Most route planners give you one number for pace and apply it to the whole track. You know from experience that's nonsense. A 4 km/h average means nothing when the day is a 600 m climb out of a valley followed by a knee-punishing descent on scree. Your cadence on a 25% pitch is not your cadence on the flat, and no single multiplier fixes that.
The Analysis tab works differently. It breaks your route into gradient bands, applies a different cadence and metabolic cost to each, and rebuilds your time and calorie estimate from the segments up. This post covers the research that underpins that approach, exactly how the app turns it into a distance-and-time estimate, and how pack weight feeds into the result.
Train hard. Fuel right. Pack smart. Go further.
The Research: Speed and Energy Are Functions of Gradient
Two bodies of work sit behind the model. Both make the same point from different directions: on real terrain, gradient is the dominant variable, and it does not act symmetrically.
Tobler: Speed Decays Exponentially With Slope
Waldo Tobler's hiking function is the standard for predicting walking speed from terrain slope [1]. It is an exponential relationship: speed falls off sharply as the ground steepens, in either direction.
W = 6 · e^(−3.5 · |S + 0.05|)
where W is speed in km/h and S is slope as a ratio (rise over run). Three things matter for route planning:
- On the flat, the function gives 5 km/h. That's the anchor most hikers intuitively recognise as a fit walker's unloaded pace.
- Speed peaks at roughly 6 km/h on a gentle −5% downhill, not on the flat. A slight descent is the fastest ground you'll cover.
- It's asymmetric. Past that gentle-descent sweet spot, both climbing and steep descending cost you speed, but the curve is not a mirror image. Moderate downhill helps; steep downhill hurts almost as much as climbing.
The practical takeaway is that a steep section eats time out of all proportion to its distance. A 1 km segment at 20% can take longer than 3 km on the flat. Averaging hides this. Banding exposes it.
Minetti: Energy Cost Follows a Different Curve
Alberto Minetti's work on the energy cost of graded walking measured how many joules per kilogram per metre it takes to move across slopes from −45% to +45% [2]. The shape of that curve is what justifies treating calories and time as two separate calculations rather than one.
- Energy cost minimises at about −10% gradient (≈0.81 J·kg⁻¹·m⁻¹): a moderate descent is the most economical ground, where gravity does useful work for you.
- It climbs steeply uphill, reaching ≈17.3 J·kg⁻¹·m⁻¹ at +45%, more than ten times the cost of that optimal descent.
- Below about −10% the cost rises again: on steep descent your muscles burn energy braking, eccentrically loading every step.
- For sustained climbing, the most efficient path gradient sits around 20–30%, steeper than most hikers expect, which is why well-built mountain trails switchback at roughly that pitch rather than going gently or going straight up.
The headline: your fastest gradient (Tobler's −5%) and your cheapest gradient (Minetti's −10%) are not the same, and neither is symmetric about flat. Speed and energy need to be modelled independently. That is precisely what the app does.
How the App Turns This Into a Distance and Time Estimate
The Analysis tab doesn't run Tobler's equation point by point. It uses a banded model built on the same principles: cadence and metabolic cost are assigned per gradient band, and your personal stride length converts cadence into real speed. Here's the pipeline.
Step 1: Segment and Classify the Track
The app walks your route point to point. For each consecutive pair it computes:
- Horizontal distance using the haversine formula (great-circle distance between the two lat/long points).
- Gradient, as the elevation change over that horizontal distance, expressed as a percentage.
- Direction, ascent or descent, from the sign of the elevation change.
Segments shorter than 0.1 m are dropped as GPS noise. Every valid segment is then filed into one of sixteen bands: eight ascent bands and eight descent bands, in 5% steps from 0% up to 35%+.
Step 2: Apply Cadence Per Band
Each band carries a cadence value in steps per minute, drawn from the research and tuned for hiking rather than lab treadmill walking. Cadence drops as the ground steepens, and the ascent and descent tables differ because climbing and descending don't load you the same way.
| Gradient | Ascent cadence | Descent cadence |
|---|---|---|
| 0–5% | 115 | 115 |
| 5–10% | 100 | 105 |
| 10–15% | 90 | 95 |
| 15–20% | 80 | 85 |
| 20–25% | 70 | 80 |
| 25–30% | 60 | 75 |
| 30–35% | 55 | 70 |
| 35%+ | 50 | 60 |
Two things to note. Descent cadence stays higher than ascent at every matching band: you keep your feet moving downhill even as each step does less climbing work. And the steep-descent bands don't collapse as far as the steep-ascent bands, which mirrors Tobler's asymmetry: a 30% descent still moves you along faster than a 30% climb.
