Help with Dive plan: Math Check

[g1138]

Haven't done an air plan in specific detail lately. I'll be doing a deep-boat dive with a class and just wanted to make sure I did my math right.
The purpose is to calculate how much air I need at a minimum to ascend and end my dive with 500psi in my tank.
I'm also trying to calculate my emergency air, should I be sharing air with another diver.

So here goes:
Tank Al 80 (32-36% EAN) => ~77.4cf to work with
Avg SAC: 0.8cf/min
M. Depth : 85'
Cylinder factor: 0.03 cf/psi

For my math calculations:
converting psi to cf = (psi/cylinder factor)
calculating cf needed at depth = (time*SAC)*[(depth/33')+1ata]

____Onto air plan___________
500psi reserve = 15cf
0:03 Safety Stop @ 20' = (3min*0.8cf/min)*[(20'/33')+1ata] => 3.85cf
0:01 Deep Stop @ 40' = (1min*0.8cf/min)*[(40'/33')+1ata] => 1.77cf
0:03 ascent from 85' = (3min*0.8cf/min)*[(85'/33')+1ata] => 8.58cf
3.85+1.77+8.58 = 14.2cf
Therefore I need 14.2cf minimum to ascend and perform my stops. For simplicity I'm just going to round up to 15cf which means I need to begin my ascend no latter than 1000psi to reach the surface with 500psi still in my tank.

Am I good so far?
Now lets assume I'm sharing air. The SAC rate on the tank will supposedly be 2.0cf/min. I won't be performing any stops on the way up.
0:03 ascent from 85' = (3min*2.0cf/min)*[(85'/33')+1ata] => 21cf
0:01 to sort out problems @ 85' = (1min*2.0cf/min)*[(85'/33')+1ata] => 7.15cf
21+7.15 = 28.15cf
Therefore I need 28.15cf or 938.33psi to reach the surface safely with a OOA diver.

So rounding up, I need a minimum of 1000psi to ascend on my own with 500psi reserve left in my tank on the surface.
With an OOA diver I need roughly 1000psi to ascend, but I'll end the dive with an empty tank.

Overall feelings:
I think I should plan my dive so I'm back on the anchor line with 1200psi.
This gives me 1800psi or 54cf to work with for my bottom time.
With a SAC rate of 0.8cf/min @ 85' I'll have an equivalent consumption rate of:
0.8(cf/min)*[(85/33')+1](ata) = 2.86cf/min @ 85'

54((cf)/2.86(cf/min @85') = 17.48 mins of bottom time; round down to 16mins of bottom time.........meh

How 'd I do? Any corrections or insight?

 

[PfcAJ]

I would reserve enough to complete my stops (safety stop, minimum deco, whatever) while sharing gas.

 

[DiveNav]

Will this be a square profile? Or a real multilevel dive profile?

Alberto (aka eDiver)

 

[Blackwood]

You're heavy on reserve, but that's not a bad thing.

For your 3 minute ascent from 85 you've computed 3 minutes AT 85 (should be at 43 for a constant ascent rate, i.e. halve that segment's requirement).

 

[g1138]

Alberto, this will be a square profile. The site will be a flat sandy bottom with a few rocky outcroppings (if even).

Blackwood: What's the reason for computing at 43' for my ascent? I don't really understand the math behind halfing the depth in the ascent calculation.

Edit:
So I just noticed that using 0.03 cf/psi for an Al 80 doesn't allow for my math to add up when converting 1200psi and 1800psi.
ie. I don't end up with 77.4 cf of air in total

When using the cylinder factor for an Al 80, would it be correct (I guess is the word) to use
80cf/3000psi = 0.026666
OR
77.4cf/3000psi = 0.0258

 

[Blackwood]

You aren't consuming gas at 1+85/33 ATM throughout the entire ascent.

At the inception you're at 85. A minute later you're at 57. A minute after that you're at 28, and a minute after that 0.

*If you truly hold a constant ascent rate* the average pressure at which your regulator will deliver air is halfway between the deepest and shallowest points. In this case it's 85-0/2. If instead you went up for a safety stop at 15, it would be 85-15/2, followed by 15-0/2.

 

[g1138]

Ahh, that makes sense now. Thanks

 

[Pullmyfinger]

In regards to halving the max depth.

Your gas consumption is variable as you ascend.

At an ascent rate of 30 ft. per min. ascending from 90 ft. to 60 ft. will require approx. 110 psi from an 80 cu. ft. tank
From 60 ft. to 30 ft. will require approx. 85 psi, and from 30 ft. to the surface will consume a little less than 60 psi.

A 3 minute safety stop at 20 ft. will take 45-50 psi per minute, so figure 145 psi for your 3 minute stop.

110 psi
85 psi
60 psi
145 psi

So that's 400 psi for you to ascend from 90 ft. (I rounded up from your stated 85 ft. depth) and make a 3 minute safety stop.
As PfcAJ mentioned, you'll need to account for your buddy...you already know this though.

Using the breakdown above equals 400 psi for a 6 minute ascent and safety stop.

Using half of your max depth consumes approx. 70 psi per minute for the same 6 minute ascent and safety stop...which equals 420 psi.

Close enough to the taking the depth segments and figuring the gas consumption for each segment.

As Blackwood mentioned....just take half the depth and look at the gas consumption that way.
Easier, and close enough.

-Mitch

 

[TSandM]

You've already been corrected on the depth, but I don't think anyone has mentioned that you have rounded UP on the tank factor for the Al80, whereas we usually round down to 2.5 cf/100 psi.

What you have learned is that, if you are going to be mindful of reserves, an Al80 is not much gas for deeper dives.

 

[DiveNav]

Alberto, this will be a square profile. The site will be a flat sandy bottom with a few rocky outcroppings (if even).....

Here you go
Max depth: 85ft (with few outcroppings)
Tank: AL80 with EAN32
Descent Rate: ~60ft/min
Ascent Rate: ~30ft/min
Safety stop @ 15ft
End Pressure: ~560PSI
End Nitrogen Loading: 58% (Moderate Conservatism)
Total dive time (including descent, bottom time, ascent and safety stop): ~26min
1 minute to create the plan .... 5 minutes to write the post

​

Alberto (aka eDiver)