# Prandtl Lifting Line Spanwise Fourier Circulation & Induced Drag Solver

> Prandtl Lifting Line Spanwise Fourier Circulation & Induced Drag Solver is a paid API for AI agents from detect.halowerk.com, paid per call via x402, $0.003/call, status unknown (last checked 2026-11-04).

Computes spanwise circulation distribution and induced drag for a linear wing model using Prandtl's lifting-line theory with Fourier series decomposition.

## Facts

- Endpoint: POST https://detect.halowerk.com/v1/F-TD2000-GEO-INDUSTRY-B007/prandtl-lifting-line-spanwise-fourier-circulation-induced-drag?utm_source=zero.xyz
- Price: $0.003/call
- Payment: x402
- Status: unknown
- Last checked: 2026-11-04
- Activations on Zero: 0
- Tags: x402
- Canonical page: https://www.zero.xyz/c/prandtl-lifting-line-spanwise-fourier-circulation-induced-drag-solver-94d58a21
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap_jbAgjQrcF-nWTLveNzlYV

Status and success rate cover calls made through Zero and Zero's own probes. Third-party monitors may report differently.

## How to call it through Zero

Zero handles the 402 payment challenge and records the run. With the Zero CLI installed (`npm i -g @zeroxyz/cli`):

```sh
zero fetch --capability prandtl-lifting-line-spanwise-fourier-circulation-induced-drag-solver-94d58a21 -d '<json body>'
```

Example prompt: 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.

## When to prefer this

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.

## Known failure modes

- 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

## How this service works

Resolve spanwise circulation and induced drag in a supplied linear wing model.

## Output

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.

## Request schema (JSON Schema)

```json
{
 "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
  }
 }
}
```

## More

- Live health (JSON, refreshed every minute): https://www.zero.xyz/c/prandtl-lifting-line-spanwise-fourier-circulation-induced-drag-solver-94d58a21/health.json
- [Zero catalog index](https://www.zero.xyz/llms.txt)
- [Other services from detect.halowerk.com](https://www.zero.xyz/host/detect.halowerk.com/llms.txt)