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The Physics of Running Faster

Part 1 - Ground Forces

Exercise Physiology teaches that running speed is determined by stride length and stride frequency.  That being the case, running speed can be increased in one of three ways: 1) increase stride length, 2) increase stride frequency, or 3) increase both stride length and stride frequency.  As a practical matter though, running speed is increased by lengthening the stride.  Stride frequency does increase some at faster running speeds, but not nearly as much as stride length.  Furthermore, it is taught that the fastest runners have both a higher stride frequency and length than slower runners.

I still recall being taught the above as an undergraduate student in exercise physiology.  However, what was not taught at the time or afterwards was, what determines stride length and stride frequency?  I mean, sure running speed can be calculated by multiplying stride length by stride frequency, but that's just a simple math equation.  It does not provide any information as to what determines stride length or frequency or what training might best improve stride length or frequency.  I wondered, when a person runs faster, what physically is happening that causes stride length to increase?  And how do we go about improving it the most?

As it turns out, I'm not the only person who has asked these questions.  In recent years exercise physiologists have researched the answers to these same questions, providing us some interesting and insightful views into the physics of running faster.  This 2-part series will explore the physics of running faster and use this information to suggest ways to improve our own running performance.

What is a stride?

In running a stride is the distance between consecutive footfalls of the same foot.  So a stride is the distance and time between the left foot contacting the ground twice or the distance/time between the right foot contacting the ground twice.  A step is the distance/time between consecutive footfalls of opposite feet.  In other words, a step is the distance and time between the left foot contacting the ground and then the right foot contacting the ground or vice versa.  A stride, then, is composed of two steps.  Exercise physiologists generally use stride, and not step, as the basis for their research, so we will use stride too in these articles.

Strides are further divided into stride length and stride frequency.  Stride length is the distance the body travels during consecutive footfalls.  Stride frequency is the number of strides during some unit of time. 

Finally, a stride can be sub-divided into ground contact time and swing time.  Ground contact time is the period during the stride when your foot is on the ground.  Swing time is the period during the stride when your foot is not on the ground, and is swinging forward for it's next ground contact.

Researching Stride Length and Frequency

As noted above, stride length varies the most as running speed increases with stride frequency increasing some but not nearly as much as stride length.  This being the case, the question natural comes up as to what is causing the increase in stride length?  In 2000, a team of four researchers set out to answer these questions (1).  They hypothesized that running speeds are determined by the amount of force applied to the ground rather than by how fast the limbs are repositioned in the air.  Let's have a look at their research, results, and the implications of those results.

The researchers recruited 33 subjects and had them run, on a level treadmill equipped with a force plate, at varying paces from a jog all the way up to each subjects fastest sprinting speed.  These subjects were physically active subjects between 18 and 36 years of age and consisted of 24 men and 9 women.  The sprinting abilities differed greatly among the subjects, with top speed varying 1.8 fold, from 6.2 to 11.1 m/s (approx 14 - 25 mph).  The researchers measured a wide variety of factors, including total stride time, ground contact time, swing time, aerial time, stride frequency, stride length, and force applied to the running surface.  Additionally, five of the subjects were subjected to a second test consisting of running to top speed on a -6° and a +9° inclination.  The research revealed the following.

"Although sprinting abilities differed greatly among subjects and the top speeds of the same runners differed considerably on the different inclines, the mechanical means by which runners increased speed from a jog to top speed varied little.  Across each individual's speed range, speed increases were achieved primarily by increasing stride lengths at lower speeds and stride frequency at higher ones."

Nothing particularly remarkable about this finding as it confirms what physiology already teaches.  But, here comes the good stuff.  What the research further revealed was that increases in speed were accomplished by applying more force to the ground.

