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Flight Dynamics (fixed-wing Aircraft)
Flight dynamics is the science of air vehicle orientation and control in three dimensions. The three critical flight dynamics parameters are the angles of rotation in three dimensions about the vehicle's center of gravity (cg), known as ''pitch'', ''roll'' and ''yaw''. These are collectively known as aircraft attitude, often principally relative to the atmospheric frame in normal flight, but also relative to terrain during takeoff or landing, or when operating at low elevation. The concept of attitude is not specific to fixed-wing aircraft, but also extends to rotary aircraft such as helicopters, and dirigibles, where the flight dynamics involved in establishing and controlling attitude are entirely different. Control systems adjust the orientation of a vehicle about its cg. A control system includes control surfaces which, when deflected, generate a moment (or couple from ailerons) about the cg which rotates the aircraft in pitch, roll, and yaw. For example, a pitching mo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Yaw Axis Corrected
Yaw or yaws may refer to: Measurement and technology Movement about the vertical axis * Yaw angle (or yaw rotation), one of the angular degrees of freedom of any stiff body (for example a vehicle), describing rotation about the vertical axis ** Yaw (aviation), one of the aircraft principal axes of rotation, describing motion about the vertical axis of an aircraft (nose-left or nose-right angle measured from vertical axis) ** Yaw (ship motion), one of the ship motions' principal axes of rotation, describing motion about the vertical axis of a ship (bow-left or bow-right angle measured from vertical axis) * Yaw rate (or yaw velocity), the angular speed of yaw rotation, measured with a yaw rate sensor * Yawing moment, the angular momentum of a yaw rotation, important for adverse yaw in aircraft dynamics Wind turbines * Yaw system, a yaw angle control system in wind turbines responsible for the orientation of the rotor towards the wind ** Yaw bearing, the most crucial and cost in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Right-hand Rule
In mathematics and physics, the right-hand rule is a common mnemonic for understanding orientation of axes in three-dimensional space. It is also a convenient method for quickly finding the direction of a cross-product of 2 vectors. Most of the various left-hand and right-hand rules arise from the fact that the three axes of three-dimensional space have two possible orientations. One can see this by holding one's hands outward and together, palms up, with the thumbs out-stretched to the right and left, and the fingers making a curling motion from straight outward to pointing upward. (Note the picture to right is not an illustration of this.) The curling motion of the fingers represents a movement from the first (''x'' axis) to the second (''y'' axis); the third (''z'' axis) can point along either thumb. Left-hand and right-hand rules arise when dealing with coordinate axes. The rule can be used to find the direction of the magnetic field, rotation, spirals, electromagnetic field ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Euler Angles
The Euler angles are three angles introduced by Leonhard Euler to describe the Orientation (geometry), 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 can also represent the orientation of a mobile frame of reference in physics or the orientation of a general Basis (linear algebra), basis in 3-dimensional linear algebra. Alternative forms were later introduced by Peter Guthrie Tait and George H. Bryan intended for use in aeronautics and engineering. Chained rotations equivalence Euler angles can be defined by elemental geometry or by composition of rotations. The geometrical definition demonstrates that three composed ''elemental rotations'' (rotations about the axes of a coordinate system) are always sufficient to reach any target frame. The three elemental rotations may be #Conventions by extrinsic rotations, extrinsic (rotations about the axes ''xyz'' of t ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Direction Cosine
In analytic geometry, the direction cosines (or directional cosines) of a vector are the cosines of the angles between the vector and the three positive coordinate axes. Equivalently, they are the contributions of each component of the basis to a unit vector in that direction. Three-dimensional Cartesian coordinates If v is a Euclidean vector in three-dimensional Euclidean space, R3, :\mathbf v = v_x \mathbf e_x + v_y \mathbf e_y + v_z \mathbf e_z, where e''x'', e''y'', e''z'' are the standard basis in Cartesian notation, then the direction cosines are :\begin \alpha &= \cos a = \frac &&= \frac,\\ \beta &= \cos b = \frac &&= \frac,\\ \gamma &= \cos c = \frac &&= \frac. \end It follows that by squaring each equation and adding the results : \cos^2 a + \cos^2 b + \cos^2 c = \alpha^ + \beta^ + \gamma^ = 1. Here ''α'', ''β'' and ''γ'' are the direction cosines and the Cartesian coordinates of the unit vector v/, v, , and ''a'', ''b'' and ''c'' are the direction angl ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rotation Matrix
In linear algebra, a rotation matrix is a transformation matrix that is used to perform a rotation in Euclidean space. For example, using the convention below, the matrix :R = \begin \cos \theta & -\sin \theta \\ \sin \theta & \cos \theta \end rotates points in the plane counterclockwise through an angle with respect to the positive axis about the origin of a two-dimensional Cartesian coordinate system. To perform the rotation on a plane point with standard coordinates , it should be written as a column vector, and multiplied by the matrix : : R\mathbf = \begin \cos \theta & -\sin \theta \\ \sin \theta & \cos \theta \end \begin x \\ y \end = \begin x\cos\theta-y\sin\theta \\ x\sin\theta+y\cos\theta \end. If and are the endpoint coordinates of a vector, where is cosine and is sine, then the above equations become the trigonometric summation angle formulae. Indeed, a rotation matrix can be seen as the trigonometric summation angle formulae in matrix form. One w ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Roll Pitch Yaw Mnemonic
Roll or Rolls may refer to: Movement about the longitudinal axis * Roll angle (or roll rotation), one of the 3 angular degrees of freedom of any stiff body (for example a vehicle), describing motion about the longitudinal axis ** Roll (aviation), one of the aircraft principal axes of rotation of an aircraft (angle of tilt to the left or right measured from the longitudinal axis) ** Roll (ship motion), one of the ship motions' principal axes of rotation of a ship (angle of tilt to the port or starboard measured from the longitudinal axis) * Rolling ''manoeuvre'', a manoeuvre of any stiff body (for example a vehicle) around its roll axis: ** Roll, an aerobatic maneuver with an airplane, usually referring to an aileron roll, but sometimes instead a barrel roll, rudder roll or slow roll ** Kayak roll, a maneuver used to right a capsized kayak ** Roll program, an aerodynamic maneuver performed in a rocket launch * Roll rate (or roll velocity), the angular speed at which an aircraft ca ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Lift (force)
