How to calculate total air consumption along ascent?

[magicfx]

Assume my RMV is 15L/min on the surface, 30L/min at 10m.
If I ascent from 10m depth to surface, ascend rate is steady 10m/min,
how much air will I consume??

If my SAC is not constant, and my ascent rate is not constant,
how could I calculate my air consumption.

Please help solve this problem in University Calculus/Physics way,
my calculus skills are rusted but if you give me a hint, I might recall the memory....
thank you.

 

[boulderjohn]

Assume my RMV is 15L/min on the surface, 30L/min at 10m.
If I ascent from 10m depth to surface, ascend rate is steady 10m/min,
how much air will I consume??

If my SAC is not constant, and my ascent rate is not constant,
how could I calculate my air consumption.

Please help solve this problem in University Calculus/Physics way,
my calculus skills are rusted but if you give me a hint, I might recall the memory....
thank you.

I don't understand the question, to be honest.

If your ascent rate is steady and your SAC is constant, then it is easy--use your SAC rate at 5m.

If one or both is not constant, I don't know how you can figure it without more information, and if you get some kind of rate on a curve, I will get off that train now. I have not taken calculus in 52 years.

 

[Wibble]

Two ways to answer this: academic or practical.

What's your ascent rate? You say 1 min from 10m to 0, so 10m/min in a linear way. Half way is 5m, which is 1.5 atm/bar. So take your SAC and multiply by 1.5. Sac=15 x 1.5 = 22.5 litres.

Now the real issue; that assumes you're a dive machine that actually does exactly that. It's much better to take the 1 minute value as the start pressure, 10m = 2ata/bar not 5m. Thus you'd use SAC=15 x 2 = 30 litres.

Extrapolating this for an ascent from 40m AND IGNORING deco stops (safety stops). At 10m / min ascent rate it would be:
1min at 40 (5bar x 15sac = 75), 1min at 30 (4bar), 1min at 20, 1min at 10 = 75 + 60 + 45 + 30 = 210 litres.

The reality is there'd also be deco stops. But lets simplify to a short NDL bounce dive to 40m for 3 mins. This would need a deco/safety stop of 5 mins at 5m. Add this to the previous ascent: 1.5bar x 15(sac) x 5m = 112.5 litres, so a total of 210 + 112.5 = 322.5 litres.

Issue is always round up and allow for safety; that's the practical aspect of dive planning. Few people actually hit 10m/min ascent, and in any case you need to accelerate and decelerate, hence erring on the side of caution.

(Have assumed a 5min safety stop).

It's all arithmetic - no integration/differentiation required.

 

[MaxTorque]

In terms of calculus, the onyl way to calculate your actual air consumption is to Integrate over time. The more samples you have, ie the shorter time peiod with which you update that information the more accurate the integration becomes. There is no theoretical answer because you have three varriables, time, depth and SAC, but of course you can form a "surface" that effectively contains each possible answer.

Why you would want to do that, i have no idea!

(as suggested, take your best estimate for SAC, take you deepest depth, and take a realistic longest ascent time and use that to calculate what should be a worst case consumption by far)

 

[Vicko]

Bum a transmitter off of someone and let a computer do the computing.

 

[broncobowsher]

Between 15 and 30 Litres. If your planning is that tight, you are pushing the limits way too much.
The general safe way to calculate it, just use 30 and what you don't use is a safety buffer. Makes the math real easy.

 

[loosenit2]

Dont overthink it. Break up your ascent into segments, like 10 ft or ATA segments and calculate consumption for that segment, then add up the segments. Using a calculus approach and trying to determine the area under a curve as the number of segments you break it up into as they approach infinity is unnecessarily complicated.

as an example, you start your ascent from 100 ft and are ascending at 30 ft a min with a 3 min safety stop at 15

segment 1 100 ft to 70 feet, avg 4 ata, should take 1 min, multiply your Sac (better to use RMV so you are measuring in volume rather than psi) times 4 and you have segment 1 consumption

segment 2 70 ft to 40 ft should take 1 min; average ata is 3; again sac x ata is segment air consumption

segment 3 40 ft to 10 ft, will take 4 min, 1 for 30 ft ascent + 3 min safety stop. Average ata is 2, so again sac x2 for 4 min

segment 4 10 ft to surface, average ata is 1, so sac for 20 seconds.

then add up gas consumption for segments and you have a planning factor.

you can break up any ascent into segments like this using any ascent profile or set of safety stops you want and calculate gas requirements for the ascent.

You would also use a very similar method for determining a gas reserve, although you have to account for 2 divers using gas well above normal sac or rmv.

 

[Wibble]

SAC (Surface Air Consumption) vs RMV (Respiratory Minute Volume) is the same thing: volume of gas consumed at 1bar/ata

Both are volumes of gas in litres/cubits?

 

[boulderjohn]

I think people are missing the point in this thread. Practical advice will not be helpful. He is trying to solve a story problem from a math class.

 

[hedonist222]

Assume my RMV is 15L/min on the surface, 30L/min at 10m.
If I ascent from 10m depth to surface, ascend rate is steady 10m/min,
how much air will I consume??

If my SAC is not constant, and my ascent rate is not constant,
how could I calculate my air consumption.

Please help solve this problem in University Calculus/Physics way,
my calculus skills are rusted but if you give me a hint, I might recall the memory....
thank you.

get an air integrated computer

set it to the most sampling rate (Shearwater is every two seconds for reference)

export the data into excel as a .csv (comma separated values)

delete the data thats irrelevant

enter a formula : divide consumption by time

plot this in a chart