Originally Posted by John@NewPaltz
While I love mathematical approaches (and due to my lack of skills in complex mathematical equations I also love simplicity), I need to disagree with optimizing in a 2-dimensional manner for the following reason (however, I tend to agree for sprint distance swimming like 25/50/100 m):
I am able to increase tempo and stroke length, but I won't be able to maintain it for more than 1-2 pool lengths. In other words, if I went with sclim's approach of finding the sweet spot, I would end up at a pace and SPL, that I cannot maintain. This is also the reason, why I tend to agree in case of sprint distance swimming: I don't need to maintain my pace for longer than the duration of my experiments in the pool.
For every other distance, I find my self left with an optimization dilemma:
Say, you're preparing for a 2.4 mile open-water swim: It is kinda obvious that "maximizing the envelope" based on a couple lengths in a 25m pool will not result in your efficiency optimum for your target distance. However, where is the optimum? It will be somewhere below your pool optimum. Is the only way to find out swimming 2.4 miles at a perfectly consistent SPM rate? And even if you did that, your stroke length might be dropping a lot over the course of the swim, because you didn't chose the optimal SPM. Averaging it out over the full length could trick you. This risk is way lower or even non-existent in sprint distance swimming.
You don't have to agree with the math, but it's really not binary as you make it out to be. The math offers choices in rate given distance and time. You have to factor perceived effort, i.e can a swimmer sustain that pace for 500m, 1.2 mile, 2.4 mile, 5k ,etc. A good test is 4x300 holding stroke length and tempo. If 2.4 mile IM swim, add on time for bottlenecks, sighting, some drift. I've been able to predict swimmers times within a minute on 1.2 mile swims and 3 mins on 2.4 mile IM swims. So it's just not time and distance, it's knowing your swimmer and using some math to help them hit their best time.
However, I've had many coaches argue with math and swear by pace clock. Pace clock is just another unit of time, elapsed time given some number of lengths. But the distance and time is generalized by lengths whether 25y or 50m and a 1 minute pace clock. Very few tools to determine potential speed.
So it's not whether you agree with the math or method of estimation, it's how it's used to help swimmers understand what they're capable of if time and distance in smaller units can be easily understood and achieved.