doi:10.3723/ut.28.051 International Journal of the Society for Underwater Technology, Vol 28, No 2, pp 51–55, 2009

The effects of high altitude on relative performance of dive computers

PL Buzzacott Technical Paper School of Population Health, University of Western Australia, Perth, Western Australia A Ruehle Department of Chemistry and Biochemistry, University of Denver, Colorado, USA

Abstract computer considered more conservative than other In this paper, -generated no decom- available models. pression limits (NDLs) in at high altitude Recreational dives are commonly made at were compared with low-altitude single, repetitive and altitude. For example, in Johannesburg, South multilevel dives. All computer-generated high-altitude Africa, where the altitude exceeds 1500m, there NDLs exceeded those published for the altitude dived. were 30 recreational dive businesses listed in Computer rankings by conservatism for single dives at business telephone directories published in 2008. low altitude had negative correlation with rankings at Likewise, there were 53 recreational dive businesses high altitude (r = −0.81). Correlation between high- above 1500m altitude listed in 2008 Colorado busi- altitude square-profile dives and low-altitude repetitive, ness directories in the United States. When diving multilevel NDLs was significantly higher (r = 0.91, at altitude, where ambient at the surface p < 0.01). We conclude sea-level single-dive NDLs, is less than at sea-level, NDLs are reduced (Bell such as those published in instruction manuals, are and Borgwardt, 1976; Wienke, 1993). Different not reliable when gauging the conservatism of dive decompression models use different methods to computers for use at high altitude. It is recommended adjust their NDLs for altitude (Hennessy, 1977; that divers using dive computers for planning high- Wienke, 1993; Egi and Brubakk, 1995). This study altitude dives to consider computer-generated real- hypothesised that relative conservativeness of pop- time NDLs as experimental. ular dive computers, ranked by single-dive NDLs at , would not be a reliable measure of relative Keywords: hypobaric, no decompression limit (NDL), conservativeness at high altitude. algorithms, altitude correction, dive computers 2. Methods 1. Introduction Recreational divers have increasingly used dive 2.1. Dive computers computers to plan no decompression limits (NDLs) Eleven popular recreational dive computers were during the past two decades (Lippmann, 1989; attached to an array and taken on 8 freshwater Sheffield, 1990; Wilks, 1990; Acott, 1994). A dives – 6 at low altitude (40m above sea level) variety of dive computers are available, using and 2 at an altitude of 3000m above sea level. different decompression models to estimate these Following arrival at high altitude, time was allowed limits (Davies, 1994; Egstrom, 2004; Doolette, for each dive computer to account for clearance 2005). When attempting to gauge the relative of residual nitrogen before the first dive. Four conservatism of dive computers, NDLs for single of the dive computers failed at high altitude and square-profile dives are often compared between are hereafter disregarded. The remaining dive dive computers over recreational depths, which computers were: two UWATEC Aladin Sport, which are less than 40m (Lippmann, 1989; Sheffield, use the Buhlmann ZH-L8 ADT model and are rated 1990; Davis, 1995; Lippmann and Wellard, 2004). to 4000m (Uwatec, 1995); two Dive Rite NiTek, These single-dive limits are often published in the using the Buhlmann ZH-L16 model and rated to dive computer instruction manuals, or displayed 6000m (Dive Rite, 1997); two Vyper, using by dive computers at point-of-sale by accessing the Reduced Gradient Bubble Model (RGBM) and the planning function (Uwatec, 1995; Dive Rite, rated to 3000m (Suunto, 2003); and a Delta P 1997; Apollo, 2001; Suunto, 2003). By comparing Technology VR3, using the Variable Permeability these limits, a recreational diver might select a dive Model (VPM) and rated to 3500m (Gurr, 1999).

