Airfoil aerodynamics
Unit 02 ended on the thing geometry cannot tell you: how much lift, at what angle, for how much drag, and where it stops working. Those answers are not in the shape. They come out of a viscous calculation, and they change with Reynolds number, which is why unit 01 asked for a speed and a rough chord.
The lift curve
Plot cl against angle of attack and most of it is a straight line. Two numbers describe that line. Where it crosses zero is the zero-lift angle, which camber sets: a symmetric section crosses at 0, and NACA 2412 should cross near −2. How steep it is, the lift slope, thin-airfoil theory puts at 2π per radian, or about 0.11 per degree, for every section regardless of thickness or camber.
Check both against the readout. At Re 200k the zero-lift angle is −2.02 degrees, which is what 2 per cent of camber should give. Walk the Reynolds number down to 50k and it moves to +0.30, the wrong side of zero: the section needs a positive angle before it lifts at all. You can see that on the plot, where the curve crosses to the right of the vertical rule. The camber is still there and it has stopped paying for itself.
The slope reads 0.093 per degree at 200k, about 15 per cent under the ideal 0.11. That gap is the boundary layer: thin- airfoil theory describes a section without one, so 2π is a ceiling rather than a target. Step through 100k, 200k, 300k and 500k and the slope barely moves — 0.096, 0.093, 0.094, 0.096 — because it is the same straight line each time. At 50k the readout gives 0.139, which is not a lift slope at all but a curve bending through its own bubble.
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At 50k the curve near zero lift is not straight at all. It goes flat between −2 and 0 and then steepens. That flat stretch is a laminar separation bubble: the flow leaves the surface, sits there, and reattaches, and while it does the section is not behaving like the one in the textbook. A 20 cm chord at 15 m/s is Reynolds 200k, so a small foamie flying slowly lives in this band, and thin-airfoil theory is the wrong tool there.
Where it stops
Follow any curve up and it stops rising. That is the stall, and the marker sits on it. For 2412 the lift at that point moves from cl 1.15 at 50k to 1.34 at 500k, and it moves later too: 10 degrees at the bottom of the band, 14 at the top. The same wing stalls at a different angle depending on how fast it is going.
Past the marker the line goes dashed, and the data stops within a couple of degrees. On some polars it stops at the marker itself, with nothing left to dash. All of that is deliberate. XFOIL solves a boundary layer, and once the flow separates in earnest it returns numbers that converge and mean nothing: the raw campaign has this section’s neighbours reporting lift doubling while drag collapses. Read the dashed part as “it stalls around here” and nothing more precise.
The drag polar
Drag is the half that decides how long you stay up. Plotted against lift instead of angle it makes a bucket: a floor where drag is lowest, and walls where it climbs at both ends. Flying at the bottom of the bucket is flying efficiently.
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Step through the Reynolds numbers on 2412 and read the best L/D off the readout: 32.2 at 50k, 66.7 at 200k, 88.1 at 500k. Nothing about the section changed. The same shape is nearly three times the glider at the top of this band that it is at the bottom, and that is the single most useful thing on this page. Chord and speed are Reynolds number, and Reynolds number is performance.
Picking one
Now compare sections at a Reynolds number you would actually fly. Thickness first: 2408 against 2412 against 4415. Thin sections carry less drag at low lift and give up earlier at the top: 2408 bottoms out at cd 0.0086 against 2412’s 0.0098, and stalls at cl 1.07 where 4415 reaches 1.40. Camber next: 0012 against 2412 against 4412. Camber buys lift at the stall, 1.08 to 1.28 to 1.37 across those three, and moves the bucket to a lift you are more likely to cruise at. It is not free. At cl 0 the symmetric section costs 0.0102 and the 4412 costs 0.0165, sixty per cent more. The order reverses at about cl 0.35, so a section that cruises below that is paying for camber it is not using.
There is no best section, only a section that suits a brief. That is what unit 01 was for. A slow floater and a fast wing want opposite ends of these trades, and the numbers here are how you argue one over the other instead of copying whatever the last build used.
What this is not
These are XFOIL results, not wind tunnel measurements. XFOIL is good at attached flow and honest people use it for exactly this, but it is a model: it over-predicts maximum lift at low Reynolds numbers, it is sensitive to the transition setting (these were run at Ncrit 9, the standard clean-tunnel value), and past stall it does not describe reality at all. Treat the slope and the bucket as reliable, the peak as approximate, and the dashed part as a warning.
Also: everything on this page is two-dimensional, a section of infinite span. A real wing is not, and what the third dimension does to these numbers is unit 04.