![]() ![]() Where F fr is the friction force, μ is the friction coefficient, and F norm is the normal force. This research also confirmed that the coefficient of friction between the tires and the road is affected by temperature and rainfall.ĭerivation using Newton’s Second Law Methodīy definition, the coefficient of friction is defined as the ratio of force of friction to the normal force: The results of research 1, in which the coefficient of friction was determined by means of measuring deceleration, identified that the anti-lock braking system (ABS) influenced the coefficient of friction: it increases with velocity increasing when using ABS and decreases with increasing velocity when ABS is not used. In this calculator, we will not consider other factors with negligible influence such as rolling drag of the tires or air drag. This distance depends on the pre-braking speed of the vehicle and the coefficient of friction between the tires and the road surface. The braking distance is the distance a vehicle travels from the moment when its brakes are fully applied to the moment when it comes to a complete stop. Where a is the acceleration, v is the final speed, v 0 is the initial speed, and t is the time. To simplify our calculations, we will assume that the vehicle is moving with constant acceleration or deceleration, which is determined using the following formula derived from the equation of accelerated (decelerated) motion: Where s brl is the brake lag distance in m, v is the vehicle speed in km/h, t brl is the brake lag time in seconds. The brake lag distance is determined using the following formula Hydraulic brakes, on the other hand, act almost instantly, two to five times faster than the air brake. In pneumatic brakes, air needs to flow through brake lines and this takes time. For pneumatic brakes, the total brake delay varies from 0.4 to 0.7 s because air brakes do not work almost instantly like hydraulic brakes. It consists of the lag time in the brake system and the deceleration rising time. The total brake delay is measured as the time from the moment the brake pedal is depressed to the moment at which deceleration has reached steady-state. The air brake lag is approximately 0.4 s and the hydraulic brake lag is about 0.1–0.2 s. Air brakes are used on almost all commercial trucks. Hydraulic brakes are used on almost all cars and light trucks. The brake lag distance depends on the type of brakes used in the vehicle. Where s hp is the human perception distance in m, v is the vehicle speed in km/h, t hp is the human perception time in seconds, and 1000/3600 is the coefficient for converting km/h to m/s (1 kilometer equals to 1000 meters and 1 hour is equal to 3600 seconds). ![]() It is calculated using the following formula The human perception distance is the distance a vehicle travels while the driver is identifying a hazard and deciding to slow down and stop the vehicle. Where s hr is the human perception distance, s hr is the human reaction distance, s brl is the brake lag distance, and s br is the braking distance. The stopping distance s stop is determined using the following formula: ![]() This distance is the sum of several distances that the car travels while the driver makes a decision, the brakes are activated and the vehicle slows down until it stops. The stopping distance is the distance a vehicle travels from the time a driver sees a hazard, takes a decision to stop a vehicle, presses on the brake pedal until the vehicle comes to a complete stop. Definitions and Formulas Stopping Distance ![]()
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