In Power up a Tower: Part 1, I showed the relationship between work
(J) and power (watts). I also introduced the power to mass ratio metric
(watts/kg) which can be used to measure the performance of different climbers
climbing the same building. Finally, I showed an example of how the power to
mass ratio of climbers depends on the height of a climb.
In
Power up a Tower: Part 2,
I built upon the principals of work & power presented in part 1 and I
showed the relationship between power output and race length. Using this
relationship, I was able develop a method to predict racer’s finish time based
on prior results in a different building (i.e. at different height and race
duration).
In
this post, I will focus on a slightly more practical topic for the average
fitness enthusiast: How many calories are burned while climbing stairs?*
*Dedicated
to Jason Larson who inadvertently sparked my interest on this topic.
To
answer this question, you first need to understand that overall calorie burn
can be broken up into two separate pieces:
1) Calories
burned due skeletal muscle exertion (e.g. using your muscles when climbing
stairs.
2) Calories
burned due to other processes occurring within the body (e.g. process of
digestion, the functioning of your brain and other organs, etc.).
As
I explain each piece, I’ll use my latest Sears Tower climb as an illustrative
example. Here are a few pieces of information you’ll need to know about my
latest climb.
Climber: Alex Workman
Mass: 80 kg
Mass of
shoes & clothes:
1 kg
Percent
Body Fat:
11%
Height
of Climb:
412 meters
Duration
of Climb:
15 minutes*
*Actually,
it only took me 14 minutes and 53 seconds, but for illustrative purposes, 15
minutes is close enough.
Calories Burned via
Bodily Processes:
The
1^{st} piece (skeletal muscle exertion) is the primary calorie burner
during vigorous exercise, but the 2^{nd} piece (bodily processes)
cannot be completely ignored. After all, the majority of your overall daily
calorie expenditure is consumed by your organs while you go about your
daytoday activities (sleeping, eating, sitting, reading, etc.). So what
exactly are your caloric needs for your internal processes? It turns out that
this topic is pretty complicated, since there are thousands of chemical
interactions happening concurrently inside your body every moment of your life.
Fortunately, you can approximate this value by using your Resting
Metabolic Rate (RMR). RMR is defined as is the amount of energy expended daily
by humans (and other animals) at rest. One method of calculating your RMR is
the Cunningham Formula:
P
= 500 + (22 x LBM)
where P is your daily caloric needs
where LBM is your Lean Body Mass in kg.
Lean
body mass is used in the formula because fat cells have negligible caloric
needs to exist, whereas muscle tissue and other organs require energy to
function, even when resting. There are several different ways to measure your
LBM directly, but as a rule of thumb, you can reference the table below
(courtesy of Wikipedia) and make an educated guess.
Body
Fat Percentage
Description 
Women

