Fundies Math

[WJL]

Dimensional analysis is just the fancy way of saying "when you cancel out units, you ought to have the right ones left over".

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Dimensional analysis can often provide some nice insights.

For example, it is easy to show that the real units of SAC aren't cfm or lpm, but instead are truly cu ft per minute per ata. It just happens that at 1ata the last part drops out. If you include the /ata at the end you can easily see for example that
1 cu ft/min/1ata = 2 cu ft/min/2ata.

Thanks, guys. Most of the time I feel guilty for wasting time on this board, but today I learned something interesting.

 

[Randy43068]

If I ever have time to go diving again, perhaps I'll put this to use. Brando would be so proud of me!

 

[shoredivr]

Charlie99, thanks for the clear information.

 

[TNdiver6387]

Totally agree with these formulas. However, your example ignores a basic math skill regarding "significant figures." 60 fsw (a measurement with 2 significant figures) is approximately 2.8 ATA (a measurement with 2 significant figures). 2.8 ATA for 50 minutes (a measurement with 2 significant figures) = 140 ata/minutes (a measurement with 2 significant figures). The gas consumed is determined by mutliplying 140 by .75 (a measurement with 2 significant figures) = 105 cf

Your example rounds up 2.8 ATA to 3.0, which replaces a measurement with 2 significant figures with a measurement that has 1 signficant figure and lowers the precision of the result. 112 is more than 6% greater than 105 and is based on an error in the measured depth of 10% (60 fsw instead of 66 fsw). What if our dive was to 3.1 ATAs or 70 fsw. Shall we round up to 4 ATAs and base our calcs on a dive to 100 fsw? The discrepancy here is too great to just ignore as imbedded conservatism. Gas planning should be more precise than that.

There's no need to invent some protocol like rounding up to the nearest 25 hundredths. If were focused on precision, mathematics already gives us one. Keep the number of significant figures the same. If you like .75 as your SAC then use ATAs to two significant figures.

For those who think computing ATAs is mentally challenging, try converting to meters first. (# fsw/10)*3. Then divide the result by 10 and add 1. Voila ... ATAs.

So 60 fsw = (60/10)*3 = 18 meters. 18 meters = (18/10) +1 = 2.8 ATAs.

I'd like to know by what logic 60 and 140 both have 2 significant figures

 

[SparticleBrane]

60 has 1sigfig, 140 has 2. Didn't catch that at first...

 

[JeffG]

blah blah blah Significant digits blah blah blah

Holy cyber diving...batman

 

[SparticleBrane]

Hey I was just responding to the question at hand. I wasn't the one who asked the question.

 

[MXGratefulDiver]

Holy cyber diving...batman

Play nice, Jeff ... we like having you here ...

... Bob (Grateful Diver)

 

[JeffG]

Play nice, Jeff ... we like having you here ...

... Bob (Grateful Diver)

Yea ok...but Significant digits?

LOL

 

[MonkSeal]

60 has 1sigfig, 140 has 2. Didn't catch that at first...

Convert this to metric and you'll have the same number of significant digits