Fundies Math

[Jasonmh]

I am not great at math, nor am I such a great note-taker at times
So I am finally getting around to going back over my notes from Fundies last year to REALLY try to understand all the equations.
There are a few things that I am just unsure of and wanted to see if someone can help.

- Time dependant equation for Gas Management:
I have in my notes: Time = volume available / SCR (in cubic feet) x ave. depth in ata
The example was:
How much time permitted with 50cf., ave depth 100ft., SCR = 1cf/min
Which I THINK should look like this:
50cf. / 1 x 4 = ?
The answer given was 12 min. Clearly I am forgetting some basic math here, so someone tell me, is the equation not calculated left -> right? If I do it left to right, as in: 50 / 1 = 50 and then 50 x 4 = 200 I get the wrong answer.
Now, here is what really screwed me up. Next I get to the "Converting psi to cubic feet" equation, which looks like this:
pressure consumed in psi / rated pressure in psi x rated capacity in cf.
The example given is:
500 psi consumed / 3000 psi rated pressure x 80cf.
The answer given is 13cf.
I get 13cf. as the answer if I do the equation left to right, but if I do it like the Time Dependant equation, with the muliplication first, then I clearly do not get the right answer.
So, in my mind (and please some one kick me if I am wrong) I see these 2 equations:
50cf. / 1 x 4 = 12
500 psi / 3000 psi x 80cf = 13
Very similar equations, but one is being calculated in a different order than the other.


- In my notes I have 2 different sets of equations for calculating SCR:
SCR = Volume in cf. consumed / average ata's / time in min.
and
SCR = Volume in PSI consumed / average ata's / time in min.

I was writing so fast and trying to keep up, that I was not sure if I made a typo on one or the other. I am assuming that both equations are correct, depending on if you are trying to calc SCR in PSI or in Cubic Feet. Is that correct?

I know it is not the most exciting topic, but any clarification would be most apprciated.
Thanks,
Jason

 

[radinator]

Hi Jason,

Kudos on trying to get a handle on this. With a little practice it becomes easier.

For your first equation, it should be 50 cf / (1 cf per min per ATA x 4 ATA) = 12.5 min.

The top part is the total gas available, while the bottom part (inside the "()") is the gas consumption per minute. The math is very different. "a/b * c" is different from "a/(b * c)".

You divide total gas available by consumption per minute, and you get the available time (minutes) of gas you have.

Now for the second one:

In this one, the equation should be
(pressure consumed in psi / rated pressure in psi) * rated capacity in cf

The first part of the equation is determining the fraction of the tank used. Notice that you have psi on the top and bottom of the fraction. These units cancel, and you end up with a dimensionless number. This is just a fraction. So 500 psi / 3000 psi = 1/6 = 0.167. You've used 16.7% of the gas in the tank.

Now you multiply this by the size of the tank. You've used 16.7% of the 80 cf tank, or 0.167 * 80 cf = 13.3 cf of gas.

As for your last point, you are correct. Both equations are correct, depending on whether you are working in psi or cf.

I hope that helps. Good luck in your studies.
Ray

 

[Jasonmh]

Thanks, that definitely does help. It makes much more sense with the () there
Not only was I missing those parens in my notes, it was also missing on the Gas Management pages in the workbook.
I guess I should review the rest of my notes to see if there are any others like that.
Thanks a ton for the help.
Jason

 

[amascuba]

I am not great at math, nor am I such a great note-taker at times
So I am finally getting around to going back over my notes from Fundies last year to REALLY try to understand all the equations.
There are a few things that I am just unsure of and wanted to see if someone can help.

- Time dependant equation for Gas Management:
I have in my notes: Time = volume available / SCR (in cubic feet) x ave. depth in ata
The example was:
How much time permitted with 50cf., ave depth 100ft., SCR = 1cf/min
Which I THINK should look like this:
50cf. / 1 x 4 = ?
The answer given was 12 min. Clearly I am forgetting some basic math here, so someone tell me, is the equation not calculated left -> right? If I do it left to right, as in: 50 / 1 = 50 and then 50 x 4 = 200 I get the wrong answer.

The way you have your equation wrote down is confusing. I think we ran across this in our presentation as well.

The equation should be:

ft3 available / (SCR x DepthinATA) = Time

Instead of doing 50 / 1 = 50 x 4 = 200; It should be 50/4 = 12.5minutes (round down to 12minutes.)

Or if your SRC = .75 and everything else the same it would be:

50 / (.75 x 4) = Time

.75 x 4 = 3

50 / 3 = 16.67minutes (round down to 16minutes)

Now, here is what really screwed me up. Next I get to the "Converting psi to cubic feet" equation, which looks like this:
pressure consumed in psi / rated pressure in psi x rated capacity in cf.
The example given is:
500 psi consumed / 3000 psi rated pressure x 80cf.
The answer given is 13cf.
I get 13cf. as the answer if I do the equation left to right, but if I do it like the Time Dependant equation, with the muliplication first, then I clearly do not get the right answer.
So, in my mind (and please some one kick me if I am wrong) I see these 2 equations:
50cf. / 1 x 4 = 12
500 psi / 3000 psi x 80cf = 13

For me it's easier to do get the GUE TF (Tank Factor) for your tank.

For example:

If you wanted to find out what the ft3 per psi (ft3/psi) was of a tank you would divide the tank rated ft3 by the tank rated pressure. So you would do:

80/3000 = .026ft3/psi

For battlefield calculations you would get the TF by taking the ft3/psi x 100psi. So:

.026 x 100 = 2.6ft3 per 100psi (2.6ft3/100psi)

To find out how much volume 500psi holds in an AL80 you would take your TF and multiply it by 5.