Men

Essential
fat

10–13%

2–5%

Athletes

14–20%

6–13%

Fitness

21–24%

14–17%

Average

25–31%

18–24%

Obese

32%+

25%+

Using
this table, you can estimate your Lean Body Mass:
LBM
= your mass – (your mass x Body Fat
Percentage)
Example 1: How many
Calories did I burn during the Sears Tower climb due to bodily processes?
Answer: My LBM = 80
kg – (80 kg x 11%) = 71.2 kg.
Using Cunningham’s
formula, my daily Caloric needs = 500 +
(22 x 71.2 kg) = 2066.4 Calories per day
Since the duration of
the climb was only 15 minutes (a quarter of an hour) I burned 2066.4/24 hours x
¼ hour = 22 Calories (rounded to nearest Calorie)
Calorie Burned via
Exercise:
Now
that we have a method for determining the calories burned due to the natural
processes within your body, let’s take a look at calories burned while stair
climbing. Using the information presented in Part 1 of this series, the total
work output needed to climb a stairwell is:
Work
= Mass x 9.81 m/s^{2} x Distance
Where:
Work is in joules
Mass is in kg (total mass including body mass
and mass of clothing & accessories worn)
Distance is in meters (i.e. the total height
of the stairwell)
Since
1 joule = 0.239 calories, and 1000 calories = 1 Calorie (aka the kilocalorie
which is the dietary Calorie we’re most familiar with) the Calories of
work for a stair climb is:
Calories
of Work Output = (Mass x Distance)/426.5
Where:
Mass is in kg.
Distance is in meters
Units for the 426.5 factor is (kg x
m)/Calorie
Example 2: How many
Calories of work output were needed to climb the Sears Tower?
Answer: My total mass
is 81 kg, which includes both my body mass (80kg) and the mass of my clothes
& shoes (1 kg). Since the vertical height of the Sears Tower climb is 412
meters, the Calories of work output = (81 kg x 412 m)/426.5 = 78 Calories
(rounded)
Looking
at the above example, you might think that something seems to be missing. How
is it possible that I only needed 78 Calories of work output (the equivalent
rate of about 313 Calories per hour) during my 15 minute stair climb?
The
truth is, studies have shown that your skeletal muscles are only about 18%25%
efficient at converting energy into work*. The remaining 75%82% of energy
spent by your body is given off as heat**. Although the studies I’ve read on
this topic were focused mainly on cycling and rowing, I believe that it also
would apply to stair climbing since it is a similarly efficient exercise.
*Compare
that with a modern combinedcycle gas turbine/steam turbine power plant that is
over 60% efficient!
**Now
you know why you sweat so much when climbing stairs.
The
last piece of the puzzle is that work performed to climb a stairwell excludes
the work performed to swing the arms &
legs and to turn around the corners in the stairwell. Fortunately a
paper published by Minetti et. al. (Skyscraper running: physiological and
biomechanical profile of a novel sport activity) offers some insight. In this
paper, the authors experimentally derived that only about 80% of the total
power output is used to climb vertically. Another 5% of the total output is
used to swing your limbs and another 15% is used while turning around corners.
However, I don’t fully agree with all of these findings. My biggest concern was
that the authors assumed that that the power needed to turn around a landing
was equivalent to the power needed to run in a 2 meter (about 6’7”) diameter
circle. From experience, I know that I make much tighter turns in the stairwell
*and* I’m using my arms to keep my center of mass as close to the hand
rail as possible. Really I’m just pivoting around the rail (on my inside foot)
rather than running around a circle. As such, I believe that the author’s model
was quite conservative. Although I have neither experimental evidence nor a
kinematic model to predict the power needed to turn around a stairwell landing,
I estimate that:
 90% of work output is used to climb vertically
 5% of work output is used to move your limbs
 5% of work output is used to turn around the landings
Including
both muscle efficiency and excess power wasted in the stairwell (on turns &
extraneous motion) we can use the following formula to calculate the total
number of Calories used to climb a stairwell:
Calories
used to Climb a Stairwell = [(Mass x
Distance)/384]/A_{eff}
Where:
Mass is in kg.
Distance is in meters (vertical height of
climb)
Units for the 384 factor is (kg x m)/Calorie*
A_{eff} is the muscle efficiency
factor, a unit less number somewhere between 0.18 and 0.25
*note: this is 90% of the 426.5 factor used in the 2nd example
Example 3: How many
Calories did I use to climb the Sears Tower?
Answer: We’ve already
shown I need 78 Calories of work output to climb the Sears Tower, but this only
represents 90% of the total work output exerted by my body.
Therefore overall
output of my body = 78 Calories/90% = 87 Calories (rounded).
Since my muscles are
pretty inefficient at converting energy into work, I burned far more than just 87
Calories  mostly in the form of heat. Assuming I’m about 22% efficient
(estimate), I burned about 87 Calories/22% = 393 Calories during the climb, which
is a rate of about 1576 Calories per hour.*
*Note: this does not
include the 22 additional Calories burned via my body’s internal processes
(which is an order of magnitude smaller than the Calories burned due to
climbing).
MET
Have
you ever used a piece of exercise equipment and noticed the term “MET” on the
electronic display? Well, MET is an acronym for “Metabolic Equivalent of Task”.
One MET is defined as 1 Calorie/(kg x hour), and it was originally considered
to be the resting metabolic rate of an “average” person. The reason why
exercise equipment manufacturers include MET is because it provides a
measurement of the intensity of a workout. For example, walking very slowly has
a MET of 2.3. This means you are burning 2.3 times as many calories (via
exercise) than your body naturally burns while at rest. Here is a short list of
common activities and their MET values (courtesy of Wikipedia):
 Watching TV: MET = 1
 Walking briskly (3.4 mph): MET = 3.6
 Jogging: MET = 7
 Pushups/Pullups: MET = 8
 Running: MET = 10+ (depending on speed)
Since
this article is primarily about stair climbing, lets calculate my MET for
climbing up the Sears Tower.
Example 4: What was
my MET for climbing the Sears Tower?
Answer: Since we’ve
already calculated my RMR in Example 1 and my Calorie expenditure due to
climbing in Example 3, the ratio should give an approximate value of MET. In my
case that was 393 Calories burned due to climbing per 22 Calories due to my
body’s internal processes. This give an approximate value of
MET_{est}= 393/22 = 17.9.
MET_{est}= 393/22 = 17.9.
However, my RMR is
not exactly the same as the an average person’s. So, taking the definition of 1
MET = 1 Calorie/(kg x hour), it looks like my actual MET is
MET_{act}= 393/(80kg x .25 hours) = 19.7
MET_{act}= 393/(80kg x .25 hours) = 19.7
Taking
the ratio of these two MET calculations (i.e. MET_{act}/MET_{est})
it appears my RMR is about 10% more than the average person.*
*Which
makes sense ‘cause I’m totally jacked.
Further Questions:
As
you can see from the examples above, stair climbing is a great way to burn
calories. However, there are several areas that require further exploration:
1) It
has been shown that a trained athlete requires less energy to perform the same
amount of work, but that is mainly because a trained athlete recruits fewer
muscles to perform a given amount of work. Unfortunately, there is a lot less information
about how muscle efficiency (i.e. translating energy into mechanical work vs.
heat) varies from person to person. Can muscle efficiency also be increased
with training? Is there a biochemical upper limit?
2) How
much extraneous work is really spent swinging the arms and legs and turning
around the stairwell turns? Minetti et. al. has piqued my interest on this
topic. In addition, I’d also like to know the effect of using the rails vs. not
using the rails when climbing. I know from experience that using the rails (i.e.
using the arms) helps to “save” my legs from anaerobic fatigue, but at the same
time, using the rails is not as mechanically efficient as using the legs. I’d
like to quantify this trade off.
3) RMR
is a very good measurement of the metabolic needs of your internal processes
when the body is at rest, but does it change during exercise? For example, I
know that intense exercise makes difficult to think, so I must assume that less
energy is used by the brain during exercise. Does the same hold true for other
organs?