The Metabolic Energy Mile (MEM) Framework: A Systems-Based Approach to Measuring the Cost of Walking a Mile

The MEM equation looks elegant and insightful. However, I noticed that the article doesn’t fully define the individual parameters — 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.

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.

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.

I become increasingly skeptical that even the most carefully developed model will have practical benefit

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:

You’re absolutely right – inter-individual variability is extreme. That’s not a flaw to correct in the MEM model; instead, it’s an inherent part of the system it’s meant to describe. The MEM framework doesn’t aim to provide a one-size-fits-all predictive model of human energy cost. Instead, it’s a conceptual and computational structure that allows each individual to quantify their own “metabolic cost per mile” under specific environmental, biomechanical, and physiological conditions.

In that sense, MEM is not intended to yield absolute predictions without calibration – it’s 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 model’s value is in predicting relationships. Once those relationships are parameterized for an individual, MEM becomes a tool for relative comparisons (e.g., “How much harder will this day feel than that one?”), 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:

You’re also correct that human performance involves countless interacting variables – fatigue, hydration, sleep, temperature, nutrition, psychological state – and these can’t 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 isn’t to perfectly predict every outcome, but to:

• Identify the dominant contributors to metabolic cost in a structured way;
• Understand how those contributors interact (terrain, load, gradient, surface, etc.);
• Offer a quantifiable framework for reasoning about tradeoffs.

In short: MEM doesn’t compete with physiological measurement (like heart rate or VO₂) – 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 isn’t in producing an app that gives hikers an exact calorie or fatigue number. It’s in:

• Helping hikers, guides, and researchers conceptualize performance tradeoffs – such as pack weight vs. terrain vs. pacing.
• Supporting training and trip-planning decisions (e.g., route difficulty normalization, recovery planning).
• Serving as a pedagogical model for understanding how energy systems behave under real-world conditions.

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 “budgeting calculator” for energy expenditure than a “metabolic oracle.”

4. On the Philosophy Behind the Framework:

I agree with the sentiment that “some things are just too complex,” 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:

• MEM ≠ universal predictor
• MEM = structured framework for personalized modeling and reasoning
• Goal: conceptual clarity, not empirical precision
• Value: improving understanding of energy dynamics and informing decision-making

Why METs Already Provide What “MEM” Is Aiming For
Below is a point-by-point comparison of the claims made for the proposed “MEM” 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.

“MEM” promise
How the MET framework already addresses it
1. “Explain why one mile feels harder than another, even under seemingly identical objective conditions.”
• A mile walked at 3 mph on flat ground ≈ 3.3 METs. Add a 10 kg pack (+≈0.9 MET) and a 5 % grade (+≈3 MET) and the same mile becomes ≈7.2 METs—more 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). “Why it felt harder” is answered quantitatively: the required VO₂ and therefore the fraction of VO₂max rose.
2. “Predict effort variability under shifting terrain, increasing fatigue, and dynamic external factors like weather or psychological state.”
• Terrain & grade: ACSM and Pandolf–Givoni–Goldman equations convert speed, grade, surface, and load into VO₂; converting VO₂ to METs yields a terrain-specific prediction.
• Environmental stressors (heat, cold, wind): ISO 9886 and NIOSH models supply correction factors (e.g., +10 % VO₂ 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. “Guide real-time decisions in route planning and pacing when standard models offer insufficient granularity.”
• 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 “energy expenditure per km.” The granularity is as fine as the GPS/barometric sample rate.
4. “Design gear and training strategies that manage not just biomechanical output but also perceptual strain and disruption-induced inefficiencies.”
• Lab studies report MET deltas for shoe mass (+1 % VO₂ per 100 g), pole usage (−3–5 % VO₂ on steep ascents), ski-skin glide, bike-packing aerodynamics, etc. Practitioners already choose gear by comparing these MET differences to performance goals.
5. “Answer 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?”
• 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 change—slowing 0.3 mph, ditching 4 kg, waiting for cooler temps—will cut the cost next time.

The Nuts and Bolts
Definition recap
• 1 MET = 3.5 mL O₂ · kg⁻¹ · min⁻¹ (≈ 1 kcal · kg⁻¹ · h⁻¹).
• Intensity (%) = (Required MET ÷ VO₂max in METs) × 100.
Terrain & load conversion (Pandolf et al., 1977; ACSM, 10th ed.)
VO₂ (mL · kg⁻¹ · min⁻¹) = 1.5 S + 0.35 S G + (E + L)(1.5 + 0.35 G)
where S = speed (m · s⁻¹), 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 × [1 + 0.01 (WBGT − 22 °C)].
For altitude: add 7 % MET per 1 000 m above 1 500 m.
Perceptual link
RPE ≈ 1.5 × MET for steady-state locomotion up to ~15 METs.
Thus, a jump from 4 → 6 METs predicts an RPE rise from ~6 → 9—“moderate” to “very hard.”

So What Would “MEM” Add?
• If MEM is just “METs plus context tags,” then it is a semantic re-labeling.
• If it intends to fold psychological and environmental multipliers into a single “felt-effort number,” that’s 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 to—or routinely layered on top of—the 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.