Need help figuring halftime compartments, please!

[Shoc369]

Can you please help me understand how to do the math to answer the following question:

In feet of pressure, how much nitrogen would the 5, 10, 20 and 60 minute halftime compartments each have after 60 minutes at 60 feet?

Any help would be greatly appreciated!

 

[Charlie99]

Are you trying to get us to do you DM classwork??

Here's some starting info......

0 depth is 1ata. When you are saturated from breathing air at sea level, you start off with (33'-1.6') x 0.79 = 24.8 fsw of N2. (1.6fsw to 2.0fsw is the typical range assumed for water vapor + CO2 vapor pressure in the lungs. 0.79 is typically used as the fraction of N2, although it's really more like 78% N2 and 1% argon.)

At 60' depth, your lungs have a partial pressure N2 of (60'+33'-1.6') x 0.79 = 72.2fsw.

For each halftime, the N2 in the compartment is assumed to move halfway between the starting point and the inspired N2. The 5 minute compartment will be fully saturated after 60 minutes, and be 72fsw. The 60 minute will be halfway between 24.8 and 72.2 fsw, or about 48.5fsw.

 

[Azza]

Sorry that imperial version threw me. Imperial seems such a backward way of doing anything but that’s not the discussion. So here it is in Metric for those that prefer Metric.

Remember the theory of halftimes is that after each halftime the compartment gets halfway to saturation, so after the 1st halftime, it is halfway.
After the second halftime it is halfway between the 1st halftime and saturation,
After the third halftime it is halfway between the 2nd halftime and saturation etc.

Think of it like a clock. Starting at 12 after the first halftime it is 6. After the second it is 9, after the third it is 10:30... and finally after 6 halftimes we say it is saturated because the increments become so miniscule that we cant be bothered getting out our atomic calculators and measuring the loading.

So 5, 10, 20, 60 minute halftime compartments, after 60 minutes at 18 MSW

60 / 5 = 12 halftimes. Tissue is saturated after 6 halftimes. Answer is 18 MSW

60 / 10 = 6 halftimes. Tissue is saturated after 6 halftimes. Answer is 18 MSW

60 / 20 = 3 halftimes.
• Halfway to 18MSW is 9MSW. (1st halftime)
• Halfway from 9MSW to 18MSW is 9MSW. 9MSW + half of 9MSW (4.5MSW) = 13.5 MSW. (2nd halftime)
• Halfway between 13.5 MSW and 18 MSW is 4.5MSW, 13.5MSW + half of 4.5MSW (2.25MSW) = 15.75 MSW (3rd halftime)
• Answer is after 3 halftimes 15.75 MSW

60 / 60 = 1 halftime. Half of 18MSW is 9MSW. Answer is 9MSW

If you want to measure in ATA then Metric is the easiest way.
10 MSW = 2 ATA absolute.
20 MSW = 3 ATA absolute.
30 MSW = 4 ATA absolute.

So the answers in ATA are

5 MIN HT = 2.8 ATA
10 MIN HT= 2.8 ATA
20 MIN HT= 2.575 ATA
60 MIN HT= 1.9 ATA

 

[Charlie99]

Azza, your numbers work only if the diver is breathing pure N2, in which case this decompression stuff doesn't really matter

 

[Azza]

Azza, your numbers work only if the diver is breathing pure N2

You sure about that?

 

[Charlie99]

You sure about that?

Yep. Your math gives the same N2 loading independent of whether the gas is air or nitrox.

 

[Requiem]

Hiya Charlie,

Azza is actually right, and if you want the word from the horses mouth so to speak. An excerpt from the PADI Instructor manual is below.

Your tissue loading can not go past the depth you are currently at, so if you are at 60fsw you cannot have 72.7 fsw pressure of N2 unless you have ascended to that depth from a deeper depth. I'm not sure what you are calculating with your sum of (33'-1.6') x 0.79 but you need to have a time factor for half times. A half time is the time it takes for a theoretical tissue to fill or empty half of its volume or remaining volume with nitrogen. Due to the very minor difference (98.5% compared with 100%), we count 6 half times as being how long it takes to fill or empty a theoretical compartment. Therefore a 60 min compartement will fill or empty in 6 hours and at 60fsw a 10 min compartment will take 60 mins to fill. It will fill to 1/2 the depth or remaining depth with every half time.

from the PADI Instructor Manual:

Example - A 5 minute halftime compartment will have
how much tissue pressure 5 minutes after taken from the
surface to 18 metres/60 feet in seawater?

