Fluid mechanics and the right way to compute rowing effort
From The Archives - I’m going back through the old blog and reposting some of the best articles.
Back in this post, I gave you a nifty chart to compute your speed at different percentages of your 2k pace. I need to update that with the new and improved chart below.
The original chart was correct in terms of speed (500m split time). If your 2k time was 8:00 and you wanted to row at 80% of that speed, you'd need to have a split time of 2:30. But that chart wasn't correct based on effort.
Back to weightlifting for a second: if you squat 200 lbs at a 100% effort, then a 160 lb squat is an 80% effort. That's because the work (F✕d) you're doing (and hence the energy you're expending) is proportional to the weight you're lifting. Effort and weight are very closely related in weightlifting.
For rowing, we noticed (and we should have thought of this sooner) our effort was non-linear with respect to our rowing speed. During Friday night's workout, Michael was the first to mention that he thought that the speeds prescribed were not matching his expectations, and he was the first person to say "non-linear". That got me thinking, and when he was done with his interval, I told him the answer was obvious: energy is a function of the square of velocity: ½mv2 so the effort should scale as the square of speed, not linear like the original chart said. Luckily, Joe was listening to us, and since he actually is a fluid mechanic (nerd gym) he pointed out that drag goes linear with velocity in addition to the kinetic energy, so really the effort you're putting into an erg is proportional to the cube of velocity you're trying to maintain.
What does that mean? If I tell you to lift twice as much weight, you have to expend twice as much energy (work twice as hard) to do it. If I tell you to row twice as fast, you have to expend eight times as much energy (work eight times as hard) to do it. That is, it takes 33% more effort to row 500m in 1:48 than it does in 2:00 even though it's only 10% faster. If you think about this, in a long race you want to keep your pace constant, why that is, is left as an exercise to the reader (or really a later blog post, that's enough math for today).
tl;dr: here's the new and improved chart that relates your 2k time to a 500m split as a function of effort - that's what we care about when we're programming anyway.