kkoski
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Recently, as an intro cave diver, I decided to practice calculating thirds with dissimilarly sized tanks. Confidently I made up a problem for myself:
Diver A is diving twin HP 100's filled to 3000 psi at the beginning of the dive. Diver B is diving twin HP 120's filled to 2800 psi at the beginning of the dive. What is the turn pressure of each diver?
Here's how I solved the problem:
First, I worked the problem for single tanks: the turn pressure for one single tank at 3000 psi will be the same as the turn pressure for two connected HP 100's at 3000 psi, which would be the same turn pressure for three connected HP 100's at 3000 psi, etc.
The dive should be turned when one diver has enough air in his tank to get both divers on the team out of the cave. The air Diver A requires to get out of the cave will be represented by A, likewise, the air Diver B requires to get out of the cave will be represented by B. We assume that Diver A requires the same air to get out of the cave as into the cave, so Diver A breathes A + A = 2A during the dive, likewise Diver B breathes 2B air during the dive. Each diver wants to reserve air for his buddy, presumably the amount the buddy breathed diving in, thus at the dive turn each diver should have A+B air in their tank, air for them (A or B) and air for their buddy (B or A). This quantity, which is in cubic feet, (A + B) tells the diver when to turn. The air in the divers tanks can be represented by:
Air in Diver A's tank= Diver A + ( Diver A + Diver B) = 2A + B (Equation 1)
Air in Diver B's tank = Diver B + (Diver A + Diver B) = 2B + A (Equation 2)
The quantity (A+B), in psi, is each divers turn pressure. This is what we want to find.
HP 100's have 35 psi/cf or 0.0286 cf/psi
HP 120's have 29 psi/cf or 0.0343 cf/psi
Diver A starts with 3000psi*0.0286cf/psi=(3000/0.0286)*(psi*cf/psi)=85.8cf
Diver B starts with 2800psi*0.0343cf/psi=(2800/0.0343)*(psi*cf/psi)=95.2cf
Plugging this in we get
85.8cf=2A+B (Equation 3)
95.2cf=2B+A (Equation 4)
From Equation 4:
A=95.2-2B (Equation 5)
Plugging Equation 5 into Equation 3:
85.8=2(95.2-2B)+B
85.8=190.4-4B+B
3B=190.4-85.8
B=34.8cf
From Equation 4:
A=95.2-2B
A=95.2-2(34.8)
A=25.4cf
The air remaining at thirds should be A+B or 25.4cf + 34.5cf = 59.9 cf
For Diver A this corresponds to 59.9cf*35psi/cf=2097psi
For Diver B this corresponds to 59.9cv*29psi/cf=1738psi
A quick check with the popular texts showed this was not the conventional way to calculate thirds. Thirds calculated conventionally would give Diver A's turn point as 2000 psi and Diver B's as 1921 psi.
Thirds calculated "my way" has Diver A turn the dive with a higher psi, while Diver B turns the dive with a lower psi. In real life, Diver A will be me, an air sipping lady, while Diver B is my beloved husband, an air gulping man's man. Since "my way" has the person with the higher SAC turn the dive at a lower psi this would work out nicely for us.
The question is (for those of you who were starting to wonder) do you think it is any less safe to dive thirds in the above manner, as compared to two divers starting with identical tanks filled to 3000 psi and each agreeing to turn the dive at 2000 psi?
-Katrina
katrina@koski.net
Diver A is diving twin HP 100's filled to 3000 psi at the beginning of the dive. Diver B is diving twin HP 120's filled to 2800 psi at the beginning of the dive. What is the turn pressure of each diver?
Here's how I solved the problem:
First, I worked the problem for single tanks: the turn pressure for one single tank at 3000 psi will be the same as the turn pressure for two connected HP 100's at 3000 psi, which would be the same turn pressure for three connected HP 100's at 3000 psi, etc.
The dive should be turned when one diver has enough air in his tank to get both divers on the team out of the cave. The air Diver A requires to get out of the cave will be represented by A, likewise, the air Diver B requires to get out of the cave will be represented by B. We assume that Diver A requires the same air to get out of the cave as into the cave, so Diver A breathes A + A = 2A during the dive, likewise Diver B breathes 2B air during the dive. Each diver wants to reserve air for his buddy, presumably the amount the buddy breathed diving in, thus at the dive turn each diver should have A+B air in their tank, air for them (A or B) and air for their buddy (B or A). This quantity, which is in cubic feet, (A + B) tells the diver when to turn. The air in the divers tanks can be represented by:
Air in Diver A's tank= Diver A + ( Diver A + Diver B) = 2A + B (Equation 1)
Air in Diver B's tank = Diver B + (Diver A + Diver B) = 2B + A (Equation 2)
The quantity (A+B), in psi, is each divers turn pressure. This is what we want to find.
HP 100's have 35 psi/cf or 0.0286 cf/psi
HP 120's have 29 psi/cf or 0.0343 cf/psi
Diver A starts with 3000psi*0.0286cf/psi=(3000/0.0286)*(psi*cf/psi)=85.8cf
Diver B starts with 2800psi*0.0343cf/psi=(2800/0.0343)*(psi*cf/psi)=95.2cf
Plugging this in we get
85.8cf=2A+B (Equation 3)
95.2cf=2B+A (Equation 4)
From Equation 4:
A=95.2-2B (Equation 5)
Plugging Equation 5 into Equation 3:
85.8=2(95.2-2B)+B
85.8=190.4-4B+B
3B=190.4-85.8
B=34.8cf
From Equation 4:
A=95.2-2B
A=95.2-2(34.8)
A=25.4cf
The air remaining at thirds should be A+B or 25.4cf + 34.5cf = 59.9 cf
For Diver A this corresponds to 59.9cf*35psi/cf=2097psi
For Diver B this corresponds to 59.9cv*29psi/cf=1738psi
A quick check with the popular texts showed this was not the conventional way to calculate thirds. Thirds calculated conventionally would give Diver A's turn point as 2000 psi and Diver B's as 1921 psi.
Thirds calculated "my way" has Diver A turn the dive with a higher psi, while Diver B turns the dive with a lower psi. In real life, Diver A will be me, an air sipping lady, while Diver B is my beloved husband, an air gulping man's man. Since "my way" has the person with the higher SAC turn the dive at a lower psi this would work out nicely for us.
The question is (for those of you who were starting to wonder) do you think it is any less safe to dive thirds in the above manner, as compared to two divers starting with identical tanks filled to 3000 psi and each agreeing to turn the dive at 2000 psi?
-Katrina
katrina@koski.net