Doing the "Math" in Scuba

[susan6868]

Hello Dr. Deco-
My son, age 14, has been diving with me for two years now. Recently, he was given an assignment in his advanced math course to write a paper on a topic and it's relationship to math. Although the teacher provided a pre-set list of topics, my son decided to be original and submitted the subject "Scuba and Math". He explained that there is so much math involeved in diving, there would be ample topics of interest of material to dicuss in his paper. I encouraged him, knowing his love for the sport would make otherwise mundane research not only fun but useful. The topics we thought might be pertinent to the topic were buoency, decompression, management of residual nitrogen, and the calculations used for safe diving. However, he's been having an awful time finding research information on these topics that he is able to comprehend. In addition, most articles use the table which provides demonstration of it's use but no mention of the mathmatical calculations used to derive the information contained therein.
In closing, could you suggest any websited, books, or even topics to "google" that might provide results concerned with the "mathmatics" used behind diving practices in a manner that would be comprehensable by the laymen, or at least an interested high school student? What we've been able to find it either too vague or so technical we are unable to decipher it.
Thank you for any suggestions you might offer. I thought it was a great idea at the time for him to not only be able to apply these theories but to understand them as it would benefit him in his diving adventures throughout his life, but didn't realize how difficult it would be to research the matter.
Again many thanks!

 

[knotical]

I applaud your son’s enthusiasm and originality to lobby for an unlisted topic.

Some of the sub-topics he’s chosen are not trivial.
Decompression theory and management of residual nitrogen can quickly become quite complex. They are lightly covered in PADI’s Divemaster manual, but it barely scratches the surface.

Buoyancy seems a better choice. PADI’s chapter on physics in either the Diving Knowledge Workbook or the more expensive Encyclopedia of Recreational Diving are reasonable candidates, and might suggest other topics to him.

I think other agencies have similar books.
Googling on “scuba physics” provides several interesting possibilities and is probably where I’d start.

best wishes,

 

[TSandM]

I would think that gas management -- calculation of SAC, RMV, gas consumption at depth, rock bottom, rules of halves and thirds, would be enough algebra to satisfy a high school paper requirement.

Add the calculations for doing nitrox mixing and figuring MODs, EADs etc. and you've got a lot of math, all of which is pretty accessible.

Getting into deco algorithms gets a little hairy for high school, I would think.

 

[MSilvia]

Wow, he really picked a difficult one with the decompression calculations. I use math a lot for my diving, but when I need to do decompression planning, I turn to my home PC to do the calculations for me. I've seen the math involved, and as knotical said, it's specialized and complex.

What I'd recommend is examining some of the other ways math is used in diving, which are both interesting and digestable. My #1 pick would be calculations related to mixed gasses like nitrox and trimix. Finding the equivalent air depth, the ideal mix for a given depth, and the maximum safe operating depth of a mix are all very useful and (I think) interesting topics. Also, if he were to combine that with surface air consumption (SAC), Respiratory Minute Volume (RMV), and rock bottom calculations to see how much gas would be required for a dive to a given depth, he'd be using no less than six complex (but managable) mathematical processes that could be presented in the context of planning a nitrox or trimix dive.

Just a thought. Wish him luck!

 

[cmalinowski]

It's funny as this morning I was thinking that we should start a thread on various calculations used in diving. I will probably start something soon, but I have to find some of my various calculations and put them all together (the reason that it came to me).

Good luck on the paper.

 

[StSomewhere]

Recreational Nitrox Diving by Robert N. Rossier.

It'll have all the Nitrox background he'd need to support the context of a paper, and all the entry-level algebra he'd want in terms of applying formulas to a real-world context.

Highly recommended!

John

 

[scubamickey]

I second the Rossier book. It assumes a basic understanding of diving and then explains Nitrox diving in pretty simple terms.
If your son understands basic math and Algebra I as well as high school physics, he should have no trouble writing a paper on the basic concepts of dive physics and the related math.
Try also doing research on Archimide's principle, Dalton's Law, Boyle...you know, all the physics laws that we refer to. It might be easier to find info that way and then relate it back to diving.

Good luck to him. Hope he earns an A+

 

[Dr Deco]

Hello readers:

Dr D. was away from the office for a while on NASA business. We were discussing decompression on the Moon. Cool!

“Easy “Stuff

That does indeed sound like a nice conjunction of math and diving. Many of the responds gave some good ideas. Gas mixtures, Dalton’s law of Partial Pressures, Density, and Buoyancy are all wonderful topics.

Decompression and Halftimes :06:

This might be described as “not easy” in comparison. In truth, there is not any way to calculate a decompression table without prior information of experience or experiments regarding what are acceptable gas loads.

That said, it is relatively easy to discuss the uptake and elimination of gas from a tissue. This is the equation that is used to calculate halftimes for radioactivity and the decay of isotopes.

Dr Deco :doctor:

 

[pickens_46929]

PADI's Encyclopedia of Recreational Diving is a good start for the gas laws and other mathematics involved in scuba. Required book for Dive Master.

 

[makomike]

wow what a great suject. I think the tables may be a little complex since they deal with complex algorithms. I enjoy math and would also recommend PADI encyclopedia of diving. They have a new color version out, but i have heard the new cd rom version is quite amazing with clips of various scientist doing experiments related to the math of diving. Boyles law is a good beginning. It does go into deco theory and explains haldane theory. good luck