Introduction
In 2015, I traversed a 50-mile stretch of a route that combined parts of the Sierra High Route, the John Muir Trail, and the Pacific Crest Trail. Skies were clear, temperatures cool, never a cloud in the sky. In spite of my heavy pack weight, elevation gain, terrain, and steepness of the route, I felt like I floated the whole way. A few years later, I returned to repeat it – same route, same terrain. But this time it rained. The rocky surfaces were slick, poor visibility slowed my pace, and temperatures were cold. But my pack was lighter, and I was in better shape. Leading up to this trek – extraordinarily long days of work, little sleep, and a stressful day of disruptive travel to California. This time, I was mentally and physically tired. I ran out of food. I finished it exhausted. The same route that seemed easy before just about broke me.
That disconnect kept rattling around in my head.
I knew that distance and elevation couldnât explain the difference in effort. The physics didnât change – this was the exact same route. But something else had, and I was determined to model it. That tension led to the birth of the Metabolic Energy Mile (MEM) model as a way of explaining why the same mile can feel radically different under changing conditions.
This paper introduces the MEM framework. It lays the philosophical groundwork – that energy cost is defined by the friction between intent and disruption. It presents a structured model for quantifying both the mechanical demands of movement and the inefficiencies that amplify those demands in the field. And it critiques the limitations of legacy models (heuristic, terrain-based, and physiological) that fail to capture the lived experience of exertion.
Future installments will extend this foundation into tools and tactics: how to quantify disruption, estimate total energy cost with field-ready proxies, and use MEM to inform gear choices, pacing strategies, route planning, training design, and performance debriefs.
MEM isnât a replacement for estimating effort based on distance or elevation gain – it just provides the missing context they ignore.
And in wild environments where calories are finite, terrain is complex, and morale is fragile, that context (and the planning required to conquer it) can make the difference between finishing strong and flaming out.
Table of Contents • Note: if this is a members-only article, some sections may only be available to Premium or Unlimited Members.
- Introduction
- Not All Miles Are Created Equal
- A Review of Existing Models
- The Five Domains that Drive Energy Cost in MEM Modeling
- Philosophy: Energy as Conflict Between Intent and Friction
- Mathematical Formulation of the MEM Model: The Disrupted Energy Costs of Moving Mass
- Case Study: One Route, Three Hikes, Three Outcomes
- Looking Ahead: How Weâll Use MEM
- Related Content
Not All Miles Are Created Equal
We tend to treat a mile as a static metric. It’s a known unit – “5,280 feet of distance” – and we often assume that covering one mile requires a predictable, repeatable amount of exertion. But every hiker, runner, or soldier is acutely aware of the reality: not all miles are created equal.
Sometimes one mile feels effortless, smooth, and even meditative. Other times, the same distance on another trail feels grueling, slow, and demoralizing. And we all know that hiking a route one day can feel very different than walking the exact same route on another day.
What explains this variability?
This is the foundational question that the Metabolic Energy Mile (“MEM”) framework is designed to explore. MEM is not a wearable device or a new caloric estimation formula. It is a conceptual and mathematical model that reframes how we understand energy expenditure in human locomotion, especially in natural environments. MEM integrates the topographical, biomechanical, environmental, physiological, and psychological factors that explain why each mile feels and costs differently.
MEM isn’t just a new variable to plug into your spreadsheet. It’s a lens, a way of seeing effort as the output of interaction between systems, and not just a linear function of time or distance.
A Review of Existing Models
Traditional models of energy expenditure – whether heuristic, empirical, or predictive – have provided useful scaffolding for estimating effort and predicting performance. But they share a critical limitation: they fail to capture the lived experience of effort in the field. The Metabolic Energy Mile (MEM) framework was created to fill this gap. It doesn’t just calculate or forecast – it interprets the felt sense of exertion, contextualizes it in real-world scenarios, and reveals what factors contribute to effort variability across time, terrain, and physical state.
MEM empowers us to:
- Explain why one mile feels harder than another, even under seemingly identical objective conditions.
- Predict effort variability under shifting terrain, increasing fatigue, and dynamic external factors like weather or psychological state.
- Guide real-time decisions in route planning and pacing when standard models offer insufficient granularity.
- Design gear and training strategies that manage not just biomechanical output, but also perceptual strain and disruption-induced inefficiencies.
