Reference frames

Question 1

Cartesian coordinate systems

Answer 1

ACartesian coordinate systemis acoordinate systemthat specifies eachpointuniquely in aplaneby a pair ofnumericalcoordinates, which are thesigneddistances to the point from two fixedperpendiculardirected lines, measured in the sameunit of length. Each reference line is called acoordinate axisor justaxisof the system, and the point where they meet is itsorigin, usually at ordered pair(0, 0). The coordinates can also be defined as the positions of theperpendicular projectionsof the point onto the two axis, expressed as signed distances from the origin.

Question 2

theright-hand rule

Answer 2

Inmathematicsandphysics, theright-hand ruleis a commonmnemonicfor understanding orientation conventions forvectorsin three dimensions.

Most of the various left and right-hand rules arise from the fact that the three axes of 3-dimensional space have two possible orientations. This can be seen by holding your hands outward and together, palms up, with the fingers curled. If the curl of your fingers represents a movement from the first or X axis to the second or Y axis then the third or Z axis can point either along your left thumb or right thumb. Left and right-hand rules arise when dealing with co-ordinate axes, rotation, spirals, electromagnetic fields, mirror images andenantiomersin mathematics and chemistry.

Question 3

Earth frame

Answer 3

Origin - arbitrary, fixed relative to the surface of the Earth

xEaxis - positive in the direction ofnorth

yEaxis - positive in the direction ofeast

zEaxis - positive towards the center of the Earth

In many flight dynamics applications, the Earth frame is assumed to be inertial with a flatxE,yE-plane, though the Earth frame can also be considered aspherical coordinate systemwith origin at the center of the Earth.

Question 4

Body frame

Answer 4

Origin - airplane center of gravity

xbaxis - positive out the nose of the aircraft in the plane of symmetry of the aircraft

zbaxis - perpendicular to thexbaxis, in the plane of symmetry of the aircraft, positive below the aircraft

ybaxis - perpendicular to thexb,zb-plane, positive determined by theright-hand rule(generally, positive out the right wing)

The body frame is often of interest because the origin and the axes remain fixed relative to the aircraft. This means that the relative orientation of the Earth and body frames describes the aircraft attitude.

Question 5

Wind frame

Answer 5

Origin - airplane center of gravity

xwaxis - positive in the direction of the velocity vector of the aircraft relative to the air

zwaxis - perpendicular to thexwaxis, in the plane of symmetry of the aircraft, positive below the aircraft

ywaxis - perpendicular to thexw,zw-plane, positive determined by the right hand rule (generally, positive to the right)

The wind frame is a convenient frame to express the aerodynamic forces and moments acting on an aircraft. In particular, the netaerodynamic forcecan be divided into components along the wind frame axes, with thedrag forcein the −xwdirection and thelift forcein the −zwdirection.

Question 6

kinematics

Answer 6

noun

the branch of mechanics concerned with the motion of objects without reference to the forces that cause the motion.

the features or properties of motion in an object.

plural noun:kinematics

Question 7

force acting on the aircraft, fixed in the +zEdirection

Answer 7

Additionally, one force acting on the aircraft, weight, is fixed in the +zEdirection.

Question 8

thrust vectoring

Answer 8

Thrust vectoring, alsothrust vector controlorTVC, is the ability of anaircraft,rocket, or other vehicle to manipulate the direction of thethrustfrom itsengine(s) or motor(s) in order tocontroltheattitudeorangular velocityof the vehicle.

Question 9

spherical coordinate system

Answer 9

Inmathematics, aspherical coordinate systemis acoordinate systemforthree-dimensional spacewhere the position of a point is specified by three numbers: theradial distanceof that point from a fixed origin, itspolar anglemeasured from a fixedzenithdirection, and theazimuth angleof itsorthogonal projectionon 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 thepolar coordinate system.

Question 10

Aerodynamic force

Answer 10

Aerodynamic forceis exerted on a body by the air (or some other gas) in which the body is immersed, and is due to therelative motionbetween the body and the gas.

.Aerodynamicforce arises from two causes:[1][2][3]

thenormal forcedue to thepressureon the surface of the body

theshear forcedue to theviscosityof the gas, also known asskin friction.

Question 11

Normal Force

Answer 11

Inmechanics, thenormalforce{\displaystyle F_{n}\ }is the component, perpendicular to the surface (surface being a plane) of contact, of thecontact forceexerted on an object by, for example, the surface of a floor or wall, preventing the object from falling. Here “normal” refers to the geometry terminology for being perpendicular, as opposed the common language use of “normal” meaning common or expected. For example, consider a person standing still on the ground, in which case the ground reaction force reduces to the normal force. In another common situation, if an object hits a surface with some speed, and the surface can withstand it, the normal force provides for a rapid deceleration, which will depend on the flexibility of the surface.