Answer: 9 msw/30 fsw of pressure
(in one halftime, compartment goes half distance from beginning
to new pressure).

Example - A 20 minute halftime compartment will have
how much tissue pressure after 40 minutes at 24 msw/80
fsw?

Answer: 18 msw/60 fsw of pressure
40 minutes = 2 halftimes for 20 minute halftime.

After first halftime, pressure goes halfway = 12 msw/40 fsw.
After second halftime, pressure goes halfway from 12 msw/40
fsw to 24 msw/80 fsw = 18 msw/60 fsw.

Example - How long would it take a 60 minute compartment
to saturate to a given depth?

Answer: 360 minutes (60 x 6 halftimes)

I hope that clears this up for you and for Shoc369

 

[Azza]

Yep. Your math gives the same N2 loading independent of whether the gas is air or nitrox.

Perhaps you would be so kind as to flick PADI an email telling them their Instructor Manual, Divemaster manual and Encyclopedia of Recreational Diving is wrong then so they dont confuse anymore people. Because if schok369 goes into a PADI DM exam with what you have said, he will fail.

 

[Charlie99]

Your tissue loading can not go past the depth you are currently at, so if you are at 60fsw you cannot have 72.7 fsw pressure of N2 unless you have ascended to that depth from a deeper depth. I'm not sure what you are calculating with your sum of (33'-1.6') x 0.79 but you need to have a time factor for half times.

Requiem and Azza, although your math may agree with PADI, it is very non-standard. As I noted before, it obviously does not take into account the breathing gas. Doesn't that raise some questions about the accuracy of the PADI manual?

Perhaps rather than reading the PADI instructors book, you should read some articles by Erik Baker, such as "INtroductory Deco Lessons", and "Understanding M-values".

What is the ppN2 at 60'? 60' depth is 60+33=93fsw (absolute depth in feet of saltwater). Multiply that by the fraction of N2, asssuming air. 93 x 0.79 73.5fsw. Let's just ignore little details such as the fact that your lungs are near 100% relative humidity at 37C, which is a vapor pressure of a foot or two.

The original poster asked the rational question, which is about NITROGEN pressure. The PADI excerpt is about some non-standard concept call tissue pressure, which doesn't seem to depend upon FN2.

I stand by my original post.

Oh, and as I stated in my original post, the (33'-1.6') x 0.79 = 24.8fsw is the calculation of the starting N2 pressure in all compartments, assuming that they all start by being saturated at sea level. The 33' is the absolute pressure at seal level. 1.6' is the H2O + CO2 correction. 0.79 is the fraction of N2 in the atmosphere.

 

[Requiem]

Hi Charlie,

Firstly we are talking about Haldanes theories. We are also talking about nitrogen loading in theoretical tissue compartments under pressure, which do not have any other part of breathing gas in them as it is either metabolised or exhaled and is not a foctor in decompression sickness and nitrogen loading, in this model. If we were talking about the lungs, and other factors of absorption and elimination as well as other factors which can cause DCS, I'd agree wiith you.

Not everyone needs to understand the full factors behind decompression models, this is relatively simple theory to allow divemasters to have an understanding of how tables work.

You obviously have a keen interest in this and have done some background reading. As a TDI Decompression proceedures Instructor and PADI Course Director I too have read quite a few different articles. The question and problem that Shoc has, relates to his Divemaster (PADI) course and is directly out of the manual, as you rightly pointed out. He obviously has a problem understanding it, I and Azza have both tried to help him clear this up and the information you are giving is too involved and unecessary.

I am not going to say your math is wrong, but it does not pertain to the problem at hand and is overcomplicating a simple calculation that is the basis of haldanean thoery which is used as a base model for all decompression tables and computers.

PADI, and many other certification agencies feel that this basic information is suffiecient for a basic understanding of decompression models. You may well disagree, however I notice that you are a PADI Rescue Diver, so you must have some faith in them as a certification agency.