The whole argument for this site is that you can check it. That only works if you can find what it was checked against. Every source the sheets rest on is here, with what it actually covers, where it stops being valid, and where to get a copy.
Airfoil data
Sheet 02's twenty-seven sections are the most source-dependent thing on the site, because model-scale section data is scarce and the tables that circulate most freely were measured at Reynolds numbers ten to a hundred times too high. These are the sources that were actually measured where models fly.
Summary of Low-Speed Airfoil Data, Volumes 1, 2 and 5
UIUC Applied Aerodynamics Group · Vol 1 (1995) Selig, Guglielmo, Broeren and Giguère · Vol 2 (1996) Selig, Lyon, Giguère, Ninham and Guglielmo · Vol 5 (2012) Williamson, McGranahan, Broughton, Deters, Brandt and Selig
Wind tunnel measurements of model-scale sections at the Reynolds numbers models actually fly at, from roughly 40,000 to 500,000. This is the single most important source behind Sheet 02 and there is no substitute for it: almost every other airfoil table in circulation was measured an order of magnitude higher up.
Used for: Maximum lift, drag polars and stall character for most of the 27 sections on Sheet 02.
Getting it: Free PDFs from the UIUC Applied Aerodynamics Group at the University of Illinois. Search for “UIUC Summary of Low-Speed Airfoil Data” and the volume number.
Airfoils at Low Speeds (SoarTech 8)
Michael S. Selig, John F. Donovan and David B. Fraser · SoarTech Publications, Virginia Beach, 1989 · 398 pp
The Princeton tests: over sixty sections measured between Reynolds 60,000 and 300,000, and the work that made low-Reynolds model data respectable. Older than the Summary volumes and still cited because it covers sections they do not.
Used for: Cross-checks on the older sections, and the stall notes for several of them.
Getting it: Out of print. A scanned PDF circulates from the UIUC group's own pages.
NACA Report 586 — Airfoil Section Characteristics as Affected by Variations of the Reynolds Number
Eastman N. Jacobs and Albert Sherman · NACA, 1937
The original systematic study of what Reynolds number does to a section, across a related family, in the variable-density tunnel. Ninety years old and still the clearest statement of the effect.
Used for: The scale-effect argument that runs through Sheet 02 and the Reynolds tool: why a table measured at Reynolds 3 million does not describe your model.
Getting it: Free from the NASA Technical Reports Server (NTRS). Search “NACA-TR-586”.
NACA Report 824 — Summary of Airfoil Data
Ira H. Abbott, Albert E. von Doenhoff and Louis S. Stivers Jr. · NACA, 1945
The canonical NACA section catalogue, and the body of work that became Theory of Wing Sections. Measured at Reynolds numbers from 3 to 9 million.
Used for: Section geometry and the high-Reynolds baseline for the NACA four- and five-digit and 6-series rows on Sheet 02.
Its Reynolds numbers are ten to a hundred times a model's. Sheet 02 uses it for shape and for the shape of the curve, never for a number quoted at model scale — that is what the UIUC volumes are for.
Getting it: Free from NTRS. Search “NACA-TR-824”.
SAND80-2114 — Aerodynamic Characteristics of Seven Symmetrical Airfoil Sections Through 180-Degree Angle of Attack
Robert E. Sheldahl and Paul C. Klimas · Sandia National Laboratories, March 1981
Symmetrical sections through the full 360°, produced for vertical-axis wind turbines and useful here because it covers angles and Reynolds numbers aeronautical data does not.
Used for: The symmetrical NACA rows on Sheet 02, and the post-stall behaviour behind their stall notes.
Only four sections were actually measured — NACA 0009, 0012, 0012H and 0015. The 0018, 0021 and 0025, and the extension to arbitrary Reynolds numbers, come from an airfoil property synthesiser code described in the report. Sheet 02 takes figures from the measured four only; its NACA 0018 row comes from Timmer instead, which is a measurement.
Getting it: Free from OSTI and from the UNT Digital Library. Search the report number.
