Exercise Not Training
(Work in Progress)
Overview
There is a distinction between training and exercise.
The basic difference is that when one is "training" one is training for a specific
goal, usually athletic in this context: running a 5K or 10K, competing in
a weight lifting contest, or being a better specific sport athlete (e.g. baseball, football, ...).
Exercise is mostly just a generic "be physically healthier" or "look better"
(e.g. carry less body fat, be more muscular) goal.
In my case, the goal is pretty much 'general health' with an emphasis on
cardio, but with no intention to run a 5K or 10K (I hate running) race.
I'd like to be stronger, or at least have more muscle and less body fat.
This makes quantitatively measuring improvement difficult :-)
Broadly, I'm paying attention to the number of pullups I can do (currently zero),
the amount of weight I can bench press, the number of calories I can burn
in an hour and the number of flights of stairs I can climb in an hour (the
last two while keeping my average heart rate to no more than 140 beats/hour).
Basic Goal
More specifically, I've been "working out" for a while now with the goals being to:
- Become generally healthier (whatever that means)
- Increase my endurance (e.g. ability to walk longer distances)
- Lose weight/fat
In addition, I have a few constraints that I'm applying:
- I'm only willing to go to the gym three times per week.
- When at the gym I'm only willing to work out for one hour at a time or maybe a bit more.
- I don't want to sustain exercising with my heart rate above about 85%
of my 'max heart rate.' 85% of my calculated max heart is about 140 beats/minute.
Exceeding 140 beats/minute for a minute or two is fine.
- My primary focus is cardiovascular health, though I'd like to
mix some weight training in as well.
With these goals and constraints I'd like to get the most value out of my
three-ish hours/week spent at the gym.
And, yes, sleep and nutrition are important, too, but that's not the focus
of this document.
So ... how do Cardiovascular and Strength Exercise work and what makes
sense for me given my goals and constraints?
Cardiovascular Exercise
Current Status
My typical cardio workout is to stretch and then get on a
elliptical machine or stair stepper for an hour while keeping
my heart rate in the 130 - 140 beats/minute range. 140 beats/minute
is 85% of my estimated HRmax as traditionally calculated
and 85% is a Mayo Clinic recommended upper limit for exercise.
So ... my current strategy is to basically go "all out" for 60 minutes
keeping in mind my desired cap to sustained heart rate. Can I do better?
There are other cardio strategies such as HIIT (High Intensity Interval
Training) and Zone 2 training. How do those work? Maybe doing one
of these would be good?
Topics
Calories and Kilocalories
For historical reasons we have two different definitions of calorie. One,
the food or dietary calorie, is the amount of energy needed to raise one
kilogram of water one degree celsius. The other, historically used in
physics and chemistry, is the amount of energy needed to raise one
gram of water one degree celsius. Obviously, the two units are different
by a factor of 1,000. This document uses the food/dietary definition of
calorie.
Max VO2
One of the factors limiting how hard and how long
you can exercise is the amount of oxygen your body can
take in over a period of time.
The amount of oxygen that your body can take in is
referred to as VO2 max, which is short for
"Volume of Oxygen Maximum" Because the oxygen is
used as the oxidizer when your body is burning fuel, the value is defined in
terms of body mass. The same amount of oxygen for a
person with ½ the mass will result in a VO2
max value twice as high.
Commonly, the VO2 max value is reported as
mL of oxygen per Kg of body mass per minute
Perhaps surprisingly, the limit here is rarely your lungs, but
instead how hard, fast and efficiently your heart can beat. [Another
limit can be how good your blood is at carrying oxgen. Blood doping
increases VO2 max by making your blood better at
transporting oxygen.]
Max Heart Rate
Many cardiovascular activities are either limited by how fast your
heart is able to beat or are limited by a desire to remain in a given heart
rate range. These ranges are usually defined relative to a person's
maximum heart rate.
The most accurate way to measure an someone's max heartrate is to
hook them up to a treadmill and a heart rate monitor and see how fast
they can actually run their heart. Most casual exercisers don't do
that, but instead use an age based forumula to estimate max heart rate.
A few common formulas can be used to estimate the max heart rate in
beats/minute requiring only the age in years of the individual:
Fox Formula: HRmax = 220 - age
HUNT Formula: HRmax = 211 - (0.64 * age)
Tanaka Formula: HRmax = 208 - (0.70 * age)
Gellish Formula: HRmax = 207 - (0.70 * age)
Gulati Formula: HRmax = 206 - (0.88 * age)
- The Fox Formula is the most commonly used formula and
is used by The Mayo Clinic
as well as The Cleveland Clinic.
