Trying to come up with a precise metric for cold water acclimatization

edited September 2013 in General Discussion
In my attempt to acclimatize to cold water, I am trying to approach this in a systematic way (a flaw of mine). When I train for a distance swim, the key metric in my training objectives is distance (km). But when my intention is to acclimatize to cold water, I am facing a dilemma. How does a a 45 minute swim in 15C water compare to a 1 hour swim in 17C water? Which one gets me closer to my goal of swimming 2 hours in 15C water? For this purpose, I came up with a ratio (CWITR...short for Cold Water Index Training Ratio) which is simply: #minutes divided by Water temp. So, in my earlier example, the CWIT Ratio of a 45 minute swim @ 15C is 3 and the CWIT Ratio of a 1 hour swim @ 17C is 3.5. This would indicate that the latter swim would be a more intense cold water training than the former and would be a better training for my 2 hour @ 15C goal (CWITR = 8).

Does this ratio make any sense to you cold water swimmers? What tweaks would you recommend to the formula (# minutes / Water Temperature) to make it more accurate to the realities of cold water training and cold water acclimatization?

Thanks a lot for your help.
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  • The ratio feels right but it'd be good to get a little science behind it. First off, you need to establish that there's an inverse relationship between water temp and difficulty. This may be tough as a 1 mile swim at 0C, while very hard, is not infinitely difficult. Second, what are the dependent variables at play here? Are these swims with sun overhead, on outcast days, or at night? What current are you swimming with/against? What's the salinity of the water? All of these come into play. I think the idea is great, it just needs to be fleshed out a little.
  • Waiting for the official MSF scientist @evmo to chime in...
  • edited September 2013
    My $0.02 - I would do it is follows:
    1) Construct a scale of difficulty (y axis) vs water temp (x axis). It might be 1-100 (y axis) or more likely a modified log function. The lowest water temp you can stand = max y, min y= temp you are most comfortable swimming at, the highest water temp you can stand (like 98.6 degrees F) =max y
    2) The "difficulty product" of a swim is then distance (or minutes) * difficulty (from #1 above)

    This follows Eric Bannister's theory of TRIMPS (TRaining IMPulSe) in running where a run's difficulty is distance * perceived effort. He used a 1-10 scale for perceived effort. Note that both Bannister's TRIMPS and what I proposed is individualized. If you wanted a "universal" scale of difficulty, maybe set max y at 32 degrees F and 98.6 F and min y to something like 70 degrees F. (Open to debate.) The shape of the line through the points would also be open to debate, but it's definately non-linear.

    -LBJ
    "Ordinarily he is insane, but he has lucid moments when he is only stupid." - Heinrich Heine
  • edited September 2013
    Leonard: After doing some research on my own, I'm entertaining the idea that water temperature difficulty could actually be linear w/r/t water temperature minus a constant, assuming equal salinity (which affects thermal conductivity) and training.

    Essentially, we are measuring the effects of thermal conduction on the effort needed to complete a swim. The more thermal conductance, the harder the body has to work in order to replace the thermal energy to maintain a core temperature of 37C. First off, the amount of power the body normally exerts to replace heat lost can be measured by black-body radiation is about 100W (around 9MJ or 2000kCal a day), but variables such as the amount of convection can make that number vary wildly. When people shiver, they use a lot more energy to maintain core temp; that number has been measured as high as 40-50% of maximum exertion.

    However, assuming equal training and body shape, the amount of heat transfer should be equivalent to the amount of effort the body needs to exert to generate the thermal energy lost. Fourier's law seems to describe this situation (assuming no movement) and states that the amount of heat transfer is roughly proportional to the surface area of the conducting surface and the temperature gradient in Kelvin. Newton's law of cooling is the discrete analog of this (http://en.wikipedia.org/wiki/Newton's_law_of_cooling#Newton.27s_law_of_cooling) and states that the amount of energy lost is proportional to the difference in temperature.

    There are some HUGE assumptions here, such as that the water isn't moving, the water doesn't change its thermal conductivity significantly when it gets colder/warmer, the human body doesn't shift to a shivering state during the swim (in this case, dip), AND we aren't trying to cool the body instead of warm it (in cases of swimming in 31C water). But, it can be used as a first case approximation. I would conjecture that instead of using straight up temperature in C, we should use an absolute difference in temperature from a steady point. Human skin temperature is 33C, and makes for a good starting point.

    TL;DR... maybe your formula for effort in the water should be (minutes swam)*(33C-water temp). This seems to fit nicely by dimensional analysis to an amount of effort exerted by rewarming your body (minus shivering) and adds credence to one of @david_barra 's adage about how his pace per mile gets slower by a constant amount every drop of 1C (did I get that right?). In your case, 45 minutes at 15C would be 810 units of exertion vs the same amount of time at 17C would be 720 units.
  • Two thoughts:

    - Air temp will have to be a factor in any cold water swimming metric. Not as important a factor as water temp, obviously, but still a factor.

    - Try quantifying how cold you feel after each swim as a dependent variable, along with water temp, air temp, & time-in-water as independent variables. For example, when you swim in Aquatic Park you can record how long it takes you to re-warm in the sauna.
  • @evmo: I REALLY like the idea of basing acclimation on how long it takes you to warm up afterwards.
  • Leadhyena said:

    After doing some research on my own, I'm entertaining the idea that water temperature difficulty could actually be linear w/r/t water temperature minus a constant, assuming equal salinity (which affects thermal conductivity) and training.

