Sources
Where our numbers come from
SmartYardage's flight model has one rule: no number without a source. Every physical constant, every aerodynamic coefficient, and every validation target in the model traces to a published reference, and anything we assume rather than source is labeled that way in the code itself. This page is the ledger.
Validation data
The model is validated by feeding published tour-average launch conditions through our physics and checking the predicted carry, peak height, and descent angle against what Trackman, the tour's reference instrument, actually measured.
- Trackman: Introducing Updated Tour Averages (May 2, 2024)
The primary validation targets: PGA Tour average ball speed, launch angle, spin rate, carry, max height, and land angle per club, from the 2023 season (40+ events, 200+ players).
trackman.com
- Trackman: Tour Averages media kit
Trackman's own downloadable renderings of the same table, in yards and meters, used to cross-check every transcribed value.
trackman.media
- Trackman Help Center: Carry (Tee to Green)
Trackman's definition of carry: distance to a landing point at the same height the ball was struck from (“Carry Flat”). This defines where our simulation stops.
support.trackmangolf.com
- Trackman: What is Carry?
Corroborates the carry definition above.
trackman.com
- Golf Monthly: How far PGA Tour players hit every club
Independent reproduction of the Trackman table, used to verify our transcription.
golfmonthly.com
- Golf Monthly: Average spin rate of a PGA Tour pro with every club
Independent reproduction of the spin column.
golfmonthly.com
- GolfGaim: How far PGA Tour players hit every club
Second independent reproduction used in cross-checking.
golfgaim.com
- Golf.com: How far PGA and LPGA Tour players hit it with every club
Reproduction of the earlier (pre-2024) vintage of the Trackman table, used to date table versions so we never mix numbers across vintages.
golf.com
- Trackman: Driver Fitting Chart (CARRY Optimizer)
Matched single-shot launch conditions and carries across a wide speed range, used as a second validation set because each row is one coherent trajectory rather than a column average. Honest caveat: these values come from Trackman's own trajectory model, so agreement here is model-to-model, not model-to-radar.
trackman chart PDF (2010)
Aerodynamics
Golf balls are the most wind-tunnel-studied sphere in sport. Our drag and lift coefficients come from published measurements, not tuned guesses.
- Ferguson, McNally & McPhee (2022): Predicting the Flight of a Golf Ball
The Engineering of Sport 14 (ISEA 2022), DOI 10.5703/1288284317493. The primary drag and lift coefficients in our flight model, fitted to over a thousand tracked shots with modern tour balls.
docs.lib.purdue.edu
- US Patent 7,887,439 B2 (Acushnet/Titleist): ball aerodynamic characteristics
Table 10 publishes measured drag and lift for a real tour ball across spin ratios. We use it as an independent cross-check on the primary coefficients; the two agree closely across the driver range.
patents.google.com
- Smits & Smith (1994): A new aerodynamic model of a golf ball in flight
Science and Golf II, pp. 340–347. The source of our spin-decay rate: how fast backspin bleeds off during flight, which matters over a six-second driver flight.
taylorfrancis.com
- Bearman & Harvey (1976): Golf Ball Aerodynamics
The Aeronautical Quarterly, Vol. 27, pp. 112–122. The foundational wind-tunnel study of spinning golf balls. We read it in full; it publishes its results as figures rather than numeric tables, so in keeping with our no-transcription-guessing rule its values are not in the model. Listed because it anchors the field.
semanticscholar.org
Standards and constants
The fixed physical facts the whole measurement rests on.
- R&A / USGA: Golf ball weight and size test protocol
The conformance limits every ball is built to: maximum mass 45.93 g (1.620 oz), minimum diameter 42.67 mm (1.680 in). These are the ball constants in our physics.
usga.org (PDF)
- ISO/IEC 7810: Identification cards (ID-1 format)
The standard that makes every credit-card-size card exactly 85.60 × 53.98 mm, which is why a card in frame can calibrate real-world scale.
wikipedia.org
- International Standard Atmosphere (ICAO)
The barometric model and reference constants (sea-level pressure 101,325 Pa, 15 °C, lapse rate 6.5 K/km) we use to compute air density from altitude and temperature.
wikipedia.org
Honest footnotes
- Trackman's tour averages are as-played across many venues and conditions; Trackman does not normalize them for altitude or weather. Where our validation must assume an atmosphere, it assumes the standard one and says so.
- The wind-tunnel coefficient data above covers a measured range of spin ratios; some real shots (especially wedges) fly partly outside it. Where the model extrapolates beyond measured data, the code marks it, and affected results carry a caveat.
- Model validation is in progress. When it's done, we'll publish the results on this site: the per-club errors, not just a pass/fail.
Why we publish this
A measurement tool that won't show its work is asking for faith, not trust. If you find an error in our sources or our physics, we genuinely want to hear about it: support@smartyardage.com
See how the measurement works