HELEN!! A measure of power increase

One of my favorite workouts! Came home yesterday and busted it out at lunch. In February I did it in 10:30. On July 15th I did it in 13:45...I want to throw up just thinking of that performance. Well, after only two and a half months of training I just completed my fastest Helen yet...

HELEN
3 rounds for time of:
400 m Run
21 Kettle Bell Swings, 55 lbs
12 Pull-Ups

Time: 9:08

Some quick physics and math and we can determine power increase... Power=Work/time. The Work (completing Helen) hasn't changed but the time to complete that Work, and therefore Power, have changed. For the sake of simplicity I am not going to use units but just derive a percentage of power change.

For the July performance I completed W (Work of Helen) in a t (time) of 825 seconds. For the sake of simplicity I am going to say the value of W is 825. I could use any value here but this just makes calculations easy as it conveniently gives me a baseline P (power) of 1, P=W/t = 825/825.
Using the same value for W and plugging in the new value for t we get P=825/548, P= 1.505. That would indicate a power increase of 50.5%

Now, from a physics stand point this is not accurate because W did actually change between July and yesterday. The fact is that I lost 6 lbs since the July performance. That means I need less F (force) to move my m (mass) across a fixed d (distance), W = F x d; therefore the amount of W performed yesterday was less than in July. Ultimately that means all of the difference in performance cannot be attributed to simply an increase of P but also a decrease in W.

From a practicle standpoint no one cares about the physics; they just see the 50.5% as a measure of performance increase (this can be said to be the true percentage increase of average velocity over a given distance as velocity = distance/time. Notice that unlike Work, distance did not change between the July and September performances). When runners compete they are all completing different W as their masses are different while they run across the same distance. People do not care about the amount of Work the runner completed as they cross the finish line; they care about who completed the task first and by how much. Regardless, we can probably find a way to reasonably account for the mass and Work differences and therefore Power difference.

The 6 lbs decrease in weight is equal to a 3.125% reduction in mass. Considering Work = mass x acceleration x distance, where any acceleration difference between July and September is negligable, we can reasonably assume for any task where I am moving my mass across a fixed distance, that the Work is decreased by 3.125%. This is a very safe assumption considering that a 55 lbs weight is added to one of the tasks of Helen, Kettle Bell Swings. This mass does not change, accounts for considerable movement distance and therefore it can be reasonably assumed that the percentage of Work decrease for the entire task of Helen is actually less than 3.125%.

Using the 3.125% reduction figure the work performed yesterday would be approximately 825 - (825 x 0.03125) = 799.218. Using this new work figure we can find a lower end Power percentage improvement: P = 799.218 / 548 = 1.458.

These two calculations show a 45.8% to 50.5% increase in Power in less than 3 months!

Finally, a last measurement is how much faster I completed the task in September compared to July: (825 sec - 548 sec) / 825 sec = 33.57% reduction in time.

Either way, this is a huge performance improvement that I am very happy with.