The Foundry Manual
How raw telemetry is forged into meaning
The physics and the maths behind each metric — the intuition, the equations, how we actually compute them from a GPX track, and how to read the numbers. We start with the power calculation.
Power
The mechanical effort behind the speed — comparable across any terrain.
Why power at all?
Speed tells you how fast the track went by; heart rate tells you how hard the engine answered. Both are symptoms. Power — the mechanical work you put out each second — is the cause underneath them, and unlike speed it is comparable across flats, climbs and headwinds. 20 km/h up a 6% hill and 20 km/h on the flat are utterly different efforts; the same wattage on both is the same effort. That is what makes power the honest currency of pacing.
The power balance
To hold a steady speed, the power a skier produces must exactly balance the power dissipated by the resisting forces of the world. Normalising by body mass (so the number is watts per kilogram and needs no scale), that balance is:
p = g·(μ·cosθ + sinθ)·v + ½·ρ·(CdA/m)·v³ + a·vmass-normalised mechanical power, in W/kg
- p
- mechanical power per kilogram (W/kg)
- g
- gravity, 9.81 m/s²
- μ
- ski–snow friction coefficient (the day's glide)
- θ
- slope angle (from the smoothed grade)
- v
- speed (m/s)
- ρ
- air density, ≈1.225 kg/m³
- CdA/m
- drag area per kilogram of body mass
- a
- acceleration (dv/dt)
The four resistances
Every term is a force the skier spends watts to overcome:
- ►Gravity (sinθ·v) — lifting body and gear up the hill. Dominant on climbs; negative on descents (the hill gives the energy back).
- ►Friction (μ·cosθ·v) — ski sliding against snow. Always present, even on the flat — this is why skiing, unlike level running, never costs zero external power.
- ►Air drag (½ρ·(CdA/m)·v³) — grows with the cube of speed, so it only bites at high speed and on descents.
- ►Kinetic (a·v) — the cost of accelerating. Averages to roughly zero over a lap (you finish near the speed you started).
What a skier can't do
A skier cannot produce negative power. On a descent gravity supplies the energy, not the muscles, so wherever the balance comes out negative we read the propulsive power as zero. Air drag also misbehaves at speed: it scales as v³, so a few fast or GPS-glitched points would otherwise blow the estimate up.
Why descents read near zero
Above roughly 9 m/s (≈32 km/h) a skier tucks and coasts rather than propels (Gløersen et al.). We cap the drag/kinetic speed there and taper propulsive power to zero by ~12 m/s — which both matches the physics and tames the v³ spikes. The headline average is time-weighted (work ÷ time), the physically correct mean power, and we smooth the signal before clipping so acceleration noise can't bias it upward.
Watts per kilo, and watts
The estimate is mass-independent, so the primary number is W/kg — directly comparable between athletes. Enter a body mass and we multiply through to absolute watts for the headline cards; the shape of the curve is identical either way.
Calibrating to the day and the athlete
Two terms — the snow friction μ and the drag area CdA — are not measured; they depend on wax, snow and posture. Literature defaults (μ≈0.03, CdA/m≈0.0075) are only a starting point. We refine them in a fallback ladder, using the most trustworthy source available for each run:
From most to least specific:
- ►This run's own climbs — steep climbs are gravity-dominated, so power there is certain regardless of μ/CdA. Heart rate on those climbs anchors the athlete's HR-to-power line, which we carry to the flats to back-solve the day's μ.
- ►The race field — everyone skied the same snow that day, so the per-run calibrations pool into one robust competition-wide μ.
- ►Literature defaults — when nothing better exists.
Conditions belong to the course
Snow friction μ changes with conditions, and drag area CdA depends on posture and the race environment. The readout first calibrates from the run's own climbs; if that evidence is insufficient, it uses robust race-field conditions from the same course and day before returning to literature defaults.
Normalized Power and zones
Normalized Power (the fourth-power mean of the smoothed trace) weights surges more heavily than a plain average, approximating the metabolic cost of a variable effort. It is a cycling concept and only loosely validated for skiing, so we label it experimental. Power zones split time by absolute W/kg bands anchored to field data.
What this is not
This is an estimate from GPS and heart rate, not a reading from a force-measuring pole. It is at its best for tracking trends and comparing terrain, not for claiming a watt is a watt. One honest limit: in an all-out race heart rate can saturate near maximum on every climb and stop tracking power, so a run may fall back to race-field conditions or literature defaults.
Pacing & grade-adjusted speed
Coming soonFlattening the terrain to see whether you faded, surged, or held.
Aerobic decoupling
Coming soonWhen the engine drifts away from the pace — durability, quantified.
Wind
Coming soonSplitting the breeze into head, tail and cross components along the course.
Want the quick one-line definitions instead? See the Metric Guide. For the research behind it all, read the thesis.