It is known to be less accurate than later models and has a fairly
large standard error of over 10 beats/minute.
- The HUNT formula was generated from a study of 3,320 healthy men
and women over a wide range of ages.
- The American College of Sports Medicine prefers the Tanaka formula.
- The Gellish Formula from "Longitudinal modeling of the relationship between
age and maximal heart rate" and is basically identical to the Tanaka forumula.
- The Gulati formula was generated by fitting data from a study on women
("Heart Rate Response to Exercise Stress Testing in Asymptomatic Women")
and this forumla is not applicable to men.
The formulas generate different max heart rate estimates, but are not
wildly different, except that the Gulati values — intended for
women only — are noticeably lower than the others:
| Age | Fox | | HUNT | Tanaka | Gulati |
|---|
| 20 | 200 | | 198 | 194 | 188 |
| 30 | 190 | | 192 | 187 | 180 |
| 40 | 180 | | 185 | 180 | 171 |
| 50 | 170 | | 180 | 173 | 162 |
| 60 | 160 | | 173 | 166 | 153 |
In 2020 the paper "Accuracy of Commonly Used Age-Predicted Maximal Heart Rate Equations"
noted that the Fox formula "has been reported to have a standard deviation of between 10 and
12 bpm, as well as significantly over and underestimating HRmax in younger and
older adults, respectively. Although the limited predictive accuracy of this equation
has been documented it is still used in clinical settings and published in resources
by well-established organizations in the field."
Resting Heart Rate
Resting heart rate is the rate at which the heart beats when the
body isn't doing anything specific. The resting heart rate is specific to
individuals and common rates for non-athletes range from 60 beats/minute
to 100 beats/minute. There is no age (or weight) based formula for this.
You need to measure it by doing something like taking your pulse early in
the morning after you have woken up but before you get out of bed.
My resting heart rate is around 72.
Heart Rate Reserve
Heart Rate Reserve is the difference between an individual's HRmax
and resting heart rate. If someone has a HRmax of 160 beats/minute
and a resting heart rate of 60 beats/minute then that someone has a Heart
Rate Reserve of 100 (160 - 60).
Energy Systems
This is the section where I am least confident of my understanding.
Bodies convert 'stored energy' (e.g. fat, ATP) to useful energy via chemical
reactions. Two of these reactions are anaerobic reactions which do
not need external oxygen. The third reaction is aerobic which
requires external oxygen. This external oxygen for the aerobic
reaction is provided by your lungs breathing in air and the oxygen is
distributed to your body by your heart via your blood.
The aerobic system can run for hours, but the two anaerobic systems
will run out of fuel fairly quickly.
The three systems are:
- The (Anarobic) ATP-CP System
The ATP-CP system is responsible for providing very short (< 10 sec)
bursts of energy. If you are running a 50 - 100 yard sprint then most
of the energy is coming from this system.
The ATP consumed by this reaction can and will be restored/replaced by
the lactic acid system though the ATP-CP system can consume APT faster
than the lactic acid system can replace the APT which is why you can't
sprint 'all out' for minutes at a time.
- The (Anarobic) Lactic Acid System
The Lactic Acid System mostly converts stored glucose to APT which
is then consumed by the ATP-CP System. The side effect of this
glycolysis is the creation of lactic acid, which you body will
attempt to remove. This system is limited by lactic buildup and
eventually by the body running out of stored glucose.
- The Aerobic System
The aerobic system burns fat using oxygen taken in from breathing.
You should have a lot of oxygen in the air around you
and, from an aerobic standpoint, lots of fat to consume. Because of
this, activities using only the aerobic system for energy can be sustained
for hours.
Different heart rates will use different mixes of the three energy systems.
Heart Rate Zones
Cardio workouts are often defined in terms of "zones." This may be
extra true right now because "Zone 2" training is popular right now. The
training zones are usually defined on the Internet as ranges of
the percent of max heart rate:
| Zone | | % Max HR |
|---|
| Zone 1 | | 50% - 60% |
| Zone 2 | | 60% - 70% |
| Zone 3 | | 70% - 80% |
| Zone 4 | | 80% - 90% |
| Zone 5 | | 90% - 100% |
This table is simple and the 10% range per zone is easy to remember. But it
is so simple that one suspects that it doesn't match the reality of human
biology as well as it might. Very specifically, it likely doesn't map terribly
well to the three energy systems.