2.6 x 5 = 13ft3

Very similar equations, but one is being calculated in a different order than the other.


- In my notes I have 2 different sets of equations for calculating SCR:
SCR = Volume in cf. consumed / average ata's / time in min.
and
SCR = Volume in PSI consumed / average ata's / time in min.

I was writing so fast and trying to keep up, that I was not sure if I made a typo on one or the other. I am assuming that both equations are correct, depending on if you are trying to calc SCR in PSI or in Cubic Feet. Is that correct?

I know it is not the most exciting topic, but any clarification would be most apprciated.
Thanks,
Jason

Your last equations are correct, depending on if you want your SCR in psi or ft3 as radiator said.

I can make copies of my handouts from class if you want. I'll just give them to you the next time we meet up at the BH. On that note we should really start pre-planning our dives this way so that we are somewhat ahead of the game for when we take cave 1. It will get us into a good habit anyways.

 

[The Kraken]

OK, simple.

Take your cubic foot volume of your tank (100) divide it by your SAC rate (1.00) and then divide that by your average depth in ATA (5)
100cf/1.00/min = 100 min. . . . 100min./5 ATA = 20 min.

Don't confuse your RMV with SAC.

RMV is in a constant state of flux. It will vary with any addition or deletion of task loading. The PSI (RMV) is the amount of gas you are consuming RIGHT NOW, and this will vary throughout your dive.

A SAC rate is a HISTORICAL consumption of gas on a given dive with specific parameters.

A SAC rate is a tool better suited for planning than analyzing the current state of a dive.

the K-alculator

 

[Jasonmh]

The way you have your equation wrote down is confusing. I think we ran across this in our presentation as well.

Yeah it is. It would be interesting to compare what you have from you class to what I have. We were using the "beta" version of the workbook, and were told that it was not final.

I can make copies of my handouts from class if you want. I'll just give them to you the next time we meet up at the BH. On that note we should really start pre-planning our dives this way so that we are somewhat ahead of the game for when we take cave 1.

Sounds good, i'll bring my waterproof calculator. The nice thing for you is, according to my math my SCR is around a negative 2, so if anything goes wrong i'll have PLENTY of gas for both of us

 

[Charlie99]

Your specific questions have been answered, so I'll just throw out a general observation .......

Equations like this are much easier to remember and use if, instead of trying to memorize specific equations, that you look at the underlying reasoning for the equation, and if you understand how the equation is derived.

For example, your first problem was 50 cu feet will last how long with SAC of 1cfm and depth of 4ata. If you just think about it a bit you will see that you have to divide the 50 by both the 1cfm and by the 4ata. One way to look at is is that your actual consumption rate at depth will be 1cfm x 4ata = 4cfm. Then you know your time available is simply 50/4=12. Or you could figure out that, on the surface you would have 50/1= 50 minutes, but at depth of 4ata this time would be reduced by a factor of 4. Again leading you to 50/4=12.

The same sort of logic applied to the psi to cf equations would leave you with a much better understanding than just applying equations by rote.

 

[amascuba]

Sounds good, i'll bring my waterproof calculator. The nice thing for you is, according to my math my SCR is around a negative 2, so if anything goes wrong i'll have PLENTY of gas for both of us

You must have a good lung capacity if you can push air back into the tank. We're usually within 100psi of each other after a dive. I would say your sac rate is somewhere between .5 - .75ft3/min.

I like to break the SRC calculation down into five parts.

1. PSI Used / Elapsed Time = PSI/min.@Depth
2. DepthinFeet / 33 + 1 = DepthinATA
3. PSI/min.@Depth / DepthinATA = PSI/min.@Surface
4. TankVolume / TankRatedPressure = TF(ft3)
5. PSI/min@Surface x TF(ft3) = SRC(ft3/min.)

For Example:

A diver has an AL80 filled to 3000psi. He at dives to 100ft. for 8 minutes and consumed 700psi. What is his SRC?

1. 700 / 8 = 87.5psi/min@depth (round up to 88psi/min@depth)
2. 100 / 33 + 1 = 4.03ATA
3. 88 / 4.03 = 21.84psi/min.@surface (round up to 22psi/min@surface)
4. 80 / 3000 = .026ft3
5. 22 x .026 = .57ft3/min.

In this case the SRC = .57ft3/min.

If you want, the next time we're at the BH we can work on finding your SRC.

We'll hover at the platform for five minutes just resting and take note of the average depth, starting pressure, and ending pressure. Then we'll get the heart rate up some by swimming around for five minutes. Again we'll take note of the average depth, starting pressure, and ending pressure. From there we'll figure the SRC from both of those and come up with an average SCR, which you can build onto after that.

 

[do it easy]

That's too much math for me! How about (700/3000)*80 then divide that by (8*4)?

The first part is how much gas he used in cft, and the second part is how he used it. I like Charlie's method better- breaking it down to the pieces you actually use for the answer you are looking for.

 

[TSandM]

One tip, when doing these sorts of things -- Look at the units you want to express the answer in (eg. cuft/min, or psi, or whatever). Look at the calculations you are doing, and make sure you are ending up with the right units. If your math gives you min/cu ft, for example, instead of cu ft/min, you're doing something backwards.

Dimensional analysis . . . It's kind of cool. You can actually derive a bunch of equations in physics (except for the constants) by just considering the units and figuring out what the relationships have to be.