{
 "version": "2026-10-20",
 "license": "Dimension sheets: CC BY 4.0. Standard and published-size files: CC BY 4.0. Xem Studio's own designs (files_license = Xem Studio Design License): free to use and sell things from, not to redistribute as files — https://xemstudio.com/license/. Other publishers' files: their own license, linked beside them.",
 "slug": "elliptical-wing",
 "name": "Elliptical wing",
 "kind": "standard",
 "category": "Aircraft design",
 "group": "Wing planforms",
 "year": null,
 "question": "Why is the elliptical wing considered ideal?",
 "tags": [
  "vehicle design",
  "wing planforms",
  "rc design",
  "aerodynamics"
 ],
 "aliases": [
  "elliptical wing",
  "elliptical planform",
  "spitfire wing",
  "elliptical lift distribution",
  "elliptical wing rc",
  "why elliptical wing",
  "oswald efficiency",
  "elliptical wing template",
  "span efficiency factor"
 ],
 "overall_mm": {
  "length": null,
  "width": null,
  "height": null
 },
 "official_cad": false,
 "xem_status": "free-files",
 "les": false,
 "free_files": 1,
 "url": "https://xemstudio.com/objects/elliptical-wing/",
 "sheet_txt": "https://xemstudio.com/objects/elliptical-wing/sheet.txt",
 "sheet": {
  "basis": "Design rules and figures from the cited sources; example geometry by Xem Studio",
  "overall_mm": {
   "length": null,
   "width": null,
   "height": null
  },
  "notes": [
   "An elliptical span loading gives span efficiency e = 1, the minimum induced drag for a given span; non-elliptical loading has e < 1 and more induced drag (TU Delft AE1101; Kitplanes).",
   "The Spitfire is the textbook elliptical wing: root chord 100 in, span 445 in, AR 5.67 and S = 242.71 ft^2 (Leishman, ERAU).",
   "Curved edges are harder to build than a straight taper, which is why a 0.45 taper is often used to approximate elliptical loading (arXiv 1801.02938 citing Torenbeek).",
   "Used on: Supermarine Spitfire.",
   "The file is a reference example built by Xem Studio from the numbers above. Sizes the sources do not fix are illustrative; scale the example to your own vehicle."
  ],
  "table": {
   "columns": [
    "parameter",
    "value or range",
    "source"
   ],
   "rows": [
    [
     "Span efficiency, elliptical loading",
     "e = 1 (minimum induced drag)",
     "TU Delft AE1101"
    ],
    [
     "Induced drag",
     "CDi = CL^2 / (pi AR e)",
     "TU Delft AE1101"
    ],
    [
     "Spitfire root chord / span",
     "100 in / 445 in",
     "ERAU (Leishman)"
    ],
    [
     "Spitfire AR / area",
     "5.67 / 242.71 ft^2",
     "ERAU (Leishman)"
    ],
    [
     "Reference build",
     "span 1000 mm, root 225 mm (Spitfire proportions scaled)",
     "computed"
    ]
   ]
  }
 },
 "sheet_text": "Elliptical wing — dimension sheet\nSource: Xem Studio, https://xemstudio.com/objects/elliptical-wing/  (sheet CC BY 4.0; files Xem Studio Design License, https://xemstudio.com/license/)\nBasis: Design rules and figures from the cited sources; example geometry by Xem Studio\nCatalog version: 2026-10-20\n\nSizes: see table below\n- An elliptical span loading gives span efficiency e = 1, the minimum induced drag for a given span; non-elliptical loading has e < 1 and more induced drag (TU Delft AE1101; Kitplanes).\n- The Spitfire is the textbook elliptical wing: root chord 100 in, span 445 in, AR 5.67 and S = 242.71 ft^2 (Leishman, ERAU).\n- Curved edges are harder to build than a straight taper, which is why a 0.45 taper is often used to approximate elliptical loading (arXiv 1801.02938 citing Torenbeek).\n- Used on: Supermarine Spitfire.\n- The file is a reference example built by Xem Studio from the numbers above. Sizes the sources do not fix are illustrative; scale the example to your own vehicle.