The American College of Sports Medicine has a
different set of values
for the various Zones:
| Zone | | % Max HR |
|---|
| Zone 1 | | <57% |
| Zone 2 | | 57% - 63% |
| Zone 3 | | 64% - 76% |
| Zone 4 | | 77% - 95% |
| Zone 5 | | > 95% |
The ACSM folks point out that the '220 - age' max heart rate estimation "formula
wasn't intended to be used for the calculation of fitness programs." Instead, the
ACSM uses the Tanaka formula for calculating max heart rates and the ACSM also sets
the Zones at different cut points (I don't know where they get the data to
set the cut points). For 55-year-old me this results in competing Zone tables:
| Zone | | beats/minute range |
|---|
| | Traditional | ACSM |
|---|
| Zone 1 | | 82 - 99 | <97 |
| Zone 2 | | 100 - 115 | 97 - 107 |
| Zone 3 | | 116 - 132 | 108 - 129 |
| Zone 4 | | 133 - 148 | 130 - 161 |
| Zone 5 | | 149 + | 162 + |
The differences aren't too big, with the maximum heart rate at the top of
Zone 2 being the only difference of consequence. The difference at the top
of Zone 4 is larger, but can mostly be ignored as folks are unlikely to be
between 90% and 95% of max heart rate long enough to care whether to consider
it to be in Zone 4 or Zone 5.
There is, however, one more wrinkle and this wrinkle matters more. Rather than
calculating Zones as a percentage of max heart rate the Zones can be calculated
as a percentage of your heart rate reserve.
The Karvonen Formula accomplishes this (and the Mayo clinic uses this method
as well as the percent of HRmax approach even though they result
in very different values for "85%"!). Using the traditional zones table
but applying the percentages to the heart rate reserve as the Karvonen
Formula does we get the following table of heart rate beats per minute
ranges for 55 year old me:
| Zone | | beats/minute range |
|---|
| | Traditional | ACSM | Karvonen |
|---|
| Zone 1 | | 82 - 99 | <97 | 119 - 128 |
| Zone 2 | | 100 - 115 | 97 - 107 | 129 - 137 |
| Zone 3 | | 116 - 132 | 108 - 129 | 138 - 146 |
| Zone 4 | | 133 - 148 | 130 - 161 | 147 - 156 |
| Zone 5 | | 149 + | 162 + | 157+ |
The difference here is obvious: The Karvonen ranges are substantially higher than any of the
other methods for the first three zones. This becomes important when the various training
styles are considered. Notice, to illustrate, that 136 beats/minute would be considered
Zone 4 using Traditional and ACSM zone definitions and as the high end of Zone 2 using
Karvonen zone definitions based on heart rate reserve.
This also calls into question discussions of Zone based training. If there are wildly
different definitions of the Zones, then generalized conclusions from different experiences
and experiments cannot be compared or merged.
Styles: SIT, HIIT, MICT and Zone 2
People can't run (or climb stairs or ...) at their maxiumum heart rate for long periods
of time, so the mix of various intensities and durations make up
different 'types' or 'styles' of cardio training. The boundaries between these styles
is not well defined and different people will use slightly different dividing lines
between the styles. Still, a reasonable set of definitions is:
| Type | Description |
|---|
| SIT | Sprint Interval Training:
This is basically exercising with
an all out effort — max heart rate (100% or higher!) —
for a short period of time, maybe 10 to 30 seconds, followed
by a relatively long recovery time of maybe 120 seconds. A
running activity done as SIT might be to sprint for 100 - 200 yards
and then walk back to the start. Then repeat as many times as
needed/desired until done. Alternately, one might repeatedly
run up three flights of stairs and then walk (not run) down them.
During Covid (2020 - 2022) while the gyms were shut down I did this
for two years. An overpass near my house had a flight of stairs
~3 floors high and I could run stairs but had no access to elliptical
machines or exercycles.
|
|---|
| HIIT | High Intensity Interval Training:
This is exercising at a high intensity
— 80% - 100% of HRmax — for 1 - 4 minutes, followed
by a recovery period that gets the heart rate back down to 55% - 70%
of HRmax. Repeat until done.
|
|---|
| MICT | Moderate Intensity Continuous Training:
This is exercising at an low enough intensity that one can
maintain the intensity for up to an hour if not more. A
heart rate of around 55% - 70% HRmax is often considered MICT.
|
|---|
| Zone 2 | This is similar to MICT and often conflated with it, but Zone 2
training is easy enough that, in theory, one can maintain it for
many hours.
|
|---|
Zone 2 Training
Zone 2 training isn't just another name for "Moderate Intensity Continuous Training."