51 Buzzacott and Ruehle. The effects of high altitude on relative performance of dive decompression computers

2.2. Dives On each dive, the array of computers was lowered at a mean rate of 29.1m/min (SD 0.8). Dive computers, in general, display an estimate of depth calculated as a function of . Typically, they are calibrated for dives in salt water at sea level. In this study, computer estimated depths were displayed in feet, recorded in feet, and then converted to metres using a conversion factor of 1ft = 0.305m. Depths displayed by dive computers were compared to measured depths using a fibre- glass surveyor’s tape measure (Hangzhou Yangyang Machinery-Equipment Tools and Hardware Co, Zhejiang Province, China). As soon as the array reached maximum depth on each dive, elapsed time and remaining NDLs displayed by each computer were then added together to calculate each computer’s total NDL for that depth and descent rate. These NDLs were recorded on a slate, and during four dives only, the array was then ascended to a shallower depth before any dive computer displayed a decompression obligation (see Fig 1). At this ‘multilevel’ depth, the adjusted NDLs displayed by each computer were added to the elapsed times displayed to give a predicted total Fig 1: The array of dive computers was ascended permissible dive time for that profile, and these to a shallower depth and multilevel NDLs recorded. NDLs were also recorded on a slate. Accordingly, 12 readings of predicted permissible NDLs dive Section 2.2. Spearman rank correlation coefficients time were recorded from each dive computer (84 were calculated between mean rankings for each data in total). Correlation between same-model dive of the four types of low-altitude NDL and the computers provided a measure of their intra-model mean rank at high altitude. Improvement in reliability. (dependant) correlation was tested for using the A repetitive dive was defined as any dive made method developed by Hotelling (1940), which within six hours of surfacing from a previous dive follows the t distribution with n − 3 degrees of (Diving Science Technology [DSAT], 1985). Five freedom. Significance was accepted at p < 0.05. types of NDLs were recorded: The formula that was used is given as follows: • Three non-repetitive (first dive of the day) s (n − 3)(1 + ryz ) square-profile (single depth) dives at low altitude t = (r − r ) (1) xy xz − 2 − 2 − 2 + • Two non-repetitive (first dive of the day) 2(1 rxy rxz ryz 2rxy rxz ryz ) multilevel-profile (two depths) dives at low where n is the sample size; rxy is the correlation altitude between square, non-repetitive rankings at low • Three repetitive (second dive of the day) square- altitude and rankings at high altitude; r is the profile (single depth) dives at low altitude xz correlation between multilevel, repetitive rankings • Two repetitive (second dive of the day) multilevel- at low altitude and rankings at high altitude; and profile (two depths) dives at low altitude r is the correlation between square, non-repetitive • Two non-repetitive (first dive of the day) square- yz rankings at low altitude and multilevel, repetitive profile (single depth) dives at high altitude. rankings at low altitude. 2.3. Statistics Data were managed using Excel and analysed 3. Results using SAS, version 9.1 (SAS Inc, North Carolina). Means are presented with standard deviations. 3.1. Reliability Pearson (r ) correlation coefficients were calculated Displayed depths differed to depths physically between NDLs from same-model dive computers. measured with a fibreglass tape by a mean vertical Dive computers were ranked for each dive by distance of −0.2m at 27.4m depth at low altitude, NDL, and mean rankings were calculated for which was less than expected for freshwater each of the five types of NDL described in dives with computers calibrated for sea water

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Table 1: Mean depths and NDLs displayed at each reading Reading Mean depth Depth range Mean NDL in NDL range in in m (SD) in m minutes (SD) minutes 1 (LA, nrep, sq) 27.2 (0.3) 26.8–27.7 19.7 (1.4) 17–21 2 (LA, rep, sq) 21.2 (0.3) 20.7–21.6 31.3 (1.7) 29–33 3 (LA, nrep, sq) 27.3 (0.3) 26.8–27.7 21.7 (2.6) 17–24 4 (LA, nrep, ml) 21.0 (0.2) 20.7–21.3 30.3 (3.1) 25–35 5 (LA, rep, sq) 27.2 (0.5) 26.5–27.7 19.1 (1.1) 17–20 6 (LA, rep, ml) 21.2 (0.5) 20.4–21.6 27.1 (1.3) 26–29 7 (LA, nrep, sq) 27.3 (0.4) 26.5–27.7 19.4 (1.3) 17–21 8 (LA, nrep, ml) 21.9 (0.3) 21.3–22.3 26.9 (2.1) 24–29 9 (LA, rep, sq) 26.1 (0.2) 25.9–26.5 20.4 (2.1) 17–23 10 (LA, rep, ml) 15.5 (0.3) 14.9–15.8 41.3 (9.1) 33–60 11 (HA, nrep, sq) 17.6 (0.4) 16.8–18.0 37.9 (4.6) 31–42 12 (HA, nrep, sq) 16.0 (0.6) 14.6–16.5 46.9 (9.8) 35–62 Total (n = 84) 22.5 (4.4) 14.6–27.7 28.5 (9.9) 17–62

