Hiking: estimated time, elevation and calories with your pack

The principle

When hiking, distance doesn't say much: 10 km on the flat and 10 km with 800 m of climbing have nothing in common. Azetta therefore takes elevation into account everywhere: to estimate how long a trail will take before you set off, to measure how much you climbed, and to calculate what you burned, pack included.

The Azetta method

Estimated time for a trail

Azetta uses Werner Munter's effort-kilometre method, used by the Swiss Alpine Club: 100 m of climbing weighs as much as one extra kilometre on the flat, as does 150 m of steep descent (grades of 20% or more). A hiker covers about 4 effort-kilometres per hour, breaks not included.

Trail elevation comes from a terrain model (SRTM data, 90 m resolution), with a point every 25 m (further apart on very long trails, 1000 points at most) and a 5 m threshold. The difficulty shown is the Swiss Alpine Club's T1 to T6 scale, read from the trail's OpenStreetMap data (the hardest section wins; with no information, no grade is shown).

The elevation you did

Without a barometer, GPS altitude wanders and spikes by 20 m or more. Each altitude goes through three filters:

1. a rolling median over 5 values, which removes isolated spikes;
2. an exponential moving average with a weight of 0.3, which smooths the rest;
3. a 5 m threshold (hysteresis) before counting a climb or a descent.

Calories

The ACSM walking equation gives oxygen consumption according to speed S (m/min) and grade G:

Summed over the whole hike, it becomes:

Descents are counted as flat (the equation is not valid for negative grades). The weight of the pack is added to your weight: for the loads a hiker carries, one kilo carried costs roughly as much as one kilo of body weight. One litre of oxygen is worth about 5 kcal.

Auto-pause

With no new metre covered for 30 s, the timer pauses and those 30 s are removed from moving time.

Why this choice

• The effort-kilometre is simple, well known to alpine hikers, and takes into account both climbing and steep descent.
• The ACSM equation directly links speed, grade and expenditure, and climbing weighs heavily in it, as it does on the ground.
• Adding the pack to body weight follows the measurements by Pandolf and colleagues on loaded walking.
• The combination of median + average + threshold is robust to the typical flaws of GPS altitude.

Limits

• The estimated time counts neither breaks, nor terrain (scree, snow), nor your fitness: it is a planning guide.
• The 90 m terrain model smooths out small bumps: actual elevation gain may be slightly higher.
• The ACSM equation was established on a treadmill; on an uneven trail, actual expenditure is often higher.

References

1. American College of Sports Medicine. ACSM's Guidelines for Exercise Testing and Prescription, 11th edition. Wolters Kluwer, 2021 (chapter 6, metabolic equations).
2. Pandolf KB, Givoni B, Goldman RF. Predicting energy expenditure with loads while standing or walking very slowly. Journal of Applied Physiology, 1977;43(4):577-581.
3. Swiss Alpine Club (SAC). Hiking difficulty scale T1 to T6.