The basic idea behind Zone 2 training is that you keep your body in its aerobic range
which means that all the energy used is burned with oxygen. Above this range the body
begins burning glycol via anaerobic glycolysis. One side-effect of this glycolysis
is that the body begins to generate lactic acid faster than the body can clear it out.
Training in the aerobic range is supposed to provide a number of benefits (e.g. mitochondrial
development/growth) which eventually manifest as being able to maintain a higher
effort (e.g. speed) at a given heart rate. For endurance runners this is important.
Dr. Phil Maffetone
Before (I think) we had Zone 2 training, Phil Maffetone was pushing the idea
that the way to run faster in endurance activities (e.g. marathons) was to
spend most of your training time beneath the upper limit of your aerobic heart rate.
Doing so would train your body to run (or bike or swim or whatever) faster at
this heart rate and thus would allow you to run faster at higher heart rates, too.
Initially, Maffetone found this for athletes by using exercise equipment
(e.g. treadmills, exercycles) and heart rate monitors.
By the early 1980s, Maffetone came up with a simple formula using age in years
to establish the heart rate upper limit to keep your heart rate in the aerobic
regime. The formula matched his machines well enough that it could be reliably
used on its own. The formula is:
MAF180 = 180 - age
A handful of adjustments are then made:
| Adj | Condition |
|---|
| -10 | If you have or are recovering from a major illness
(heart disease, any operation or hospital stay, etc.),
are in rehabilitation, are on any regular medication,
or are in Stage 3 (chronic) overtraining (burnout)
|
| -5 | If you are injured, have regressed or not improved in
training (such as poor MAF Tests) or competition, get
more than two colds, flu or other infections per year,
have seasonal allergies or asthma, are overfat, are in
Stage 1 or 2 of overtraining, or if you have been inconsistent,
just starting, or just getting back into training
|
| +5 | If you have been training for more than two years without
any of the problems listed above, have made progress in
your MAF Tests, improved competitively and are without injury
|
In addition, below age 16 Maffetone says to use 165 as an upper heart rate to
stay in the aerobic regime. Over 65 may require adjusting up by as many
as 10 beats/minute.
Maffetone notes that the Maffetone heart rate doesn't correspond to any
specific physical measurement (e.g. VO2 max, lactate threshold, ...).
It is simply the individual's maximum aerobic heart rate.
Since Zone 2 training tries to accomplish the same thing that Maffetone advocates
— keeping the training heart rate in the aerobic heart rate range —
we can see how this matches up. For 55 year old me the heart rate to not
exceed using the various approaches is:
| Approach | bpm range | % of Fox HRmax |
|---|
| Zone 2 using Fox HRmax & Decile zones | 100 - | 115 | 60-70% |
| Zone 2 using Tanaka HRmax & ACSM zones | 97 - | 107 | 59-65% |
| Zone 2 using Fox HRmax, Karvonen HR reserve & Decile zones | 129 - | 137 | 78-83% |
| Maffetone HR180 | 125 - | 130 | 76-79% |
It is interesting that the last two rows are fairly similar and that the first
two rows are fairly similar but that the two pairs are quite far apart. A reasonable
belief might be that the aerobic heart rate range ends at around 80% of HRmax
for me. Since I try to avoid exceeding 85% of my HRmax as calculated using
the Fox formula, this means that I'm (probably) mostly exercising in the aerobic heart rate range.
The Original Conundrum & My Conclusion
Initially, this analysis began with me attempting to make consistent the
Traditional Decile Zone table above and HIIT:
My HRmax, using the Fox formula (220 - 55), is 165 beats/minute.
85% of my HRmax is 0.85 × 165, or 140 beats/minute.
I can sustain an average of 132+ beats/minute (or 80% of my HRmax) for
over an hour. The 80+% puts my heart rate in the (low end of the) intense
part of HIIT using the traditional zone definitions. The 60+ minutes puts my
heart rate in the MICT regime.
I am in reasonably good cardiovascular shape, but by no means an "athlete." So
what gives?
The key insight seems to be the difference between defining zones using
the Karvonen HRmax approach, which uses percent of Heart Rate Reserve, and the
approaches that define zones using the percent of HRmax. The Karvonen Formula has the nice
property that it puts my typical cardio workout at the top of Zone 2 rather in Zone 4.
Since I can maintain my 132+ beats/minute heart rate for over an hour, thinking of this
as Zone 2 rather than Zone 4 makes a lot more sense. In addition, the Karvonen Formula
gets values similar to Maffetone so that would be another data point in favor of believing
that the decile Zone definitions as percentages of HRmax are just wrong (assuming
that we want them to correspond to anything physical).