MEM isnât meant to replace conventional metrics such as speed, distance, or VOâ-based energy estimates. Instead, it answers a different question – one that’s more relevant in dynamic backcountry environments:
Why did this mile feel harder than the last one, how can I predict that effort in the future, and what is within my control to reduce that effort?
To understand what MEM contributes, it helps to examine where current models fall short. Most fall into one of three buckets: heuristic models, terrain-speed models, and physiological models.
Heuristic Models
Before we had GPS apps, digital elevation profiles, or wearable sensors, hikers and mountaineers still needed a way to predict how long it would take to get from point A to point B. Enter the heuristic model – a rule-of-thumb approach rooted in simplicity, practicality, and broad generalization.
Some of the most well-known examples include Naismithâs Rule, which dates back to 1892 and provides a baseline estimate of travel time based on distance and elevation gain. Then came refinements like Petzoldtâs Energy Mile and Langmuir Adjustments, which attempted to incorporate additional terrain factors. These models were never meant to be precise: they were meant to be good enough for back-of-the-napkin estimates, especially in the era of paper maps and analog compasses. They gave backcountry travelers a quick mental model to assess route difficulty and make planning decisions without needing a calculator.
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Discussion
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Companion forum thread to: The Metabolic Energy Mile (MEM) Framework: A Systems-Based Approach to Measuring the Cost of Walking a Mile
The Metabolic Energy Mile (MEM) Framework redefines hiking effort beyond distance. It integrates terrain, fatigue, and environment for accurate energy cost prediction.
The MEM equation looks elegant and insightful. However, I noticed that the article doesn’t fully define the individual parameters â for example, the specific forms or estimation methods for the parameters.
How should these parameters be determined or approximated in practice?
Are you planning to publish quantitative definitions or field-measurable proxies for them in future installments of the MEM series?
This will be an article series, we’re unpacking each parameter one by one. The next piece we’re working on publishing is the steepness (grade) / pacing / pack weight model.
My 9-5 occupation for years included developing objective models to predict subjective experiences as is attempted here.
Some experiences can be modelled because there is very little variability between subjects and the variability that does exist can be constrained through training. For example cognition (hearing, vision) thresholds are surprisingly similar between highly trained subjects if the subjects have similar age and no damage.
In this case, MEM tries to objectively model:
Why did this mile feel harder than the last one, how can I predict that effort in the future, and what is within my control to reduce that effort?
The person to person variability in this will be so extreme that the only way to make it work is for each individual user to experimentally quantify the model parameters for their own personalized model through many field trips.
Give that, I’m not sure how this can be used in practice.  Once I know how hard 35km+2000m+scrambling is, I don’t need a parameterized model, I have the experience.
This was my thought as well. And if you add in cumulative fatigue effects from multiple days, hydration and other variable conditions that are difficult to measure, I become increasingly skeptical that even the most carefully developed model will have practical benefit. Even predicting the relative effort of different activities for a given person is improbable, because different people have different balances of strength, aerobic conditioning, and metabolism. As @David D mentions, any useful model would have to be so thoroughly calibrated for each person, that the model would become little more than an empirical interpolation. As I’ve monitored this thread, I’ve been imagining that the ultimate goal is to create an app, and I’ve been trying to picture how it could have practical utility.
As a scientist, I appreciate the efforts to quantify things, and I do understand that it’s often just a fun activity during the off-season. But it takes a lot of training and experience to understand the confidence limits of quantitative predictions (especially with human subjects), so I don’t take these calculations too seriously.
There are so many factors at play and they can affect each other so deeply.
One good purely objective proxy is to instead use heart rate monitoring to determine effort and stress levels. However, I’ve even seen oddly contradictory trends in my heart rate. Last month I took a 4 day trip with 25-30km per day which is usually no problem. First two days were fine. Third day was an elevated struggle even in the same terrain type but the heat had spiked significantly. I was hydrating properly and taking my salt. Oddly enough, my heart rate was at hard to understand lows (~ 90 bpm moving @ ~ 6kph) even though I was feeling it. Fourth day was the longest but felt easy enough, on the same terrain.
Was the watch reading wrong? Did I get a bad sleep the night before? Did I take my saltsticks too late? No model could have predicted the impact of any of this.
I’ve been focusing my models on a much easier task, estimating caloric burn. For that I’m getting close to accurate outcomes over varied terrain, as I explain here.
