{"uid":"cap_jbAgjQrcF-nWTLveNzlYV","slug":"prandtl-lifting-line-spanwise-fourier-circulation-induced-drag-solver-94d58a21","name":"Prandtl Lifting Line Spanwise Fourier Circulation & Induced Drag Solver","description":"Resolve spanwise circulation and induced drag in a supplied linear wing model.","url":"https://detect.halowerk.com/v1/F-TD2000-GEO-INDUSTRY-B007/prandtl-lifting-line-spanwise-fourier-circulation-induced-drag?utm_source=zero.xyz","method":"POST","headers":{},"bodySchema":{"type":"object","properties":{"artifact":{"type":"object","required":["liftingLine"],"properties":{"liftingLine":{"type":"object","required":["data","claim"],"properties":{"data":{"type":"object","required":["span","reference_area","speed","density","stations"],"properties":{"span":{"type":"number","maximum":100,"minimum":0.1},"speed":{"type":"number","maximum":100,"minimum":1},"density":{"type":"number","maximum":10,"minimum":0.1},"stations":{"type":"array","items":{"type":"object","required":["chord","angle_radians","zero_lift_radians","lift_slope_per_radian"],"properties":{"chord":{"type":"number","maximum":100,"minimum":0.001},"angle_radians":{"type":"number","maximum":0.2,"minimum":-0.2},"zero_lift_radians":{"type":"number","maximum":0.2,"minimum":-0.2},"lift_slope_per_radian":{"type":"number","maximum":10,"minimum":0.1}},"additionalProperties":false},"maxItems":16,"minItems":4},"reference_area":{"type":"number","maximum":1000,"minimum":0.01}},"additionalProperties":false},"claim":{}},"additionalProperties":false}},"additionalProperties":false}}},"responseSchema":null,"example":null,"exampleRequest":null,"tags":["x402"],"displayCostAmount":"0.003","displayCostAsset":"USDC","priceDynamic":false,"priceHint":null,"priceStatus":"priced","priceSource":"probe","requiresHandshake":false,"reviewCount":0,"rating":{"score":"0.00","successRate":"0.00","reviews":0,"stars":null,"state":"unrated"},"availabilityStatus":"unknown","priceObserved":null,"sessionDeposit":null,"pricing":{"kind":"static","summary":"$0.003/call","primary":{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.003","per":"call","confidence":"exact"},"accepted":[{"kind":"static","protocol":"x402","network":"base","amountUsd":"0.003","per":"call","confidence":"exact"}]},"paymentMethods":[{"uid":"pm_SRTy1KWyb7uope5JShNEM","protocol":"x402","methodType":"crypto","chain":"base","mode":"charge","costAmount":"0.003","costPer":"request","priority":0,"asset":"0x833589fCD6eDb6E08f4c7C32D4f71b54bdA02913","unit":"request","depositMicros":null,"planRef":null}],"brandName":null,"brandSlug":null,"brandBaseUrl":null,"brandDocsUrl":null,"whatItDoes":"Computes spanwise circulation distribution and induced drag for a linear wing model using Prandtl's lifting-line theory with Fourier series decomposition.","exampleAgentPrompt":"I need to solve the spanwise circulation and induced drag for a straight wing with a 10-meter span, 15 square meters of reference area, flying at 30 m/s in air density 1.225 kg/m³ — I have 8 spanwise stations each with chord 1.2 m, angle of attack 0.08 rad, zero-lift angle -0.02 rad, and a lift slope of 5.9 per radian.","exampleUseCases":[{"title":"Induced drag analysis for glider wing","prompt":"Can you compute the induced drag and spanwise circulation for my glider wing? It has a 15-meter span, 10.5 square meters of reference area, flying at 25 m/s in standard sea-level air density of 1.225 kg/m³. I have 6 spanwise stations all with chord 0.7 m, angle of attack 0.06 rad, zero-lift angle -0.015 rad, and a 2π lift slope of 6.28 per radian."},{"title":"Tapered wing aerodynamic performance check","prompt":"Run a Prandtl lifting line analysis on my tapered wing design — 8-meter span, 9 square meters reference area, speed 40 m/s, density 1.2 kg/m³. I have 4 stations with chords 1.4, 1.1, 0.8, 0.5 meters respectively, all at 0.1 rad angle of attack, zero-lift at -0.03 rad, and lift slope 5.73 per radian."},{"title":"UAV wing spanwise load distribution","prompt":"I'm designing a UAV and need to verify the spanwise circulation and induced drag for my wing — 3-meter span, 0.6 square meters reference area, cruising at 20 m/s at a density of 1.1 kg/m³. Use 8 stations each with chord 0.2 m, angle of attack 0.05 rad, zero-lift angle 0.0 rad, and lift slope 5.5 per radian."}],"resultDescription":"Returns the resolved spanwise circulation distribution across the wing stations and the computed induced drag, derived from the Fourier series coefficients of Prandtl's lifting-line equation. Output typically includes per-station circulation values and an overall induced drag coefficient or force.","failureModes":["Fewer than 4 or more than 16 spanwise stations provided — schema validation error","Span, speed, density, chord, or angle values outside allowed numeric ranges — rejected with validation error","Degenerate wing geometry (e.g. zero or near-zero chord at multiple stations) causing numerical instability","Missing required fields in any station object — schema validation error","Claim field missing or malformed — authentication/authorization failure","Network timeout if compute load is high"],"whenToPreferThis":"Use this endpoint when you need a fast, analytically grounded computation of spanwise circulation and induced drag for a linear, incompressible wing model using classical Prandtl lifting-line theory with Fourier decomposition. Prefer this over CFD-based approaches when you have a discretized spanwise wing description (4–16 stations) and need a quick, physics-based aerodynamic estimate without full Navier-Stokes simulation overhead. Best suited for conceptual and preliminary wing design stages.","instructions":null,"reviewSummary":null,"reviewSummaryHighlights":null,"reviewSummaryConcerns":null,"reviewSummaryGeneratedAt":null,"activationCount":0,"lastUsedAt":null,"lastSuccessfullyRanAt":null,"lastHealthCheckAt":"2026-11-04T06:41:12.004Z","isFirstParty":false,"canonicalSlug":"prandtl-lifting-line-spanwise-fourier-circulation-induced-drag-solver-94d58a21"}