# Perfect Gas Oblique Shock Complete Weak & Strong Polar Branches

> Perfect Gas Oblique Shock Complete Weak & Strong Polar Branches 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 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.

## Facts

- Endpoint: POST https://detect.halowerk.com/v1/F-TD2000-GEO-INDUSTRY-B008/perfect-gas-oblique-shock-complete-weak-strong-polar-branches?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/perfect-gas-oblique-shock-complete-weak-strong-polar-branches-148e8fc8
- Structured record (JSON): https://api.zero.xyz/v1/capabilities/cap__aF0v5bTwmX9QVyd2OXDy

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 perfect-gas-oblique-shock-complete-weak-strong-polar-branches-148e8fc8 -d '<json body>'
```

Example prompt: 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.

## When to prefer this

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.

## Known failure modes

- 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

## How this service works

Enumerate both attached-shock states for a supplied supersonic turning model.

## Output

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.

## Request schema (JSON Schema)

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

## More

- Live health (JSON, refreshed every minute): https://www.zero.xyz/c/perfect-gas-oblique-shock-complete-weak-strong-polar-branches-148e8fc8/health.json
- [Zero catalog index](https://www.zero.xyz/llms.txt)
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