Question 12

Pressure

Answer 12

Pressure(symbol:porP) is theforceapplied perpendicular to the surface of an object per unitareaover which that force is distributed.Gauge pressure(also spelledgagepressure)[a]is the pressure relative to the ambient pressure.

Question 13

Shear force

Answer 13

Shearing forcesare unalignedforcespushing one part of a body in one direction, and another part of the body in the opposite direction. When the forces are aligned into each other, they are calledcompression forces. An example is a deck of cards being pushed one way on the top, and the other at the bottom, causing the cards to slide. Another example is when wind blows at the side of a peaked roof of a home - the side walls experience a force at their top pushing in the direction of the wind, and their bottom in the opposite direction, from the ground or foundation.

this is also known as Skin friction drag

Question 14

Viscosity

Answer 14

Theviscosityof afluidis a measure of itsresistanceto gradual deformation byshear stressortensile stress.[1]For liquids, it corresponds to the informal concept of “thickness”; for example,honeyhas a much higher viscosity thanwater.[2]

Question 15

Skin friction drag

Answer 15

Skin friction dragis a component ofprofile dragthat acts on a body in a fluid flow. “Skin friction drag” applies not only to the “skins” of an aircraft but also to flow of fluids within and about any body subjected to a fluid flow. Friction drag begins as laminar drag but may become turbulent drag at some point along the body in the fluid flow direction. Skin friction drag is calculated or measured and is additive with other forms of drag acting on a body.

Question 16

Aerodynamic drag

Answer 16

Inaerodynamics,aerodynamic dragis thefluid drag forcethat acts on any moving solid body in the direction of the fluidfreestreamflow.[1]From the body’s perspective (near-field approach), the drag results from forces due to pressure distributions over the body surface, symbolized{\displaystyle D_{pr}}, and forces due to skin friction, which is a result of viscosity, denoted{\displaystyle D_{f}}.

Question 17

Lift (force)

Answer 17

Afluidflowing past the surface of a body exerts aforceon it.Liftis thecomponentof this force that is perpendicular to the oncoming flow direction.[1]It contrasts with thedragforce, which is the component of the surface force parallel to the flow direction. If the fluid is air, the force is called anaerodynamic force. In water, it is called ahydrodynamic force.

Question 18

Direction cosine or rotation matrices

Answer 18

Inlinear algebra, arotation matrixis amatrixthat is used to perform arotationinEuclidean space. For example, using the convention below, the matrix

{\displaystyle R={\begin{bmatrix}\cos \theta &-\sin \theta \\sin \theta &\cos \theta \\end{bmatrix}}}

rotatespointsin thexy-Cartesian planecounter-clockwise through an angleθabout the origin of theCartesian coordinate system. To perform the rotation using a rotation matrixR, the position of each point must be represented by acolumn vectorv, containing the coordinates of the point. A rotated vector is obtained by using thematrix multiplicationRv.

Question 19

Euler angles

Answer 19

TheEuler anglesare three angles introduced byLeonhard Eulerto describe theorientationof arigid bodywith respect to a fixedcoordinate system.[1]They can also represent the orientation of a mobileframe of referencein physics or the orientation of a generalbasisin3-dimensionallinear algebra.

Question 20

Quaternion

Answer 20

Inmathematics, thequaternionsare anumber systemthat extends thecomplex numbers. They were first described by Irish mathematicianWilliam Rowan Hamiltonin 1843[1][2]and applied tomechanicsinthree-dimensional space. A feature of quaternions is that multiplication of two quaternions isnoncommutative. Hamilton defined a quaternion as thequotientof two directed lines in a three-dimensional space[3]or equivalently as the quotient of twovectors.

Question 21

Tait–Bryan angles

Answer 21

The second type of formalism is calledTait–Bryan angles, afterPeter Guthrie TaitandGeorge H. Bryan. It is the convention normally used for aerospace applications, so that zero degrees elevation represents the horizontal attitude. Tait–Bryan angles represent the orientation of the aircraft with respect to the world frame. When dealing with other vehicles, differentaxes conventionsare possible.

Question 22

Slip / sideslip angle

Answer 22

Aslipis anaerodynamicstate where anaircraftis movingsomewhatsideways as well as forward relative to the oncoming airflow orrelative wind. In other words, for a conventional aircraft, the nose will be pointing in the opposite direction to the bank of the wing(s). The aircraft is not incoordinated flightand therefore is flying inefficiently.

Question 23

velocity

Answer 23

Thevelocityof an object is therate of changeof itspositionwith respect to aframe of reference, and is a function of time. Velocity is equivalent to a specification of itsspeedand direction ofmotion(e.g.60km/hto the north). Velocity is an important concept inkinematics, the branch ofclassical mechanicsthat describes the motion of bodies