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Vectors. A vector is a graphic representation of a quantity that must be described using magnitude and direction. Examples of vector quantities are. Acceleration. Thrust. Lift. Weight. and. Drag. Vector Addition. When more than two forces acting on a point of origin. - PowerPoint PPT Presentation
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WeightWeightWeightWeight
VectorsVectorsVectorsVectors
A vector is a graphic representation of aA vector is a graphic representation of aquantity that must be described usingquantity that must be described usingmagnitude and direction. magnitude and direction.
Examples of vector quantities areExamples of vector quantities are
A vector is a graphic representation of aA vector is a graphic representation of aquantity that must be described usingquantity that must be described usingmagnitude and direction. magnitude and direction.
Examples of vector quantities areExamples of vector quantities are
AccelerationAccelerationAccelerationAcceleration ThrustThrustThrustThrust LiftLiftLiftLift andandandand DragDragDragDrag
Vector AdditionVector AdditionVector AdditionVector Addition
When more than two forces acting on When more than two forces acting on a point of origin a point of origin When more than two forces acting on When more than two forces acting on a point of origin a point of origin
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Establish a point thatEstablish a point thatat which all forcesat which all forcesare considered to beare considered to beconcentratedconcentrated
Establish a point thatEstablish a point thatat which all forcesat which all forcesare considered to beare considered to beconcentratedconcentrated
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Resultant
From the point of origin, From the point of origin, draw a vector corresponding to draw a vector corresponding to the magnitude and direction of the magnitude and direction of one of the forces. one of the forces.
From the point of origin, From the point of origin, draw a vector corresponding to draw a vector corresponding to the magnitude and direction of the magnitude and direction of one of the forces. one of the forces.
From the head of this vector From the head of this vector draw another vector showing draw another vector showing magnitude and direction ofmagnitude and direction ofanother of the forces.another of the forces.
From the head of this vector From the head of this vector draw another vector showing draw another vector showing magnitude and direction ofmagnitude and direction ofanother of the forces.another of the forces.
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Resultant
The resultant will be the sameThe resultant will be the sameregardless which order theregardless which order thevectors are added. vectors are added.
The resultant will be the sameThe resultant will be the sameregardless which order theregardless which order thevectors are added. vectors are added.
ParallelogramParallelogramParallelogramParallelogram
Used to represent solutions when only two Used to represent solutions when only two forces are acting on an object.forces are acting on an object.
Lift and drag vectors on an airfoil are goodLift and drag vectors on an airfoil are goodexamples of the parallelogram method of examples of the parallelogram method of vector solutionvector solution
Used to represent solutions when only two Used to represent solutions when only two forces are acting on an object.forces are acting on an object.
Lift and drag vectors on an airfoil are goodLift and drag vectors on an airfoil are goodexamples of the parallelogram method of examples of the parallelogram method of vector solutionvector solution
LiftLiftLiftLift
DragDragDragDrag
Total Aerodynamic ForceTotal Aerodynamic Force
(TAF)(TAF)Total Aerodynamic ForceTotal Aerodynamic Force
(TAF)(TAF)From point of origin, draw vectorFrom point of origin, draw vectorparallel to reference plane parallel to reference plane From point of origin, draw vectorFrom point of origin, draw vectorparallel to reference plane parallel to reference plane
Draw second vector at appropriateDraw second vector at appropriateangle to first vectorangle to first vectorDraw second vector at appropriateDraw second vector at appropriateangle to first vectorangle to first vector
Complete parallelogramComplete parallelogramby drawing oppositeby drawing oppositesides parallel to knownsides parallel to knownsidessides
Complete parallelogramComplete parallelogramby drawing oppositeby drawing oppositesides parallel to knownsides parallel to knownsidessides
Draw a line from the originDraw a line from the originof the two vectors to the of the two vectors to the opposite corner of the opposite corner of the parallelogramparallelogram
Draw a line from the originDraw a line from the originof the two vectors to the of the two vectors to the opposite corner of the opposite corner of the parallelogramparallelogram
The length of the line represents The length of the line represents the magnitude of the vector in thethe magnitude of the vector in thedirection indicateddirection indicated
The length of the line represents The length of the line represents the magnitude of the vector in thethe magnitude of the vector in thedirection indicateddirection indicated
Triangular SolutionsTriangular SolutionsTriangular SolutionsTriangular SolutionsOften used to solve navigation problems Often used to solve navigation problems Often used to solve navigation problems Often used to solve navigation problems
From a point of origin, draw a vector corresponding to the From a point of origin, draw a vector corresponding to the directiondirection and and magnitudemagnitude of one of the forces. of one of the forces.From a point of origin, draw a vector corresponding to the From a point of origin, draw a vector corresponding to the directiondirection and and magnitudemagnitude of one of the forces. of one of the forces.
From the head of this vector, draw the other vector corresponding to the From the head of this vector, draw the other vector corresponding to the directiondirection and and magnitudemagnitude of the other force. of the other force.From the head of this vector, draw the other vector corresponding to the From the head of this vector, draw the other vector corresponding to the directiondirection and and magnitudemagnitude of the other force. of the other force.
From the point of origin, draw the From the point of origin, draw the resultantresultant vector to the head of the last vector to the head of the lastforce.force.From the point of origin, draw the From the point of origin, draw the resultantresultant vector to the head of the last vector to the head of the lastforce.force.
CourseCourseCourseCourse
WindWindWindWind
TrackTrackTrackTrack ResultantResultant
Desired Track Desired Track (100 NM)(100 NM)
Desired Track Desired Track (100 NM)(100 NM)
Wind (20 kts)Wind (20 kts)45° RT crosswind45° RT crosswind
Wind (20 kts)Wind (20 kts)45° RT crosswind45° RT crosswindResultant Track
Resultant Track
(90 NM)(90 NM)Resultant TrackResultant Track
(90 NM)(90 NM)
Example #2 Example #2 100 KIAS Point A toward Point B100 KIAS Point A toward Point BExample #2 Example #2 100 KIAS Point A toward Point B100 KIAS Point A toward Point B
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ResultantResultant
Questions ?Questions ?Questions ?Questions ?
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