Your wing doesn't lift evenly
A wing lifts hardest at one station and gives up at another, and the planform you drew decides where those are. The distribution matters for two reasons. It sets how much induced drag you pay to hold the thing up, and it tells you which part of the wing is closest to its lift limit when you pull too hard.
All of that is in the textbooks. It lands better when you move a slider and watch it happen, which is what this post is. Every plot below comes from the same solver behind Wing Builder: a real vortex lattice, running on your machine while you read.
Lift per unit span, and the elliptic shape
March along the span and ask each slice how much lift it makes, then plot the answers. That curve is the spanload. What this page plots is the equivalent nondimensional quantity cl·c / MAC; at a fixed dynamic pressure, its area tracks the wing's total lift coefficient.
For a planar wing carrying a given lift over a given span, classical lifting-line theory gives exactly one minimum-induced-drag distribution: an ellipse. It produces uniform downwash across the span, and any departure from it costs more induced drag for the same lift and the same span.
The dashed line below is that reference, scaled to carry the same lift as the solid curve. Drag the taper ratio and watch your wing chase it.
That is the classic result for an unswept, untwisted, straight-tapered wing: λ ≈ 0.4–0.5 can get very close to elliptic loading with straight ribs and straight edges. It is a good place to start. It is not the right taper for every wing.
A caveat on that number. The lab reports span efficiency e, where 1.0 is the elliptic result for this planar, fixed-span comparison. You will sometimes see it read slightly above 1.0. That is numerical error, not a wing beating the theoretical limit: on a coarse lattice the vortex-lattice method under-counts induced drag, and e converges down onto 1.0 as you add panels. We keep the panel count low so the thing stays interactive in a browser tab. Compare e between planforms; do not read it as an absolute.
Notice what the lab holds fixed: span, root chord, and angle of attack. Moving the taper slider therefore changes wing area, aspect ratio, and total lift at the same time. Use the curve and e to compare the loading. Do not rank complete wings by the raw CDi number unless you first bring them to the same required lift and flight condition.
Local cl, the curve that shows your stall margin
Spanload is lift per unit span. It is not the same as local cl, which is how hard each slice is working relative to its own chord. In symbols, L' = q·c·cl: divide the spanload by dynamic pressure and local chord, and you get local cl.
The distinction matters because a section stalls when its local cl reaches that section's cl,max, not simply where lift per metre is largest. If every station had the same airfoil, Reynolds number, surface finish, and cl,max, the highest local cl would reach the limit first. That simplifying assumption is what the lab marks.
Taper is where this bites. It shrinks the chord towards the tip faster than it sheds load: the load falls, the chord falls faster, and the ratio climbs. Taper the wing hard enough and the hardest-working section is no longer at the root. It is out where your ailerons are.
Play with that one until the trade is in your hands. λ = 1 gives you a gentle inboard cl peak and misses the elliptic loading. λ = 0.2 misses the elliptic loading in the other direction and pushes the clpeak outboard, so it buys you less than “slipperier” suggests. The useful numbers sit in the middle, and they are a compromise.
Sweep changes the trade again
In this straight-tapered, untwisted wing, sweeping the leading edge back moves the local cl peak outboard. On its own the shift is gradual. Stacked on top of taper, it spends some of the outboard margin you thought taper had left you.
There is a second reason designers care. If the outer wing lies behind the centre of gravity and loses lift first, part of the aircraft's nose-down contribution disappears; that can produce pitch-up and drive the angle of attack higher. Whether a whole aircraft does this depends on the tail, CG, airfoil moments, and separated flow. A wing-only linear VLM cannot answer that question, but an outboard cl peak is still a warning worth investigating.
Washout, and what it costs you
Twist the tip down a couple of degrees. Now the tip meets the air at a lower geometric angle than the root, so its local cl comes down and the peak moves inboard. That is washout, and two degrees of it does more than you might guess in this example.
Read the drag numbers carefully here. At the same geometric angle of attack, washout also reduces total lift, so a lower CDidoes not prove a drag win. At the same required lift, you would have to raise the whole wing's angle of attack and compare again. Twist can improve the loading at one design lift coefficient and worsen it away from that point; when it is chosen for root-first stall behaviour, some off-design induced-drag penalty is often part of the bill.
Taper, sweep and twist are not independent style choices. Between them they set the spanload and the local cl distribution. Pick a design point, then check both curves at the lift coefficients your aircraft is going to fly.
What to take to the bench
- Taper ratio around 0.4–0.5 is a strong first look for an unswept, untwisted, straight-tapered wing. It is not a universal optimum.
- Sweep and taper can stack. In the geometry shown here, both move the local
clpeak outboard. Check your actual combination. - Washout moves the loading inboard. Judge its drag cost at the same required lift, not merely the same angle of attack.
- Local cl is only half the stall map. Compare it with the local
cl,max, including airfoil and Reynolds-number changes along the span.
None of this needs a CFD licence or a wind tunnel. It needs the planform you were going to build anyway, and a few minutes of moving sliders.
Open Wing Builder and do it for your wing →
This post does not predict stall. The solver models an attached, thin lifting surface; it does not model viscosity, thickness, Reynolds number, surface condition, or the airfoil's cl,max. It shows where demand is highest under an equal-section-limit assumption. Use that as a screening result, not as flight clearance.