Partial Pressure Explained (hopefully)
Imperial units
One of the harder
things for new
In the above diagram
we can see the approximate composition of air, there are about 1% of other
trace elements in this mix and oxygen is generally referred to as having 20.9%
of oxygen and nitrogen as 78% but for our purposes we will refer to air as
21/79.
Pressure is defined
as the movement of the gas particles bouncing around and impacting everything
they are exposed to. Gas, unlike water,
or solids, is
easily compressible and the pressure of the air around us is about 14.7 pounds
per square inch at sea level. This
pressure is created by gravity, pulling the planets surrounding atmosphere
toward the core of the earth. Gas, like
anything, has mass, and mass attracts mass according to
So…
1 ATM = 14.7 Pounds
per square inch or PSI = 1 BA
We must remember to
include the pressure of our surrounding atmosphere when we do our
calculations. We are going to compare our
pressures to a perfect vacuum, or zero pressure or 0 psi. We also call this type of pressure measuring
“absolute pressure”. So we are
surrounded by 1 ATA, which means Atmosphere Absolute. If our atmosphere was twice as thick, we
would have 29.4psi of
atmospheric pressure, 2x14.7psi=29.4psi.
So, what does water
weigh? Lets use
that same one square inch tube we used for the air measurement. We will find out that our water column only
has to be 33 feet high to get to that same 14.7 pounds, so to double the
ambient pressure around us, we would have to dive 33 feet below the surface and
then the pressure would be 29.4psi, or 2 ATA.
So we have all the atmosphere above us, 1 ATA, and an additional 33 feet
of water, another ATA, added together gives us 2 ATA of pressure. If we went down another 33 feet under water,
we would be at 3 ATA and so on. So depth
can be expressed in feet, meters, BA
ATA 
PSI 
Volume 
FSW 
PO2 
PN2 



1 
14.7 
1 
0 
.21 
.79 



2 
29.4 
1/2 
33 
.42 
1.58 



3 
44.1 
1/3 
66 
.63 
2.37 



4 
58.8 
1/4 
99 
.84 
3.16 



5 
73.5 
1/5 
132 
1.05 
3.95 



6 
88.2 
1/6 
165 
1.26 
4.74 



7 
102.9 
1/7 
198 
1.47 
5.53 



8 
117.5 
1/8 
231 
1.68 
6.32 



9 
132.3 
1/9 
264 
1.89 
7.11 



Also notice
Some Fun Stuff to tease your OC buddies with.
Lets toss in another
advantage of diving a rebreather and compare how we utilize an aluminum 80
compared to a single 13cf oxygen cylinder we might have on our rebreather. The divers
OPEN CI
FSW 

