# shock

Physical size
Surname shock
Formula symbol ${\ displaystyle j}$
Size and
unit system
unit dimension
SI m · s −3 L · T −3
cgs cm · s −3 L · T −3

Jerk is a term from kinematics . It is the instantaneous rate of change in the acceleration of a body over time . The SI unit of the jerk is . As a formula symbol is usually chosen, based on the English terms jerk or jolt . ${\ displaystyle \ mathrm {m} / \ mathrm {s} ^ {3}}$${\ displaystyle j}$

When developing elevator systems and gears , the aim is to achieve values ​​for the jerk that guarantee comfort and safety in operation. In the case of rail vehicles , the choice of the routing elements ensures that travel is as smooth as possible when crossing bends. Even with roller coasters , the stress on the human body is reduced by appropriate transitions.

Formally, the jerk is the derivative of the acceleration with respect to time, i.e. the second time derivative of the speed and the third time derivative of the distance :

${\ displaystyle j (t) = {\ dot {a}} (t) = {\ ddot {v}} (t) = {\ overset {...} {x}} (t)}$

where are time , acceleration, speed and location. ${\ displaystyle t}$${\ displaystyle a}$${\ displaystyle v}$${\ displaystyle x}$

If a body-fixed coordinate system is assumed, the jerk can be determined separately for each coordinate direction, e.g. B. as a longitudinal jolt or transverse jerk , or generally vectorially as a derivative of the acceleration with respect to this reference system. In particular, this definition ensures that a uniform circular movement is jolt-free, which corresponds to general usage and application in technology.

The jerk is not defined for shock processes .

Although the physical quantity 'jerk' is defined for every change in acceleration, the term is usually only used colloquially for short "jerky" changes in acceleration (see web links ). These occur z. B. when starting with a non-pretensioned tow rope. “Jerky” here means that the gradient of the kinematic jerk has a high value .

## Example elevator

Interplay between jerk (red), acceleration (green), speed (blue) and location (turquoise) over time. See text for explanation.

The diagram shows the relationship between jerk, acceleration, speed and path for an exemplary movement of an elevator from position −6 to position +6 (the piecewise linear course of the acceleration is typically the same for a jerk change (fourth derivative of the path according to time) Zero):

• In the first phase (0–1) the jerk is constantly greater than zero and the acceleration increases linearly, the speed increases as a square and the distance covered increases as a cubic.
• In the second phase (1-2) the jerk is zero, the acceleration is therefore constant. The speed changes linearly and the distance covered quadratic.
• In the third phase (2-3) the jerk is constantly less than zero and the acceleration decreases linearly. The speed thus increases more and more slowly.
• In the fourth phase (3–4) the jerk and also the acceleration are zero. The speed is constant and the distance covered increases linearly.
• In the fifth phase (4-5) the jerk is constantly less than zero. The acceleration becomes more and more negative, i.e. it acts as a deceleration, and the speed decreases more and more.
• In the sixth phase (5-6) the jerk is zero and the acceleration is at a constant negative value. The speed decreases linearly.
• In the seventh phase (6–7) the jerk has a positive value again, the negative acceleration becomes zero and the speed goes back to zero. At the end of the seventh phase, the movement comes to a standstill at position 6.

The entire timing is controlled in such a way that the end position of the elevator is reached exactly. For acceleration and jerk, values ​​are taken into account that are perceived as pleasant and comfortable.

With other numerical values, the example could also be applied to a moving train that drives over a switch onto a parallel track. The represented variables jerk, acceleration, speed and location are then to be understood in the transverse direction.

The jerk courses shown are more of a theoretical nature. In operation z. B. in cable lifts vibrations can occur, whereby the accelerations are significantly greater than the setpoints.

## Jerk in vehicles

In vehicles, the reason for jerks is often a change in load (e.g. during partial load jerks ). A distinction is made between a longitudinal and transverse jerk. The longitudinal jolt is the change in the longitudinal acceleration over time, while the lateral jolt is a change in the lateral acceleration over time . This clearly means that the longitudinal jolt in a vehicle is caused by sudden starting or braking, whereas the lateral jolt is caused by a sudden change in the steering wheel angle in a moving automobile. With electronic steering systems, the additional functions can also cause jerks without actuating the steering wheel. For safety reasons, these must be limited to 5 m / s 3 ( ECE R79 ).

The designations longitudinal and transverse already indicate that these accelerations are components in a reference system that is fixed to the vehicle. If the components do not change, the jerk is zero. With stationary circular travel, the acceleration vector always points to the center of the circle; so viewed from the outside it changes. In contrast, in the vehicle-fixed coordinate system, the same acceleration vector remains constant.

### Longitudinal jerk

The faster braking is initiated or ended, the greater the jolt. An abruptly initiated braking (emergency braking) is associated with a high jolt. If the occupant does not adjust to it quickly enough and does not support himself, he will be thrown forward when driving forward (caught by the belt in the car) and pushed into the seat when driving backward. Since the actuation of the brake takes a certain amount of time even in the event of emergency braking, the jerk remains a finite value.

