Where your wing's lift actually goes
Your wing does not lift evenly. It lifts hardest somewhere, gives up somewhere, and the two places are not the same. Where they land is shaped by the planform you drew. That distribution affects two things you care about: how much induced drag you pay to hold the thing up, and which part of the wing is closest to its lift limit when you pull too hard.
You can read that in a book. It is more convincing to move a slider and watch it happen, so that is what this post is. The solver behind every plot here is the same one behind Wing Builder — a real vortex lattice, running on your machine, not a picture of one.
Lift per unit span, and the elliptic shape
March along the span and ask each slice how much lift it makes. Plot it. That curve is the spanload. This page plots the equivalent nondimensional quantity cl·c / MAC; at a fixed dynamic pressure, its area tracks the wing's total lift coefficient.
Here is the part with consequences. For a planar wing carrying a given lift over a given span, classical lifting-line theory has one minimum-induced-drag distribution: an ellipse. It produces uniform downwash across the span; departures from it cost more induced drag for the same lift and 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 useful starting point, not a magic taper ratio for every wing.
One honest note about the number. The lab reports span efficiency e, where 1.0 is the elliptic result for this planar, fixed-span comparison. You will see it read slightly above 1.0, which 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. Read e as a comparison between planforms, not as an absolute.
Also 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.
The other curve — the one that shows 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.
And here is the trap. Taper shrinks the chord towards the tip faster than it sheds load. The load falls; the chord falls faster; 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, because it is the whole reason taper is a decision and not a default. λ = 1 gives a gentle inboard clpeak but misses the elliptic loading. λ = 0.2 is not simply “slipperier”: it also misses the elliptic loading and pushes the cl peak outboard. The useful numbers in the middle are a compromise, not a free lunch.
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 the whole aircraft actually 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 is one fix, and it is not free
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.
That is the actual lesson. Taper, sweep, and twist are not independent style choices; together they set the spanload and local cl distribution. The job is to choose a design point, then check both curves at the lift coefficients your aircraft will actually 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 →
What this post does not predict is 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.