GAS USED 60 MIN 
DM 
GAS USED 60 MIN 


0 
17LPM 
1020L /72CF 
1LPM 
60L 2.1CF 


33 
34 
2040L /144CF 
1 
60L 


66 
51 
3060L /216CF 
1 
60L 


99 
68 
4080L /288CF 
1 
60L 


132 
85 
5100L /360CF 
1 
60L 


So, as you can see,
our diver diving open circuit must take down 360 cubic feet of gas to do the
same one hour dive at 132 feet as our rebreather diver does on 2.1 cubic feet of oxygen. Now we must also add that we will actually use
more gas than this because of mask clearing and equalizing as well as the gas
we bleed off during ascent, but the facts still show the
Lets calculate how much oxygen is in an
aluminum 80. 80 CF of gas, of which 21%
is oxygen, so 80x.21=16.8 cubic feet of oxygen, converted to liters is
16.8x28.3= 475 liters of oxygen, this amount of oxygen would allow the
Ok, back to the lesson…
Lets go back to our Air mix.
The oxygen component
of air is 21%, or in decimal, .21 or 21/100 of the whole amount. If the whole amount is 1, as in 1ATA, then
the Partial Pressure of the oxygen in air, at the surface, is .21, easy,
right? Now if we go under water to the
33 foot level, we just added another atmosphere of pressure didn’t we? So the total
pressure we now have is 2 ATA, but the F
So…
2 ATA(our
depth measured in ATA)
This works for
nitrogen too, if nitrogen is 79% of the whole of air, or .79 in decimal, then
it stands to reason that at 2 ATA our partial pressure of nitrogen is…
2
ATA x .79 = 1.58 PPN2 or partial pressure of Nitrogen.
Lets see a graphical representation of that
formula.
Some folks call this
the Pigs on top formula, some call it the T formula, call it whatever you want.
This is something you
might want to memorize, it will come in handy as long
as you are a diver.
To use this formula,
you cover the data you want to find and do the resulting math. For example, cover the PPg,
what’s left? Fg
and Depth, so Fg (or
Fraction of Gas x Depth (in ATA) = the Partial pressure of that particular gas,
at that depth.
Cover the Depth and you are left with PPg “over” Fg, so if you need the
depth where a fraction of oxygen reaches, say, 1.6 PPO2, the Fg (fraction of gas) or oxygen content of your mix is 32%,
or .32, then you divide (remember PPg/Fg, same as PPg divided by Fg) 1.6 (our PPg) divided by .32 (the O2 of our mix) equals 5. OK 5 what?
Lets do some more examples.
If we had a nitrox
mix of 32% oxygen, and we wanted to know what the PPO2 would be at 100 feet,
how would we do it? Well we want the PP
of a gas, in this case oxygen, so we put our thumb over the PPg
part of the formula and we are left with Fg
and Depth, so we multiply our Fg by our Depth in ATA.
Ok, the fraction of
oxygen is 32%,or expressed as a decimal, .32. So Fg=.32 multiply that by
our depth, but we cannot use 100 feet, because that is not in ATA.
So how do we get ATA
from feet of water? Simple, just think
about what is over your head, 100 feet of water, plus the earths
atmosphere. How many 33’s are in
100? 100/33=3.03 (lets call it 3) So that is 3 ATA of
water we have, now add that to the pressure of the atmosphere 1 ATA so 3+1=4
ATA of pressure at 100 feet.
Now take our fraction
of gas, .32 and multiply that by 4, which is our depth, but measured in
ATA. .32 x 4 ATA = 1.28 ATA of oxygen in
that 32% mix at a depth of 100 feet.
Since the human body can tolerate between .16 (hypoxia)and
1.6 (hyperoxia) partial pressure of oxygen, this 1.28 is right in the ballpark.
More about units,
where are we going to see these units.
PP: This
will be the readout on our PPO2 meter at depth or when we calibrate sensors.
This will also be a way to figure how much narcosis we can tolerate, if
we start getting narc’ed at around 100 feet of depth,
on air, then we need to keep in mind we want our gas mixes to not allow a PPN2
higher than 3.2. more
on how to do this later.
You may not need this, but you can also figure what the PP of your
helium is in a particular mix. We are
more concerned with PP’s of Oxygen and Nitrogen than helium but it is a good
way to check your math at the end of mix calculations.
Depth in ATA: This is our depth unit, we will need to
convert this to feet to make it useful to us, if we are plugging in a depth in
feet, we divide that number by 33 and
then add one to it. Feet into ATA (D in
feet/33)+1 = D in ATA. If we are pulling depth out of the formula
in ATA and converting to feet, we subtract one and multiply by 33. (Depth in
ATA – 1) / 33 = Depth in feet. Instead of
remembering the formulas remember the concepts.
What’s over your head? if you are given depth in ATA, subtract the weigh of the
air, and only count the water.
Fg:
This is our fraction of gas, if we are pulling this out of the formula,
we might be mixing some gas up for a dive.
If we are plugging this into the formula, then we might be figuring out
how deep we can take a particular mix, either limiting by Oxygen limits, or
Narcosis limits.
So here are some more
ways we can use this formula.
Best mix:
We want to do a dive
to 175 feet to a wreck and want a bottom mix, or diluent to be a maximum of 1.6
PPO2 and a max narcotic depth to be equivalent of air at 100 feet. So this will be a trimix blend. First figure how much oxygen will be in the
mix. So this would be a fraction of
gas. We cover the Fg of the formula.
Leaves us with PPg over
Depth. The PPg
is going to be 1.6ATA, the max PP of oxygen we feel safe with. The depth is going to be 175 feet, but we
cannot use this measurement, so convert to ATA, divide by 33 and add 1 to the
quotient. 5.3+1=6.3 ATA of depth.
Now 1.6 divided by
6.3, remember our algebra, the top number is divided by the bottom, the answer
is .254 and now which way do we round?
Think about what we are doing here, figuring an oxygen content of a mix
to be used at 175 feet! Do we want to round up, hell no! Yeah, round down to .25 or 25% oxygen content
in our mix.
Ok, now we know how
much O2 to put in our mix, how about the other two gasses. Well the most important component of our mix
is the oxygen, so we figured that first.
The next most important component is the nitrogen and remember
we wanted the narcosis to be like air at 100 feet. So what is the PP of nitrogen, on air, at 100
feet? What is the unit we want out of
our calculations? OK PPN2, that’s the
top of the formula, cover it, what’s left?
Fg and depth. The fraction of nitrogen in air is .79 or 79%
(mathematically the same). So .79 X depth. Our
depth is 100 feet (remember we want the PPN2 on air at 100 feet) Depth is (100/33)+1
= 4.03ATA Lets do the math (I always
wanted to say that). Fg of .79 X 4.03 Depth in ATA=3.18 PPN2. So we are happy with a PPN2 of 3.18, or
3.2. Narcosis is so variable it wont
matter which way we round this. So now
we have a safe PPN2 of 3.2 and we want to know what Fg, or fraction of N2 in our mix will yield a PPN2 of
3.2 at 175 feet. Cover the Fg, plug in the PPN2 of 3.2 in the top of the formula and
divide by the Depth in ATA, we already figured it to be 6.3ATA so 3.2 divided
by 6.3 = .507 or .51 = 51% of nitrogen, so we have 25% oxygen, and 51%
nitrogen, what do we use to fill the rest of the mix? Helium, of course. We will end up with 25% O2, 51% N2 and 49% HE. Or
TMX 25/49. There are
several ways to state trimix blends, one comes from the Compressed Gas Industry,
one used by divers and ANDI has there own.
It doesn’t matter what you use, just so everyone involved is using and
understands the same units.
Check our sensors at
depth:
Many of us manual CC
Below is a table for
even ATA’s on air or 21 % oxygen mixtures. It is normal to have some variation in oxygen
sensors, do not expect them to agree exactly.
33 FSW = .42 PO2 
165 FSW = 1.3 
66 FSW = .63 
198 FSW = 1.5 
99 FSW = .84 
231 FSW = 1.7 
132 FSW = 1.1 



