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it is valid for a vector to have a magnitude of zero.
Correct. It is NOT valid for a scalar to have a directional component Correct. and it is meaningless to have an AOA with no directional component and magnitude Incorrect. I can give you many examples of such AOAs. Can you give me an example of an AOA that =itself= has a direction and magnitude? (Not that it's derived from things that have direction and magnitude, but that it, =itself= has such) The two aspects of the AOA is referenced to the wing chord and relative wind, not the fuselage. The two aspects of the AOA are referenced to each other. I refereneced them to the same other thing (fuselage) and then derived their relation to each other. I'd say that it is often "OK" to PRESUME the directional components and IGNORE their value if they are unimportant to usages where only the angle is needed. It is not OK to presume anything in math. Things are what they are defined to be. You might be thinking of "unit vectors" in which case a magnitude of one is used, but they are defined that way. Or you might be thinking of the algebraic sign (which is part of a scalar quantity). We're not talking about generic "angles", but an "Angle Of Attack" An angle of attack =is= an angle. All angles are scalars. Therefore, an angle of attack is a scalar. Which part of this do you disagree with? i.e., a specific usage which is defined by and inseparable from the components of motion (aka relative wind). Defined by, yes. Inseperable from, no. The price to earnings ratio (PE) of a stock is =defined by= the dollar price of a stock, and the dollar earnings of the company divided by the number of shares outstanding. Without those components, you don't have a PE ratio. But the PE is a pure number. It is not a dollar amount. Jose -- "Never trust anything that can think for itself, if you can't see where it keeps its brain." (chapter 10 of book 3 - Harry Potter). for Email, make the obvious change in the address. |
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