Two-Dimensional Low-Reynolds Number Wind Tunnel Results for Airfoil NACA 0018
W. A. Timmer · Wind Energy Section, Delft University of Technology · Wind Engineering 32(6), 525–537, 2008
A careful two-dimensional measurement of the NACA 0018 from Reynolds 150,000 to 1,000,000, including the laminar separation on the lower surface that decides its behaviour.
Used for: The NACA 0018 row on Sheet 02, whose quoted 1.06 at Reynolds 300,000 rising to 1.11 at 1 million comes from here.
It starts at Reynolds 150,000. Below that the 0018 is not described by this source or, so far as I know, by any other measurement — which is why Sheet 02 does not offer the section below 200,000.
Getting it: Paywalled at the publisher; the author's copy is in the TU Delft repository.
Wind tunnel tests of wings at Reynolds numbers below 70 000
E. V. Laitone · Experiments in Fluids 23, 405–409, 1997
The bottom of the range, where almost nothing else has been measured: rectangular wings down to Reynolds 20,000, comparing a NACA 0012 against thin flat and cambered plates.
Used for: The warning that runs through Sheet 02 and the Reynolds tool about what happens below 50,000.
Getting it: Paywalled at Springer. The abstract alone carries the result that matters: below Reynolds 70,000 a thin plate with 5% circular-arc camber beat every conventional section tested, and the NACA 0012 was badly affected by both Reynolds number and turbulence below 50,000.
Methods
Aircraft Design: A Conceptual Approach
Daniel P. Raymer · AIAA Education Series
The standard conceptual-design text, and the source of the component form factors that turn a skin-friction coefficient into a component drag.
Used for: The form factors in the drag build-up on Sheet 07.
Getting it: In print. Any edition carries the form factor relations.
Boundary-Layer Theory
Hermann Schlichting · McGraw-Hill
The reference for boundary layers, and the source of the turbulent skin-friction relation usually written as Prandtl–Schlichting.
Used for: Turbulent skin friction on Sheet 07 and in the Reynolds tool: Cf = 0.455 / (log₁₀ Re)^2.58. The laminar companion is Blasius, Cf = 1.328 / √Re.
Getting it: In print, and in every aerodynamics library.
The viscosity of gases and molecular force
William Sutherland · Philosophical Magazine, 1893
The temperature dependence of dynamic viscosity, still the relation used for air a century and a third later.
Used for: Viscosity in the shared atmosphere block, which means every Reynolds number on the site.
Getting it: Long out of copyright; the relation is in any fluids text.
The ICAO Standard Atmosphere, and the Magnus form for water vapour
ICAO Doc 7488 / ISO 2533 · the Magnus–Tetens saturation vapour pressure relation
The barometric relation for the standard day, plus the correction for humidity that most calculators skip.
Used for: The whole of the atmosphere block: pressure, temperature, density, density altitude and the speed of sound.
Getting it: The standard atmosphere tables are widely reproduced. The Magnus coefficients used here are the common meteorological set.
14 CFR Part 23 — Airworthiness Standards: Normal Category Airplanes
US Federal Aviation Administration
Not because a model is certified — it is not — but because the gust and speed conventions in it are the ones the whole field reasons with.
Used for: The sharp-edged gust convention on Sheet 10: full gust at Vc and half at Vd, 50 and 25 ft/s. Also the lift-off speed convention Sheet 13 departs from, and says so.
Part 23 was rewritten to performance-based standards at Amendment 23-64, effective 30 August 2017. The numeric gust velocities the sheets quote are from the prescriptive text that preceded it, so a reader who opens today's Part 23 will not find them. They remain the convention in practice and in the accepted means of compliance.
Getting it: Free from the eCFR. The pre-2017 text is archived and easy to find.
