It is very quick and easy to work out a MOD from first principles. This is one of the reasons why a Nitrox course is so recommended: because you learn the theory behind it.
You basically want to work out the depth at which your mix has the maximum partial pressure of oxygen (ppO2) you are willing to tolerate. This is almost universally 1.4 atm for non-resting portions of the dive. You can do this in 2 distinct steps.
1. First you work out the required ambient pressure to get 1.4 atm by diving (Edit: meant to be dividing. What a Freudian slip!) your mix O2 % into 1.4.
Assuming you are using 28% the calc is 1.4/0.28 = 5.
2.Then you work out what depth gives you that ambient pressure.
In metric you subtract 1 (to account for sea lvl pressure) and multiply by 10 (assuming you are in sea water, not fresh*).
(5-1)*10 = 40metres.
Imperial is just as easy except instead of multiplying by 10 you multiply by 33.
You can combine the two steps and you get the formula which PADI and other agencies make their students learn by rote/off by heart.
Depth = [(1.4/mix%)-1] * 10
Depth = 14/mix% - 10
I find that using first principles is much easier to remember and you know for certain that you understand exactly what it is you are working out.
Edit: that little example also shows why EAN28 is considered generally safe for all recreational depths. Because if you go deep enough to violate the MOD you are violating the 40m/130ft recreational limit.
*Remember: 10 metres of seawater ~ 1 atm/bar of pressure. So 30 metres of seawater exerts ~ 3 atm/bar. That is why you multiply by 10.
Similarly 33 feet of seawater exert ~ 1 atm/14.7 psi which is why you multiply by 33 when using the imperial system.
You basically want to work out the depth at which your mix has the maximum partial pressure of oxygen (ppO2) you are willing to tolerate. This is almost universally 1.4 atm for non-resting portions of the dive. You can do this in 2 distinct steps.
1. First you work out the required ambient pressure to get 1.4 atm by diving (Edit: meant to be dividing. What a Freudian slip!) your mix O2 % into 1.4.
Assuming you are using 28% the calc is 1.4/0.28 = 5.
2.Then you work out what depth gives you that ambient pressure.
In metric you subtract 1 (to account for sea lvl pressure) and multiply by 10 (assuming you are in sea water, not fresh*).
(5-1)*10 = 40metres.
Imperial is just as easy except instead of multiplying by 10 you multiply by 33.
You can combine the two steps and you get the formula which PADI and other agencies make their students learn by rote/off by heart.
Depth = [(1.4/mix%)-1] * 10
Depth = 14/mix% - 10
I find that using first principles is much easier to remember and you know for certain that you understand exactly what it is you are working out.
Edit: that little example also shows why EAN28 is considered generally safe for all recreational depths. Because if you go deep enough to violate the MOD you are violating the 40m/130ft recreational limit.
*Remember: 10 metres of seawater ~ 1 atm/bar of pressure. So 30 metres of seawater exerts ~ 3 atm/bar. That is why you multiply by 10.
Similarly 33 feet of seawater exert ~ 1 atm/14.7 psi which is why you multiply by 33 when using the imperial system.
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