I noticed some days I seem to be pretty tired after a training session, and others not at all. I know some of these is related to how much sleep I got, and other physical factors, but I was thinking that if there was a way to measure my workout's overall "effort" it would be a useful metric to track.
I realize that there is probably alot of technical research on this sort of thing, but I decided to try and derive my own equation that I can use that roughly fits with my intuition.
First I was thinking that I would just take a sum of weighted effort for each set. Since it seems like more speed is clearly more effort, I tried writing out the following equation:
E_tot = S1*T1 + S2*T2 + S3*T3 + ......
However since D (distance) =S*T, E_tot just ends up equaling the entire distance spent, which doesn't seem to be an accurate metric of the effort I spent. This logic implies that it doesn't matter how fast I swim a certain length, because the extra effort I spend will get balanced by the fact I am swimming for less time, and the total effort will remain the same.
Since effort clearly isn't related to just the distance spent I tried the following:
E_tot = D1*S1 + D2*S2 + D3*S3 + ...
Here, swimming the same distance faster, or swimming the same speed longer distance will give an increase in total Effort.
However, this too seems generally wrong because clearly I should get more tired doing sprints at (say) twice the speed of normal laps when compared to just doing double the laps at the normal speed, whereas this equation implies the two would yield the same effort.
Squaring the speed factor seems like it would give a more accurate result:
E_tot = D1*(S1^2) + D2*(S2^2) + D3*(S3^2) + ...
This equation has the problem where 4 laps of 25m is the same effort as 1 lap of 100m (at the same speed), which clearly isn't true. So I give distance only a half power:
E_tot = (D1^1.5)*(S1^2) + (D2^1.5)*(S2^2) + (D3^1.5)*(S3^2) + ...
= SUM
If we have L laps and they are all the same speed, we can simplify to this:
E_tot = L (Dl^1.5) (Sl^2)
Now swimming the 4 laps together will give a 2x effort.
Of course, this doesn't take into account the rests within a set (like 4 laps of 25m with 10 seconds in between each)
To try to that, lets define a few more variables:
Ts = time to do a lap (or larger continuous set)
Tr = rest between each lap (or larger continuous set)
This clearly varies a great deal between people, but lets assume for now that if Tr >= Ts, then the person has fully recovered and there is no effect on the next lap. However, if Ts = 0, then its as if they are swimming all the laps together - as I said above with the latest equation this results in a 2x effort for 4 laps, basically SQRT(laps).
So if we try to fit all these factors together, we get something like this:
Let Rc (non-rest constant) = (Ts - Tr) / Tr
(If Tr happens to be greater than Ts, then set it to Ts to make the logic work out)
So that:
Rc = 0 when Tr = Ts (a good amount of rest, fully recovered)
Rc = 1 when Tr = 0 (no rest)
E_tot = L ^ (1 + Rc/2) * (Dl^1.5) (Sl^2)
So using this, lets try an example:
4 25m laps at 20s, 5 sec rest:
Sl = 25/20 = 1.25
Rc = (20-5)/20 = .75
E_tot = 4^(1+.75/2) * (25^1.5)*(1.25^2)
= 6.72*125*1.4
= 1176
Of course, this number is useless unless compared against another workout.
Lets compare to 15 sec rest:
E_ tot = 4^(1+(.25/2)*125*1.4
= 4.75*125*1.4
= 831
Now lets try 4 25m laps at 15s, 15 sec rest:
Sl = 25/15=1.66
E_tot = 4^(1+(0))*(25^1.5)*(1.66^2)
= 4*125*2.75
= 1375
For multiple sets, assuming that there is enough rest between, just can add up the E_tot for each set to get the E_tot for the workout.
Another thing this doesn't account for is incremental improvements in efficiency, but those happen slowly so don't think it would have a major effect. Also the relative efforts for per-stroke would be different due to differences in muscles used and swimmer's technique, etc, though this could be compensated using estimated constants for each stroke.
Does anyone think this equation is reasonibly useful for comparing the relative effort of different workouts?
