/SSN 014/08/4. Journa/ o/Ihe Soriel)' /or Undemaler Techno/ag)'. Vo/. 23. No. 4. pp. /81-186, /999 Technology Nomograms for Improving Diver Safety ca -u T. G. ANTHONY* and B. J. HORNt oe'e u * DERA AlverslOke, Fort Road. Gosport. Hampshire POI22DU. UK. G) t Departmel1l of Mathematics and Statistics. University of Call1erbury. Christchurch, NZ. ••• Abstract Similarly, decompression schedules require a diver to breathe appropriate gas mixtures; an Divers are increasingly required to perform error in identifying the gas mixture used, and 'safety to life' calculations which, if incorrect, the associated decompression schedule, may may result in a serious incident. The application result in severe Decompression Illness (DCI). of an 'old fashioned' manual computational Traditional training presents the diver with technique, the Nomogram, is proposed as a equations for the required calculations and cheap and simple tool for performing safety to teaches mathematical tricks such as 'Magie life calculations. The Nomogram is friendly to triangle, Dalton's T and the Rotating rectangle' non-mathematicians, applicable to the marine to help simplify their use for the non- environment and may significantly reduce the mathematician [2]. Unfortunately, with serious risk of calculation error. Example Nomograms mistakes being made, these techniques do not are illustrated and the advantages for always result in a successful outcome. A improving diver safety presented. significant advance in training being encouraged by the recreational diver training agencies is to eliminate where possible the use of mathematical 1. Introduction formulae and equations and replace them by 'Look Up' tables. 'Look Up' tables are in the Observation of current commercial, military and main easy to use, suitable for use in the extremes recreational diver training procedures shows that of a marine environment and eliminate the risk of divers are increasingly required to undertake calculation errors. They have !imitations, 'safety to life' calculations on the physiological however, in that they can only present a aspects of their breathing gases and their dive limited 'calculation' range and require variables profiles [I, 2]. This is particularly apparent in to be at given values. A large number of tables the growing area of 'Nitrox' and other may need to be produced to cover all combina- 'Technical diving'. These calculations may easily tions of an equation's variables to the required be subject to error either by a simple mistake 01' accuracy. the inappropriate mathematical aptitude of the In our modern electronic and microcomputer diver. In addition, calculations often have to be world, an alternative approach to eliminating the performed in an extreme marine environment. problems of mathematical calculations is to · Typical 'safety to Iife' calculations currently embed them within user-friendly pre-pro- being undertaken by divers include the grammed calculators or computer software. This following: is in many ways an ideal solution giving correct • Conversion of gas percentage to partial pres- and accurate solutions to a given problem, pro- sures (and vice versa), including the determi- viding the computer adage 'GIGO' (Garbage In nation of maximum safe depth. Garbage Out) is avoided. However, this would require all trainees and divers to obtain these • Calculation of Equivalent Air Depth (EAD) devices or have them available for use. The cost far decompression procedures. of this option may be prohibitively expensive to • Determination of safe flow rates and gas some divers, schools and businesses. mixtures for semi-closed circuit re-breathing The principle presented in this paper is that in a diving apparatus. microcoinputer-based world, an 'old fashioned' A simple calculation error in respect of choosing manual computational technique (i.e., the an appropriate gas mixture, gas flow rate or safe Nomogram) may be app!ied successfully to maximum depth for a dive may easily result in a increasingly complex diving requirements and diver losing consciousness underwater from the application of this technique may significantly hypo- or hyperoxia with a fatal outcome. reduce the risk of diving incidents due to calcula- tion errors. The simplicity, cost and durability of © Crown Copyright 1998-DERA. Publishedwith the the system are appropriate to divers who are non- permission of the Controller of Her Britannic mathematicians and takes account of the Majesty's Stationery Office. extremes of their marine environment. 