Originally Posted by WFEGb
good Image to think about.
OK, (3) expands the area of your envelope. Very good! Otherwise you will get best area if you "design" your envelope with both sides equal-lengthed...
...Damned not everybody likes squared envelops, and damned, both sides don't have the same unit of measurement... :-))
Interesting that the concept of a mathematical value being the product of two factors can be easily related in our minds to the real world situation of area = side a x side b. In this real world case the units are the same (that is, linear dimensional distance) which makes the concept a little more concrete. But if you just extend the analogy a bit more and think abstractly, you can abandon your insistence that the dimensional units stay the same, and if you need an image to help anchor your mental visual construction, think of a graphic plot with the x and y axes being your two variables. The product will be the area of the rectangle formed on the graph, and the dimensional unit of the product will be xy (TT number x SPL, that is, duration per stroke multiplied by number of strokes per 25 metres = Time in seconds per 25m). To be truly accurate, I guess you have to also include the number of beeps during the push-off glide.
The equivalent of a nearly square envelope would be the sweet-spot point at which dropping the Tempo Trainer time by your smallest usual decrease interval results in an increase in SPL by one, and vice-versa, at which time you are very close to your optimum efficiency for that distance, and practicing and aiming for this point should in theory prepare you for the greatest likelihood of being able to swim at your current maximum efficiency.