NACA TM 948 — A Simple Approximation Method for Obtaining the Spanwise Lift Distribution
O. Schrenk · NACA Technical Memorandum 948, 1940
The approximation that averages an elliptical lift distribution with one shaped like the planform itself. It is not exact and does not pretend to be; it is close enough for sizing a spar and simple enough to do by hand, which is why it has outlasted better methods.
Used for: The spanwise load on Sheet 10, the centroid it puts the lift at, and the root bending moment the spar caps are sized against.
Getting it: NASA's technical reports server. It is a translation of a 1940 Luftwissen paper, and the method is reproduced in most structures texts if the memorandum itself is awkward to get.
Cross-Country Soaring
Helmut Reichmann · Soaring Society of America
The standard treatment of speed-to-fly: how fast to push between thermals, and why the answer depends on the climb you expect next rather than on the glide you are in. The theory is usually attributed to Paul MacCready, whose name the setting still carries.
Used for: Sheet 14's speed to fly. The sheet derives the optimum from its own drag polar and the expected climb rather than reproducing a ring or a published table, so this is where to read the theory properly rather than where a figure came from.
Getting it: In print, and in most gliding club libraries.
Tools worth having
XFOIL and XFLR5
XFOIL: Mark Drela, MIT · XFLR5: an open-source front end to it
A panel method with an integral boundary layer, and the only practical way to get a polar for a section nobody has put in a tunnel at your Reynolds number.
Used for: nothing on this site is computed with it. Sheet 02 recommends it where a section's figures are marked as computed rather than measured, because running it yourself is the honest next step.
A computed polar is not a measurement, and at the Reynolds numbers that matter here the difference is largest. XFOIL's transition model is a correlation, and the laminar separation bubble it is predicting is exactly the thing that is hardest to predict. Treat its numbers the way this site treats its own computed ones.
Getting it: both are free. XFLR5 is the easier start.
What has no source
Some numbers on this site are not from anywhere. They are compiled — assembled from practice, from what people build and fly, and from figures that recur across enough places to be worth using but cannot be traced to one measurement. The site labels every one of them, in those words, next to the number.
Every one, checked against the sheet that carries it:
- Sheet 03 — the centre-of-gravity and tail volume bands your layout is judged against.
- Sheets 04 and 06 — Oswald span efficiency, and motor and controller efficiency from typical hobby hardware. Sheet 06's practice minimums are rules of thumb, and it says so.
- Sheet 05 — the areal densities for covering and structure, from build practice.
- Sheet 07 — the drag-area figures for wheels, legs and the other add-ons, on frontal area.
- Sheet 08 — the blade-quality factor behind the actuator-disc efficiencies, and the figure of merit behind static thrust.
- Sheet 09 — cell voltages and pack energy density, from current cells rather than from yours.
- Sheet 10 — every figure in the materials table.
- Sheet 11 — hinge moment coefficients, the servo ratings, and the tail dynamic-pressure ratio behind the elevator authority.
- Sheet 12 — the fin dynamic-pressure ratio, the ±3° wing-position allowance, and the spiral and Dutch roll bands.
- Sheet 13 — rolling resistance for model wheels, and the 28 km/h hand-launch speed, which the sheet calls a convention rather than a measurement in the box itself.
- Sheet 15 — the minimum wheel diameters and the side-force coefficient for a parked aeroplane.
- Sheet 16 — the usable fraction of a pack, and the default avionics draw: three watts is a receiver, four servos and a small camera, from practice rather than from a measurement of yours.
That is a long list, and publishing it as a list is the point. A site that is honest about which of its numbers are soft is more useful than one that presents everything at equal confidence. If you have a measurement for any of them, it is worth more than what is there now.
How to check the work
The methods themselves — every formula, its source and where it stops being valid
— are set out sheet by sheet in CALCULATIONS.md in the repository.
Each sheet also carries its own scope statement saying what it does not model, and the
nomenclature page says what every symbol and every
sign means.
Sheet 02 marks each pitching moment as measured or computed. Fifteen of the twenty-seven are measured; twelve are computed and say so. That convention is being extended across the site rather than left on one sheet.