Refining The Ramp Rate

You will find a graph illustrating the two training ramp rate strategies listed earlier, i.e., linear, and geometric. My son, Thomas suggested a Fibonacci Sequence strategy.

As you'll recall, the beautiful Fibonacci sequence begins with zero, then one, and each subsequent number in the sequence is created by adding the previous two i.e., 0, 1, 1, 2, 3, 5, 8...

The Fibonacci sequence was used by Indian mathematicians as early as 200 BC. In 1202, the first Western mention of it was made by Leonardo of Piza, a.k.a. "Fibonacci" in the book Liber Abaci in which he introduced the use of Arabic numerals to European mathematicians.

Math students know that the ratio of any two successive Fibonacci Numbers  approximates the Golden Ratio of 1.618025751... and the ratios of successive Fibonacci Numbers approaches the Golden Ratio in the infinite.

Practical use of the Fibonacci Sequence and Golden Ratio can be found in art, music, architecture, economics and applied mathematics. Elegant examples in nature can be seen in the arrangement of a sunflower's seeds, branching in trees, and (my favorite) in the pedigrees of [idealized] honeybees.

     * If an egg is laid by an un-mated female, it hatches a male or drone bee.
     * If, however, an egg was fertilized by a male, it hatches a female.
     * Thus, a male bee always has one parent, and a female bee has two.

     * If one traces the pedigree of any male bee (1 bee), he has 1 parent (1 bee), 2 grandparents, 3                 great-grandparents, 5 great-great-grandparents, and so on.

Unfortunately, the Fibonacci sequence seems like a recipe for late-season injury if used un-adjusted as a training ramp rate. It's too little mileage early on and too aggressive towards the end. A"Modified Fibonacci" training plan is shown in purple. It is the Fibonacci sequence plus a fixed 21 miles. It's still too light in the early spring and too steep by the fall.

But, if you want to leave your training buddy's head spinning, you can explain that this year you've decided to follow: "A hybrid of Fibonacci and Geometric endurance training  ramp rates targeting late season optimization." The subsequent discussion should carry you several miles and be worth at a Tall Mocha Latte.