Haldane and his compartments

[up 4 it]

If something has a half time of 5 mins, how long will it take to reach 95% saturation?

Cmon Nigel, help me out on this one

Steve

[Lazlo]

Originally Posted by up 4 it

If something has a half time of 5 mins, how long will it take to reach 95% saturation?

Cmon Nigel, help me out on this one

Steve

1 half-time = 50%
2 half-times = 50% + 25% = 75%
3 half-times = 50% + 25% + 12.5% = 87.5%
4 half-times = 50% + 25% + 12.5% + 6.25% = 93.75%
5 half-times = 50% + 25% + 12.5% + 6.25% + 3.125% = 96.875%

So just under 5 half-times - about 25 mins.

This stuff IS in the Encyclopedia - honest.

Incidentally - new PADI guidelines starting next year will make the Encyclopedia and Knowledge Workbook compulsory reading for new Divemaster candidates.

[up 4 it]

Thanks Ian

that was one of the questions in my BSAC First Class Diver theory exam on Saturday...... I knew I'd got it wrong

[Paul Oliver]

Hi Steve

Try this post by Mark Powell, covers it rather well

http://www.yorkshire-divers.co.uk/fo...ad.php?t=20184

[nigelH]

Originally Posted by up 4 it

If something has a half time of 5 mins, how long will it take to reach 95% saturation?

Cmon Nigel, help me out on this one

Darn slave drivers.

Number of half times = -ln(1-N)/ln(2)

where N is the fraction so 95% = 0.95
so 1-N = 0.05
ln (natural log) of 0.05 is -2.99 so negate that is 2.99
divide by 0.695 (natural log of 2) gives 4.31 half times
multiply by 5 gives 21.55mins

I think. Possibly. If you're lucky.
I'm going to bed as I have to get up at 5.

Incidentally why is http://www.yorkshire-divers.co.uk/ giving me a 403 error?
You don't have permission to access / on this server
I can only get in via my history list.

[Rick Huggins]

I’ll take a stab at a “Gradient Factors For Dummies (Condensed)”. Here goes.

Everything in the gradient factor decompression algorithms revolves around Buhlmann’s tissue model. Currently this means 16 hypothetical tissue compartments (TCs) that are constantly tracked during a dive in order to determine each TC's inert gas pressure.

As you ascend all those TCs start to off gas as the outside ambient pressure is decreased. The question is – How fast can you let those TCs off gas?

Buhlmann answered that question by coming up with an “M-value”. Basically, an M-value is a maximum overpressure value that tells you that, if you exceed the value, Buhlmann thinks you’re crazy and believes you are about to get bent. Because M-values are “overpressure” values, an M-value for a given depth will be above the ambient pressure for that depth (that is, you are not going to hit an M-value if your tissue compartment pressure is less than ambient pressure) .

One ascent strategy, therefore, would be to move up until the pressure in your TCs just reaches Buhlmann’s M-value and then let your tissues off gas a bit (reduce pressure), rise to the next level, etc. In this strategy, you would keep going up in such a way that you never let your TCs exceed Buhlmann’s M-value.

Unfortunately, deco sickness does not exactly track M-values. More sickness occurs at and above the M-values and less sickness occurs when divers never reach Buhlmann’s M-values. So, GFs were invented as a consistent way to never reach Buhlmann’s M-value.

Gradient factors are calculated as :

GF = ( TCInertGasPressure – AmbientPressure ) / ( MValue – AmbientPressure)

So what does this formula tell us? First, it tells us that at a GF=1.0, you are at Buhlmann’s M-value. Therefore, staying at or below GF=1.0 seems important. Second, it tells us that when our TC pressure just reaches ambient pressure, then the GF= 0.0.

Another ascent strategy might be to shoot up to a GF=0.8 and ascend in such a way as not to exceed that value. In this way you know that your tissue compartments are never over 80% of the distance between ambient pressure and Buhlmann’s M-value. Dive computers implementing GFs usually let you set two GF parameters. Moving straight to GF=0.8 and ascending in such a way that you always keep your TCs at GF=0.8 would be equivalent to setting your dive computer to 80/80.

ErikBaker’s strategy was NOT to ascend directly to a high GF. Instead, he said “Let’s all ascend to a lower GF initially, then slowly move to higher GFs.” So, let’s say you want to first ascend to a GF=0.25 and then slowly move to reach GF=0.75 as you surface. This setting on your computer is likely 25/75. As reference, I believe the Shearwater computer uses 30/85 as it's default setting.

So what is happening when you use a GF setting of 30/85? First, your dive computer allows you to ascend until the pressure in your TCs first reaches a GF=0.3. This means your TC pressure is 30% of the way between ambient pressure and Buhlmann’s M-value. Then you sit there until your TCs drop enough pressure so that you can ascend to your next stop.

How much pressure must leave your TCs before you can ascend? Assume you hit your first stop (GF=0.3) at 110 ft. Well, then, we now have two known points. Point 1 is (110,0.3) – that is at 110 ft we are at a GF of 0.3. Point 2 is (0, 0.85), or at the surface we want to be at a GF=0.85. A natural way to ascend then (and this is what Baker did) is to create a line from the two points and ascend in such a way that you never exceed the GF generated by that line. The formula for the MaxGF at any depth, then, is

MaxGF = HiGF + (HiGF-LoGF)/ ( HiGFDepth – LowGFDepth ) * CurrentDepth

= HiGF - (HiGF-LoGF)/ LowGFDepth * CurrentDepth ( HiGFDepth is at the surface, or 0)

Therefore, if you hit your first GF=0.3 at 110ft, then your LowGFDepth=110. Before you can ascend to 100ft you must let enough TC pressure off so that, when you arrive at 100 ft, the GF of your TCs does not exceed 0.35 calculated as

MaxGF = 0.85 - (0.85-0.3)/ 110 * 100.

You can ascend to 90 ft when your TCs let off enough pressure at your 100ft stop so that when you reach 90 ft your TCs GF does not exceed 0.40 calculated as

MaxGF = 0.85 - (0.85-0.3)/ 110 * 90.

The GF method just walks the line all the way to the surface.

If you understood the above explanation, then you should see why some of the divers on this forum say that setting your GF parameters to 10/90, or 10/80, etc. helps generate deep stops. The low GF of 10 means a stop must be generated when your TCs are only 10% of the way between ambient pressure and Buhlmann’s M-value, rather than 30% if you were to set the low GF to 30. Simply, the GF line just starts deeper.

[GLOC]

Thanks for that Frogman. Makes sense, although I didn't quite follow the maths.