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Half times easily explained...

Discussion in 'Decompression Theory' started by Bluebottle, May 14, 2005.

  1. Bluebottle

    Bluebottle Guest

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    can anyone explain the half times theory to me, in easy language?

    it's all very complicated and i did my divemaster's ages ago and have forgotten it all.. IDC coming up soon and i gotta get it right.

    any links or straight answers would be much appreciated.

    Thanks
    bluebottle :brain:
     
  2. Mark Powell

    Mark Powell Scuba Media & Publications

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    Half times are a common concept in science. The most famous use of half times is in relation to nuclear materials where the half time is the time it takes a radioactive substance to decay to half of its current size. This is exactly the same concept applied to the uptake of Nitrogen by a tissue compartment. The half time of a compartment is the time it takes for the compartment to become half saturated, or if we are ascending to become half desaturated.

    So if we consider a compartment with a half time of 5 minutes this means that compartment will become 50% saturated within 5 minutes. It will then take a further 5 minutes for the compartment to move from the current state to half way to saturation, i.e. 75%. The table below shows the progression of the tissue saturation at 5 minute intervals.

    5 min 50%
    10 min 75%
    15 min 87.5%
    20 min 93.75%
    25 min 96.88%
    30 min 98.44%

    We can see from this that the largest movement takes place during the first half time period, each subsequent half time period then sees a smaller and smaller change. If we draw a graph of gas uptake over time we can see a smooth line that initially shoots up but then gets ever shallower as it reached 100%.

    [​IMG]


    Mathematically the tissue will never reach 100% as it only moved half of the way from where it is towards 100% at each stage so it takes smaller and smaller steps towards it’s goal but always has the other half of the last step to cover. However, for practical purposes, after 6 periods we can consider the tissue saturated as it is at 98.44% saturation and after 24 hours we would consider the tissue to be completely saturated.

    Each compartment will saturate at a different rate. As we have seen after 5 minutes the 5 min tissue is 50% saturated but the 10 min tissue will take 10 minutes to become 50% saturated and so on. This means that each of the tissues will have a different level of saturation with the fast tissues absorbing gas and moving towards saturation faster than the slow tissues. However, as the diver ascends and the pressure is reduced the fast tissues will also release inert gas faster as the half time also refers to the time it takes to release 50% of the absorbed gasses. This means that fast tissues will also release gases faster then slow tissues.

    [​IMG]

    From the graph above we can see the behaviour of a number of compartments when considered together. As we have seen above the 5 min compartment is 50% saturated after 5 minutes, at 10 minutes it is 75 % saturated and so on until 30 minutes or 6 half-time periods it is effectively saturated (98.44%). The 10 min compartment is 50% saturated after 10 minutes. After 40 minutes the compartment is not yet saturated as this has only been 4 half time periods. It would require 6 half-time periods (60 minutes) for this compartment to become effectively saturated. The 40 min compartment is at 50% saturation at 40 minutes but all of the slower compartments; 80, 120, 160 and 200 min, are less then 50% saturated.

    At 40 minutes the pressure is released and the compartments start to desaturate. The 5 min compartment was the most saturated but as it desaturates equally fast the level of saturation quickly drops to below that of the 10 min compartment and soon drops below the other compartments until at time 60 minutes, 20 minutes after the pressure was released, the 5 min compartment is less saturated than all of the other compartments. The 10 min compartment also drops quickly so that at 48 mins it drops below that of the 20 min compartment.
     
  3. Bluebottle

    Bluebottle Guest

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    hi Mark

    thank you for such an indepth reply... i am printing it off, will take a close look and then get back...

    much appreciated.
    BB
     
  4. Charlie99

    Charlie99 Solo Diver

    # of Dives: 500 - 999
    Location: Silicon Valley, CA / New Bedford, MA / Kihei, Maui
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    A simple example of halftimes is a tall cylindrical bucket that is full of water.

    Assume that you drill a small hole in the side, down near the bottom. Eventually the bucket will empty down to the level of the drilled hole, but for a small hole it will take a while.

    The rate that the water exits through the hole is proportional to the difference between the water level in the bucket and the level where the hole is drilled. When the water level is high, there is more water coming out of the hole. When the water level approaches the drill hole, the water flow nearly stops. (All processes that have this sort of rate-proportional-to-the-amount-left characteristic will have a halflife or exponential decay behavior. That's why it is so common).

    It will take a certain length of time for the water level to drop half the distance from the starting point to the level of the hole. This is the "halftime". Since the water flow is now slower (less pressure because of the lower water level), it will take that same "halftime" for the water to drop half the distance from this new starting point to the drill hole level. After this 2nd halftime, the water flow is even slower and ......

    A very tiny hole will drain the water very slowly and the "halftime" or time to empty the bucket halfway will be very long. Drill a bigger hole and the halftime is shorter. In both cases, though, the bucket empties fastest when full, and empties slower and slower the closer the water level gets to where you drilled the hole.
     
  5. miketsp

    miketsp Solo Diver

    # of Dives: 500 - 999
    Location: São Paulo, Brazil
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  6. Bluebottle

    Bluebottle Guest

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    hi hi hi!

    well finished my exams, 80 90 90 100 100 90.. not too bad for a rusty old s0d! hehehehe

    thanks for all your help guys.. we are now two days into the IDC and it's getting interesting... candidates from all walks of life so let's see...
     

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