In a special session on military physiology ultimately week’s American College of Sports Medicine convention, 2 groups of researchers offered new information on one thing known as the “Pandolf equation,” which has been used for the reason that 1970s to estimate how a lot power it takes to hump a pack. A British staff explored how load distribution patterns have an effect on the estimates, since fashionable troopers carry weight somewhere else because of issues like physique armor, as a substitute of getting their full load crammed right into a backpack. And a U.S. Army staff looked into variations between women and men, since girls at the moment are filling fight roles that require carrying heavy hundreds.
The outcomes of those research are mildly fascinating. (In temporary, fashionable troopers burn extra power than the equation predicts, as a result of it’s extra environment friendly to hold hundreds in your again. And males burn extra power than girls whereas carrying a given weight, however the equation isn’t fairly proper for both.)
But the actual revelation to me was the unique Pandolf query. Here’s a easy device that tells you what number of energy you’re burning as a perform of your weight, your pack’s weight, your mountain climbing velocity, the incline of the slope you’re strolling on, and the character of the terrain. Amazing! Even if it has some gentle inaccuracies within the absolute numbers it calculates, it gives an goal method of answering a few of the logistical questions that you simply face when planning a backpacking journey. How a lot additional power will it value you to haul an elective luxurious like your camp chair? How a lot will you decelerate on a chronic climb or in sandy terrain should you keep a roughly fixed effort stage? What’s probably the most environment friendly velocity should you’re carrying a very heavy pack? Or a very gentle 1?
I spent a while enjoying round with the equation to see what it tells us, utilizing the instance of a 150-pound individual carrying a 50-pound pack at 4 miles per hour on a gravel path because the reference case. The equation itself isn’t notably revealing, however for the file right here it’s:
M = 1.5 W + 2.0 (W + L)(L/W)2 + n(W + L)(1.5V2 + 0.35VG)
Here M is the metabolic fee, which is how shortly you’re burning power. This equation provides you a worth in watts, however that’s simple to transform to different models like energy per hour.
The inputs into the equation are:
- W: your weight (kg)
- L: the load of your pack (kg)
- V: your mountain climbing velocity (m/s)
- G: the grade of any incline (%)
- n: a “terrain factor” that adjusts the outcomes for various surfaces (for instance, a paved highway has a terrain issue of 1.0, however a gravel highway is 1.2, because it takes extra energy to stroll on a mushy or uneven floor)
For the equation to work as written, you need to use the models I’ve listed above. For the rest of this text and for the interactive calculator on the backside of the web page, I’ve transformed to kilos for the weights and miles per hour for mountain climbing velocity.
So should you plug my reference case numbers into the equation, you discover that this hypothetical hiker (let’s name him “Alex H”) is burning about 555 energy per hour. That implies that over a six-hour mountain climbing day, he’d be burning 3,330 energy. That’s a variety of GORP.
To be honest, not all of these energy are immediately associated to mountain climbing. Notice that the equation has 3 phrases in it. The first time period displays the power value of merely standing nonetheless, supporting your individual weight. In this case, that’s 88 energy per hour. The 2nd time period displays the power of standing nonetheless with a pack on. The pack provides one other 17 energy per hour. And the 3rd time period is the place the motion is, incorporating the power wanted to stroll at a given velocity, with the impact of gradient and terrain included—on this case, an additional 450 energy per hour.
That provides us a baseline estimate of the caloric calls for of backpacking, so now we will discover what occurs when the situations change. For instance, what’s the impact of accelerating your pack weight between 20 kilos and 100 kilos (proven alongside the horizontal axis)? And how does that change should you stroll at completely different speeds from 1 mph to five mph (proven with completely different strains)?
Admittedly, the conclusions right here aren’t earth-shattering. The heavier your pack, the extra power you burn. At 4 mph, doubling your pack weight from 40 lbs to 80 lbs will increase your calorie burn from 526 per hour to 657 per hour, a rise of about 25 %. You pay a steeper penalty for including 20 kilos to a heavy pack than to a lightweight pack.
