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Recently, Gary Drescher posted:
"Neil Gould" wrote in message .. . This makes *no* reference to the amount of lift that a stalled wing provides beyond it being inadequate to support flight, Interestingly enough, a stall occurs at the critical angle of attack, which is the AOA at which the coefficient of lift is the *maximum possible*. Just past the critical angle of attack (that is, further into the stall), the lift coefficient is no longer maximal, but is still well above what it is in ordinary cruise flight. What *does* happen just past the critical AOA--that is, just into the stall--is *not* that there's insufficient lift to support the plane's weight, but rather that there's a loss of *vertical damping*. John Denker (a physicist and a pilot) has a nice explanation he http://www.av8n.com/how/htm/vdamp.ht...rtical-damping. Thanks for that! I'm not sure that resolves the issue of trying to land with these parameters. Wrong. "To be a scalar" it needs to be a single value. And it is. Angle-of-attack is just an angle. A single value. Wrong. A scalar can not contain elements of direction by definition. Ergo, AOA has no meaning as a scalar. No, an angle is unquestionably a scalar, not a vector. Check any introductory math text. If an angle were a vector, then a symbol representing an angle would be set in boldface; but it is not. Mathematically, an "angle" by itself *is* a scalar, and I'm not arguing otherwise. I'm saying that "Angle Of Attack" requires direction to have meaning. Without direction, there is no AOA. You're right that an angle is defined by reference to vectors, but so is (for example) the *dot product* of two vectors (yet the dot product is a scalar); or so is the *magnitude* of a vector (but the magnitude is a scalar). So being defined by reference to vectors does not preclude a quantity from being scalar. Well, OK. Then, how do you determine the AOA when the aircraft is parked? If the component of direction is inseparable from the definition of AOA, how can it be a scalar? Neil |
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Mathematically, an "angle" by itself *is* a scalar, and I'm not arguing
otherwise. I'm saying that "Angle Of Attack" requires direction to have meaning. Without direction, there is no AOA. [...] Well, OK. Then, how do you determine the AOA when the aircraft is parked? If the component of direction is inseparable from the definition of AOA, how can it be a scalar? How long is it between 11 AM and 1:30 PM? The answer is 150 minutes. Now, is that 150 minutes AM or 150 minutes PM? In order to form the difference, you NEED to know whether the original times are AM or PM, but the result is a pure number of minutes. 11 AM is a =time of day=, 1:30 pm is a =time of day= but the difference is =not= a time of day, it is just a number (of minutes). In a similar vein, in order to form an angle (a pure number), you need to have not just one direction, but two. You need TWO quantites that have direction (they don't even have to have magnitude!). However, the result (the angle between them) has no direction (beyond the algebraic sign). When you say: I'm saying that "Angle Of Attack" requires direction to have meaning. all you're really saying is that you don't have an angle of attack if you don't have the requisite components (a relative wind, and a chord). But don't confuse the components with the result. Area is made up of length and width, but area is not in itself one dimesional. Cakes are made with raw eggs and flour, but I'm not likely to confuse the two any time soon. ![]() 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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Recently, Jose posted:
Mathematically, an "angle" by itself *is* a scalar, and I'm not arguing otherwise. I'm saying that "Angle Of Attack" requires direction to have meaning. Without direction, there is no AOA. [...] Well, OK. Then, how do you determine the AOA when the aircraft is parked? If the component of direction is inseparable from the definition of AOA, how can it be a scalar? [...] When you say: I'm saying that "Angle Of Attack" requires direction to have meaning. all you're really saying is that you don't have an angle of attack if you don't have the requisite components (a relative wind, and a chord). I'm not sure that I follow your analogies, here, Jose. But, it may be a good idea for you to look up the definition of "scalar". It *can not* include a directional component. Conversely, AOA can not exist without one. Neil |
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Neil Gould wrote:
But, it may be a good idea for you to look up the definition of "scalar". It *can not* include a directional component. Conversely, AOA can not exist without one. Angle of attack does not "include a directional component". It is just an angle, which is a scalar quantity. You have evidently looked up the dictionary definition of scalar, and you read it, but you didn't understand it. Dave |
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Recently, Dave Butler posted:
Neil Gould wrote: But, it may be a good idea for you to look up the definition of "scalar". It *can not* include a directional component. Conversely, AOA can not exist without one. Angle of attack does not "include a directional component". It is just an angle, which is a scalar quantity. If what you think is true, then it is possible to determine the AOA when the aircraft is parked. Do so, and I'll revise my thinking. The wonderful thing about this level of mathematics is that it is not ambiguous. If any usage results in a violation of the definition, then the usage is wrong, period. Neil |
#6
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Neil Gould wrote:
If what you think is true, then it is possible to determine the AOA when the aircraft is parked. Do so, and I'll revise my thinking. The wonderful thing about this level of mathematics is that it is not ambiguous. If any usage results in a violation of the definition, then the usage is wrong, period. I don't give a flip whether you revise your thinking or not. Your loss. |
#7
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Recently, Dave Butler posted:
Neil Gould wrote: If what you think is true, then it is possible to determine the AOA when the aircraft is parked. Do so, and I'll revise my thinking. The wonderful thing about this level of mathematics is that it is not ambiguous. If any usage results in a violation of the definition, then the usage is wrong, period. I don't give a flip whether you revise your thinking or not. Your loss. Not really. Have a nice weekend, and fly safely. Neil |
#8
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I'm not sure that I follow your analogies, here, Jose.
