The rectangular wing cannot have the same span than the real one, or its area and all associated forces and moments would be higher. You are right, the two definitions you quote are not compatible. This rectangular wing can either have the same area or the same span as the real wing, but not both together, unless the real wing is rectangular, too. if you wand to calculate pitch motion, you need a wing of the correct MAC.if you want to calculate induced drag, you need a wing of equal span.if you want to calculate lift, you need a wing of equal area. The area of a circle is times the radius squared, which is written: A r 2.By doing all calculations on the correctly sized rectangular version, the more complicated calculations on the real one could be avoided. The MAC has been invented to convert arbitrary wing planforms into much easier to calculate rectangular wings. The resulting rectangular wing will have a larger area than the original, tapered wing but the same pitch damping! In case of a delta wing, MAC will grow to be ⅔ of the root chord, and for an elliptical wing it will be 90.5% of the root chord. Since the chord is squared, deeper sections of the wing are overrepresented in the result. Here $b$ denotes wing span, $y$ the spanwise coordinate and $S$ the wing area. That is why the formula for the mean aerodynamic chord divides the square of the local chord by the wing area: Pitch characteristics need to include pitch damping, and pitch damping grows with the square of the local chord. Why? Because the mean aerodynamic chord is the mean chord of a rectangular wing that has the same pitch characteristics as the "real" wing. (previous) .The mean aerodynamic chord is only identical to the mean chord for rectangular wings. This kite’s diagonals are two chords that cross each other, so you can use the Chord-Chord Power Theorem. 2008: David Nelson: The Penguin Dictionary of Mathematics (4th ed.) . To get the area of a kite, you need to know the lengths of its diagonals.1998: David Nelson: The Penguin Dictionary of Mathematics (2nd ed.) .When this work has been completed, you may remove this instance of from the code. To discuss this page in more detail, feel free to use the talk page. In particular: Once it has been written, this would be on Definition:Chord of Curve If you have access to any of these works, then you are invited to review this list, and make any necessary corrections. When this has been completed, the citation of that source work (if it is appropriate that it stay on this page) is to be placed above this message, into the usual chronological ordering. As such, the following source works, along with any process flow, will need to be reviewed. This page may be the result of a refactoring operation. Results about chords can be found here.There are other sorts of chords, still to be documented. In the diagram above, the lines $AB$ and $C$ are chords. In the above diagram, $DF$ is a chord of polygon $ABCDEFG$.Ī chord of a parabola is a straight line segment whose endpoints are on the parabola. In the diagram above, the line $AB$ is a chord.Ī chord of a polygon $P$ is a straight line connecting two non- adjacent vertices of $P$: In the diagram above, the lines $CD$ and $EF$ are both chords.Ī chord of an ellipse is a straight line segment whose endpoints are on the perimeter of the ellipse. The angle that lies between a tangent and a chord is equal to the angle subtended by the same chord in the alternate segment. A chord of a circle is a straight line segment whose endpoints are on the circumference of the circle.
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