The Harris Benedict equation for BMR

Here’s a lighter one for a change. No politics, no grand solutions to grand problems, just a playful way to extract a life lesson or two (it will require some elementary maths though):

If one purpose of this blog is to make me and you more literate in sustainability “beyond green”, Energy Literacy must be a part. We need our intuition, because our language is full of sustainability terms that don’t mean a thing! “Carbon footprint”, or “food miles” are my favourites.

Imagine someone saying “the carbon footprint of an Audi is X“. Depending on the audience, we can visualize them nodding or disagreeing violently, but not one will question whether this statement means anything at all: But that is the question we must ask, because you can put almost any number for X, depending on what “carbon footprint” means:

• Does it mean CO2 emissions?
• If yes, who is the user and their driving pattern?
• Do we include the energy put into producing the Audi?
• If yes, do we include the energy put into producing the materials?
• If yes, do we factor in whether that energy was renewable or not?
• How do we handle other emissions? [1]

X becomes meaningless if we simply assume “carbon footprint” is a well-defined term. It isn’t. An environmental activist will give you one number, and the marketing head of Audi another, and both are right in their own little world. “Carbon footprint” by itself is a term that most often is meant to obfuscate, not educate. “Food miles” is even worse.

What matters, is sustainability thinking, not sustainability talking. Going back to basics, most sustainability thinking is first and foremost about “effortless action”, which is the art of getting the most of a desirable outcome (diversity, health, well-being) with a minimum of effort (resources, time, energy) and waste. It should not be more complicated than that (VIF — very important footnote [2]). And yes, most often it’s an art and not a science.

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So let’s start our tour towards energy literacy on the most human of scales: With the kcal or “food calorie”.

One kcal is the amount of energy needed to raise the temperature of 1kg of water by 1 degree Celsius.

One kcal equals approximately 4,200 J (“Joule”). One Joule (the proper metric unit of energy) is the energy expended by moving something with a force of 1N (Newton) by a distance of 1 meter. Our intuition of force will require us to use the weight of one kilogram, which equals 9.81N.

1 kcal (4,200 J) will lift a weight of 85kg by 5m (because 85 x 5 x 9.81 = aproox. 4,200). If that is your weight and you climb 5m, you have expended 1 kcal of physical work. However, the bio-mechanical efficiency of your body is only around 20-25%, so you actually “burn” 4-5 kcal of food energy for every kcal of actual work performed. The rest goes into body heat and ambient heat through friction (mostly in your muscle-fibres, but also in your joints, between your tendons, etc.). In reality, you “burn” about 1 kcal by climbing 1m, but less than a quarter of that turns into mechanical energy needed for this movement.

On top of the bio-mechanical (in-)efficiency of  your body, there’s the effect that you don’t use all your (food) energy to actually do stuff. Far from it. You actually burn most of your food just keep you alive, i.e. to metabolize (breathing, blood circulation, brain activity, keeping at the right body temperature, re-building damaged tissue, growing, etc. etc.) before you actually do any physical work; The amount of energy you need to do just that is called the base metabolic rate (“BMR”), and it depends on several factors. For men, it is given by the equation at the top of this article, so for a man of 85kg, 180cm, 40yrs (try this yourself!), it is approximately 1,860 kcal.

1,860 kcal, the base metabolic rate would be enough to lift that person by 9,370m (=7,800,800 J/ 85 kg / 9.81 m/s2), more than from the sea level to the top of Mt. Everest. Even with the limited bio-mechanical efficiency of the body, that person would have to climb some 2,000m (6,000 ft) or more just to burn his daily BMR through exercise.

For the average person, the work they perform in a day is maybe a fifth of a 2,000m climb, (if that!) so we can guess that 15%-20% of your food intake is used to move around and do work.

Is that intuitive? Well, it depends. How much more do you eat on a long day of hiking vs. on a day in the office? Probably less than twice the normal amount, so you see that even almost continuous work all day will raise your food intake by less than what it already is normally. Doing physical work will never massively increase your body’s energy consumption.
It is said that Olympic swimmers burn at most 5,000 kcal a day during peak practice, more than perhaps any other sport demands, and even that is just over twice the BMR.

Now, use your newly acquired intuition: To fight obesity, should we try to get people to (a) exercise more, (b) eat less?

Our examples show that for a relatively average person, a doubling of your physical work every day is equivalent (in terms of energy balance) to eating just about 15% less. What is easier: Cut that Mars bar (242kcal) from your diet, or climb 242m (80 flights of stairs)? I know what I would opt for! (hint: the thing that takes less time)

But there is more fun stuff we can do with the Harris Benedikt equation above.

It says that for men, the base metabolic rate goes up with weight, by 13.5 kcal per kg of body mass, and for women this figure is 9.5 kcal / kg. So if you eat one Mars bar (242 kcal) too many every day, then as a man your weight will stabilize at some 18kg higher than it should (for at that point your body will need that Mars bar just to maintain its weight), and for a woman this might be 25kg more. That might be a shocker, but instructive it most certainly is.

Another game with that weight/BMR relationship: if one flight of stairs equals 3 kcal (for a man) and call it 2.3 for a woman, say (because of lower average weight), then climbing just 4 flights per day will lower your long-term weight by almost 1kg. That is worth a thought, no? [3] [4]

[1] This alone can cause huge differences, even up to factors of 10 or more. You can count them as “CO2-equivalent”, meaning you count as much CO2 as would be “needed” to make the non-CO2 emission as potent as CO2 emission. You can count them 1-for-1, or not at all. All these conventions are used and mixed in practice.

[2] It is because I believe that sustainability is ultimately, and most often about “effortless action” that I believe the captains of finance and industry, the leaders and managers in the real world, are so well equipped to do well in the sustainability sphere once their attention and goals are directed properly: because they are – inherent to their day-to-day jobs – always trying to optimize outcomes and minimize inputs. We all are, in a way, but management requires social intelligence, leading by example, and many soft skills that are generally under-appreciated (and often also under-supplied) by environmental activists.

[3] This is because your body has to “find” the missing 13.5 kcal somewhere, and it does it by starting, until the BMR has shrunk by 13.5 kcal through weight-loss (which, according to the equation, happens after 1 kg of weight loss).

[4] For completeness, we can also estimate how long it may take you to get there, and it is a somewhat depressing analysis. One kg of fat has 9,000 kcal. To lose that much, by saving 9 kcal a day (as in the case of a woman climbing four extra flights of stairs a day) would take 1,000 days or almost three years. Definitely don’t check your weight every day if you are opting for this “diet”!