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?
You are assuming the water temperature is the same and therefore your formula is always correct.
Your body's metabolism will work harder or easier depending on the varying temperature of the pool and air.
Please add this into your equation because currently it is incomplete and the results would deviate from the rectilinear path of ethical rectitude.
:2cents:
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?
Without having performed a comprehensive research of all that's currently available out there, I don't think I am far from the truth in stating that Dr.Phil Skiba definitely has a serious lead on all the others in quantifying swim training load.
The main difference with Skiba, is that prior trying to lay down his own forumulas, he carefully studied what was available
1) in other sports
2) in swimming based on the works of Toussain (to name only these)
I remain convinced to this day (at the risk of becoming slightly controversial) that for a scoring model to be robust, Relative intensity factors are mandatory.
He proposes the only model (that I know) which takes this *mandatory* step into account.
Also, he based his model on one that also takes into account a very important element. And to present it to you, I prefer to let the father of these new models talk directly:
To derive an appropriate algorithm for calculating IF, blood lactate data collected from a large number of trained cyclists exercising at intensities both below and above their LT were analyzed. This choice was made because many physiological responses (e.g., muscle glycogen and blood glucose utilization, catecholamine levels, ventilation) tend to parallel changes in blood lactate during exercise – in this context, then, blood lactate levels can be viewed as an overall index of physiological stress. To reduce variability between individuals, the data were normalized by expressing both the power output and the corresponding blood lactate level as a percentage of that measured at LT. The normalized data were then used to derive a best-fit curve. Perhaps not surprisingly, an exponential function provided the best fit, but a power function of the following form proved to be nearly as good:
(Center)blood lactate (% of lactate at LT) = power (% of power at LT)3.90; R2=0.806, n=76 (/center)
Based on these data, a 4th-order function was used in the algorithm for determining the IF (the exponent was rounded from 3.90 to 4.00 for simplicity’s sake).
A good scoring model can not be obtained without minimal understanding of those physiological responses that are taking place as a result of intensity increase.
So, Skiba first got inspired by this:
home.trainingpeaks.com/.../normalized-power,-intensity-factor,-training-stress-score.aspx
Which he then turned into this:
home.trainingpeaks.com/.../normalized-power,-intensity-factor,-training-stress-score.aspx
After being inspired among other things by this:
jap.physiology.org/.../2506
Best of luck and keep us posted.
ASCA has good info on quantifying training effort in a workout based on the type of set(s) and their corresponding energy zones. They give a way of deriving the workout effort. They also explain how effort should be varied and/or cycled. You may be able to go to ASCA and get this info. It would be in the general literature for swim coaches. This is what I recall.
It's interestesting you try to express it mathmatically. I believe you would need to base your equations off of your threshold pace which is required to determine which energy zones you are working in. You are thinking about it which is good. Alot of swimmers just "wing it".
This information about baseline training may be useful. Good Luck, Coach T.
swimming.about.com/.../baseline_train.htm
Without having performed a comprehensive research of all that's currently available out there, I don't think I am far from the truth in stating that Dr.Phil Skiba definitely has a serious lead on all the others in quantifying swim training load.
The main difference with Skiba, is that prior trying to lay down his own forumulas, he carefully studied what was available
1) in other sports
2) in swimming based on the works of Toussain (to name only these)
I remain convinced to this day (at the risk of becoming slightly controversial) that for a scoring model to be robust, Relative intensity factors are mandatory.
He proposes the only model (that I know) which takes this *mandatory* step into account.
Also, he based his model on one that also takes into account a very important element. And to present it to you, I prefer to let the father of these new models talk directly:
A good scoring model can not be obtained without minimal understanding of those physiological responses that are taking place as a result of intensity increase.
So, Skiba first got inspired by this:
home.trainingpeaks.com/.../normalized-power,-intensity-factor,-training-stress-score.aspx
Which he then turned into this:
home.trainingpeaks.com/.../normalized-power,-intensity-factor,-training-stress-score.aspx
After being inspired among other things by this:
jap.physiology.org/.../2506
Best of luck and keep us posted.
You are cruising down an energy type path. A fellow by the name of Toussaint has published a lot of good work showing that power in crawl swimming is proportional to the velocity cubed.
So for a given swim, Energy = time * velocity^3
Add them all up for a session and there you are.
The swim score that Phil Skiba proposes takesa the above and adds in some rolling averages to account for time for your metabolism to respond and then takes that number and raises it to the 4th power to incorporate a lactate reponse model.
For my money, if you're traveling that path then the Sharp Stress Score that was developed by Rick Sharp is the easiest way to proceed. The easiest place to find that imeplemented is in the personal swim manager software by hy-tek. You tell it the workout and your 30 minute swim pace and it will tell you the stress of your workout. It is based on lactate responses and the set types that ASCA and others have been using for a while i.e. the en1, en2, sp1, sp2 definitions.
The swimscore has a rolling average in it that accounts for resting between intervals. The Sharp Stress Score has set construction guidelines with it. So a given set of 100s at a given speed can be scored differently based on the rest in between.
So a lactate tolerance set can only be scored as lactate tolerance if you follow the set construction guidelines for appropriate rest.
I really don't know if team manager has it at what level. It is part of the workout manager block, but I think personal swim manager is based on a previous version and that function might not be included anymore.
The swimscore has a rolling average in it that accounts for resting between intervals. The Sharp Stress Score has set construction guidelines with it. So a given set of 100s at a given speed can be scored differently based on the rest in between.
So a lactate tolerance set can only be scored as lactate tolerance if you follow the set construction guidelines for appropriate rest.
I really don't know if team manager has it at what level. It is part of the workout manager block, but I think personal swim manager is based on a previous version and that function might not be included anymore.
Thanks everyone for the replies, I learned much from the replies.
Is the delay time between sets taken into account with any of the mentioned formulas? If I have a workout of 6 different sets (each with a few laps), and I perform those sets back-to-back with no delay between sets, and compare that to doing the same 6 sets with 1 minute rest in between each set, surely there is a different difference in the amount of "effort", right? Though the same amount is being swam, the heart rate will be very different - and also something related to 'lactate response' though that is out of my domain of understanding at the moment.
Related to this, do I really need to worry about this rest time between sets? I try to time the rest in between sets (swim a lap, wait 5 seconds, swim a lap, etc.) but sometimes I am lax about the time between sets and wondering if this could have a big impact on my workouts.
For my money, if you're traveling that path then the Sharp Stress Score that was developed by Rick Sharp is the easiest way to proceed. The easiest place to find that imeplemented is in the personal swim manager software by hy-tek. You tell it the workout and your 30 minute swim pace and it will tell you the stress of your workout. It is based on lactate responses and the set types that ASCA and others have been using for a while i.e. the en1, en2, sp1, sp2 definitions.
Does the "Bronze" version of the "Team manager" package contain the functionality you mention?
