Models & assumptions.

Check the units and limits below before planning. The field guides work through examples with each model.

Loaded walking

Pandolf estimates gross metabolic power (watts). W: body mass kg. L: carried mass kg. V: speed m/s. G: grade percent, not degrees. η: terrain multiplier.

M = 1.5W + 2(W+L)(L/W)²
  + η(W+L)(1.5V² + 0.35VG)
kcal = M × seconds / 4184

The ±25% band is a sensitivity illustration, not a confidence interval. Research reports substantial underprediction in some load-carriage conditions. Software bounds: adult mass 35–180 kg, pack up to 50% of mass or 40 kg, speed 0.5–6 km/h, uphill grade 0–15%, time up to 12 h. These bounds do not assert physiological validation. Downhill, heat, altitude, fitness, daily food and fluid requirements are excluded.

A-frame geometry

For width W across the ridge, length L along it and height h: floor width = 2√((W/2)²−h²); triangular volume = floor width × h × L / 2; roof slope = asin(2h/W). Height must be below W/2.

Line estimate: two ridge guys of √(h²+r²), four 1.5 m corner lines, plus 2 m total tying allowance. Real anchors and knots change it. Wind is a plan view, with no load, stability, thermal or stake-holding model. Sun orientation is a separate tool.

Rope and knots

Hypothetical remaining strength = entered breaking strength × assumed retained fraction. No knot percentage, safety factor or working-load limit is prescribed. Diagrams are simplified path rehearsals; verify practical tying with an instructor.

Sun and daylight

NOAA fractional-year equations estimate declination and equation of time, including leap years. UTC inputs; east-positive longitude; azimuth clockwise from true north. Unobstructed sunrise/sunset use 90.833° zenith. The obstruction slider subtracts a uniform angle, a rough terrain scenario. Daily events use noon terms. Polar no-crossing states are reported explicitly. Civil dawn and dusk use a 96° zenith (sun centre 6° below the true horizon); the obstruction slider does not move them.

This approximation differs from detailed ephemerides. Atmosphere, clouds and real terrain affect observations. Phone headings may be magnetic or uncalibrated, so manual true bearings remain primary.

Water decisions

Rules separate suspected dissolved contamination from germs and preserve an unknown state. They do not detect contaminants or certify water. Follow current advisories and actual product instructions.

Power budget

Label Wh = mAh ÷ 1000 × cell volts
Usable Wh = label Wh × assumed efficiency
Demand Wh = watts × hours/day × days
Solar Wh = panel watts × sun-hours/day
           × days × efficiency

The same simplified end-to-end efficiency applies to battery delivery and the solar path. It is not a weather forecast or charging simulation. Verify battery chemistry, label voltage, temperature, age and reserve needs.

Trail time

Naismith’s rule (1892): one hour per 5 km of map distance plus one hour per 600 m of ascent. The tool exposes both rates: flat pace in km/h and a climb allowance in minutes per 100 m (10 by default). Langmuir’s descent corrections are optional: subtract 10 minutes per 300 m of descent for gentle 5–12° slopes, add 10 minutes per 300 m for slopes steeper than 12°.

moving min = distance ÷ pace × 60 + ascent ÷ 100 × climb ± descent correction
total min  = moving × (1 + rest per hour ÷ 60)
equivalent flat km = distance + pace × ascent × climb ÷ 6000

The gentle correction is refused when the descent averages steeper than 12° over the whole distance. Terrain, load, weather, navigation, group pace and fatigue are not modelled.

Map slope

ground m = map mm × scale ÷ 1000
rise m   = contour interval × intervals crossed
grade %  = rise ÷ ground × 100;  angle = atan(rise ÷ ground)
speed    = 6 × e^(−3.5 × |S + 0.05|) km/h   (S = ±rise ÷ ground)

Tobler’s hiking function (1993) gives walking speed over horizontal distance; downhill legs use a negative S. Off-path legs multiply the speed by 0.6. A map gradient is an average over the measured leg: short steps can be far steeper, and a 1 mm measuring error is 25 m on a 1:25,000 map.

Feels like

wind chill = 13.12 + 0.6215T − 11.37V^0.16 + 0.3965T·V^0.16

T in °C, V in km/h at the standard 10 m height; applied only at T ≤ 10 °C and V above 4.8 km/h. Risk levels and freezing times are Environment and Climate Change Canada’s bands. The heat index follows the NWS procedure in °F: the simple formula first, then the Rothfusz regression with the low- and high-humidity adjustments when the result reaches 80 °F; categories are the NWS caution bands. Neither index accounts for sun, clothing, exertion or acclimatisation.

Altitude

pressure hPa = 1013.25 × (1 − 2.25577×10⁻⁵ × h)^5.25588
log10(P mmHg) = 8.07131 − 1730.63 ÷ (233.426 + T °C)
temperature  = trailhead °C − lapse × (elevation − trailhead) ÷ 1000

Pressure follows the International Standard Atmosphere in the troposphere; real pressure moves several hectopascals with the weather. The Antoine constants used are tabulated for −20 to 100 °C. Lapse rates are chosen assumptions: 6.5 °C per km (standard atmosphere), 9.8 (dry air) or about 5 (saturated air). Inversions and local weather break them. Boil times follow CDC: 1 minute, or 3 minutes above 1,981 m (6,500 ft).

Pack ledger

Base weight is the sum of carried items excluding consumables (food, water, fuel) and worn items. Total pack weight adds consumables, taking 1 litre of water as 1 kg; skin-out adds worn items. The pack share is total pack mass divided by body mass. The ultralight (under 4.5 kg) and lightweight (under 9 kg) labels are community conventions, not standards.

Food carry

g per person per day = kcal ÷ (kcal per 100 g) × 100 × (1 + packaging %)

The daily energy target is your input; the tool does not estimate anyone’s needs. General Atwater factors (FAO) explain energy density: about 9 kcal per gram of fat and 4 kcal per gram of protein or carbohydrate. Water content lowers density.

Verification

Arithmetic fixtures, invalid inputs, high latitudes, leap years and contamination branches are checked in release tests, along with published reference points: the NWS wind chill and heat index charts, the CDC 1,981 m boiling boundary and a 100 °C sea-level boiling point. No human field validation or equipment certification is claimed. Sources & release notes.