There are examples of Zone confusion on the Internet. One such is
here:
Zone 2 training involves running or
cross-training at a pace that keeps your
heart rate within 60-70% of your maximal heart rate.
...
Zone 2 is defined by a heart rate range of 60-70% of your maximum heart rate.
If you know your maximum heart rate, you can use that; otherwise, you can estimate
your heart rate using the following formula:
- Maximum Heart Rate for Males = 208.609-0.716 x age
- ...
For example, if you're a 36-year old male: 208.609-0.716 x 36 = 183 bpm.
Once you have your maximum heart rate, you need to calculate your heart
rate reserve (HRR), which is your maximum heart rate minus your resting
heart rate (HRR = Maximum heart rate - resting heart rate).
Measure your resting heart rate first thing in the morning while you're
still lying in bed. For example, if your maximum heart rate is 180 bpm
and your resting heart rate is 60, your heart rate reserve is 120 bpm.
From there, you can determine your zone 2 heart rate with the following formula:
- Lower end of the heart rate range = 0.60 x HRR + resting heart rate
- Upper end of the heart rate range = 0.70 x HRR + resting heart rate
With an HRR of 120 bpm, for example, you would end up with the following:
- Lower end of the heart rate range = 0.60 x 120 + 60 = 132 bpm
- Upper end of the heart rate range = 0.70 x 120 + 60 = 144 bpm
This means the runner's Zone 2 heart rate is 132-144 bpm.
The flaw with the analysis here is that 60% - 70% of an HRmax of 180 gives
a range of 108 - 126 beats/minute, not the calculated 132 - 144 beats/minute. 132 - 144
beats/minute is 73% - 80% of a HRmax of 180 beats/minute. Other sites calculate
Zone 2 for an individual with a HRmax of 180 as falling in the range
of 108 - 126 beats/minute so there is certainly inconsistency about what defines Zone 2.
My tentative conclusion is that I am doing Zone 2 or Moderate Intensity Continuous
Training workout (mostly) and many of the folks who think they are doing HIIT training
are not unless they actually get well into the traditional Zone 4 beats/minute range.
Additionally, I believe that meaningful "Zones" — Zones that correspond to something
physical such as aerobic threshold — need to be estimated as percentages of Heart Rate
Reserve rather than a percentages of HRmax
One more piece of information that supports the conclusion that my Zone 2 is more
likely to be in the 129 - 137 range comes from Peter Attia, MD. Dr. Attia
has a Youtube Chanel that focuses on longevity. A large part of that is exercise.
He has a video from late 2023 or early 2024 titled "This is what Zone 2 training
looks like."
In this video, he rides a stationary bicycle in what he claims is
Zone 2 and speaks to the camera. Part of what he says (at around the
45 second mark) is this:
"Heart rate today right now about 137. It's been as high as 142, low as 134,
meaning throughout the past couple of weeks"
--
This is what Zone 2 training looks like
Attia is 50 years old, so his Zone 2 should be about 5 beats/minute higher
than mine. If his numbers are Zone 2 then 129 - 137 for me is about right
and 100 - 115 is below Zone 2.
For reasons not entirely clear, the heart rate needed to sustain a given level
of moderate to high intensity activity drifts higher over time. In short, the
heart rate needed to run a mile in a given time (e.g. 10 minutes) for the first
mile will be lower than the heart rate needed to run the same mile in the same
given time after running a number of miles.
About ½ of the drift seems to be accounted for by (1) an increase in the
body's core temperature which requires energy to cool and (2) dehydration leading
to thicker blood (thus requiring more work for the heart to pump). Staying hydrated
counters this ½ of cardiac drift.
I've been doing cardio workouts like this:
- I get on a machine (e.g. elliptical, stair stepper)
- I exercise for about an hour.
- I try to avoid having my heart rate go above 85% of my Fox HRmax
The machines report calories burned during your workout and seem
to be consistent (if not accurate!) as long as I enter my weight.
My results over time on the elliptical machine look like this:
| | | Calories |
|---|
| Date | Avg HR | Duration | Overall | 10 min | 30 min | 40 min |
|---|
| 18-Sep-2022 | 131 | 60:01 | 837 | | | |
| 19-Jan-2023 | 136 | 62:10 | 900 | 160 | 455 | |
| 24-Jan-2023 | 135 | 60:50 | 900 | | 455 | 605 |
| 31-Jan-2023 | 131 | 61:50 | 900 | 165 | 447 | 595 |
| 16-Feb-2023 | 132 | 60:16 | 900 | | | |
| 19-Feb-2023 | 134 | 60:00 | 904 | | 462 | 609 |
| 12-Mar-2023 | 130 | 60:00 | 914 | 163 | 472 | 619 |
Progress over past six months is going from around 840 calories/hour burned
with an average heart rate of 131 beats/minute to almost 915 calories/hour burned
with an average heart rate of 130 beats/minute. So about a 9% improvement
in six months.