Below is a table for
10/50 trimix.
33 FSW = .2 PO2 
231 = .8 
66 FSW = .3 
264 = .9 
99 FSW = .4 
297 =1.0 
132 FSW = .5 
330 =1.1 
165 FSW = .6 
363 = 1.2 
198 FSW = .7 
396 = 1.3 
Equivalent Air Depth EAD
This refers to
comparing the nitrogen content in the mix you are breathing and matching it to
a like nitrogen exposure if one was diving air.
This is helpful if one is calculating decompression for a nitrox mix and
the only thing you have to use is air tables.
In my humble opinion, one should stick a crow bar in your wallet and buy
the correct tables, or a nitrox computer rather than waste time learning to use
this formula. ‘nuff said.
Equivalent Narcotic Depth END
Now here is a
comparison I can reason with. If a diver
knows that he/she will likely become narced at any depth below 130 FSW, then
one would plan your mixes to have an equivalent narcotic depth of less than
that, say 100 fsw or less. Like we did in the best mix calculations above. The PN2 of air at 100 feet is about 3.2. If you don’t know how I got that number, you
have not been paying attention, go back to the T formula and catch up with the
rest of us later. So, to make a mix with
a PN2 of 3.2 or less, we will want to pull from our T formula a Fg, or fraction of gas, in this
case nitrogen. If our depth is to be 140
FSW (5.2 ATA), again you should know by now how we got the 5.2, we covered the Fg, and 3.2 PN2/5.2 ATA Depth =
.61, or 61% of nitrogen. So what is the
rest of the mix? Well lets try oxygen,
100% 61% = 39% of gas we need to make the rest of our mix. But 39% oxygen at 140 FSW is a bit hot, like
2.0 PO2, that’s likely to make you do the funky chicken, bad at any depth. So
what would work? Well at 5.2 ATA of
depth, we might want the mix to be a 1.5 PO2, so same formula, different gases,
1.5 PO2 of oxygen/5.2 ATA of depth =.29 or 29 % oxygen, so our mix is now 29%
O2 and 61 % N2 which is 90% of the full monty, OK, 10
% helium will make the best mix for this dive.
There is no reason to use more HE than you
need, pick an END that you are comfortable with and plan your mixes
accordingly.
Interesting comparisons.
When we dive on a
closed circuit rebreather, we are said to be diving a constant PO2. What exactly does that mean?
Ok, as an open
circuit diver we calculate our PO2 at the deepest part of the dive and mix our
gas for that depth so as to not go over 1.6 PO2, the reason we get as close to
that as possible, is so that we do not take on as much nitrogen and have to
spend too much time on the deco line.
The only depth that mix is really good for is at the deepest part of the
dive. As we ascend, that mix becomes
less and less PO2 so that as technical divers we bring along extra mixes with
higher PO2’s to increase the gradient of oxygen and speed up
decompression. Lets
look at another table.
depth 
OC PO2 32% mix 
OC mix fraction 
CC SP 1.2 
CC mix fraction 

