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A yaw rotation is a movement around the yaw axis of a rigid body that changes the direction it is pointing, to the left or right of its direction of motion. The yaw rate or yaw velocity of a car, aircraft, projectile or other rigid body is the
angular velocity In physics, angular velocity or rotational velocity ( or ), also known as angular frequency vector,(UP1) is a pseudovector representation of how fast the angular position or orientation of an object changes with time (i.e. how quickly an object ...
of this rotation, or rate of change of the heading angle when the aircraft is horizontal. It is commonly measured in degrees per second or radians per second. Another important concept is the yaw
moment Moment or Moments may refer to: * Present time Music * The Moments, American R&B vocal group Albums * ''Moment'' (Dark Tranquillity album), 2020 * ''Moment'' (Speed album), 1998 * ''Moments'' (Darude album) * ''Moments'' (Christine Guldbrand ...
, or yawing moment, which is the component of a
torque In physics and mechanics, torque is the rotational equivalent of linear force. It is also referred to as the moment of force (also abbreviated to moment). It represents the capability of a force to produce change in the rotational motion of th ...
about the yaw axis.


Measurement

Yaw velocity can be measured by measuring the ground velocity at two geometrically separated points on the body, or by a
gyroscope A gyroscope (from Ancient Greek γῦρος ''gŷros'', "round" and σκοπέω ''skopéō'', "to look") is a device used for measuring or maintaining orientation and angular velocity. It is a spinning wheel or disc in which the axis of rot ...
, or it can be synthesized from
accelerometers An accelerometer is a tool that measures proper acceleration. Proper acceleration is the acceleration (the rate of change of velocity) of a body in its own instantaneous rest frame; this is different from coordinate acceleration, which is acce ...
and the like. It is the primary measure of how drivers sense a car's turning visually. It is important in electronic stabilized vehicles. The yaw rate is directly related to the lateral acceleration of the vehicle turning at constant speed around a constant radius, by the relationship :tangential speed*yaw velocity = lateral acceleration = tangential speed^2/radius of turn, in appropriate units The sign convention can be established by rigorous attention to coordinate systems. In a more general manoeuvre where the radius is varying, and/or the speed is varying, the above relationship no longer holds.


Yaw rate control

The yaw rate can be measured with accelerometers in the vertical axis. Any device intended to measure the yaw rate is called a yaw rate sensor.


Road vehicles

Studying the stability of a road vehicle requires a reasonable approximation to the equations of motion. The diagram illustrates a four-wheel vehicle, in which the front axle is located ''a'' metres ahead of the
centre of gravity In physics, the center of mass of a distribution of mass in space (sometimes referred to as the balance point) is the unique point where the weighted relative position of the distributed mass sums to zero. This is the point to which a force may ...
and the rear axle is ''b'' metres towards the rear from the center of gravity. The body of the car is pointing in a direction \theta (theta) while it is travelling in a direction \psi (psi). In general, these are not the same. The tyre treads at the region of contact point in the direction of travel, but the hubs are aligned with the vehicle body, with the
steering Steering is a system of components, linkages, and other parts that allows a driver to control the direction of the vehicle. Introduction The most conventional steering arrangement allows a driver to turn the front wheels of a vehicle using ...
held central. The tyres distort as they rotate to accommodate this mis-alignment, and generate side forces as a consequence. From
directional stability Directional stability is stability of a moving body or vehicle about an axis which is perpendicular to its direction of motion. Stability of a vehicle concerns itself with the tendency of a vehicle to return to its original direction in relation ...
study, denoting the angular velocity \omega, the equations of motion are: :\frac=2k\frac\beta-2k\frac\omega :\frac=-\frac\beta+(1-2k)\frac\omega with M the mass of the vehicle, V the vehicle speed and \beta = \theta - \psi the vehicle's overall angle. The coefficient of \frac will be called the '
damping Damping is an influence within or upon an oscillatory system that has the effect of reducing or preventing its oscillation. In physical systems, damping is produced by processes that dissipate the energy stored in the oscillation. Examples i ...
' by analogy with a mass-spring-damper which has a similar equation of motion. By the same analogy, the coefficient of \beta will be called the 'stiffness', as its function is to return the system to zero deflection, in the same manner as a spring. The form of the solution depends only on the signs of the damping and stiffness terms. The four possible solution types are presented in the figure. The only satisfactory solution requires both stiffness and damping to be positive. If the centre of gravity is ahead of the centre of the
wheelbase In both road and rail vehicles, the wheelbase is the horizontal distance between the centers of the front and rear wheels. For road vehicles with more than two axles (e.g. some trucks), the wheelbase is the distance between the steering (fron ...
(b>a), this will always be positive, and the vehicle will be stable at all speeds. However, if it lies further aft, the term has the potential of becoming negative above a speed given by: ::V^2=\frac Above this speed, the vehicle will be directionally (yaw)
unstable In numerous fields of study, the component of instability within a system is generally characterized by some of the outputs or internal states growing without bounds. Not all systems that are not stable are unstable; systems can also be mar ...
. Corrections for relative effect of front and rear tyres and steering forces are available in the main article.


Relationship with other rotation systems

These rotations are
intrinsic rotations The Euler angles are three angles introduced by Leonhard Euler to describe the orientation of a rigid body with respect to a fixed coordinate system.Novi Commentarii academiae scientiarum Petropolitanae 20, 1776, pp. 189–207 (E478PDF/ref> They ...
and the calculus behind them is similar to the Frenet-Serret formulas. Performing a rotation in an intrinsic reference frame is equivalent to right-multiply its characteristic matrix (the matrix that has the vector of the reference frame as columns) by the matrix of the rotation.


History

The first aircraft to demonstrate active control about all three axes was the Wright brothers' 1902 glider.{{cite web , url=https://www.grc.nasa.gov/WWW/K-12/airplane/rotations.html , title=Aircraft rotations , date=2015-05-05 , publisher=
Glenn Research Center NASA John H. Glenn Research Center at Lewis Field is a NASA center within the cities of Brook Park and Cleveland between Cleveland Hopkins International Airport and the Rocky River Reservation of Cleveland Metroparks, with a subsidiary facilit ...
, access-date=2018-10-13


See also

*
Adverse yaw Adverse yaw is the natural and undesirable tendency for an aircraft to yaw in the opposite direction of a roll. It is caused by the difference in lift and drag of each wing. The effect can be greatly minimized with ailerons deliberately designed to ...
*
Aircraft principal axes An aircraft in flight is free to rotate in three dimensions: '' yaw'', nose left or right about an axis running up and down; ''pitch'', nose up or down about an axis running from wing to wing; and ''roll'', rotation about an axis running from ...
* Coriolis acceleration *
Directional stability Directional stability is stability of a moving body or vehicle about an axis which is perpendicular to its direction of motion. Stability of a vehicle concerns itself with the tendency of a vehicle to return to its original direction in relation ...
*
Flight dynamics Flight dynamics in aviation and spacecraft, is the study of the performance, stability, and control of vehicles flying through the air or in outer space. It is concerned with how forces acting on the vehicle determine its velocity and attitude ...
*
Six degrees of freedom Six degrees of freedom (6DOF) refers to the six mechanical degrees of freedom of movement of a rigid body in three-dimensional space. Specifically, the body is free to change position as forward/backward (surge), up/down (heave), left/right ...
*
Vehicle dynamics For motorized vehicles, such as automobiles, aircraft, and watercraft, vehicle dynamics is the study of vehicle motion, e.g., how a vehicle's forward movement changes in response to driver inputs, propulsion system outputs, ambient conditions, air ...
* Yaw rate sensor


References

Dynamics (mechanics) Attitude control