Table 2: Rankings and NDLs for low-altitude, square, non-repetitive readings Dive Computer Reading 1: Reading 3: Reading 7: Mean rank Rank (depth, NDL) Rank (depth, NDL) Rank (depth, NDL) Aladin 1 6.5 (27.7, 21) 3.0 (27.7, 21) 5.0 (27.7, 20) 4.83 Aladin 2 4.0 (27.7, 20) 2.0 (27.7, 20) 5.0 (27.7, 20) 3.67 Suunto 1 4.0 (27.1, 20) 6.5 (27.1, 24) 5.0 (27.4, 20) 5.17 Suunto 2 6.5 (27.1, 21) 6.5 (27.1, 24) 7.0 (27.1, 21) 6.67 Dive Rite 1 2.0 (27.0, 19) 4.5 (27.4, 23) 2.5 (27.2, 19) 3.00 Dive Rite 2 4.0 (27.1, 20) 4.5 (27.1, 23) 2.5 (27.4, 19) 3.67 VR3 1.0 (26.8, 17) 1.0 (26.8, 17) 1.0 (26.5, 17) 1.00

(Suunto, 2003), and by −3.7m at 21.3m depth (mean SD 0.3m) and 1.5m (mean SD 0.5m) at high at high altitude. This larger difference at high altitude. At depth, the mean range of NDLs at low altitude is in keeping with depth table adjustments altitude was 7.3 minutes (mean SD 2.6 minutes), for dives at 3000m altitude (Smith, 1976), and yet at high altitude, the mean range was 19 minutes the 0.3m-plus 3% correction per 300m altitude (mean SD 7.2). cited elsewhere (Lenihan and Morgan, 1975; 3.3. Correlation Lippmann, 1996, National Oceanic Atmospheric At each reading, computers were ranked by Administration [NOAA], 2001). increasing magnitude of NDLs recorded. Rankings The NDLs displayed by the two Aladin computers and displayed NDLs are presented in Tables 2–4. over 12 readings had a correlation coefficient of Dive computer NDL rankings for the two 1.00, meaning that each Aladin computer displayed high-altitude dives had a correlation coefficient information that was identical to the other at every of 0.86, indicating a high level of agreement recording. The 12 NDLs displayed by the two (for computer estimated depths between 14 and Suunto Vyper computers were also identical to each 18m). There was negative correlation between other and thus also had a correlation coefficient mean rankings for the two high-altitude, non- of 1.00. The two NiTek computers had a correlation repetitive, square profile NDLs and mean ranking coefficient for NDLs recorded over 12 readings for low-altitude, non-repetitive, square profile NDLs of 0.99. (r = −0.81), suggesting the dive computers used in this study did not uniformly adjust for altitude. 3.2. NDLs Likewise, correlation between mean rankings for Table 1 presents mean depths and NDLs, as well as high-altitude, non-repetitive, square profile NDLs the ranges of each for each reading. Also indicated and low-altitude, non-repetitive, multilevel NDLs are if the readings were low altitude (LA), high was −0.90. This suggests NDLs for first dives of the altitude (HA), repetitive (rep) or not repetitive day were paradoxically ranked in conservativeness (nrep), and if the reading was taken initially at the between high and low altitude, and that this nega- deepest depth – as in a square profile (sq) – or at tive correlation increased with multilevel diving at a subsequently shallower depth – as in a multilevel low altitude. profile (ml). Mean differences in depth readings Correlation between mean rankings for between dive computers at low altitude were 0.9m, high-altitude, non-repetitive, square profile NDLs