181 T. G. Anthony and B. J. Horn. Nomogramsfor fmproving Diver Safety Moreover, although the concept has been pro- of oxygen is injected into the breathing circuit at a posed here far diving applications, it is likely to be constant mass flow. The percentage of oxygen of use in any scenario where ca1culations have to inspired by a diver using the apparatus is depen- be undertaken by operators with limited math- dent upon the percentage of oxygen in the gas ematical skills andfor in extreme environments. mixture, the rate of gas flow and the diver's work rate (expressed as the volume of oxygen 2. The Nomogram consumed in one minute [\'02])' The relationship between the inspired percentage of oxygen and The Nomogram has been used for engineering the percentage of oxygen in the gas mixture, and other applications for many years and was rate of gas fIow and diver's work rate is repre- particularly applicable before the development sented by the 'counter-lung equation'. of computer technology [3]. A Nomogram is a two-dimensional diagram representing a math- 0/0 (%02 Mix x 0.01 x Flow) - Y02) /0 2 Ins = . ematical equation in which each variable is repre- (Flow - Y02) sented by one or more graduated lines. To perform the 'ca1culation' a furt her line (known x 100 (3) as the index line) is superimposed on the where Nomogram such that it intersects with each of the graduated lines at the required value of the %02 Ins percentage of oxygen in the breath- variable. (Examples of calculations using ing circuit inspired by the diver (%) Nomograms are given in Figures 1, 3 and 4 in %02 Mix percentage of oxygen in gas mixture the next section.) entering the breathing circuit (coun- The graduated lines which form the ter-Iung) (%) Nomogram can be straight or curved' depending Flow gas mixture flow rate (litres per min- I on the equation and the method of construction. ute [Imin- ] at Standard Nomograms may be classified by the number of Temperature and Pressure Dry variables involved: [STPD]) 1 Second class Nomogram represents two vari- Y02 divers oxygen consumption (1min- ables STPD) X = y2 (1) It can be seen from this that to a non-mathe- Third class Nomogram represents three variables matician the 'counter-Iung equation' may be quite daunting and that there is significant scope for X = y2 +2 (2) error in its use. As indicated earlier, a transposi- When constructing Nomograms, the simplest tion or calculation error using this equation may and first approach may result in scales that are lead to an inappropriate gas mixture being not practical in use. A range of Nomogram for- breathed with dire consequences. mats have been identified to overcome these prob- The 'counter-lung' equation has four variables lems [3]. One particular derivation of a third class and can be represented as a fourth Class Nomogram is the 'Circular Nomogram', which Nomogram as shown in Figure I. Note that the we have found particularly applicable to some percentage of oxygen in the gas mixture is given of the equations used in diving. Examples are pre- on a set of lines, each line representing a different sen ted in the next section. value of V02. An example use of the Nomogram is also included in Figure I. 3. Nomograms for Divi ng Appl ications 3.2 Equivalent Air Depth (EAD)for It is not the intention within this paper to show decompress ion the method of constructing a Nomogram but to When considering dive decompression require- illustrate the principles ofuse and application for ments using oxygen in nitrogen gas mixtures improving diver safety. Nomograms applicable to other than air a principle known as the several diving applications have been developed Equivalent Air Depth may be applied. This deter- to illustrate the use of the technique and are pre- mines the depth breathing air that would give an sented below. The examples also show how to use equivalent partial pressure of nitrogen to the different formats to ensure useable and practical maximum depth that the gas mixture is being scales. breathed. Decompression may then be conducted using the equivalent air depth as opposed to the 3.1 Gas control in semi-closed circuit re- actual depth. The calculation for this is repre- breathing diving apparatus sented by Equation 4. Although this may be Simple mechanical semi-closed circuit re- viewed as being simpler than the counter-lung breathing diving apparatus uses agas control equation, providing the user can successfully principle to maintain a safe level of inspired identify, remember or derive the equation, it still oxygen whcrc agas containing a fixeu percentage has the potential for miscalculation. 182 Underwater Technology, Vol. 23 No. 4, 1999 %OXYGEN IN MIXTURE %OXYGEN I I rM1XTUREI EXAMPLE 1 2 3 V0 lmin-1 (STPD) 1 2 3 ~tm-llSTPOJ 2 20 r i j:20 20 20 A 15.0 litres per minute flow rale 01 ! ! 40 % oxygen in nitrogen gas into the i~~~~ counterlung with a 2.0 Ittre V02 will '" f f ~ ':n~~ give a 31 % oxygen in nitrogen 1/ and mixture within the counter-Iung k'._ 2 'ttre per minute I'" V02 30 30 I 50 t i 50 50 I 40 40 r70 (!) I z ; ::> ...J 50 ci: 50 1: 15.0 Ittres per minute w f10w rate into I- counterlung Z DERA ::> ---45673 9 10 " 12 13 U 17 1! 19 ~ 21 ~ n ~ ~ o 'lOW RATE .lmin-1 (STPD) ü60 60 ~ Z W (!) >- 70 70 oX cf.