In this picture, how do you determine the amount of the camber? Is it the average difference in the distances between the mean camber line and the chord line from the leading edge all the way down to the trailing edge?
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The mean camber line is the locus of points halfway between the top surface and the bottom surface (which are sometimes referred as upper and lower cambers). For a symmetrical airfoil, it is merged with the chord line.
This curve is described by a polynomial function at each point along the chord axis. An airfoil may have a camber line which changes direction at one or more point, and which possibly crosses the chord.
All measures are taken perpendicular to the chord which is considered having a length of 1 or 100%.

Adapted from Wikipedia.
What you ask for is the maximum camber, which is determined by the value of the maximum difference between chord and mean camber line, and the distance from the leading edge.

Adapted from Wikipedia.
mins
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So it looks like there is no such thing as the "average camber." Then, when deployed flaps are said to increase the camber, what exactly does it mean? Does it mean the maximum camber increases? – lemonincider Mar 06 '17 at 07:15
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1@lemonincider: The "average" camber is likely the "mean" camber. when flaps are extended, the chord line changes because the trailing edge is lowered, this increases the maximum camber. – mins Mar 06 '17 at 07:22
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Is the mean camber different from the mean camber line? Then, is it the "mean camber" that is referred to when the flaps are commonly said to increase the camber? – lemonincider Mar 06 '17 at 07:31
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@lemonincider: No, this is a shortcut, like chord line and chord. – mins Mar 06 '17 at 07:53
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I probably would have located the leading edge point of the chord line at the mid-point of the leading edge radius (slightly higher, in the "middle" of your drawing above). But the implication is that the leading edge chord line is anchored where the leading edge of the mean camber line starts. Is that correct? – PeterT Mar 06 '17 at 15:42
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@PeterT: Correct. Endpoints of both (mean) camber line and chord line are the identical. Mean camber line, near the leading edge, is the median of outer surfaces, it also where the stagnation point (the point where upper and lower streamlines separate) will be. This is more clear on turbine-blade-like airfoil. – mins Mar 06 '17 at 20:20
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@mins I thought I understood you but seems like I did not. Let me ask you once again. So when we say "this airfoil has a greater camber than that airfoil does," how exactly is it determined? Based on what? What's the criterion? The maximum camber? Or the average of the difference between the mean camber line and the chord line? Or something else? – lemonincider Jul 11 '17 at 23:53
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@lemonincider: "this airfoil has a greater camber than that airfoil does" is not particularly clear, in particular if the airfoil has a camber inversion (reflex camber. What would that mean in this case?)... – mins Jul 12 '17 at 00:11
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1... The more the airfoil is cambered, the more it is asymmetric , at some point the bottom face becomes concave (by definition of the mean line) and the chord is outside of the airfoil. So yes, when the camber is not reflexive (no inflection point), this is a measure of the difference with the chord. – mins Jul 12 '17 at 00:18
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@mins I came back to this question, because I came across the phrase "the flaps increase the camber" but couldn't understand exactly what was meant by that. Thanks. – lemonincider Jul 12 '17 at 00:19
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@lemonincider: That's true, they move the trailing extremity of the chord line down, so the camber has increased (and the airfoil bottom is more concave). – mins Jul 12 '17 at 00:24