"We undertook this study to test the hypothesis that the different top speeds of human runners are determined by the amount of force applied to the ground rather than how rapidly limbs are repositioned in the air and found this to be the case in each of our two experimental tests.  Both the greater top speeds of faster vs. slower level runners and those attained during declined vs. inclined running were achieved by the application of greater support forces to the ground while the legs were repositioned in nearly the same minimum time.  Here, we also put forth a mechanical explanation for the limit to running speed with a more concrete physiological basis than the considerations of maximal stride lengths and frequencies that have typically framed this question.  Because of the narrow constraints on the minimum swing times and maximum contact lengths that runners can use, speed is conferred predominantly by an enhanced ability to generate and transmit muscular force to the ground."

What this means is that their study shows that increasing your running speed is mostly accomplished by the muscles of your legs generating more force.  This greater propulsion results in a longer stride length - i.e. your body travels farther from each step you take.  Stride frequency plays a minor role in increased running speed, but increased stride length caused by greater muscle force being generated is at the core of running faster.

It sounds like all you would need to do to run faster is to increase the strength of your muscles, doesn't it?  Indeed, I suggest that this explains why strength training has been shown to improve running performance at distances of 10k and less. 

However, you might think that if strength were the primary factor in top running speed then the strongest people should be the fastest sprinters too.  But, we know that isn't the case.  Powerlifters aren't necessarily the best sprinters, are they?   The research shows there is another factor at work, a factor that balances out greater muscular force.

The research shows that swing time - the period during a stride when the foot is not in contact with the ground - varies little at top speed.  Even though there was a wide difference in top sprint speeds across the 33 subjects, "swing times...did not vary significantly in relation to their top running speeds."  Despite running at very different top speeds, swing time was about the same for all the runners.  The major difference was found in ground contact time.  The faster the pace the less the foot-ground contact time.  What this means is that as your speed increases your foot is on the ground an increasingly lesser amount of time.  Ground contact time is the factor that balances out generating greater muscular force.

These two factors - force generation and ground contact time - counteract each other to limit maximum running speed.  As you run at ever faster speeds, your muscles have to increasingly generate more force faster.  But, at ever faster speeds, you have less and less time to generate those forces against the ground and provide propulsion for your body.  There comes a point when the force and speed at which your muscles are producing power uses all the available ground contact time.  To run even faster requires more force faster, since an increase in speed further reduces ground contact time, but your muscles don't have the power or speed to generate the required force.

"Although the support forces applied to the running surface increased with increasing speed and reached individual maximums at the top speeds of different runners, the relatively larger reductions in foot-ground contact times that accompanied the greater support forces applied at faster running speeds resulted in reductions in both the aerial and swing periods of the stride.  In each case, top speed was reached when increases in speed and decreased in foot-ground contact times reduced effective impulses and aerial time to the minimum values providing sufficient time to swing the leg into position for the next step..."

As you can see, running speed ultimately comes down to the force generating capacity of your muscles.  To run faster, your muscles have to produce more force and they have to produce that greater amount of force increasingly faster.

"Accordingly we suggest that the mechanism by which faster muscle fibers confer faster top running speeds...is not by decreasing minimum swing times but by increasing the maximum rate at which force can be applied to the ground."

This finding explains why sprinters have an abundance of fast twitch muscle fibers.  Fast twitch muscle fibers are both more powerful and contract at a faster rate than slow twitch fibers.  This capability of fast twitch fibers provides the needed force and speed required to run at faster velocities.  Slow twitch fibers cannot produce as much force as fast as fast twitch fibers, explaining why those with an abundance of slow twitch fibers are slower sprinters.

The implication of this is that if you want to increase the speed at which you run, especially at sprinting speeds, you have to train your muscles to produce greater amounts of force at increasingly faster speeds.  This likely explains why plyometrics and explosive training produces improved running performance.  You can use this same information to improve your running performance.  Train your muscles to produce more force faster and your running performance will improve.

Part 2:  The structural basis of running

References:

1.  Weyand P, Sternlight D, Bellizzi M, Wright S., Faster top running speeds are achieved with greater ground forces not more rapid leg movement, J Appl Physiol, 2000, 89, 1991-1999.