This could possibly be helpful to know for trip-planning, for instance, to determine how far you may fairly count on to make it in a given period of time. But should you’ve already determined how a lot distance you’re going to cowl, then you need to think about that the sooner you hike, the much less time you’ll spend mountain climbing. That implies that mountain climbing sooner may typically really be extra environment friendly general, because you’re burning extra energy however for a shorter time. So let’s look once more on the identical information, however expressed as energy per mile as a substitute of energy per hour:
Now issues get a bit of extra complicated. In this case, the 2 worst choices are the slowest (1 mph) and quickest (5 mph) mountain climbing speeds, with the very best choices someplace within the center. Some of the strains cross one another, so it’s arduous to determine why that is. To get a clearer image, let’s take a look at the identical information 1 final time, however this time swap issues round in order that mountain climbing velocity is on the horizontal axis and pack weight is proven with completely different strains:
This exhibits that strolling actually slowly is inefficient, notably should you’re carrying a heavy pack. That is sensible: should you take too lengthy to cowl your distance, you’re spending pointless time with an enormous pack weighing you down. So going sooner is extra environment friendly—however should you hold dashing up, the price of making an attempt to stroll quick takes over. The candy spot between strolling too quick and supporting the pack for too lengthy, on this pattern case, is between 2 and three mph. The heavier your pack, the sooner the optimum strolling velocity will get.
It’s vital to notice that this evaluation is just contemplating the power value of strolling with a pack. There are different elements that make backpacking arduous. For me, at the very least, protecting a heavy pack on for lengthy durations of time will get uncomfortable irrespective of how well-fitted it is. My hips and shoulders begin to fatigue and typically chafe. So I typically discover that I want a faster-than-“optimal” velocity, which burns some additional energy however minimizes the period of time I have to hold the pack on. Still, these graphs provide you with some concepts of how the energetics of backpacking change as you modify parameters like pack weight and strolling velocity.
There are different elements we will mess around with. For instance, how does calorie burn change as a perform of slope? Here’s some information for my reference case at slopes from 0 to 15 %, with strolling speeds from 0.5 to 4 mph proven alongside the horizontal axis:
Yes, it takes much more power to stroll uphill. But we will extract some extra helpful data, too. Let’s say you’re used to schlepping alongside at 4 mph with a 50-pound pack on stage floor. Now you’re planning a visit that may contain some extended uphill. What velocity must you count on to keep up should you plan to expend roughly the identical quantity of effort (or, extra particularly, the identical quantity of power)? At a 5-percent grade, you’d must decelerate to 2.9 mph. At a 10-percent grade, it will be 2.2 mph.
The final element I’ll pull out is the impact of terrain. All of the above calculations have used a “terrain factor” of 1.2, which is what the Pandolf equation recommends for gravel or filth roads. But these numbers can change fairly dramatically should you’re on different surfaces. A paved highway has a terrain issue of 1.0; swamp has a terrain issue of three.5. (There’s been numerous analysis and debate on the suitable terrain elements over time; I’m utilizing values from a 2015 paper on the topic.)
Here’s the calories-per-mile information for numerous terrains at 3 completely different speeds between 2 and 4 mph:
You can see that unhealthy terrain takes a disproportionately massive toll at sooner speeds. If you’re planning a route by troublesome terrain and also you don’t consider a big slowdown, you’ll be pushing your self very arduous to remain on tempo. If you’re clipping alongside at 4 mph on a gravel path, then come to a bit of ice (terrain issue 1.7), you’ll decelerate by about 15 % to three.4 mph should you keep the identical power output. Sand is a bit more sophisticated: its terrain issue is (1.5 + 1.3/V^2), which means that it adjustments with mountain climbing velocity, in order that the slower you go, the tougher it will get.
So that’s the Pandolf equation. Exactly what it tells you’ll rely upon the particular particulars of your journey, which is why we’ve designed a easy calculator that means that you can calculate your individual caloric value. Simply plug in your weight and your pack’s weight (in kilos), your mountain climbing velocity (in miles per hour), and the grade you’ll be mountain climbing on (in %), and choose one of many terrain choices, and the calculator will estimate your caloric value in energy per hour and energy per mile. Have enjoyable enjoying with it… and at all times pack an additional day’s meals simply in case.
My new ebook, Endure: Mind, Body, and the Curiously Elastic Limits of Human Performance, with a foreword by Malcolm Gladwell, is now obtainable. For extra, be part of me on Twitter and Facebook, and join the Sweat Science email newsletter.