53 Buzzacott and Ruehle. The effects of high altitude on relative performance of dive decompression computers

Table 3: Rankings and NDLs for low altitude, multilevel, repetitive readings Dive Computer Reading 6: Reading 10: Mean Rank Rank (depth, NDL) Rank (depth, NDL) Aladin 1 4.5 (21.6, 27) 5.5 (15.8, 42) 5.00 Aladin 2 2.0 (21.6, 26) 5.5 (15.8, 42) 3.75 Suunto 1 2.0 (21.3, 26) 1.5 (15.5, 33) 1.75 Suunto 2 2.0 (21.3, 26) 1.5 (15.5, 33) 1.75 Dive Rite 1 6.5 (20.4, 29) 3.0 (15.6, 39) 4.75 Dive Rite 2 6.5 (21.0, 29) 4.0 (15.5, 40) 5.25 VR3 4.5 (20.7, 27) 7.0 (14.9, 60) 5.75

Table 4: Rankings and NDLs for high altitude, square, non-repetitive readings Dive Computer Reading 11: Reading 12: Mean Rank Rank (depth, NDL) Rank (depth, NDL) Aladin 1 4.0 (18.0, 39) 3.5 (16.5, 46) 3.75 Aladin 2 3.0 (18.0, 38) 3.5 (16.2, 46) 3.25 Suunto 1 1.0 (17.7, 31) 1.5 (16.5, 35) 1.25 Suunto 2 2.0 (17.4, 32) 1.5 (16.2, 35) 1.75 Dive Rite 1 6.5 (17.8, 42) 6.0 (16.5, 54) 6.25 Dive Rite 2 6.5 (17.8, 42) 5.0 (15.8, 50) 5.75 VR3 5.0 (16.8, 41) 7.0 (14.6, 62) 6.00

and low-altitude, repetitive square profile NDLs most conservative on the first dive of the day (mean was 0.59. Correlation between mean rankings for rank = 1), yet amongst the least conservative for high-altitude, non-repetitive, square profile NDLs repetitive dives (mean rank = 5.0), and similarly at and low-altitude, repetitive, multilevel NDLs was high altitude, they were ranked on average the sixth 0.91. This suggests NDLs for repetitive square most conservative out of the seven dive computers. profile dives at low altitude were ranked similarly to The scale by which dive computers adjust NDLs non-repetitive, square profile dives at high altitude, for altitude is significantly more similar (p < 0.01) and that this positive correlation increased with to the scale by which they compensate for multilevel multilevel diving at low altitude. Compared with profiles during repetitive dives at low altitude the mean ranking of computers by non-repetitive, (r = 0.91) than to their initial ranking at sea level square profile NDLs at high altitude, correla- during single square-profile dives (r = −0.81). tion to mean NDL rankings at low altitude for repetitive, multilevel profiles was significantly better 4. Discussion (p < 0.01) than correlation to mean rankings at low altitude for single-dive, single-depth NDLs. In this small pilot study, intra-model agreement was excellent for displayed estimates of depth and inter- 3.4. Order reversal computer variation low (mean standard deviation At low altitude, the Suunto Vypers were consistently for depth readings less than 0.6m). Despite the amongst the least conservative during the first high level of agreement between these seven dive dives of each day (non-repetitive dives), whether computers with respect to depth, the range of square or multilevel profile (mean rank = 6.2). NDLs recorded at high altitude was relatively wide. At high altitude, however, they were consistently Furthermore, all computer-generated NDLs at the most conservative, mean rank = 1.5. As their altitude were less conservative than NDLs published intra-model correlation (reliability) was high, and in tables. At a mean displayed depth of 17.6m, their reported depths were within the range at each NDLs ranged from 31–42 minutes and, for 16.0m, reading, it can only be concluded their method of from 35–62 minutes, yet tables published for 3000m adjustment for altitude was the most conservative altitude recommend NDLs of just 10 minutes at (severe). For repetitive dives at low altitude, how- 15m depth and 5 minutes at 18m (Boni et al., 1976). ever, the Vypers were consistently amongst the most Further research, perhaps in controlled chamber conservative, suggesting (at least for the dive pro- trials, would shed more light on the behaviour files in this study) that the decompression model of various dive computers at high altitude and they use gives less credit for gas washout during over a wider depth range. Manufacturers might surface interval than the other computers used in also uniformly publish anticipated NDLs for dives this study. The opposite can be said for the VR3. at a standard altitude within their respective dive At low altitude, the VR3 NDLs were consistently the computer instruction manuals – for example at