A fluid flowing around an object exerts a force on it. Lift is the component of this force that is perpendicular to the oncoming flow direction. It contrasts with the drag force, which is the component of the force parallel to the flow direction. Lift conventionally acts in an upward direction in order to counter the force of gravity, but it can act in any direction at right angles to the flow. If the surrounding fluid is air, the force is called an aerodynamic force. In water or any other liquid, it is called a hydrodynamic force. Dynamic lift is distinguished from other kinds of lift in fluids. Aerostatic lift or buoyancy, in which an internal fluid is lighter than the surrounding fluid, does not require movement and is used by balloons, blimps, dirigibles, boats, and submarines. Planing lift, in which only the lower portion of the body is immersed in a liquid flow, is used by motorboats, surfboards, windsurfers, sailboats, and water-skis. Overview A fluid flowing arou ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Aerodynamic Drag
In fluid dynamics, drag (sometimes called air resistance, a type of friction, or fluid resistance, another type of friction or fluid friction) is a force acting opposite to the relative motion of any object moving with respect to a surrounding fluid. This can exist between two fluid layers (or surfaces) or between a fluid and a solid surface. Unlike other resistive forces, such as dry friction, which are nearly independent of velocity, the drag force depends on velocity. Drag force is proportional to the velocity for low-speed flow and the squared velocity for high speed flow, where the distinction between low and high speed is measured by the Reynolds number. Even though the ultimate cause of drag is viscous friction, turbulent drag is independent of viscosity. Drag forces always tend to decrease fluid velocity relative to the solid object in the fluid's path. Examples Examples of drag include the component of the net aerodynamic or hydrodynamic force acting opposite to the di ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Aerodynamic Force
In fluid mechanics, an aerodynamic force is a force exerted on a body by the air (or other gas) in which the body is immersed, and is due to the relative motion between the body and the gas. Force There are two causes of aerodynamic force: *the normal force due to the pressure on the surface of the body *the shear force due to the viscosity of the gas, also known as skin friction. Pressure acts normal to the surface, and shear force acts parallel to the surface. Both forces act locally. The net aerodynamic force on the body is equal to the pressure and shear forces integrated over the body's total exposed area. When an airfoil (such as a wing) moves relative to the air, it generates an aerodynamic force in a rearward direction, at an angle determined by the direction of relative motion. This aerodynamic force is commonly resolved into two components, both acting through the center of pressure: *'' drag'' is the force component parallel to the direction of relative mo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Thrust Vectoring
Thrust vectoring, also known as thrust vector control (TVC), is the ability of an aircraft, rocket, or other vehicle to manipulate the direction of the thrust from its engine(s) or motor(s) to control the attitude or angular velocity of the vehicle. In rocketry and ballistic missiles that fly outside the atmosphere, aerodynamic control surfaces are ineffective, so thrust vectoring is the primary means of attitude control. Exhaust vanes and gimbaled engines were used in the 1930s by Robert Goddard. For aircraft, the method was originally envisaged to provide upward vertical thrust as a means to give aircraft vertical (VTOL) or short (STOL) takeoff and landing ability. Subsequently, it was realized that using vectored thrust in combat situations enabled aircraft to perform various maneuvers not available to conventional-engined planes. To perform turns, aircraft that use no thrust vectoring must rely on aerodynamic control surfaces only, such as ailerons or elevator; aircraft ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Right-hand Rule
In mathematics and physics, the right-hand rule is a common mnemonic for understanding orientation of axes in three-dimensional space. It is also a convenient method for quickly finding the direction of a cross-product of 2 vectors. Most of the various left-hand and right-hand rules arise from the fact that the three axes of three-dimensional space have two possible orientations. One can see this by holding one's hands outward and together, palms up, with the thumbs out-stretched to the right and left, and the fingers making a curling motion from straight outward to pointing upward. (Note the picture to right is not an illustration of this.) The curling motion of the fingers represents a movement from the first (''x'' axis) to the second (''y'' axis); the third (''z'' axis) can point along either thumb. Left-hand and right-hand rules arise when dealing with coordinate axes. The rule can be used to find the direction of the magnetic field, rotation, spirals, electromagnetic field ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Spherical Coordinate System
In mathematics, a spherical coordinate system is a coordinate system for three-dimensional space where the position of a point is specified by three numbers: the ''radial distance'' of that point from a fixed origin, its ''polar angle'' measured from a fixed zenith direction, and the ''azimuthal angle'' of its orthogonal projection on a reference plane that passes through the origin and is orthogonal to the zenith, measured from a fixed reference direction on that plane. It can be seen as the three-dimensional version of the polar coordinate system. The radial distance is also called the ''radius'' or ''radial coordinate''. The polar angle may be called '' colatitude'', ''zenith angle'', '' normal angle'', or ''inclination angle''. When radius is fixed, the two angular coordinates make a coordinate system on the sphere sometimes called spherical polar coordinates. The use of symbols and the order of the coordinates differs among sources and disciplines. This article will us ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
