{
  "schema": "authored-scalar-cutback/v1",
  "scope": "Centered90degree nozzle ID-to-parentOD scalar contact; idealstraightcircularheader anddepictedcenteredLRquarter-circle elbow. Not a fullprofile/template,reinforcement,bevel orweldqualification.",
  "straight": {
    "expression": "Ch=sqrt((Dh/2)^2−(dn/2)^2)",
    "quantities": {
      "Dh": "Header outside diameter, length",
      "dn": "Nozzle inside diameter, length",
      "Ch": "Positive upper bore-edge contact height from header center, length"
    },
    "conditions": "Consistentunits/circularparent/centered90degreeID-to-ODcontact, radicand≥0; actualprofile/oval/offcenter/angle notsupplied",
    "selected_historical_dimensions_in": {
      "header_NPS": "6",
      "header_OD": 6.625,
      "nozzle_NPS": "2",
      "nozzle_OD": 2.375,
      "standard_wall": 0.154,
      "standard_ID": 2.067,
      "extra_strong_wall": 0.218,
      "extra_strong_ID": 1.939
    },
    "independent_geometry": {
      "standard_radicand_in2": 9.904534,
      "standard_Ch_in": 3.147146961932347,
      "heavier_radicand_in2": 10.032726,
      "heavier_Ch_in": 3.167447868552851
    },
    "selected_raw_lookup": {
      "units": "inches",
      "axes": "Header nominal designation is column; nozzle nominal designation is row",
      "entries": [
        {
          "nozzle": "2",
          "header": "6",
          "standard_weight": "3-1/8",
          "extra_heavy": "3-3/16",
          "state": "LITERAL_VALUE"
        },
        {
          "nozzle": "2",
          "header": "2",
          "standard_weight": "0",
          "extra_heavy": "0",
          "state": "LITERAL_ZERO",
          "qualification": "Notproof ofzeroactualcirclecutback; unexplainedphysical/table convention remains"
        },
        {
          "nozzle": "3",
          "header": "2",
          "standard_weight": "",
          "extra_heavy": "",
          "state": "UNPROVIDED",
          "qualification": "Blanknotzero/notinferredfabricationpermission"
        }
      ],
      "rounding": "Selectedlookup versuscircle results distinct; no universalroundinglaw orallcellformulaidentity claimed"
    },
    "raw_zero_counterexample": {
      "header_OD_in": 2.375,
      "nozzle_ID_in": 2.067,
      "circle_Ch_in": 0.5848367293527311,
      "raw_lookup": "0",
      "disposition": "Resolveactualdetail, do notreplaceeitherbasis silently"
    },
    "blank_counterexample": {
      "header_OD_in": 2.375,
      "nozzle_ID_in": 3.068,
      "radicand_in2": -0.9429997500000002,
      "disposition": "Norealintersectioninthismodel; blank remainsunprovided, notgeneraloutletprohibition"
    },
    "datums": {
      "header_center_in": [
        0,
        0
      ],
      "positive_nozzle_axis": "Outward/upward fromheadercenter",
      "bore_edge_contacts_in": [
        [
          -1.0335,
          3.147146961932347
        ],
        [
          1.0335,
          3.147146961932347
        ]
      ]
    }
  },
  "elbow": {
    "expressions": [
      "Z=R+De/2",
      "S=dn/2",
      "Y^2=Z^2−(R+S)^2",
      "X=R−Y"
    ],
    "quantities": {
      "R": "Actualcenterlinebendradius, length",
      "De": "Elbowoutsidediameter atbend, length",
      "dn": "Nozzleinside diameter, length",
      "Z": "Outsidebendcircleradius, length",
      "S": "Nozzleborehalfwidth, length",
      "Y": "Positivehorizontal distance fromcurvaturecentertoloweredgecontact, length",
      "X": "Signedhorizontal contactcoordinatefromvirtualtangentintersection, positive towardhorizontalend, length"
    },
    "datums": {
      "V_in": [
        0,
        0
      ],
      "O_in": [
        9.0,
        9.0
      ],
