Newton's Running Formula (with apologies to Jack Daniels)

When we hear new things, we think about the new information in terms of what we already know and believe to be true, and decide if it both fits and adds something new. With engineers, this process includes thinking about new information in terms of scientific principles and laws.

Now, Newton (Isaac, not the South African running Arthur - though both would be fun to talk to about this) observed in his laws of motion that the acceleration of a body is proportional to the force acting on the body, and is inversely proportional to the mass m of the body, i.e., F = ma (see Wikipedia).

I thought of the F = ma law when I read that sprinters exert a force equal to several (five?) times their own weight on the track. For larger runners this can be many hundreds of pounds of force (think about a large football running back accelerating to record his best 40 yard time).  I'm trying to reconcile this with the idea that runners might want to be "light on their feet". For sprinters this doesn't seem to be possible while applying such large forces.  The track has to take that pounding!

Getting back to Newton, and knowing that the distance traveled equals 1/2 a * t^2 we could make some dramatically simplifying assumptions and think about running 100 meters fast (most importantly, this calculation assumes acceleration is constant over the entire race, and it isn't - Usain Bolt seems to hit top speed and then cruises a good portion of even 100 meters ...).

But since distance (d) = 100 meters, and Mr Bolt's time in London 2012 was 9.63 seconds, let's assume we can solve for Usain Bolt's acceleration - it is about 2.157. We can call that number "one Usain Bolt".

Let's run Usain's numbers for a hypothetical 9.5 second run ... it is a 1.3% improvement in time but he's going to need an acceleration of 2.216,which is a 2.7% improvement in "Usain Bolt" force. Now Usain Bolts acceleration, just like everybody else s is proportional to the force he can apply and his own mass. This is a lot because there really isn't much he can do to get his mass down (run naked?).  And he's awfully strong already.

In addition to appreciation for the real forces involved, one can only accelerate during the time that force is being applied. The implication is that when you stop pushing and pick that back foot up, acceleration stops. Once you are off the ground you are decelerating. A long 'push time' would seem to be good.

Now, referring back to our man Newton, he tells us an object in motion tends to remain in motion ... doesn't a distance runner only need to accelerate for a very short period, and then simply remain in motion? Why does it feel like it continues to take significant effort? Drag (wind resistance) is actually very low at my running speed. There is little friction with the ground (the foot is not providing sliding friction, but is closer to a rolling wheel). I think the largest component of drag must come from the landing foot. In essence the landing (forward) foot is providing a stopping force, that needs to be matched during the push if we are going to maintain speed.

Joe Friel just blogged about cyclists who might try to 'pull up' in addition to pushing down on the pedals. He concludes that it isn't possible to provide a real contribution to pedaling force by pulling up, that at best one can only partially compensate for the effort it takes the downward pushing foot  to lift the rising pedal. In other words, the best one can do is reduce the amount of drag caused by the rising foot..

The same thing must be happening with running - an efficient runner wants to reduce the drag coming from landing force and minimize the corresponding force required to maintain constant speed.  Fitting this in with what we think is true about running form means that landing the forward foot under your center of gravity (very close to where it can start to push!) is a good thing.  And looking at the stride angles of elite distance runners, they actually do keep that pushing foot on the ground through quite a few degrees of the running stride cycle.

gear update

There's nothing like getting new shoes to mark the early days of a new training cycle ... I just got the new Brooks Cascadia 8 trail shoes.

Brooks Cascadia 8 trail shoes

I have run in the Cascadia shoes a lot over the past years.  I've been buying and wearing the size 15 shoes, because I have pretty big feet and like some room in the toe box.  The new Cascadia 8 shoes fit differently - I actually found the size 15 to be too big.  Maybe I'm shrinking (I wish!).  But for now I'm happy running in size 14's for a change.

Another gear update is coming.  I've had my Garmin FR60 watch for a while now.  I like the feature set (I run with the heart rate monitor, and the shoe pod that gives me speed, stride turnover rate, and distance).  And I really want to keep resisting going to a watch with GPS, as the required charging discipline guarantees 1) the watch will be dead when I need it and 2) I'm going to leave that charger behind on some trip one day. The FR60 system just works for me. BUT ...when the FR70 came out with the same feature set, it seems one of the real changes was a better band.  A lot of users were reporting the non-replaceable band on the FR60 was breaking.  My own FR60 is now showing the signs that the band is failing.

Garmin FR60 watch band cracking

I'll probably go with an FR70 when the band breaks.  The one big (unlikely?) improvement I would like to see in the FR70 is a barometer that would record the elevation profile for a run.