I’ve been recently calibrating this model against my son’s hero trips to check if it was over-personalized for me only and to see how it holds up under more extreme hikes. Last week to finish his 46 he did the Great Range Traverse in the ADKs plus another mountain all in one day (~40km/3500m elevation gain over tough terrain) then followed it up the very next day with another ~40 plus ~ 2km elevation in similar conditions.  My predictive model was within a couple percent of his coros watch’s calorie count.
Equating this to weight loss or gain has been near impossible to arrive at in a generalized model though. It’s close for me but I have two additional excellent data points, where 2 researchers tracked every calorie over a long trail through-hike (IIRC one was PCT, one was AT) and they arrived at wildly different results for their weight loss based on calorie deficiency over the duration of the entire thru.
Its comforting to try and get a sense of order in the world, and us scientific/engineering types have a temptation to do this through modeling. But some things are just too complex and we need to come to a serene acceptance of the limitations.
It is fun and interesting exploring though and I commend Ryan for giving it a shot. At worst, it can help provide a better understanding of some of the factors at play.
I become increasingly skeptical that even the most carefully developed model will have practical benefit
As far as I can see, none of them make any allowance for the possibility of something as simple and common as a basic rhinovirus. (ie, a sniffle) But we all know what effect that can have on the day!
Cheers
1. On Individual Variability and Calibration:
Youâre absolutely right – inter-individual variability is extreme. Thatâs not a flaw to correct in the MEM model; instead, it’s an inherent part of the system itâs meant to describe. The MEM framework doesnât aim to provide a one-size-fits-all predictive model of human energy cost. Instead, itâs a conceptual and computational structure that allows each individual to quantify their own âmetabolic cost per mileâ under specific environmental, biomechanical, and physiological conditions.
In that sense, MEM is not intended to yield absolute predictions without calibration – itâs a framework for personal modeling, much like metabolic equivalents (METs) or aerobic threshold testing, where the utility comes from personalization over time rather than generalization across people.
But my goal is to make the calibration process as simple as possible (initially) and then allow the model to learn and adapt in response to you increasing the amount of personal data you feed into it.
The modelâs value is in predicting relationships. Once those relationships are parameterized for an individual, MEM becomes a tool for relative comparisons (e.g., âHow much harder will this day feel than that one?â), rather than absolute predictions.
However, absolute predictions are possible with the model in its current form – you just have to understand that there is normal stochastic variability (a range defined by a low and a high) and not a single number.
2. On Complexity and the Limits of Predictive Precision:
Youâre also correct that human performance involves countless interacting variables – fatigue, hydration, sleep, temperature, nutrition, psychological state – and these canât all be reliably modeled with predictive modeling. The MEM approach explicitly acknowledges this by treating it as a systems-based model, not a single-variable regression for all possible variables. Some of these have narrower stochastic noise in their predictions, others have wider noise.
The goal isnât to perfectly predict every outcome, but to:
In short: MEM doesnât compete with physiological measurement (like heart rate or VOâ) – it complements them by organizing the problem space so we can reason systematically about energy cost under complex conditions.
3. On Practical Utility:
The practical utility of MEM isnât in producing an app that gives hikers an exact calorie or fatigue number. Itâs in:
If the MEM framework ever informs an app, it would likely function like a personalized decision-support tool, not a real-time predictor – more akin to a âbudgeting calculatorâ for energy expenditure than a âmetabolic oracle.â
4. On the Philosophy Behind the Framework:
I agree with the sentiment that âsome things are just too complex,â and that acceptance of those limits is part of the scientific process. The MEM model is not about simplifying reality but about structuring complexity – giving us a map of what domains reflect the most uncertainty, how big it might be, and how we might bound it experimentally.
In that sense, the MEM framework is a lens for planning and analysis, not a closed-form solution. Its greatest potential is as an “adaptive-heuristic” framework (dynamic and feedback-driven; it begins as a heuristic, but it can learn or update its parameters in response to new data or changing conditions) vs. a pure heuristic (empirical) framework.
In short:
Why METs Already Provide What âMEMâ Is Aiming For
Below is a point-by-point comparison of the claims made for the proposed âMEMâ metric against what the Metabolic Equivalent of Task (MET) framework already does (or is routinely used to do) in exercise physiology and outdoor-performance science.
âMEMâ promise
How the MET framework already addresses it
1. âExplain why one mile feels harder than another, even under seemingly identical objective conditions.â
⢠A mile walked at 3 mph on flat ground â 3.3 METs. Add a 10 kg pack (+â0.9 MET) and a 5 % grade (+â3 MET) and the same mile becomes â7.2 METsâmore than double the metabolic cost.