    This assumption seems troubling to me. At the very least, it's a quadratic, I think. @evmo has posted other places that his pace is pretty constant between 68F and 82F (if I remember the numbers correctly), but outside of that range, on either side, his pace slows. Unless you are assuming that you are operating close enough to one end of the curve, I think your trend line will give you some pretty misleading results.

  • Look, if your goal is a two hour swim in 15 degrees, I can assure you of one thing. It will be easier to just go and do it rather than try to understand the maths. Or put it another way, I can spend the next two hours studying this thread, or I can put my speedos on and go for a two hour swim.

    But seriously though, once you have swam a few 7 degree miles, you will find doing one your first 6 degree mile no more difficult than the first 7 degree mile. Then after a few 6 degree miles, you will find your first 5 degree mile no more difficult than your first 6.

    Indeed, my first official Ice Mile3.5 degrees, mile seemed comparitively easy after the many training ice miles previously swam. Acclimatising makes colder temps easy, but you would expect colder temps to be tougher. It's a paradox that will mess with your head.

    So concentrate on swimming not maths.
  • @Mauprieto, I asked myself a similar question some years. Like you, the largely rational side of my mind wanted to be able to quantify all the factors leading to heat loss. I kept asking myself why there was such variability in people's cold tolerance, where there wasn't an apparent great physical difference. It lead to me writing the first long series on my blog, on cold adaptation in swimmers. I read a lot of papers, where I could find them, I even tried using Wolfram Alpha to get answers to certain questions like trying to treat the human body as a black box.

    As @leadhyena says, the variables are significant, wind speed and air temperature are huge factors and some are internal and can't easily be measured. The externals alone are long, (add wind direction and speed, air humidity, water surface state). The physiological variables include weight, size, body fat, stroke rate, heart rate, presence of stress hormones, possible low level undetected infection, sleep, recent food intake & glycogen levels. The stress hormone and heart rate items are something that are a good measurement of experience. Early in cold adaptation both will high, even precipitating elevated respiration and noticeable cardiac palpitations whereas even though you know it will uncomfortable or even painful once you've done it enough times, you are still completeley calm.

    I eventually gave up the idea (for myself anyway). In fact, and I'm not telling you to do this, but letting go of trying to quantify cold ability so rigourously I think helped me, maybe because I relaxed a bit more, stopped trying to be the same as other people whom I perceived as better (and I believe one of the best if not the actual best cold water swimmer in the world is a Sandycove swimmer), and because I saw cold as a moving target.

    Because you have more than two variables and most of those you can't adjust (water temp and air temp are the closest to adjustable from a practical viewpoint) there's no way I think to come up with an independent scale. If you've seen a Four-Corner experiment with less variables, but which can be quantified,let's say four, as I recall the maths get complicated to assess the best outcomes (rather than where you have two variables and you simply adjust until you get the best result), and even if we could adjust, it would be even more complex. This is irrelevant since we can't even measure many of variables practically.

    What you could do, and I did it for myself about five or six years ago, is to create a diary of how long you can swim at each full or half degree drop, what you feel like mentally at each temperature drop and your recovery time. You also want to record initial shock effects (e.g. I won't get sinus pain until under 7C).

    It then becomes like the medical scale for assessing pain (almost literally) and easier to measure progression season on season. It had three primary benefits:
    1. I could establish an initial personal baseline.
    2. I could subsequently gauge personal improvement.
    3. It does allow you a scale to allow discussion with others.
    It's not a short term project, but doing now going into autumn is a good time to start.

    Another thought is having an hour swim target. Assuming I do any winter swimming, I know that at 10C water temp and 10c air temp I should be able to swim an hour (I can do more if I specifically stay in longer at lower temperatures but a five minutes variation can be very significant if you are approaching Moderate hypo. (One friend calls it the combined 20). If adding air and water temps equals 20C, this allows him to swim for an hour comfortably .)
  • Loneswimmer forgets that acclimatising will make the lower temps easier. I remember gasping for breath entering at 12 degrees, but now think nothing of getting in at 5. Does that mean 12 was colder than 5? Crumbs, after a season of ice swimming 12 will feel toasty. Bur after a summer of 17, 12 will feel chilly. I can't see how you can calculate anything meaningful. Other than simply recording the dates temps and durations of your swims and how you felt and how you recovered.
  • Haydn said:

    Look, if your goal is a two hour swim in 15 degrees, I can assure you of one thing. It will be easier to just go and do it rather than try to understand the maths. Or put it another way, I can spend the next two hours studying this thread, or I can put my speedos on and go for a two hour swim.

    I hear you, and I started my question saying that I have the flaw of trying to approach things in a systematic way. The fact is that I am curious into how things work, and was intrigued in finding out from the cold swimmer gurus out there if my rule of thumb (minutes/temperature) is a somewhat adequate metric for the relative difficulty of a cold water swim. Concentrating on maths helps my swimming. I end up putting my speedos more often if I set myself specific objectives. I find value in understanding how 60 minutes @ 15C compares with 70 minutes @ 15.5C water.

    I will gladly sacrifice a day's swim in exchange for the insights gained from @Loneswimmer, @evmo, @Leadhyena, @IronMike, @Leonard_Jansen, @timsroot, and @Haydn. Nothing wrong with learning something new now and then, so definitely time well spent for me. MSF allows me to learn from the best out there and get input from different perspectives in order to draw the right conclusions for me, and this thread is a great example. Thanks you all for the time dedicated to shed light into my question.
  • edited September 2013
    @Haydn, I didn't forget acclimatisation. I was trying to give @Mauprieto something that might him, that helped me early on, coming from a similar mindset.
    It's why I said that a personal log demonstrates a changing and improving ability, i.e. acclimatisation.

    Plus I like writing about cold.
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