Monday, December 12, 2016

New Math

I took a run the other day near our house in the mountains.  It looked like this:














Now running a half dozen miles in an hour isn't anything spectacular, even for a late blooming runner like me.  The interesting part is taking that same run in the mountains with elevations above 9,000ft on dirt roads with grades above 10%.  Now your talking about some effort. 

I find that a big part of training for an expedition has to do with practicing what will be experienced during the climb.  So for example, simply carrying a heavy pack up a steep hill at the highest elevation available is good direct practice for the actual climb.  So too is basic suffering in whatever forms you care to inflict on yourself.  Personally I like this form of training because I think more than half of the effort needed to climb a big mountain is mental.  Whether the suffering is listening to the tent flap in high winds all night long while camping on a Colorado 14er in winter, struggling with the day's load carrying because you're low on calories through effort and staying warm or pushing yourself on an hour-long run, it's all good training.

This brings us back to the run.  Usually when suffering I like to let my mind wander.  Like anyone who daydreams, I think it's fun to see where the mind goes.  Sometimes we're surprised at the thoughts we have and other times we may be inspired with creativity.  My favorite is when a big chunk of time goes by and I really wasn't thinking of anything in particular.  These are the times when the rhythm of the task at hand leads to a release of the type A conscious mind and allows us to simply live in the moment.  I've had the best experiences when climbing in the snow tethered by a rope to my teammates during the small hours of the morning.  I simply call this situation "kicking steps" and it's something I long for starting about six months after my last expedition.

But "kicking steps" isn't at all what I was doing on the morning of that run.  I was in full engineer brain mode solving many of the world's problems and generating a few new ones of my own.  then I started to think about the different types of training I was doing and how different the effort felt between one task and the other.  Is running fast on hills for an hour more difficult than carrying a heavy pack up a mountain?  Is carrying a heavy pack on a treadmill for 45 minutes at a 10% grade at a 3.5-4.0 mph speed (my morning workout) easier than carrying the same pack at a normal pace for 3 hours?

I thought, surely there must be formulas, equations, constants and factors in the engineering world to describe the effort and boil it down to numbers which can be compared, cataloged and tallied.  Well of course there are, with units like ft-lbs, Newtons, Joules, etc.  But these units are boring and don't capture the real essence of what's involved, at least for me. What I decided was that the world needed a new unit of measure that would truly capture the value of effort put forth in mountaineering type activities.  This new unit would be a measure of the load carried with how much elevation gain over what distance.  Formula looks like:

Mountaineering Work = (Pounds Carried) x (Elevation Gain in Feet) x (Distance Traveled in Miles)

...Pounds x Feet x Miles...  I'll call the new unit PFM!

What a revelation I thought!  Here was something truly exceptional and I'm surely the first person to invent the unit PFM.  Let's try a few examples:

If David were to run for 6 miles with no backpack and achieve a total elevation gain of 1,000 ft, how much PFM would that be?  The weakness of my formula was exposed immediately.  I wasn't carrying any weight so the answer would be (0) x (1,000) x (6) = 0.  Total waste of time.  This conclusion occurred descending the last hill and thinking about the lung searing ascent that was to follow.  I needed to find a solution fast in order to feel good about the morning efforts.

Aha I thought, the reason running is difficult is because we have self-weight.  So, the person's weight needs to be part of the equation also.  Let's try again:  David weighs 175 lb and runs for 6 miles with no backpack and gains 1,000 ft in elevation.  (175) x (1,000) x (6) = 1,050,000 PFM! 

It's interesting to do mental math while running fast on a dirt road.  As the numbers get bigger, your (my) concentration on the math needs to increase which takes focus from the placement of your (my) feet on the road and the constant avoidance of rocks and potholes.  Thankfully I didn't fall completely on my face and only the birds flying overhead noticed the stumble, arm flail and subsequent recovery...

Well, very impressive, over 1 million PFM's for an hour run.  This is kind of like going to a third world country and exchanging 10 bucks for a million of their money only to realize that a million of their "bucks" only gets you a sandwich.  Too many zeros!  I was falsely rich in PFM's and needed another adjustment.

By then I was heading back up the last hill and needed to finish the equation.  It became obvious that weight needed to be more of a factor of one's own weight and not just a sum.  What if I weighed 350 pounds instead of 175?  Would it be twice as hard to cross the room?  Yes, at least twice as hard. So let's take the person's body weight plus the weight they're carrying and divide that sum by their body weight.  This seemed like a better equalizer and would keep the numbers down to something reasonable.

the first example now became rounded off in my head because my lungs were dry and legs almost burned out but I knew this was the solution!  For completeness, here it is:

[(175+0)/175] x (1,000) x (6) = 6,000 PFM

Okay, this is a reasonable number.  Lets try another example:

David and his wife Kriss climbed Mt. Bancroft.  It looked like this:



According to the GPS, the climb was 4.28 miles with 2,491 ft of elevation gain and I was carrying a reasonable 45 pound pack.

Mountaineering Work = [(175+45)/175] Pounds x 2,491 Feet x 4.28 Miles = 13,403 PFM

Now that seems pretty reasonable to me.  The climb took 4-1/2 hours but it was at a reasonable pace with a few breaks for snacks, etc.  Definitely more than twice the overall effort of the run but not 3 or 4 times the effort.  The view from the top looked like this:



This equation will now serve as part of my training log and I'll report on my progress periodically.  Feel free to track your own PFM's and spread the word about our new math.  It's Pure Freakin' Magic!