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Beginner's Guide to Propulsion
Forces in a Climb -Vectors

  1. Using the first equation: L cos (c) + F sin (c) -D sin (c) - W = ma (vertical)
    and the third equation: F -D = Fex , explain and show how to obtain
    the fourth equation: L cos (c) + Fex sin (c) - W = ma (vertical).

    Factor sin (c) out of last two terms and substitute F
    ex for (F - D).

  2. Using the second equation and the third equation, explain and show how to obtain the fourth equation.
    In the second equation, factor cos (c) out of the first and third terms and substitute as in above.

  3.  Why isn't W multiplied by a sine or cosine?
    Weight is a downward force, so it would be W sin (90) or just W. (sin 90 is 1).

  4. Using the given diagram, theorems/postulates of geometry, and vectors, explain each term in the first two equations.

    Vertical Component.
    Vertical Component

    1. V1 = F sin 10 positive (upward) vertical

      V2 = L cos 10 positive vertical

      1. angle 1 + angle 2 = 90 Lift is perpendicular (vertical) to flight path

        angle 1 + angle 3 = 90 Acute angles of a right triangle are complementary.

        Therefore angle 1 + angle 2 = angle 1 + angle 3

        Then angle 2 = angle 3

        Since angle 2 = 10 then angle 3 must also.

      V3 = D sin 10 negative (downward) vertical

      V4 = W

    Horizontal Component 
    Horizontal component

    1. H1 = F cos 10 Positive (forward)

      H2 = L sin 10 Negative (backward)

      H3 = D cos 10 Negative (backward)

      "W" only affects the vertical, not horizontal, or W cos 90 = 0




Related Pages:
Aerodynamics Activity Index
Aerodynamics Index
Propulsion Activity Index
Propulsion Index


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Editor: Tom Benson
NASA Official: Tom Benson
Last Updated: Thu, May 13 02:38:39 PM EDT 2021

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