{"uid":"cap__aF0v5bTwmX9QVyd2OXDy","slug":"perfect-gas-oblique-shock-complete-weak-strong-polar-branches-148e8fc8","name":"Perfect Gas Oblique Shock Complete Weak & Strong Polar Branches","description":"Enumerate both attached-shock states for a supplied supersonic turning model.","url":"https://detect.halowerk.com/v1/F-TD2000-GEO-INDUSTRY-B008/perfect-gas-oblique-shock-complete-weak-strong-polar-branches?utm_source=zero.xyz","method":"POST","headers":{},"bodySchema":{"type":"object","properties":{"artifact":{"type":"object","required":["obliqueShock"],"properties":{"obliqueShock":{"type":"object","required":["data","claim"],"properties":{"data":{"type":"object","required":["upstream_mach","gamma","deflection_degrees"],"properties":{"gamma":{"type":"number","maximum":1.67,"minimum":1.05},"upstream_mach":{"type":"number","maximum":20,"minimum":1.01},"deflection_degrees":{"type":"number","maximum":60,"minimum":0}},"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_2-Vgg2_z4zsGys0Si7eOY","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 both the weak and strong attached-shock solutions (complete polar branches) for a perfect-gas oblique shock given upstream Mach number, specific heat ratio, and flow deflection angle.","exampleAgentPrompt":"For a supersonic flow with an upstream Mach number of 2.5, a specific heat ratio (gamma) of 1.4, and a deflection angle of 15 degrees, compute both the weak and strong oblique shock solutions — give me the full polar branch results.","exampleUseCases":[{"title":"Supersonic inlet design shock analysis","prompt":"I'm designing a supersonic inlet with an upstream Mach of 3.0, gamma of 1.4, and a wedge deflection of 20 degrees — can you give me both the weak and strong oblique shock states so I can compare which attached solution is relevant?"},{"title":"Aerodynamics textbook problem verification","prompt":"Verify my homework: for a perfect gas with gamma 1.3 at Mach 1.8 and a 10 degree flow deflection, what are the complete weak and strong shock polar branch solutions for the oblique shock?"},{"title":"CFD boundary condition setup","prompt":"I need both oblique shock solutions — weak and strong — for a Mach 4.0 freestream with gamma 1.67 and a 25 degree turning angle, so I can set up the correct boundary conditions in my CFD simulation."}],"resultDescription":"Returns both the weak-shock and strong-shock enumerated states for the oblique shock polar, including shock wave angles, downstream Mach numbers, pressure/density/temperature ratios, and other post-shock flow properties for the given upstream conditions and deflection angle.","failureModes":["Deflection angle exceeds maximum attached-shock angle for the given Mach number (detached shock condition) — no real solution exists","Upstream Mach number below 1.01 or above 20 — out of range error","Gamma outside supported range [1.05, 1.67] — validation error","Deflection angle is zero or negative — degenerate case may return trivial or error response","Malformed artifact/obliqueShock object — schema validation failure","Payment not included or insufficient — x402 payment required response"],"whenToPreferThis":"Use this endpoint when you need both the weak and strong shock solutions simultaneously (the complete polar), rather than just one branch. Ideal for aerodynamics analysis, CFD pre-processing, supersonic inlet/nozzle design, and educational verification where the full solution space of attached oblique shocks is required. Prefer over manual computation or single-branch solvers when you need verified, closed-form perfect-gas results with both branches in one call.","instructions":null,"reviewSummary":null,"reviewSummaryHighlights":null,"reviewSummaryConcerns":null,"reviewSummaryGeneratedAt":null,"activationCount":0,"lastUsedAt":null,"lastSuccessfullyRanAt":null,"lastHealthCheckAt":"2026-11-04T06:38:26.116Z","isFirstParty":false,"canonicalSlug":"perfect-gas-oblique-shock-complete-weak-strong-polar-branches-148e8fc8"}