Intuition The ONE core ideaAn airfoil is a shape whose only purpose is to turn passing air downward so the air shoves the wing up . Every symbol on the parent page — c y c y t θ α c ℓ that shape and how much air it turns .
Before you can read the parent note, you need a small toolbox. Below is every symbol and idea it uses, built from nothing, each one earning the next. Read top to bottom.
Everything starts with one image: a slice through a wing, like a slice of bread cut off a loaf. This flat 2D shape is the airfoil . Air flows past it from left to right.
Definition Leading edge (LE) and trailing edge (TE)The leading edge is the front point of the slice — the part that meets the air first. The trailing edge is the back point — the sharp tail where air leaves.
Picture: the nose and the tail of the slice. Why we need them: they are the two anchor points every measurement is pinned to.
Before any airfoil symbol, we need a grid to place points on.
x y
x along the airfoil, front to back . We set x = 0 x = c y up or down from a reference line. Up is positive, down is negative.
Picture: x y Why: every curve of the airfoil (top skin, bottom skin, skeleton) is written as a height y x
Definition Chord line and chordc chord line is the straight line from the leading edge to the trailing edge. Its length is the chord c Picture: the straight ruler drawn nose-to-tail (dashed line in the figure below).
Why the topic needs it: c ruler . Every other length (camber, thickness, positions) is quoted as a fraction of c , e.g. "0.02 c
Intuition Why measure in fractions ofc 2% 0.02 c same shape at any size. Fractions of c scale-free .
Definition Upper and lower surfaceThe upper surface is the top skin of the airfoil; the lower surface is the bottom skin. At each x y U y L Picture: the two curved lines bounding the shaded slice — top curve and bottom curve.
Why: the actual airfoil is these two curves. Everything else (camber, thickness) is a way of summarising them.
t ( x ) y t ( x ) x thickness t ( x ) gap between the upper and lower skins — how "fat" the slice is there. The half-thickness y t ( x ) = t ( x ) /2 half that gap.
Picture: a vertical (or skeleton-perpendicular) double-arrow spanning top to bottom; y t Why y t t When we build the surface, we add + y t above the skeleton and − y t below it. Splitting the gap in half is what lets us wrap thickness symmetrically around the centre.
Definition Maximum thicknesst ma x t ma x t ( x ) thickness ratio is t ma x / c t ma x / c = 0.12 Picture: the fattest point of the slice, measured against the ruler c
Definition Mean camber liney c ( x ) mean camber line is the curve of points exactly halfway between the upper and lower skins . Its height at each x y c ( x ) z ( x ) Picture: the "spine" or skeleton running down the middle of the slice.
Why: it is the airfoil's backbone . If we know the spine y c y t
The camber is the biggest gap between the mean camber line and the chord line , as a fraction of c Picture: the largest vertical distance between the curved spine and the straight ruler.
If the spine sits exactly on the ruler everywhere, camber = 0 symmetric .
Common mistake Camber is NOT curviness or fatnessA thick symmetric airfoil looks curvy and full, but if its spine lies on the chord line, its camber is zero . Camber is only about the spine vs the ruler — nothing else.
The parent writes d x d y c slope of the camber line — the tool that answers "how tilted is the spine at this point?"
Definition Slope = rise over rund x d y c y c x Picture: the steepness of a little ramp tangent to the spine at a point.
Why a derivative? We need the local tilt at each point, because the tilt changes along the airfoil. The derivative is exactly the tool for "instantaneous steepness".
The parent writes θ = arctan ( d x d y c )
Intuition Why we need an ANGLE, not just a slopeTo wrap thickness perpendicular to the spine , we must know which direction is perpendicular . "Perpendicular" is a rotation — and rotations are described by angles , not slopes. So we convert slope → angle.
The slope d x d y c ratio : rise over run. Draw the little tangent ramp as a right triangle: the horizontal side is the "run", the vertical side is the "rise", and the ramp itself is the hypotenuse. The angle θ
tan θ = adjacent opposite = run rise = d x d y c .
tan tan opposite the angle divided by the side next to it (adjacent). It measures steepness : steeper ramp → bigger tan
arctan arctan tan − 1 reverse of tan arctan undoes tan Why arctan Because we have a ratio (slope) and want an angle — that is exactly the question arctan
Intuition Why this stays safe for airfoilsFor camber lines the slope is gentle and x θ 0 − 9 0 ∘ + 9 0 ∘ arctan x d x d y c = 0 θ = 0 θ > 0 θ < 0
Definition Angle of attackα angle of attack α chord line and the oncoming air .
Picture: tilt the whole slice nose-up into a horizontal wind — that tilt is α Why: tilting also turns air downward, so α
Definition Zero-lift angleα L 0 zero-lift angle α L 0 α no lift at all . For a symmetric airfoil α L 0 = 0 negative (you can tilt nose-down a bit and still get zero lift).
Why: it's the single number that records "how much free lift the camber already gives you".
Definition Lift coefficientc ℓ c ℓ scale-free score for how much lift the airfoil makes, with the raw size, air density and speed divided out. Bigger c ℓ Why a coefficient? Just like using fractions of c c ℓ Lift and Drag Coefficients .
leading and trailing edges
thickness t and half thickness yt
tilt angle theta via arctan
sin and cos give the normal
Each foundation feeds the ones below it, and all of them converge on the parent topic, the airfoil geometry note .
Cover the right side and test yourself. If you can answer all of these, you're ready for the parent page.
What is the chord line, in one sentence? The straight line from the leading edge to the trailing edge; its length is c
Why do we quote lengths as fractions of c So the same numbers describe the shape at any physical size — they are scale-free.
What is the mean camber line? The curve of points exactly halfway between the upper and lower surfaces.
Difference between camber and thickness? Camber = how far the spine bows off the chord line; thickness = the gap between the two skins. A thick symmetric airfoil has zero camber.
What does the slope d y c / d x The local steepness of the camber line at each point x
What does tan θ Opposite over adjacent of the tangent triangle — the steepness of the spine.
What does arctan Takes a slope (a ratio) and returns the angle that produced it — it undoes tan
Why do the surface formulas use sin θ cos θ They split the perpendicular thickness offset into its sideways (sin cos
What is the angle of attack α The angle between the chord line and the oncoming air.
What is α L 0 The angle of attack at which lift is zero; camber makes it negative.
Why use c ℓ It divides out size, density and speed so shapes can be compared fairly.
