Air consumption calculation; SAC Rate and RMV

With some simple mathematical operations, you can know approximately how much air you will consume at a certain dive. Boyle's Law tells us that whenever we go deeper in a dive, the ambient pressure increases and the volume of the gas decreases, so to inhale the same volume of gas when we go deeper we need to inhale more amount of gas following Avogadro's Law. This is the reason why you consume your air faster in a deep dive than in a shallow one. In order to calculate how much air, you consume at a certain dive you need a reference value of your air consumption; that's when the SAC rate or/and the RMV comes in.

SAC Rate

The Surface Air Consumption Rate or SAC rate for short, is the equivalent amount of air pressure you consume at 1 atmosphere. After knowing this we can know how much air we consume at a given depth/pressure. In order to calculate the SAC rate, we use the next equation:

SAC = C/(t*Pa)

Where SAC is the surface air consumption, C is the air pressure consume from your tank, t is the time and Pa is the absolute pressure. The SAC rate is different for every tank size, and we will show you how to calculate the equivalent SAC rate for the different sizes in the section named "RMV and SAC Rates of Different Tank Sizes" of this same article.

Example 1.- Calculate the SAC rate

Imagine you are at sea level and you go diving for 30 minutes at a depth of 20 meters and you consume 1500 psi from a certain tank size. What's your SAC rate?

What we know:

t = 30 min

Depth = 20 meters

C = 1500

The first thing you must do is calculate the pressure of the depth you are in. Remember every 10 meters of depth is approximately 1 atmosphere of pressure (see Pressure and Depth). So, if you are at sea level and at a depth of 20 meters you will have and ambient pressure (Pa) of:

Sea level = 1 atm

20 meters depth = 2 atm

Pa = 1 atm + 2 atm = 3 atm

Then the only thing we must do to calculate the SAC rate is:

SAC = C/(t*Pa)

SAC = 1500 psi / (30 min * 3 atm) = 16.60 psi/min atm

So, your SAC rate for this tank is 16 psi/min atm.

Air Consumption Calculation with SAC Rate

When you have your SAC rate for a certain tank size you are ready to calculate your air consumption or time of a certain dive. To do this you just have to use the SAC equation we showed before and make some clearance like it's shown next:

SAC = C/(t*Pa)

C = SAC* (t*Pa)

t = C/(SAC * Pa)

Where C is the air consume, t is the time and Pa is the ambient pressure. Next we show an example of this calculation.

Example 2.- Calculate Your Air consumption with the SAC Rate

Imagine you have a SAC rate of 16.60 psi/ (min atm) for a certain tank and you want to know in how much time you will consume 2000 psi at a depth of 40 meters with the same tank.

What we know

SAC = 16.60 psi/ (min atm)

C = 2000 psi

Depth = 40 meter

The first thing you must do is to calculate the pressure of the depth you are in. Remember every 10 meters of depth is approximately 1 atmosphere of pressure (see Pressure and Depth). So, if you are at sea level and at a depth of 40 meters you will have and ambient pressure (Pa) of:

Sea level = 1 atm

40 meters depth = 4 atm

Pa = 1 atm + 4 atm = 5 atm

Next you use the SAC equation.

t = C/ (SAC * Pa)

t = 2000 psi / (16.60 psi/ (min atm) * 5 atm) =24 min

t = 24 min

So you will consume 2000 psi in 24 minutes.

RMV

Because the SAC rate is in pressure units, we can't use the same SAC rate for different tank sizes. For this we must use the tank volume. The Respiratory Minute Volume or RMV for short, determines how much air volume goes in and out your lungs in a certain time, so if you know your RMV and the tank gas volume you can calculate the amount of gas left in your tank. To calculate the RMV the only thing we must do is the next:

RMV = SAC (V/P)

Where V is the equivalent volume of the tank at 1 atmosphere and P is the working pressure.

Example 3.- RMV calculation

Imagine you use an 80 ft³ tank with a working pressure of 3000 psi and your SAC rate is 16.60 psi/(min*atm). What's your RMV?

What we know:

V = 80 ft³

P = 3000 psi

SAC = 16.60

RMV = SAC (V/P)

RMV = 16.60 psi/(min*atm) * (80 ft³/3000 psi) = 0.44 ft³ /(min*atm)

RMV = 0.44 ft³ /(min*atm)

RMV and SAC Rates of Different Tank Sizes

The SAC rate is different depending on the tank volume adn working pressure, but the RMV is the same every time. So, if you know your RMV you can calculate the equivalent SAC rate for any tank you use.

Example 4.- SAC Rate of Different Tanks Sizes

Imagine your SAC rate for an 80 ft³ tank with a working pressure of 3000 psi is 13 psi/(min*atm) and you want to know what's your SAC rate for a 105 ft³ tank with a working pressure of 2250 psi. First, we must calculate the RMV.

What we know:

Volume of tank 1 = V₁ = 80 ft³

Pressure of tank 1 = P₁ = 3000 psi

SAC for tank 1 = SAC₁ = 13 psi/(min*atm)

Volume of tank 2 = V₂ = 105 ft³

Pressure of tank 2 = P₂ = 2250 psi

SAC for tank 2 = SAC₂ = ?

RMV = SAC₁(V₁/P₁)

RMV = 13 psi/(min*atm) * (80 ft³/3000 psi) = 0.35 ft³ /(min*atm)

RMV = 0.35 ft³ /(min*atm)

Then to calculate the SAC rate of the second tank we do some clearance.

RMV = SAC₂ (V₂/P₂)

SAC₂ = RMV₂ (P₂/V₂)

SAC₂ = 0.35 ft³ /(min*atm) * (2250 psi / 105 ft³) = 7.5 psi/(min*atm)

April 10, 2020 Tags : All , Book , Physics Applied to Diving

Friday, April 10, 2020

Air consumption calculation; SAC Rate and RMV