Stair stepper progress is similar. 225 flights of stairs took 73 minutes to
climb in May 2022. The same 225 flights takes about 62 minutes in January 2023.
Since it appears that I've been mostly exercising with my heart rate in a
"real" Zone 2 as defined by the aerobic heart rate range or, alternately,
near the Maffetone upper heart rate limit a reasonable conclusion
is that exercising in this range can/will increase performance at the same heart
rate.
Additionally, one can see cardiac drift at work in the calorie counts at
various times during a given workout. Comparing the 30 minute calorie count
to the final count shows this pretty clearly as the second half of any given
session burns fewer calories than the first half [and, in addition, the earlier
thirty minutes includes some time ramping my heart rate up from baseline
to whereever it eventually stabilizes for that session].
Your body needs to do work just to keep itself alive. A body's base
metablolic rate (BMR) accounts for this work as calories.
As with HRmax estimation formulas there are a number of estimation
formulas for your base metabolic rate (expressed in terms of calories/day).
One is the Mifflin-St Jeor equation:
Males: BMR = 10 × W + 6.25 × H - 5 × A + 5
Females: BMR = 10 × W + 6.25 × H - 5 × A - 161
- W is weight in kg
- H is height in cm
- A is weight in age in years
The estimate makes no specific assumptions about an individual's lean
body mass vs fat percentage. Better estimates can be made if this is
known.
Gross calories is all the calories burned in a given time. Net calories
are the additional calories burned beyond what your body was going to burn
keeping itself alive with the base metabolic rate.
The two values can be quite different and it is common for various claims
and reports to not make clear which is being discussed.
As an example, if a base metabolic rate for a person burns ~100 calories
per hour then an exercise that burns an additional 300 calories/hour will
have a Gross calorie burn of 400 calories/hour, but a Net calorie burn
of only 300 calories/hour.
There exist functions to provide calorie burn estimates given heart rate, weight, age and sex.
One such is this (allegedly from "Target heart rates for the development of cardiorespiratory
fitness" by Swain, et.al.):
Male: Gross Calories/min = ((-55.0969 + (0.6309 × HR) + (0.1988 × W) + (0.2017 × A))/4.184)
Female: Gross Calories/min = ((-20.4022 + (0.4472 × HR) - (0.1263 × W) + (0.074 × A))/4.184)
[NOTE: The 4.184 divide converts kJ into dietary calories]
Where:
- HR is Heart Rate in beats/minute
- W is weight in kg
- A is age in years
NOTE: The estimates are valid only from about 60% of HRmax and above.
The Gross Calories/min estimate makes no specific assumptions about an
individual's VO2 max and can be improved if the VO2 max is known:
Male: ((-95.7735 + (0.634 × HR) + (0.394 × W) + (0.271 × A) + (0.404 * VO2max))/4.184)
Female: ((-59.3954 + (0.450 × HR) + (0.103 × W) + (0.274 × A) + (0.380 * VO2max))/4.184)
Additionally, the formulas can be combined to show the VO2 max assumed in the
forumulas that don't require it as an input.
Male/Female Differences
The difference between estimated male and female gross calorie burns
at the same heart rate, weight and age can be large and the difference
grows with weight. Using the Gross Calorie estimation formulas that
make no VO2 max assumptions results in this table:
| | | Estimate | |
|---|
| Age | Weight | HR | Male | Female | |
|---|
| 25 | 50 | 130 | 600 | 477 | |
| 25 | 100 | 130 | 743 | 387 | |
| 30 | 75 | 150 | 868 | 565 | |
| 55 | 100 | 130 | 830 | 418 | ← Almost 2:1 |
In all likelihood not all weights are valid. I don't know the range of valid weights.
The amount of energy needed to raise one kilogram one meter in Earth's
gravity field (9.81 m/s2) is 9.81 Joules. The energy required
to raise a 100 kg body one meter in Earth's gravity field is 981 Joules.
Moving a 100 kg body up three meters (almost a full building floor), maybe by
taking the stairs instead of the elevator, requires ~3,000 Joules
~3,000 Joules is ~0.70 nutritional calories.
So if a 100 kg person climbs 100 flights of stairs they will burn 70 calories?
Seems low.
