Diving Equations
Highlights of important math for diving – primarily focused on deco diving.
Depth to Pressure
To convert feet to a unit of pressure (atmosphere or bar) we take the depth, divide by 33 (how many feet are in an atmosphere), and remember to add the surface atmosphere. This example uses 100ft.
100ft/33ft/atm =3atm+1atm = 4ata
Pressure to Depth
Going from atmosphere to feet is the opposite.
4 ata-1atm = 3atm*33ft/atm = 100ft
How Do I Calculate Minimum Ascent Pressure?
To calculate the pressure for ascent we take the bottom time, pressure, and SAC rate to manually calculate the cubic footage we will use assuming we stay at the bottom for the estimated time. We then convert the cubic footage to PSI using our cylinder baseline.
Variables:
- Depth: 100ft
- Surface Air Consumption Rate: 0.8cuft/min @ 1 ATA
- Time: 20min
- Cylinders: Aluminum 80s, 3000psi working pressure
First, convert depth to pressure:
100ft/33ft/atm =3atm+1atm = 4ata
Then determine the gas used per minute at 1 ATA:
0.8 cuft/min *20min = 16cuft
Then factor in the pressure to get the cubic footage used:
16cuft*4ata = 64cuft
Determine the cylinder baseline and multiple by 2 for doubles:
(80cuft/3000psi = 0.026cuft/psi)* 2=0.053cuft/psi
Convert cubic footage to psi
64cuft/0.053cuft/psi = 1207psi
How do I calculate Rock Bottom?
Our first step is to find the time. Find the distance from the maximum depth to the next gas – if we have no deco gas that’s the surface, if we have oxygen that’s 20ft. Planning on an ascent speed of 33ft/min calculate the time it will take. Next we need to figure out the pressure. There are two methods for this. Maximum or average. Maximum is easier but more conservative.
Variables:
- 100ft
- SAC 0.08cuft/min@1ata
- Oxygen deco gas
- 33ft/min ascent rate
- Double AL80s
First, determine the time it will take to ascend:
100ft-20ft=80ft
80ft/33ft/min = 2.4mins
Let’s add 2 minutes at depth to start the gas share and get organized – Call it 5 mins total
Next, convert depth to pressure:
100ft/33ft/atm =3atm+1atm = 4ata
Max Depth Method – Use the deepest pressure
5 mins at 4 data with a SAC rate of 0.8cuft/min@ 1 ata
We double the SAC rate. Your SAC+ your buddy’s.
0.8cuft/min*2 = 1.6cuft/min*5mins*4ata= 32cuft
32cuft/0.053cuft/psi=~600psi
Average Depth Method – Average the pressure of the ascent.
Our deepest ata is 4, the shallowest is 1.6 (20ft). Let’s call 2.5ata the average.
5 mins at 2.5 data with a SAC rate of 0.8cuft/min@ 1 ata
We double the SAC rate. Your SAC+ your buddy’s.
0.8cuft/min*2 = 1.6cuft/min*5mins*2.5ata= 20cuft
20cuft/0.053cuft/psi=~380psi
Cell Linearity
For CCR diving we can calculate the expected mV of a cell in oxygen using this formula. Expect some variance, but not much. Input the reading from the cell’s mV in air where “AIR mV” is to complete the formula.
(AIR mV/.21)*.98
Equivalent Narcotic Depth (END)
When using trimix we want to be able to baseline the mix we’re using with air. For example, we typically shoot to have an END of 100ft, so that we’re not at a higher PPN2 at depth than using air at 100ft.
END = (depth + 33) × (1 − fraction of helium) − 33
Cave Bailout
When planning CCR dives in the cave we will use one of two formulas to determine our bailout limits.
Gas needed for a certain distance. Used when we have a specific place in the cave we want to go to.
Gas= sac *ATA*(distance/speed)*SF
Maximum distance allowed. Used when we want to know the limits of our cylinders.
Distance= (vol/(SAC*ATA*SF))*speed
Dalton’s Triangle
If there is one equation to memorize in technical diving it’s dalton’s triangle. This quick math reference is super practical at the dive shop and when planning dives.
Dissimilar Cylinder Volume
Cave divers need to be able to compensate for dissimilar volumes by doing the math associated. Memorizing tank factors or carrying a reference card are more practical for daily use.