Equations Used In Dive Planning
Here are the most common equations I use when planning a dive. I broke them out into 4 categories: General Diving, Nitrox, Cave, and Trimix. Each category builds upon the previous one. So there are no repeats. Each formula has an abbreviated name. So further down the list, you may encounter an abbreviation inside a formula. Look back up the page to see what this abbreviation means and how it is calculated (assuming multiple formulas are used to derive one answer). This article does not cover every aspect (i.e. decompression software running, contingency tables, pressure group determination, CNS, OTU's, residual CNS, residual nitrogen, etc because they require more than just a formula to determine) of dive planning, but gives you a good head start.
GENERAL DIVING
Tank Baseline (TB) = (Tank volume / Rated pressure) x 100
Example: (80 cf / 3000 psi) x 100 = 2.67 cf/100 psi. Be sure to include 10% overfill of the working pressure in the rated pressure if you are dealing with LP steel tanks.
Also, if you are using doubles, then multiply the TB answer you get by 2. For example, 2.67 cf/100psi x 2 = 5.33 cf/100 psi.
Depth in Atmospheres Absolute (DATA) = (Depth / 33) + 1
Example: (130 ft / 33) + 1 = 4.94 ATA
Converting DATA to depth (ATAD) = (DATA - 1) x 33
Example: (4.94 ATA - 1) x 33 = 130 ft
Converting tank pressure to volume (PSICF) = (Pressure / 100) x TB
Example: (3100 psi / 100) x 2.67 cf/100 psi = 82.7 cf
Converting volume to tank pressure (CFPSI) = (Volume / TB) x 100
Example: (82.7 cf / 2.67 cf/100psi) x 100 = 3097.4 psi
Beginning Volume (BV) = PSICF if your starting pressure for the dive is used in the above formula.
Example: (3100 psi / 100) x 2.67 cf/100 psi = 82.7 cf
Ending Volume (EV) = PSICF if your ending pressure for the dive is used in the above formula.
Example: (500 psi / 100) x 2.67 cf/100 psi = 13.3 cf
Volume Used (VU) = BV - EV
Example: 82.7 cf - 13.3 cf = 69.4 cf
Surface Air Consumption Rate (SAC) = (VU / Time) / DATA
Example: (69.4 cf / 20 min) / 4.94 ATA = .70 cf/min at surface
Average Depth Surface Air Consumption Rate (ASAC) = (VU / Time) / DATA. You will calculate DATA by using the average depth of your dive if your dive computer gives it to you.
Example: (69.4 cf / 20 min) / 3.12 ATA = 1.11 cf/min at surface. This example assumes the dive computer gave you an average depth of 70 ft for this hypothetical dive. Using the ASAC formula for a dive when you have required decompression is useless because the shallow stops skew the average depth the computer calculates.
Turn PSI (TPSI) = Starting pressure x .66
Example: 3100 psi x .66 = 2046 psi
Contingency PSI (CPSI) = Starting pressure x .33
Example: 3100 psi x .33 = 1023 psi
Turn Time (TT) = Planned dive time / 2
Example: 20 min / 2 = 10 min
Turn Volume (TV) = PSICF if your TPSI for the dive is used in the above formula.
Example: (2046 psi / 100) x 2.67 cf/100 psi = 54.6 cf
Contingency Volume (CV) = PSICF if your CPSI for the dive is used in the above formula.
Example: (1023 psi / 100) x 2.67 cf/100 psi = 27.3 cf
Gas requirement for dive (GR) = Time x DATA x SAC
Example: 20 min x 4.94 ATA x .7 sac = 69.2 cf
Gas requirement for dive with thirds reserve (GR3) = (Time x DATA x SAC) x 1.5
Example: (20 min x 4.94 ATA x .7 sac) x 1.5 = 103.8 cf
CAVE
Penetration Speed (PS) = Penetration distance / Penetration time
Example: 1500 ft / 30 min = 50 ft/min
Exit Speed (PS) = Exit distance / Exit time
Example: 1500 ft / 25 min = 60 ft/min. This assumes an exiting current is present.
Stage Bottle Drop Pressure (SB) = ((Tank's beginning pressure - 200 psi) / 2) + 200 psi
Example: ((3000 psi - 200) / 2) + 200 psi = 1600 psi
Deco Gas Requirement (DGR) = Stop time x DATA at stop depth x SAC
Example: 10 min x 1.6 ATA x .7 sac = 11.2 cf
Deco Gas Requirements with Reserve (DGR3) = (Stop time x DATA at stop depth x SAC) x 1.5
Example: (10 min x 1.6 ATA x .7 sac) x 1.5 = 16.8 cf
Dissimilar Tank Turn Pressure (DTTP): This requires several steps. Let's say I'm diving double 130's rated to 3460 psi with a starting pressure of 3800 psi. My buddy is diving double LP steel 95's rated to 2640 psi with 10% overfill with a starting pressure of 3500 psi.
NITROX
Best Mix (BM) = 1.4 ATA / DATA
Example: 1.4 ATA / 4.94 ATA = 28% O2 in nitrox mix for a dive to 130 ft.
Maximum Operating Depth (MOD) = 1.4 ATA / O2%
Example: 1.4 ATA / .28 = 5 ATA. Then use the ATAD formula above to convert 5 ATA to 132 ft.
Contingency Operating Depth (COD) = 1.6 ATA / O2%
Example: 1.6 ATA / .28 = 5.7 ATA. Then use the ATAD formula above to convert 5.7 ATA to 155.5 ft.
Partial Pressure Of O2 (PPO2) = O2% x DATA
Example: .28 x 5 ATA = 1.4 ATA
Equivalent Air Depth (EAD) = ((1 - O2%) / .79) x (D + 33) - 33.
Example: ((1 - .28) / .79) x (130 ft + 33) - 33 = 115.3 ft
TRIMIX
Equivalent Narcotic Depth (END) = ((1 - O2% - He%) / .79) x (D + 33) - 33.
Example: ((1 - 21% - 35%) / .79) x (190 ft + 33) - 33 = 91.8 ft
Best Mix for nitrogen in trimix (BMN) = 105.07 / (Depth + 33)
Example: 105.07 / (190 ft + 33) = 47% N2 in the trimix. 100% - 21% O2 - 47% N2 = 32% He needed in mix.
Shallowest Breathable Depth (SBD) = .16 ATA / O2%
Example: .16 ATA / 10% O2 = 1.6 ATA. Use the ATAD formula above to convert 1.6 ATA to a depth equivalent of 19.8 ft. Any mix containing 16% or more O2 can be breathed at the surface.
Adjusted Penetration (or Bottom) Turn Time (APT) = (((Planned bottom time + Ascent time) - Descent time to first deco stop) / 2) + Descent time to first deco stop
Example: (((20 min + 4 min)- 4 min) / 2) + 4 = 14 min. At 14 minutes bottom time, you must turn the dive and begin your exit (or return to anchor line) to ensure you reach your first deco stop at the time you cut your tables for.
Deco/BT Ratio (D/BT) = Required Decompression / Bottom Time
Example: 77 min / 25 min = 3.08 min. In other words, for every minute bottom time, it will require 3.08 minutes deco. The ratio of 3.08:1 means that if you spent an hour on the bottom for this dive, then you'd have 3 hours 5 minutes of deco. Deco is not linear, but it gives you an idea.