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Will...I am no expert, but have been diving for a few quite a few years and due to where I have lived over the past 15 years I do a lot more reading about diving, that actually diving....I used to also be an elite cyclist in Europe, so I know the importance of oxygen & breathing!!
Firstly!!
Please do not do wet statics without an experienced buddy!!!
With that said....
The info you also gave is also a little cryptic as there are many factors that affect dive times...e.g. correct weighting.
When you say bottom time, do you mean the time you are under the surface or the actual time you are lying on the seabed? Sorry if this sounds like a daft question, but it is important...because...if you have bottom time of 45-60 sec at say 10-12 meters then that would be quite good since if you descend/ascend at 1m/sec this would give you a dive time of roughly 80 seconds. Which is not bad at all.
However, if you are in fact referring to your actual dive time, as being 45-60 sec i.e. from the time you start your dive to the bottom and then breach the surface this is a whole different matter. I am guessing, but I think this is what you meant by bottom time in your original post?
Dive times...
Breath Hold....3 min static VS 45-60 sec dive time
Seems pretty accurate to me.
Very, very briefly (so please do not take this as science lesson critics out there!)
When you are exercising, your muscles convert oxygen to energy...less movement, the longer your oxygen supply lasts.
So
When you are static, you muscles are not using oxygen at even remotely the same rate as they would when you dive...
Static...relaxed mental state, slower breathing, muscles not moving etc.
Diving...slightly more stressed mental state/focus brain highly active (processing data fish/dangers/etc), legs kicking, arms moving etc
See the difference? Your oxygen supply is going to be used quicker....
HOWEVER
You should be able to hold your breath longer with proper training. Do a free diving course...worth every penny.
Teaches you how to practice breath hold, safety and will so you in a safe environment how long you can in fact hold your breath for...when your body starts screaming for air and you feel the cramps (contractions) in your stomach/diaphragm, you have usually got a fair bit of O2 left...
The psychology of breath holding is by far the most important aspect in attaining longer breath holds. This has to be trained.
Met a guy once...great wet static 5min + ... could not dive more than 5 metres without turning back to the surface...dive time 20 sec...
Let's face it most of us do have a little/lot of fear (which is a good thing I believe) when diving down into the deep...Who knows? There could be a big arse spearo eating fish down there taking revenge...We cannot conclusively prove the non-existence of these critters either, since they usually eat the witnesses and are big due to never being caught....
This fear could be causing you to head up earlier....
In a nutshell, I reckon you are on track...just dive, dive, dive! You will get better.
When it comes to the snorkel/breathing issue...! It seems like you are breathing in too many breaths...relax...deeper breaths into your belly, focus...attach a small bottle of water to your buoy and have a sip every so often to remove all the salt from your throat...
It is not the bore which is the problem, rather the volume of air passing into your throat...bigger bore just allows for a quicker flow...
Hope this helps you my friend! Keep at it, do a freediving course, read this...
http://www.amazon.com/Manual-Freediving-Underwater-Single-Breath/dp/1928649270&tag=deeperbcom-20
Safe diving!