      "lower_ID_contact_A_in": [
        1.8637170739943327,
        -1.0335
      ],
      "upper_ID_contact_in": [
        -0.3878929478344606,
        1.0335
      ],
      "tangent_end_center_in": [
        9.0,
        0
      ]
    },
    "worked_geometry": {
      "R_in": 9.0,
      "De_in": 6.625,
      "dn_in": 2.067,
      "Z_in": 12.3125,
      "S_in": 1.0335,
      "radicand_in2": 50.926534000000004,
      "Y_positive_in": 7.136282926005667,
      "X_signed_in": 1.8637170739943327
    },
    "raw_selected_standard_weight_lookup": {
      "nozzle_NPS": "2",
      "elbow_NPS": "6",
      "value": "1-7/8",
      "units": "inches",
      "qualification": "Separatehistorical lookup; R9 teachinginput notassertedforallactualLRell"
    },
    "eligibility": "PositiveY branch fordepictedleftcirclepoint; radicand/signX/actualquarterarc/bothboreedge andnozzlewall/preparation/tangents needverification, notrealrootalone",
    "boundary_cases": [
      {
        "R_in": 0.75,
        "De_in": 0.84,
        "dn_in": 0.1,
        "Z_in": 1.17,
        "S_in": 0.05,
        "radicand_in2": 0.7288999999999997,
        "Y_positive_in": 0.8537564055396596,
        "X_signed_in": -0.10375640553965959,
        "disposition": "Realroot withnegativeX; opposite sideofV frompositiveXlayout; do nottakeabsolutevalue"
      },
      {
        "R_in": 9,
        "De_in": 6.625,
        "dn_in": 6.625,
        "Z_in": 12.3125,
        "S_in": 3.3125,
        "radicand_in2": 0.0,
        "Y_positive_in": 0.0,
        "X_signed_in": 9.0,
        "disposition": "Yzero tangent-enddegeneracy, notqualifiedattachment"
      },
      {
        "R_in": 9,
        "De_in": 6.625,
        "dn_in": 7,
        "Z_in": 12.3125,
        "S_in": 3.5,
        "radicand_in2": -4.65234375,
        "Y_positive_in": null,
        "X_signed_in": null,
        "disposition": "Negative radicand, no realcontact"
      }
    ]
  },
  "length_chain": {
    "hypothetical_inputs_in": {
      "H": 24.0,
      "flange_face_to_weld_end_af": 2.0,
      "flange_to_nozzle_gap_gf": 0.125
    },
    "straight": {
      "expression": "Lref=H−af−gf−Ch",
      "standard_geometry_Lref_in": 18.727853038067654,
      "heavier_geometry_Lref_in": 18.707552131447148,
      "standard_lookup_Lref_in": 18.75,
      "extra_heavy_lookup_Lref_in": 18.6875,
      "axial_coordinates_in": {
        "header_center": 0,
        "standard_geometry_contact": 3.147146961932347,
        "terminal_flange_face": 24,
        "flange_welding_end": 22,
        "nozzle_butt_end_after_gap": 21.875
      }
    },
    "elbow": {
      "terminal_coordinate_in": [
        -24,
        0
      ],
      "expression": "Lref=H+X−af−gf",
      "geometry_Lref_in": 23.738717073994334,
      "lookup_Lref_in": 23.75,
      "wrong_subtraction_Lref_in": 20.011282926005666,
      "axial_coordinates_in": {
        "terminal_flange_face": -24,
        "flange_welding_end": -22,
        "nozzle_butt_end_after_gap": -21.875,
        "virtual_intersection": 0,
        "geometry_contact": 1.8637170739943327
      }
    },
    "length_definition": "Nozzle buttend todefinedbore-edgeintersection; fullwallblank/profile/preparation/trim convention notautomaticallysupplied; nofive-decimal shopprecisionclaim"
  },
  "figures": {
    "straight": {
      "svg": "c17-straight-cutback.svg",
      "geometry_scale_px_per_in": 42.264150943396224,
      "axial_chain_scale_px_per_in": 30,
      "separate_panel_scale": true
    },
    "elbow": {
      "svg": "c17-elbow-cutback.svg",
      "geometry_scale_px_per_in": 40,
      "axial_chain_scale_px_per_in": 25,
      "separate_panel_scale": true
    }
  }
}