⢠Because METs are directly proportional to steady-state oxygen consumption, they map closely to heart-rate drift and Rating of Perceived Exertion (RPE). âWhy it felt harderâ is answered quantitatively: the required VOâ and therefore the fraction of VOâmax rose.
2. âPredict effort variability under shifting terrain, increasing fatigue, and dynamic external factors like weather or psychological state.â
⢠Terrain & grade: ACSM and PandolfâGivoniâGoldman equations convert speed, grade, surface, and load into VOâ; converting VOâ to METs yields a terrain-specific prediction.
⢠Environmental stressors (heat, cold, wind): ISO 9886 and NIOSH models supply correction factors (e.g., +10 % VOâ per 10 °C WBGT increase). These factors are routinely expressed as MET multipliers.
⢠Fatigue/psychology: field practitioners overlay heart-rate variability or RPE onto MET curves to account for central fatigue. The metric is still MET; the modifiers are explanatory covariates.
3. âGuide real-time decisions in route planning and pacing when standard models offer insufficient granularity.â
⢠Hikers, cyclists, and runners already feed grade, temperature, wind, and pack weight into wearables or apps (e.g., Garmin Climb-Pro, TrainingPeaks) that output real-time METs or âenergy expenditure per km.â The granularity is as fine as the GPS/barometric sample rate.
4. âDesign gear and training strategies that manage not just biomechanical output but also perceptual strain and disruption-induced inefficiencies.â
⢠Lab studies report MET deltas for shoe mass (+1 % VOâ per 100 g), pole usage (â3â5 % VOâ on steep ascents), ski-skin glide, bike-packing aerodynamics, etc. Practitioners already choose gear by comparing these MET differences to performance goals.
5. âAnswer the question: Why did this mile feel harder than the last one, how can I predict that effort in the future, and what can I control to reduce it?â
⢠By decomposing METs into controllable (speed, load, grade, cadence) and uncontrollable (altitude, weather) contributors, a simple spreadsheet or watch widget tells you exactly which variable raised METs on that segment and what changeâslowing 0.3 mph, ditching 4 kg, waiting for cooler tempsâwill cut the cost next time.
The Nuts and Bolts
Definition recap
⢠1 MET = 3.5 mL Oâ ¡ kgâťÂš ¡ minâťÂš (â 1 kcal ¡ kgâťÂš ¡ hâťÂš).
⢠Intensity (%) = (Required MET á VOâmax in METs) Ă 100.
Terrain & load conversion (Pandolf et al., 1977; ACSM, 10th ed.)
VOâ (mL ¡ kgâťÂš ¡ minâťÂš) = 1.5 S + 0.35 S G + (E + L)(1.5 + 0.35 G)
where S = speed (m ¡ sâťÂš), G = grade decimal, E = external load, L = body weight.
Divide by 3.5 to get METs.
Environmental corrections (Gonzalez, 1988)
For heat: MET_adj = MET_base Ă [1 + 0.01 (WBGT â 22 °C)].
For altitude: add 7 % MET per 1 000 m above 1 500 m.
Perceptual link
RPE â 1.5 Ă MET for steady-state locomotion up to ~15 METs.
Thus, a jump from 4 â 6 METs predicts an RPE rise from ~6 â 9ââmoderateâ to âvery hard.â
So What Would âMEMâ Add?
⢠If MEM is just âMETs plus context tags,â then it is a semantic re-labeling.
⢠If it intends to fold psychological and environmental multipliers into a single âfelt-effort number,â thatâs already what many practitioners call Adjusted METs or Physiological Cost Index.
⢠If it aims for real-time decision support, modern wearables already expose MET-based estimates continuously.
In other words, the explanatory, predictive, and prescriptive functions claimed for MEM are inherent toâor routinely layered on top ofâthe existing MET construct. Reinventing the acronym does not create new physiology; it only risks fragmenting a vocabulary that is already standardized across research, coaching, and clinical practice.
Richard, this is gold, thanks for taking the effort to put this all down. It will take some time to research and study more deeply. As someone forced to wear boots often, the shoe mass penalty is an eye opener.
From these formulae, is the variation between subjects fully expressed then by vo2max and body weight? And is this accurately predictive of the variance in practice?
In the PAL studies I’ve read, caloric burn was reasonably well correlated with overall body plus skin out weight, consistent with E+L in your equations.
Ryan, it’s late and I will digest your response more tomorrow, thanks for replying.
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