It is. The human body is not 100% efficient at converting energy to work. A
reasonable estimate for human body efficiency is around 20% (though slightly
lower values and also values up to 25% are also common. As with much of this,
if the actual value is important then it will have to be measured for the
specific individual doing the specific task ...). So our 100 kg person climbing
100 flights of 3 meter stairs will burn around 70/0.2 = 350 calories!
It is important to be clear about whether one is measuring/reporting calories
burned (accounting for the human body's efficiency) or the Newtonian energy
of the movement (stair climbing, running, etc.). For exercise one almost always
cares about calories burned.
Some cites:
- From a University of Birmingham press release,
Stair climbing reduces energy bills,
summarizing a 2011 study:
Dr Frank Eves, a Reader in Lifestyle Physical Activity from the University
of Birmingham's School of Sport and Exercise Sciences commented "...
Humans work at only 20% efficiency when climbing stairs and each calorie
expended when climbing produces four calories of heat.""
- From Physiological effects of exercise
by Deborah Anne Burton, Keith Stokes and George M Hall:
The maximum efficiency for the conversion of energy nutrients into muscular work is 20-25%.
The remainder is released in a non-usable form as heat energy, which raises the body temperature.
Another way that exercise effort is reported is in METS (Metabolic EquivalenTS).
1 MET is intended to be the amount of energy (and thus Oxygen) needed for
the body to sustain itself. Basically, the amount of energy needed while
at 'rest'.
METS are thus a multiple of this.
1 MET seems to be fairly commonly 3.5 ml O2/kg of body weight.
The 3.5 value is a common convention, but as with so much of health information
has a problem:
The value equating 1 MET to a VO2 of 3.5 ml/kg/min was derived from a single 70 kg,
40-year-old male subject's resting oxygen consumption (VO2). This decade long convention
based on one healthy non obese male's energy expenditure has been widely used in
individuals of all ages, sexes, phenotypes and disease states.
—
METS to VO2: An Accurate Analysis (2020) (underlining added by me)
The article/paper goes on to claim:
A total of 272 people were reviewed. Mean Resting VO2 for all patients was noted to be
3.37 ml/kg/min. This is significantly different from conventionally assumed resting VO2
of 3.5 (95% CI 3.24-3.49, P 0.0379). Additionally, resting Vo2 was noted to be significantly
different for patients aged 60 and over (3.3), Patients with BMI <25 (3.88), Patients with
BMI >30 (3.12) and females (3.29). 169 patients were noted to reach maximal exercise based
on RER <1.15 while 102 patients could not reach maximal exercise. Maximal Vo2 to maximal
MET ratio for patients with maximal studies was noted to be 2.28 (95% CI 2.13-2.43) and for
patients with sub-maximal studies was 2.81 (95% CI 2.38-3.24). Both these values were
significantly different from conventionally accepted relationship of 3.5.
Still, the average value from the group of 272 people, 3.37 ml/kg/min, is not terribly
far off the estimate of 3.5 ml/kg/min — being just 4% lower. The primary problem
with the conventional 3.5 value is that it:
- overstates the average for older (60+ year old) people
- overstates the average for women
- overstates the value for people considered obese using BMI (30+)
- understates the value for people considered "normal" or "underweight" using BMI (25-)
3.5 is probably fine as an estimate for slightly overweight middle aged men. Fortunately,
that describes me :-)
Conveniently, the units of METS translate directly into the same units used by VO2 max:
1 MET is ~3.5 ml O2/kg of body weight; 10 METS is ~35 ml O2/kg of body weight.
The ~3.5 can be adjusted if one knows more about BMI, age and sex.
This means that VO2 max can be converted into METS and METS can
be thought of a a percent of VO2 max.
The National Academy of Sports Medicine provides this helpful (though wrong!)
shortcut formula:
Gross Calories/min = METS × 3.5 × W / 200
Where 'W' is weight in kg.
This formula appears on many sites. It is probably wrong, even as a estimation. Note
that 1 MET for a 100 kg person works out to 1.75 calories/min. For an entire day this
is 2520 calories. Using the Mifflin-St Jeor BMR estimation formula from above, we get
these BMR estimates (using 165 cm (5' 5") for the women and 180 cm (5' 11") for the men):
| | BMR (calories/day) |
|---|
| | Mifflin-St Jeor | NASM |
|---|
| Age | Weight | Male | Female | |
|---|
| 30 | 75 | 1,730 | 1,470 | 1,890 |
| 30 | 100 | 1,980 | 1,720 | 2,520 |
| 55 | 75 | 1,630 | 1,370 | 1,890 |
| 55 | 100 | 1,880 | 1,620 | 2,520 |
The difference between the NASM estimate at 1 MET and the Mifflin-St Jeor
equation is large.
