Archive for November 14th, 2017

Equations are abbreviated definitions that simplify and  clarify complex concepts and data. They may be used to calculate, which may either reveal past events or predict future outcomes. Qualitatively, they enable the understanding of interrelationships between variables, which may not be obvious otherwise. On the other hand, not all relationships within an equation are the mere product of their juxtapositions within an equation. Rather, some variables owe their interaction to feedback loops within their physical situations. For instance, according to the equation below, in order to have the best period (race time), both power and endurance must be at their maximum. But in physical reality, for a runner, when power is maximum, endurance must be low. Sprinters are not endurance runners. Conversely, when endurance is high, then power must be low. Long distance runners are not sprinters. Actually the equation does reveal this relationship, because if you move the power variable to the other side of the equation you get po = 1/e, or more accurately, power is inversely proportional to endurance. That is, as endurance increases, power decreases.

From the equation you may also see that pace and distance should be inversely proportional. But the opposite is true. A longer distance requires requires a slower pace, that is, larger number.

And when distance is increased, endurance must increase and power must decrease.

The Runner efficiency variable may not be able to be determined, though I think that athletic physiologists are trying desperately to do so with VO2 max, respiratory exchange ratio, fast twitch/slow twitch muscle, body mass, % body fat, and running mechanics. Strength training and anaerobic sprints seem to be two popular methods for increasing runner efficiency. Diet must not be discounted as a way to build better runners.

The constant, K, is a factor that converts the other five variables into a race time, T. At this level of development of the equation, it is nothing more than a fudge factor to make five variables equal to the one.


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The best race time (T) is what every runner, coach, and spectator is after. Thinking through this equation might help the runner and coach better design training that will secure that result. Are you training for power, the sprint, or endurance, the long distance run? What training regimens do you need to perform to meet these goals? How much is it reasonable to increase both power and endurance? What are the limits of one, given the other?

I feel certain that good runners and their coaches have all of the relationships dialed in, so that an equation seems silly, but I benefit in my thought about running by the simple definition called an equation.

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