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1500m – to enable more valid comparison between Diving Science and Technology (DSAT). (1985). The Wheel dive computers intended for use at altitude. Until Instructions for Use and Study Guide. Santa Ana, CA: Diving then, it is recommended that high-altitude divers Science and Technology. Doolette D. (2005). Gas-content versus bubble decom- using dive computers also consult appropriate pression models. South Pacific Underwater Medicine Society decompression tables, such as those published by Journal 35(2): 71–75. (Boni et al., 1976), though even these are untested Egi SM and Brubakk AO. (1995). Diving at altitude: a review in water above 2000m altitude. of decompression strategies. Undersea and Hyperbaric At this stage in the understanding of high- Medicine 22(3): 281–300. altitude diving, despite modern dive computers Egstrom GH. (2004). . In: Bove A (ed.). . Philadelphia: Elsevier Inc., 37–51. providing dive decompression information up to Gurr K. (1999). Proplanner Decompression Software. Bristol, UK: 6000m altitude, the higher the altitude at which Delta P. Technology. dives are to be made, the more the NDLs should be Hennessy TR. (1977). Converting standard air decompres- considered experimental in nature, especially for sion tables for no-stop diving from altitude or habitat. repetitive, multilevel and/or decompression dives. Undersea Biomedical Research 4(1): 39–53. Hotelling H. (1940). The selection of variates for use Therefore, when selecting a dive computer for in prediction with some comments on the problem altitude diving, it is of little use to compare sea-level of nuisance parameters. Annals of Mathematical Statistics NDLs for single dives, even if these are the only 11(3): 271–283. NDLs available at the point of sale. Lenihan D and Morgan K. (1975). High Altitude Diving. Santa Fe, NM: U.S. Department of the Interior. National Acknowledgements Parks Service. Lippmann J. (1989). Dive computers. South Pacific Underwater The authors wish to thank Dr R Vann and Medicine Society Journal 19: 5–12. Dr N Pollock of the for their Lippmann J. (1996). Deeper into diving. Carnegie, VIC: advice and assistance. J.L. Publications, 610pp. Lippmann J and Wellard M. (2004). Comparing dive References computers. South Pacific Underwater Medicine Society Journal Acott C. (1994). The diving incident monitoring study 34: 124–129. dive tables and dive computers. South Pacific Underwater National Oceanic and Atmospheric Administration Medicine Society Journal 24: 214–215. (NOAA). (2001). NOAA Diving Manual: Diving for Apollo. (2001). Apollo computer gauge. Nano. Instruction Science and Technology. Fourth Edition. Flagstaff, AZ: Best manual. Tokyo: Apollo Sports Co. Publishing Company, 660pp. Bell RL and Borgwardt RE. (1976). The theory of Sheffield PJ. (1990). Flying after diving guidelines: a high-altitide corrections to the U.S. Navy standard review. Aviation, Space and Environmental Medicine decompression tables. The cross corrections. Undersea 61(12): 1130–1138. Biomedical Research 3(1): 1–23. Smith CL. (1976). Altitude procedures for the ocean diver. Boni M, Schibli R, Nussberger P and Buhlmann AA. Colton, CA: National Association of Underwater Instruc- (1976). Diving at diminished : air tors, 46pp. decompression tables for different altitudes. Undersea Suunto. (2003). Suunto Vyper User’s Guide. Vantaa, Finland: Biomedical Research 3(3): 189–204. Suunto Oy. Davies D. (1994). Diving with computers. South Pacific Uwatec. (1995). Aladin Sport no-stop dive computer operating Underwater Medicine Society Journal 24: 216–218. manual. Hallwil, Switzerland: Uwatec AG. Davis R. (1995). The regulation of recreational Wienke BR. (1993). Diving above sea level. Flagstaff, AZ: Best in Queensland. South Pacific Underwater Medicine Society Publishing Company, 66pp. Journal 25: 10–18. Wilks J. (1990). Kitting up: An equipment profile of Dive Rite. (1997). NiTek Dive Computer User Guide. City, Queensland divers. South Pacific Underwater Medicine Society FL: Lamartek Inc. Journal 20: 200–205.

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