The analogy is merely that you can use one kind of quantity to derive another kind of quantity. You can use eggs to derive cake, you can use "time of day" to derive "time", you can use length to derive area, and you can use vectors to derive scalars. The simplest example, I suppose, is a ratio. Fifteen kilograms is THREE times as much as five kilograms. Fifteen inches is THREE times as much as five inches. The "three" in both cases is the same - it is a pure scalar quantity. It is the same "three" as the number of fingers on my hand that are surrounded by other fingers and the number of days in a long weekend. Fifteen kilograms is =not= three times as much as five inches. The units are important when =deriving= the result, but once the result is correctly derived, it has its own units (or lack of them). Similarly, two vectors can intersect at an angle. The angle is not a vector, it is a scalar. As an aside, two vectors (of the same units) can also define an area; that area is not a vector, it is a scalar (with units of square fubars, where "fubars" are the unit both vectors are measured in). A vector has magnitude and direction. AOA has no direction in and of itself. To see this, imagine a wing chord which is inclined three degrees (the leading edge higher) from some reference plane (say, the fuselage), and a relative wind which is blowing up from ahead and underneath at an angle of eighteen degrees to that same fuselage, at seventy knots. This is typical of an approach in a light aircraft. What is the angle of attack? To be a scalar, it would have just magnitude (which could include an algebraic sign). To be a vector, it would have to have magnitude AND direction. In this case, the angle of attack is twenty-one degrees. It is the difference between the two angles given (with reference to the same fuselage). There is no "direction" to this angle (except perhaps an algebraic sign). So it is not a vector. One source of confusion arises because in other contexts angles are also used to define direction, for example wind velocity is a vector whose angle is a direction component, not a magnigude component. For example, "zero three zero at ten knots" is a vector, where the magnitude part is ten knots, and the direction part is 30 degrees East of North. However, if you put a weight on an old fashioned butcher scale, the pointer moves through some angle. That angle does =not= represent a direction, it is a magnitude only, and thus a scalar (related to the weight of the meat put in the pan). And if you weigh two cuts of meat, note the angles of the pointer for each weighing, and subtract those angles, the result is also an angle - a magnitude with no direction component. This is a scalar. So, depending on context, angles can be magnitudes =or= directions, but not both at once. 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. |
#9
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Recently, Jose posted:
[...] A vector has magnitude and direction. AOA has no direction in and of itself. [...] What is the angle of attack? To be a scalar, it would have just magnitude (which could include an algebraic sign). To be a vector, it would have to have magnitude AND direction. However, it is valid for a vector to have a magnitude of zero. It is NOT valid for a scalar to have a directional component, and it is meaningless to have an AOA with no directional component and magnitude (e.g. parked aircraft have no AOA). Ergo, to have an AOA, you *must* also have velocity (magnitude) and direction. [...] In this case, the angle of attack is twenty-one degrees. It is the difference between the two angles given (with reference to the same fuselage). The two aspects of the AOA is referenced to the wing chord and relative wind, not the fuselage. There is no "direction" to this angle (except perhaps an algebraic sign). So it is not a vector. 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. But, that's quite a different situation than calling AOA something it can't be by definition. [...] So, depending on context, angles can be magnitudes =or= directions, but not both at once. We're not talking about generic "angles", but an "Angle Of Attack", i.e., a specific usage which is defined by and inseparable from the components of motion (aka relative wind). Without those components, AOA doesn't exist. Neil |
#10
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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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