\n\nparameter  value or range  source\nSpan efficiency, elliptical loading  e = 1 (minimum induced drag)  TU Delft AE1101\nInduced drag  CDi = CL^2 / (pi AR e)  TU Delft AE1101\nSpitfire root chord / span  100 in / 445 in  ERAU (Leishman)\nSpitfire AR / area  5.67 / 242.71 ft^2  ERAU (Leishman)\nReference build  span 1000 mm, root 225 mm (Spitfire proportions scaled)  computed\n\nFiles elsewhere (not hosted by Xem Studio; license as stated by the publisher):\n- TU Delft OpenCourseWare: AE1101 Introduction to Aerospace Engineering, Aerodynamics 6 — web — Publisher's page; dimensions are facts — https://ocw.tudelft.nl/wp-content/uploads/AE1101-Aero-6.pdf\n- Embry-Riddle (Leishman), Introduction to Aerospace Flight Vehicles: Wing Shapes and Nomenclature — web — Publisher's page; dimensions are facts — https://eaglepubs.erau.edu/introductiontoaerospaceflightvehicles/chapter/wing-shapes-and-nomenclature/\n- Kitplanes (B. Wainfan): Design Process: Planform Effects on Span Loading and Drag (2020) — web — Publisher's page; dimensions are facts — https://www.kitplanes.com/design-process-planform-effects-on-span-loading-and-drag/\n- arXiv 1801.02938 (citing Torenbeek, Synthesis of Subsonic Airplane Design, 1976): Systematic design methodology for a variable pitch quadrotor biplane VTOL UAV — web — Publisher's page; dimensions are facts — https://arxiv.org/pdf/1801.02938\n\nFree files (Xem Studio Design License, Xem Studio; STEP + STL, 1 parts): https://xemstudio.com/files/hardware/elliptical-wing/index.json\nAPI: https://xemstudio.com/api/geometry?object=elliptical-wing\n",
 "sources": [
  {
   "publisher": "TU Delft OpenCourseWare",
   "title": "AE1101 Introduction to Aerospace Engineering, Aerodynamics 6",
   "url": "https://ocw.tudelft.nl/wp-content/uploads/AE1101-Aero-6.pdf",
   "formats": [
    "web"
   ],
   "license": "Publisher's page; dimensions are facts",
   "license_verified": true,
   "hosted": false
  },
  {
   "publisher": "Embry-Riddle (Leishman), Introduction to Aerospace Flight Vehicles",
   "title": "Wing Shapes and Nomenclature",
   "url": "https://eaglepubs.erau.edu/introductiontoaerospaceflightvehicles/chapter/wing-shapes-and-nomenclature/",
   "formats": [
    "web"
   ],
   "license": "Publisher's page; dimensions are facts",
   "license_verified": true,
   "hosted": false
  },
  {
   "publisher": "Kitplanes (B. Wainfan)",
   "title": "Design Process: Planform Effects on Span Loading and Drag (2020)",
   "url": "https://www.kitplanes.com/design-process-planform-effects-on-span-loading-and-drag/",
   "formats": [
    "web"
   ],
   "license": "Publisher's page; dimensions are facts",
   "license_verified": true,
   "hosted": false
  },
  {
   "publisher": "arXiv 1801.02938 (citing Torenbeek, Synthesis of Subsonic Airplane Design, 1976)",
   "title": "Systematic design methodology for a variable pitch quadrotor biplane VTOL UAV",
   "url": "https://arxiv.org/pdf/1801.02938",
   "formats": [
    "web"
   ],
   "license": "Publisher's page; dimensions are facts",
   "license_verified": true,
   "hosted": false
  }
 ],
 "xem": {
  "status": "free-files",
  "sheet_free": true,
  "mesh_price_usd": null,
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  "tolerance_mm": null
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 "related": [
  "rectangular-wing",
  "tapered-wing",
  "swept-wing",
  "forward-swept-wing",
  "delta-wing",
  "cranked-double-delta-wing"
 ],
 "fits": [],
 "dimensions": "exact (nominal, no printing tolerance)",
 "dimension_rule": "All geometry on Xem Studio is exact (nominal, true size) with no printing tolerance. Where a part meets another part, the object lists its mating features (feature, exact size, what it mates with, fit class: press, slide, run, socket, clamp or designed). Apply your process's allowance to those features only; 'designed' gaps are part of the design and stay as drawn.",
 "mating": [],
 "faq": [
  {
   "q": "Is an elliptical planform needed for elliptical lift?",
   "a": "No; taper (about 0.45) or twist can approach it (Torenbeek via arXiv 1801.02938; Kitplanes)."
  }
 ],
 "files_license": {
  "name": "Xem Studio Design License",
  "holder": "Xem Studio",
  "url": "https://xemstudio.com/license/",
  "note": "Xem Studio's own design: free to use, print, modify and sell things made from it; not to be republished or redistributed as files."
 },
 "offers": [
  {
   "file": "elliptical-wing-wing",
   "formats": [
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   "license": "Xem Studio Design License",
   "step": "https://xemstudio.com/files/hardware/elliptical-wing/elliptical-wing-wing.step",
   "stl": "https://xemstudio.com/files/hardware/elliptical-wing/elliptical-wing-wing.stl",
   "note": "elliptical planform: span 1000, root 225, tip 0 mm, LE sweep 0°, dihedral 3°, NACA 2412"
  }
 ],
 "markdown": "https://xemstudio.com/objects/elliptical-wing/index.md"
}