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Aerodynamic Vectors

Aerodynamic Vectors
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2018-11-07 23:32
VectorTrigonometryGeometric Construction
This example demonstrates the geometric representation of aerodynamic vectors. Key mathematical concepts include vectors, cosine, and angles. Using GeoGebra commands such as Line, Vector, and Translate, a dynamic model of aerodynamic vectors can be constructed. Suitable for high school physics and mathematics education.

GeoGebra Commands & Parameters

  1. Line(A, Cp) → f
  2. OrthogonalLine(Cp, f) → g
  3. Point(g) → B
  4. Vector(Cp, B) → Vt
  5. Point(f) → C
  6. Vector(Cp, C) → Vi
  7. Translate(B, Vi) → B'
  8. Vector(B, B') → u
  9. Segment(C, B') → h
  10. Segment(B', B) → i
  11. Vector(Cp, B') → Vr
  12. Point(Circle[Cp, 5]) → Pas
  13. Segment(Cp, Pas) → j
  14. Ray(Pas, Cp) → Corde
  15. OrthogonalLine(Pas, Corde) → k
  16. Point(Corde) → D
  17. OrthogonalLine(D, Corde) → l
  18. Point(k) → E
  19. Line(E, Corde) → m
  20. Intersect(l, m) → F
  21. Point(Vr) → I
  22. Point(Corde) → J
  23. CircleArc(Cp, I, J) → c
  24. Point(Vt) → K
  25. Point(Corde) → L
  26. CircleArc(Cp, K, L) → d
  27. Length(c) → a
  28. PointIn(c) → Pointc
  29. Length(d) → b
  30. PointIn(d) → Pointd
  31. Angle(K, Cp, L) → α
  32. Angle(I, Cp, J) → β

AI Drawing Prompt Reference

Draw an aerodynamic vector diagram with a point Cp as the starting point. Draw two perpendicular lines f and g from Cp, and find points B and C on g and f respectively. Use vectors Vt and Vi to represent the vectors from Cp to B and C. Then, translate point B along Vi to get B', and use vector u to represent BB'. Draw line segments h and i from B to B', and vector Vr from C to B'. Find point Pas on the circle centered at Cp, and use vector u and arc c to represent the vector and arc from Cp to Pas. Use points I and J to represent the endpoints of arcs c and d, and angles α and β to represent the central angles of arcs c and d.
The prompt above was compiled from the original drawing commands and is for reference only.