Relationship of Power and Pace

I was thinking some more about the Royle training categories after the calculator post and how Royle's schema adds to or subtracts from a base split. For instance, for Cat III, you subtract 2 seconds from your 20-minute split. There seems to be an implication that it doesn't much matter what your base split is; 2 seconds subtracted from one split is the same as 2 seconds subtracted from to another split. But is that right?

The answer would seem to be: "Duh, a second is a second is a second." But, on cursory examination, I think it's readily apparent that two seconds or five or ten added or subtracted is quite different depending on the pace.

The easiest way to see this is to look at the power (watts) associated with a split. If you row on a Concept II ergometer, you can adjust the display to show watts (or you can look up the watts in the Concept II website watt-pace calculator). You'll see that at a 500m split of around 3:00, each second faster requires roughly one additional watt of power (see below). The power-pace relationship here seems linear: drop a second, add one more watt of power.

Split	Watts
3:00	60.01
2:59	61.03
2:58	62.06
2:57	63.12
2:56	64.20
2:55	65.31

At a pace of 2:00, each second faster requires roughly 5 additional watts.

Split	Watts
2:00	202.55
1:59	207.70
1:58	213.02
1:57	218.53
1:56	224.23
1:55	230.13

When you get to a split of 1:30, each additional second faster now requires almost 16 watts of additional power.

Split	Watts
1:35	408.22
1:34	421.39
1:33	435.13
1:32	449.47
1:31	464.46
1:30	480.11

 
At this point, you can clearly see that: a second is worth more or fewer watts depending on the pace. It should also be clear that the relationship between power and pace is not a linear one. Just how non-linear this relationship is may surprise some. Here's an example:

If your 500m split is 4:00, then the power associated with that effort is about 25 watts. If you row twice as fast, i.e., at a 2:00 pace, the power associated with that effort is 200 watts. In other words, to go twice as fast, you need 8 times as much power.

Another easy (mathematical) example: rowing on the ergometer at a pace of 3:00 requires about 60 watts, while rowing twice as fast--at a pace of 1:30 minutes--requires about 480 watts, again 8 times as much. Doubling your pace requires 8 times as many watts.

A rower at 2:00 pace looking to increase his pace by 15 seconds has to boost his power by 100 watts. In this case, the rower has to increase his power by 50% to drop just 15 seconds. In other words, to row a 1K in 3:30 takes 50% more power than a 1K at 4:00.

If this seems impossible, consult the Physics of Rowing for more explanation. Basically, this phenomenon applies on the water and on the rowing machine.

Graphically, you may be able to see (from my fairly inept graph below) that as the pace picks up, the watts pick up even more. In other words, the faster you go, the harder it is to go faster!

Let's return to Royle's training categories. My 20-minute 500m pace (a few years ago!) was about 1:50. Now, let's compare me with someone whose 20-minute pace is 2:40 and let's look at a Royle Cat III recommended pace of split minus 2 seconds. Below is a table with the pace and associated watts. You can see that there is a significant difference between the scenarios, but both people reduced their split by just 2 seconds.

	20-minute Split	Watts	Cat III Split (minus 2 seconds)	Cat III Watts	Watts Difference
Me	1:50	263	1:48	277.8	14.8
Other Rower	2:40	85.4	2:38	88.7	3.3

To row at a pace two seconds faster, I required almost 5 times as much additional wattage than the other rower required. So a second is not equal to a second when it is added or subtracted from different split time.

If you're in a group workout and the coach is asking you to drop your split by 10 seconds, those 10 seconds will mean different things depending on your pace. For example, the watts of a rower at 3:00 pace is about 60, whereas the rower at 2:00 pace looking to increase his pace by 10 seconds has to boost his power by the same 60 watts, but he's already "doing" 200 watts.


What does this mean for the Royle Cat system?
It seems to me that the non-linear relationship of pace and power on an ergometer such as the Concept II presents some challenges to Royle's system, which use the same time ranges (add or subtract the same number of seconds) independent of the base pace.

I have a difficult time pinpointing what the precise problem would be or how it would show up. I suspect that some workouts will be more intense for some than for others because of this. As I pointed out in the previous post, the 3 x 20 minute workout at 20-minute pace plus 2 seconds is a no-go for me, but for others I suspect it may work.

Again, Royle's system seems to provide a useful framework for folks using it.

Future Questions

1. How do Royle's categories compare with other training zone systems?
2. Would a power-based system (using watts) make more sense?
3. If you are all asked to row at a stroke rate of say, 24, then there is a noticeable difference between a rowing at a pace of 2:10 and a pace of 1:50, because obviously the power required is substantially greater. Because power equals force x velocity, the force per stroke has to go up substantially at the higher pace. The rower at the faster pace may feel the "load" is way too high and want to increase his or her rate to reduce the force per stroke and keep "the load" the same as before. This seems logical to me.  What is this physiological implication of this? For a boat--say a quad--of physiologically different people, who have to row at the same rate in the water, what is the solution?