Step 3: Convert Cadence to Speed With Your Stride
Cadence alone isn't speed. The app multiplies it by your stride length, taken from your profile measurements, to get a real pace for each band:
speed (km/h) = (stride_cm ÷ 100) × cadence × 60 ÷ 1000
So a 75 cm stride at the flat-ground cadence of 115 steps/min gives 0.75 × 115 × 60 ÷ 1000 ≈ 5.2 km/h, which lands almost exactly on Tobler's flat-ground 5 km/h and confirms the band table is calibrated sensibly. A longer stride scales every band up; a shorter stride scales everything down. This is why setting your stride accurately in your profile matters more than any other single input.
Step 4: Time Per Band, Then Sum
For each band the app already knows the total distance you'll cover in it (accumulated in Step 1) and the speed for it (Step 3). Time is simply:
time = distance ÷ speed
It sums the per-band times to give your total estimated hiking time, and sums the per-band distances for total route distance. Because steep bands carry low speeds, a route with lots of climbing automatically produces a longer estimate, without you applying any fudge factor. The gradient breakdown you see in the Analysis tab is these same bands, showing how your distance is distributed across slope steepness.
This is the core insight: distance is geometry, but time is distance reweighted by gradient. The app never reports a flat average; it reports the sum of sixteen separate pace calculations.
How Pack Weight Adjusts the Result
A loaded pack slows you down and costs you energy. The app models both and keeps them separate, because they don't scale the same way.
Speed: A Load-Ratio Penalty
Pack weight is expressed as a ratio to your body weight, then converted into a speed penalty:
pack ratio = pack_kg ÷ body_kg
speed factor = 1 − (0.5 × pack ratio), clamped to [0.5, 1.0]
The rule of thumb baked in: for every 10% of body weight you carry, your speed drops by about 5%. An 80 kg hiker carrying a 16 kg pack is at a 20% load ratio, so a 10% speed reduction: every band's pace is multiplied by 0.90. The factor is floored at 0.5, so even an extreme load never drops your modelled speed below half. That floor is a deliberate guard against nonsense estimates, not a claim that a monstrous pack only halves your pace.
This penalty is applied uniformly across all sixteen bands. It scales the cadence-derived speed before time is computed, so a heavier pack lengthens every segment of the day, flat and steep alike.
Energy: Weight Is Added to the Mass You Move
Calories are handled through METs (metabolic equivalents) [3], with each band carrying its own value: higher for ascent than descent, rising with steepness, exactly as Minetti's curve predicts [2]. The calorie calculation is:
calories = METs × (body_kg + pack_kg) × time_hours
The pack weight is added directly to the mass being moved. So a heavier pack hits your calorie burn twice: it adds to the moved mass in this equation, and it lengthens `time_hours` through the speed penalty above. That double effect is the model's way of capturing what every loaded climb already tells you: weight costs you on both the clock and the energy budget.
Your daily calorie figure then layers your BMR (Mifflin-St Jeor [4], from your height, weight, age and sex) on top of the hiking burn, spread across the number of days the route takes at your set hiking hours per day.
What This Means for Your Planning
The reason the Analysis tab's estimates hold up against real trail time is that they're built the way the terrain actually behaves: gradient first, asymmetric between up and down, with stride and load as personal multipliers. A few things worth doing with that:
- Set your stride length accurately. It's the biggest lever on every estimate. Pace out a known distance and divide rather than guessing.
- Enter realistic pack weight per section. A loaded approach day and a summit-push day with a stripped pack will produce genuinely different time estimates, and they should.
- Read the gradient bands, not just the total. Two routes of equal distance can differ by hours. The band breakdown tells you where the time goes, which is where you plan your water carries, camp spacing, and bail-out points.
The model is an estimate, not a promise. Terrain underfoot, fatigue, weather, and rest stops all live outside it. But it's an estimate based on how human locomotion actually responds to slope and load, which is a long way better than one number times your distance.
Train hard. Fuel right. Pack smart. Go further.
Back in Pack: backgear for every trail, every mountain, every adventure.
References
- Tobler W. Three Presentations on Geographical Analysis and Modeling: Non-Isotropic Geographic Modeling; Speculations on the Geometry of Geography; and Global Spatial Analysis. National Center for Geographic Information and Analysis, Technical Report 93-1. 1993. Tobler's hiking function (Wikipedia)
- Minetti AE, Moia C, Roi GS, Susta D, Ferretti G. Energy cost of walking and running at extreme uphill and downhill slopes. Journal of Applied Physiology. 2002;93(3):1039–1046. journals.physiology.org
- Ainsworth BE, Haskell WL, Herrmann SD, et al. 2011 Compendium of Physical Activities: a second update of codes and MET values. Medicine & Science in Sports & Exercise. 2011;43(8):1575–1581.
- Mifflin MD, St Jeor ST, Hill LA, et al. A new predictive equation for resting energy expenditure in healthy individuals. American Journal of Clinical Nutrition. 1990;51(2):241–247.
