The winter of our discontent
In Delhi, in winter, the temperature is finally comfortable,
and you feel inclined to go for a walk or a jog. Except…for the fact that in
winters especially, Delhi is smog-ridden at world record levels, beating Beijing hollow!
This year (2016) has been especially bad because of low speed surface wind which does not disperse pollution, as well as an anticyclone
(accompanied by a temperature inversion) which has put a lid on the suffocating
pollution pot that is Delhi, created by drivers, construction workers, celebrators of Diwali, and with a little help from crop-stubble-burning friends in Punjab and Haryana... (the list is not exhaustive, but I'm exhausted already).
So, go buy a room air purifier and an N99 face mask. Well, I
did that.
Go for a walk or
jog (only if wearing a face mask) in the afternoon, when pollution may
be lower.
So, is there a recommended speed for walking or jogging, to
minimize the amount of PM2.5 that you will get into your lungs?
This is similar to the question: should you walk or run in
the rain? But it’s a lot simpler to answer.
So, the question really is: how much do you breathe (in
L/min) when you walk or jog at a certain speed (in m/min or km/hr)?
VO2 max refers to the maximum amount of oxygen that an
individual can utilize during intense or maximal exercise. We are not
interested in VO2 max but in the simple VO2 value. After we get that number, we
just multiply by 5 (assuming that oxygen is 20% of the air content, which is
not exact, but never mind!). Then assume a given level of PM2.5, and I will go
with 500 mg/m3
, which is about 10X of what India’s lax regulations say it should be (again,
never mind!). The units for VO2 are mL/kg/min, so we also have to multiply by
the body weight. I have chosen 70 kgs – a value which I have not yet reached.
The simple expressions most often mentioned by walkers and
runners are:
VO2W = 3.5 + 0.1v
VO2R = 3.5 + 0.2v
where v is in m/min.
The formulas followed by American College of Sports Medicine
(ACSM) include the slope:
VO2W = 3.5 + 0.1S + 1.8 S G,
Where S is the speed in m/min and G is the grade of the
slope (e.g. in an inclined treadmill).
And:
VO2R = 3.5 + 0.2S + 0.9 S G
But these formulas do not account for the gait transition
between walking and running at a given speed.
So I dug out a free-to-view
paper on the Internet by D.Sentija & G.Markovic “The Relationship Between
Gait Transition Speed and Aerobic Thresholds for
Walking and Running” in Int. J. Sports Med. 30
(2009) 795-801.
The authors give the
expression for running as:
VO2R = 6.7 + 3.2v
where v is in km/hr. Using a conversion factor of 1000/60
=16.67, the value 3.2 becomes 0.192, which agrees with the ACSM expression. But
the intercept for zero speed is almost double – which may not matter since you
can jog at slow speed, but not at close to zero speed. Or can you?
The expression for walking is more complicated:
VO2W = 44.63v – 76.6 + 0.438v3 – 7.41 v2
These two equations for walking and running intersect at a
speed of 8.18 km/hr, which is the transition speed between the two gaits.
However, the problem with the expression for walking is that
it gives a negative value of VO2 for zero speed. This is ok for Sentija and
Markovic since they are only interested in the gait transition. But this flies
in the face of the expectation that you breathe air even when you are not
moving!
So I arbitrarily took the data points from ACSM for a speed
of less than 4 km/hr and the points from S & M at higher speeds, and
generated a new expression fitting both data sets pretty well (which I must
emphasize I have not empirically validated – but, so what?):
VO2W = 3.51 + 1.47v + 0.0473v2+ 0.023v3
As mentioned above, the total mass of particles inhaled is
then:
M = (PM2.5) (5)(70) (VO2) t
Where t is the time required to walk a given distance. This
time will obviously decrease if walking or jogging speed increases.
The results for the VO2 vs speed are:
The gait transition speed is now 8.6 km/hr (instead of 8.19) an increase which would make Sentija & Markovic unhappy, but we will glide over it, to obtain the inhaled mass vs speed plot:
The results show that if you are jogging, you should jog as
fast as you can.
If you are walking, don’t try to walk too fast, it’s not going
to help you. And don’t walk too slowly either. Anyway, the differences between
walking/running at 4 km/hr and 5 km/hr are a few percent. Nothing much to worry
about.
Most people walk at speeds between 4-6 km/hr anyway,
because that is the most comfortable speed, for mechanical reasons (resonance
in the pendulum-dominated mode).
It is probably better to walk than to jog, because even if
you run at 20 km/hr you still only reach 30 mgm,
still greater than the ‘best’ value attained by walking at 4 km’hr: 25 mgm. In fact the value of
PMR asymptotically approaches about 30 as running speed increases
(not shown in the plot above) – with the caveat: the expression of VO2R may
not be valid at such high speeds.
How bad is a few micrograms of PM2.5in you lungs?
How much gets in your blood? Your brain? Dunno! What does it do? Heart attacks, strokes
etc.