If the brake remains effective with its maximum force to a standstill, a theoretically infinitely high jolt occurs at the end of the braking distance, because the deceleration (= negative acceleration) ends suddenly, i.e. in the period of zero. As a result, the occupant is thrown into the chair by his own muscular force (support force) or, if he has behaved completely passively, by the force exerted by the belt and then thrown back by the spring force of the chair. However, time passes for these movements. As a result, the jolt is finite, i.e. it is softened. In addition, elastic elements on the vehicle (tires, wheel suspension, etc.) relax, which also takes at least a certain amount of time.

In normal operation, the experienced driver slowly releases the brake before the vehicle comes to a standstill and thus extends the decrease in deceleration over time, so that the jolt is reduced to a minimum.

### Cross jerk

Lateral jerk and centripetal acceleration in a vehicle that is cornering at a constant speed. In the diagrams below, the time or arc length is plotted horizontally, not the horizontal vehicle position.

The lateral jolt as a special case of jerk is the change in centripetal acceleration as a function of time : ${\ displaystyle k}$ ${\ displaystyle a_ {r}}$${\ displaystyle t}$

${\ displaystyle k = {\ mathrm {d} a_ {r} (t) \ over \ mathrm {d} t}}$

The centripetal acceleration of a vehicle is dependent on its speed and the curvature of the path, where the radius of the circle of curvature is: ${\ displaystyle v}$ ${\ displaystyle \ kappa = {\ tfrac {1} {r}}}$${\ displaystyle r}$

${\ displaystyle a_ {r} = {\ frac {v ^ {2}} {r}} = v ^ {2} \, \ kappa \ Rightarrow k = v ^ {2} \, {\ dot {\ kappa} }.}$

The curvature of the routing elements used is given as a function of the route . With this results for the lateral jolt: ${\ displaystyle s}$${\ displaystyle {\ dot {\ kappa}} = v \ cdot {\ frac {\ mathrm {d} \ kappa (s)} {\ mathrm {d} s}}}$

${\ displaystyle k = v ^ {3} \, {\ frac {\ mathrm {d} \ kappa (s)} {\ mathrm {d} s}}.}$

A lateral jolt occurs, for example, when the radius of a circular movement changes. If in a route , z. B. a railroad track, a circular arc immediately follows a straight line, the centripetal acceleration changes abruptly at this point in rail-bound vehicles. That is, the time for this change is almost zero and the lateral jolt becomes extremely large. If a clothoid is used as the connecting element between the straight line and the arc , the centripetal acceleration changes linearly during the time it takes to drive through the clothoid. The lateral jolt is therefore correspondingly lower.

The centripetal acceleration does not change in sections in which the vehicle is moving in a straight line or at constant speed on a circular path. The lateral jolt is therefore zero.

When planning routes, depending on the rated speed and the driving comfort that you want to achieve for a route, you must ensure that the lateral jolts do not exceed a limit value of 0.4 to 0.6 m / s³. In extreme cases, for example in the case of high-speed trains , the use of transition curves other than the clothoid can ensure that the lateral jolt at the beginning of the transition curve does not start suddenly, but gradually.

## Jerk change

The jerk change s (jounce, snap), sometimes called bang , is a term from the analytical modeling of the driving dynamics of rail vehicles and the first derivation of the jerk according to time.

${\ displaystyle s (t) = {\ dot {j}} (t)}$

where are the time , the acceleration, the speed and the location (as well as the jerk). The SI unit of the change in jerk is accordingly . ${\ displaystyle t}$${\ displaystyle a}$${\ displaystyle v}$${\ displaystyle x}$${\ displaystyle j}$${\ displaystyle {\ frac {\ mathrm {m}} {\ mathrm {s} ^ {4}}}}$

The change in jerk plays a theoretical role in these models, in which, at least in the case of a piecewise continuous differentiation or integration, the change in jerk is assumed to be equal to zero and in this way a solution of the associated system of equations becomes possible.

## Individual evidence

1. Bruno Assmann, Peter Selke: Technical Mechanics. 3. Kinematics and Kinetics. Oldenbourg Wissenschaftsverlag, 2004, ISBN 3-486-27294-2 , p. 30.
2. Example of a roller coaster
3. Drewer, Sebastian: Development of tools for planning and the comparison of variants of transport systems in buildings using the example of elevators . KIT Scientific Publishing, 2016, ISBN 978-3-7315-0490-0 . : ( limited preview in Google Book search)
4. Ágnes Lindenbach: Roads and Railways Lecture 4. Archived from the original on May 8, 2014 ; Retrieved May 7, 2014 .
5. Konrad Zilch (Ed.): Spatial planning and urban development, public building law / traffic systems and traffic facilities . Springer, 2013, ISBN 978-3-642-41875-4 , pp. 2152 ( limited preview in Google Book search).
6. Dietrich Wende: Driving dynamics. Transpress VEB Verlag for Transport, Berlin 1983, p. 15.