33 
.64 
32% 
1.2 
60% 

66 
.96 
32% 
1.2 
40% 

99 
1.28 
32% 
1.2 
30% 

132 
1.6 
32% 
1.2 
24% 

155 
1.92 
32% 
1.2 
20% 

The diver on open circuit’s PO2 is
steadily increasing as he descends and maxes out at 132 feet with a 1.6. The closed circuit diver is using a setpoint of
1.2 and as he descends his PO2 remains at 1.2 throughout the whole dive, while
his Fg, or fraction of gas decreases from a high of
60% to a low of 24% at 132 fsw. He does
not have to run his mix as high as 1.6 at any time,
this reduces his OTU’s or Oxygen Tolerance Units, a measure of the pulmonary
toxicity of oxygen. The CC diver has his
FG increasing during ascent and this helps with the gradient of oxygen and
washes out the inert gas faster. Look at
the same diagram with air as an OC dive gas.
depth 
OC PO2 21% mix 
OC mix fraction 
CC SP 1.2 
CC mix fraction 

33 
.42 
21% 
1.2 
60% 

66 
.63 
21% 
1.2 
40% 

99 
.84 
21% 
1.2 
30% 

132 
1.03 
21% 
1.2 
24% 

155 
1.26 
21% 
1.2 
20% 

Now the OC diver is
really not getting washed out of nitrogen, at 155 feet the mix is almost
exactly the same, but our CC diver is at his worst fraction, it only gets
better as he ascends. The OC diver will
take a much longer time to decompress.
Its even worse at the safety stop, our CC diver is breathing the
equivalent of 80% O2 at 15 feet while our OC diver is breathing .31, quite the
opposite of what you would want to do.
I ran a couple
profiles on GAP http://www.gapsoftware.com/
deco software, 2 dives to 132 fsw, one diver on CC with a 1.2 setpoint, the
other on air Open circuit, the bottom time was 20 minutes, the air OC diver had
a total runtime including deco of 57 minutes and stops beginning at 70 feet,
showing more nitrogen loading than the CC
Lets do another thinking exercise. Lets say you are
diving your CC
depth 
OC PN2 air 
CC SP 1.2 
CC PN2 

33 
1.6 
1.2 
.8 

66 
2.4 
1.2 
1.8 

99 
3.2 
1.2 
2.8 

132 
3.95 
1.2 
3.8 

155 
4.7 
1.2 
4.8 

188 
5.5 
1.2 
5.8 

Ok lets
look at our nitrogen uptake, think about this.
Our air computer is thinking we are breathing 79% nitrogen on open
circuit. As long as we are not breathing
a higher concentration of nitrogen than that, we will fall below the model and
be diving more conservative than the computer thinks we are.
But where does this
model break down? Look at the table above.
AT 33 fsw the computer thinks we are breathing 1.6 partial pressure of
nitrogen, we are actually only breathing .8.
Terrific! How about at 132 feet, computer thinks we are sucking on 3.95
PN2 while we are at only 3.8, still pretty good. But what about if we drop down to 188 keeping
that 1.2 setpoint, whoops, we just blew the model and are actually taking on
more nitrogen than the model thinks we are, in fact we are only breathing the
equivalent of 17% oxygen whereas the model thinks we are breathing 21%. How to fix this? Glad you asked. Its quite simple really, we just increase the
Setpoint of our rebreather to 1.5 for the time we are at that depth. Do the math.
Thanks to
Problems for the
student:
Given:
An OC dive to 185
feet to a wreck with no penetration planned.
Max PPO2 to be 1.5 ATA at depth/deco stops. Max Narcotic depth to be
equal to 90 fsw. Gas changes at
70 fsw and 30 fsw.
Find:
Best Bottom Mix
Two deco gases
Closed circuit
rebreather dive to 183 feet, two sensors do not agree, your diluent is normoxic
trimix and you do a flush with that, what should your PPO2 read?
If your great
grandmother gets narced anytime she dives below 70 fsw, figure her out a batch
of trimix that will allow her to dive happily to 245 FSW, assuming you like
your great g’ma, so no hot mixes.
Open circuit dive to
165 feet, you are dropped off by a skiff on a lovely wreck, do your bottom time
and there is a swim in on a shelf for about 15 minutes at 65 feet before you
reach another wall. What mix would you
carry for your first deco mix to take advantage and off gas most efficiently
during that 15 minute swim?
OK, I guess I have
confused everyone enough for now. If
this helped you, please let me know, if it confused you irretrievably, let me
know that too. If I have missed anything, or you find errors in my math, call my math
teacher and bitch at him.
3 Dec 2004