brakes at the same speed on an asphalt road VS an icy road
The Conditions: Good tyres and good brakes. (normal road conditions) Formula: Remove zero from the vehicles speed Braking Distance (D) = (S x S x 0.4) (Speed x Speed x 0.4 constant *good road conditions)
Example 1: Approximate calculation Calculation Car speed (S)= 30km/h Braking distance (D) = 3 x 3 x 0.4 = 3,6 meter
Example 2: Approximate calculation Calculation Car speed (S)= 90km/h Braking distance (D) = 9 x 9 x 0.4 = 32,4 meter Compare the calculated amount with the quadratically function amount at the start of this section Formula: speed 2 x braking distance
Example 3: More accurate calculation Formula: Braking Distance (D) = (S ^{2} / 250x F) D = braking distance in metres (to be calculated). S = speed in km/h. 250 = Constant F = coefficient of friction, approx. 0.8 on dry asphalt, 0.7 normal road and 0.1 on ice. Calculation Car speed (S)= 30km/h Braking distance (D) = (30 ^{2} ) / (250 x 0.8) = 4,5 meter
Calculation Car speed (S)= 90km/h Braking distance (D) = (90 ^{2} ) / (250 x 0.8) = 40.5 meter
Stopping distance overview
Stopping distance combines reaction distance and braking distance together.
Stopping distance = reaction distance + braking distance
Calculate the stopping distance
Question: Calculate the stopping distance given the following details Condition: Dry road, Good tyres, Good brakes Car speed (S) = 90km/h Reaction time = 1.2 seconds Formula: Stopping distance = reaction distance + braking distance. 1st calculate reaction distance 80 km/h = 8 (Remove the zero) 8 * 1.2 (reaction time) * 3 (Constant) = 28,8 ~ 29 metres reaction distance 2nd calculate brake distance 80 km/h = 8 8 x 8 x 0,4= 25,6 ~ 26 meters 3rd calculate brake distance 29 + 26= 55 meters stopping distance
Question: Calculate the stopping distance given the following details Condition: very wet road, Good tyres, Good brakes Car speed (S) = 120km/h Reaction time = 1 seconds Friction coefficient = 0,6 Formula: Stopping distance = reaction distance + braking distance. 1st calculate reaction distance 120 km/h = 12 (Remove the zero) 12 * 1 (reaction time) * 3 (Constant) = 36 metres reaction distance 2nd calculate brake distance 120 km/h = 12 Braking distance (D) = (120 ^{2} ) / (250 x 0.6 (friction coefficient)) = 96 meter 3rd calculate brake distance 36+ 96 = 132 meters stopping distance (Chances is good that the car will spin out of control at this speed)
During the exam which formula should you use?
You can use the most convenient formula. The test answers will be given with approximate values , thus choose the answer that is the closest to your calculations.