Another commonly seen equation is this:
METS = 1.163 * Watts / W
Where 'W' is weight in kg.
This one gets bizzarly low results when using Newtonian mechanical energy
for the Watts component, but the results are reasonable (which doesn't mean
correct!) when an efficiency factor of ~20% is applied to account for the
chemical energy in Watts that one's body uses to generate the Newtonian mechanical energy.
The equation then becomes:
METS = 5.815 * Newtonian-Watts / W
The assumption here is that an alive body cannot be using 0 Watts.
This calculates ~10.7 METS for 180 (Newtonian Mechanical) Watts by
a 100 kg person. This seems to be roughly in the range that ~10
METS would be. See the energy calculation below under Equipment Reported Calorie Usage.
Getting accurate calorie counts from exercise equipment can be tough.
The good news is that you can still track progress as long as the equipment is
consistent. More good news is that the equipment from a given vendor seems to
be internally consistent :-)
To illustrate the problems we can perform some basic Newtonian physics
mechanical energy calculations for a machine where we know what is happening
fairly well: the step mill.
Using me as an example we can calculate the amount of mechanical energy that must be
expended to climb a certain number of stairs and then compare that to what the
machine reports. So, from an actual exercise session:
- My weight: ~220 pounds (~100 kg)
- Flights of stairs climbled: 218
- Stair height: 7.5" (Machine's spec; OSHA specifies that step "riser height shall be from 6 to 7.5 inches")
- Stairs/flight: 16.25
- Flight height: 10' 1.875" (121.875", 3.125 meters; reasonable for residential buildings)
- Time: ~62 minutes (3,720 seconds)
Raising ~100 kg ~681.25m in a one gravity field (9.81 m/s2, such as we have on Earth)
takes 100×681.25×9.81 ~= 668,306.25 joules of energy.
668,306 joules / 3,720 seconds ~= 180 joules/sec = 180 watts (for 62 minutes)
1 Wh = 0.86 calories
180 watts for 62 minutes ~= 160 calories
The machine reports ~900 calories for the hour. 900 isn't close to 160. What gives?
We need to account for several things:
- Gross vs Net Calories
- Human Body Energy Efficiency
- The Machines Have Limited Information
Gross vs Net Calories
The first thing to do is to account for Gross vs Net calories. At zero
flights of stairs per hour the calorie burn isn't 0 calories/hour
but instead is whatever the resting metabolic rate is for the person on
the step mill. The machine doesn't know my resting metabolic rate, but
resting metabolic rate can be estimated from weight, sex and age.
The machine, however, only knows my weight. It is
plausible that 1 calories/hour/kg is what the machine uses as a crude
estimator. 1 calories/hour/kg would be close the NASM
"Gross Calories/min = METS × 3.5 × W / 200" forumula with
a METS value of 1 (for resting). For me this would work out to ~100
calories/hour or ~2,400 calories/day. This value, obviously, won't
be as good as one that takes into account age and sex as well, but
it isn't terrible and the machine doesn't ask for age or sex.
If the 900 calories/hour reported is the Gross calorie burn, then removing
the estimated resting metabolic rate gives the Net calorie burn
for doing the stairs rather than sitting quietly: 900 - 100 = 800
calories.
Human Body Energy Efficiency
800 calories is closer to 160 calories than 900 calories is, but 800
is still not particularly close. The next adjustment is to take into
account the fact that the human body is not 100% efficient at converting
chemical energy into mechanical energy.
The efficiency varies by both individual and activity, but 20% efficiency is
a plausible value. It has the additional property that 20% of 800
is 160, which is ... pretty much the number we are hoping to find.
The Machines Have Limited Information
Now, are the 20% efficiency factor and the 100 calories/hour
resting metabolic rate accurate estimates? Probably not very, but they are
also probably not horribly far off — especially for slighly overweight
middle-aged men. More importantly, as long as
they are consistent for a given individual then progress will be
accurately reported even if the progress is over or under-stated.
Still, if the true resting metabolic rate is closer to 1,900 calories/day
instead of 2,400 and the true efficiency is 25% rather than 20% (though
20% is a MUCH better guess for metabolic efficiency ...) then
the actual gross calories burned will be closer to 720 (160 × 4 + 80)
instead of 900 (160 × 5 + 100). This would have
the 900 overstate the gross calories burned by 25%! Still, it will be
difficult for the machines to do much better given how little information
they have to work with.
Strength Training Exercise
TBD
Flexibility and Range of Motion
TBD
Balance and Agility
TBD