# Ratio Deco – is it nonsense?

[This is a post by Rick Walsh but this information got lost when this blog moved to a new server.]

When I mentioned to one of my dive buddies I was considering taking a GUE Tech 1 course, his response was “I wouldn’t trust that ratio deco crud”. Another explained calculating ratio deco by: average the depth of your dive; double it; add the last two digits of the serial number of your bottom timer; divide by the number of divers in your team, which is always three; then subtract the number you first started with.

For better or worse, there is a perception among many of us non-DIR (or not yet DIR) decompression divers that ratio deco is dangerous voodoo that should be avoided. But could it be justified?

Let me state now that I have no training in ratio deco, have never used it myself, and I am not advocating its use. If you are interested in applying it to your diving, I encourage you to take a course that covers it and how and when it can be used, and most importantly its limitations. Do not take reading something on the internet as a substitute for appropriate training. This post is intended to discuss the concept of ratio deco far more than the practice. I mention GUE, but the concept applies just as well to other versions of “ratio deco”.

What is Ratio Deco?
Ratio deco is a method for calculating or adjusting a dive decompression profile, which does not require referring to a decompression dive computer, tables or software. As such, the plan can be adjusted or re-calculated on-the-fly during the dive without relying on a dive computer’s decompression calculations.

To many, that sounds too good to be true. Almost all decompression software, dive computers and tables in current use are based on Buhlmann or VPM-B decompression models or some varient thereof. These models have received theoretical and real-life testing, include calculation for sixteen different theoretical tissues, and permit unlimited combinations of dive depths, durations, breathing gasses. Surely this cannot be replaced by a new decompression model calculated on-the-fly by the diver.

In science, engineering, medicine, and many other disciplines, there are countless complicated mathematical models that cannot be generalized by a simple function. However, by controlling some variables, the relationship between others become simplified. It is possible to use linear approximations for non-linear functions over limited ranges with acceptable levels of accuracy.

In reality, ratio deco is not a decompression model. Rather it is a series of approximate relationships and trends that can be observed from ascent schedules calculated using existing models. Searching the internet suggests GUE Ratio Deco is derived from either VPM-B with +2 conservatism, or Buhlmann with approximately 30/85 gradient factors. Either way, it is attempting to replicate a bubble model profile, so comparing it to VPM-B +2 is justifiable.

Whether bubble models generally, or VPM-B specificaly, are the best choice of decompression model is another topic or much debate. But if we think of ratio deco as an approximation of VPM-B used within set limits, the concept is not so radical.

Simplifying a complex model
What variables can be controlled that would permit the simplification of a decompression model?
– Bottom gas
– Decompression gasses
– Ascent and descent rates

GUE and related organizations have adopted standard gas mixes, selected according to dive depth, and have standard ascent and descent rates. With these known, for a set depth and over a limited range in duration, it should be possible to find a linear approximation of the relationship between bottom time and decompression time.

Example profiles
An internet search for “Ratio Deco” brings up a number of hits, including a Team Foxturd blog post. The post gives a procedure for using ratio deco in line with GUE Tech 1 practice. Adopting a bottom gas of either 21/35 or 18/45 trimix, and deco gas of 50% nitrox, the ratio of bottom time to deco time for a 45m dive is given as 1:1. For dives in the 30-48m depth range, the deco time should be adjusted by 5min per 3m depth greater or less than 45m. For example, a 25 minute bottom time at 48m would result in a deco time of 25min (1:1 ratio) + 5min (+3m depth adjustment) = 30min. For a 30min bottom time at 38m, the deco time would be 30min (1:1 ratio) – 10min (-6m depth adjustment) = 20min. GUE Tech 1 limits dives to 30 minutes planned decompression, so implicitly this approximation is applicable within this limit.

Of course, there is more to the decompression profile than the decompression time. Common to both Buhlmann and VPM-B models, a typical ascent profile comprises an initial ascent off the bottom up to the first stop, followed by a series of decompression stops and a final ascent to the surface from the last stop at 3m or 6m. The Team Foxturd blog post divides the ascent into portions:
(a) ascend from the bottom to 80% of the bottom ambient pressure (approximately three quarters of bottom depth) at 9m/min
(b) slow ascent rate to 6m/min to allow “deep stops” to clear while ascending to the gas change and start of “intermediate stops” at 21m
(c) spend the first half the calculated deco time on the “intermediate stops” (the 21m to 9m stops, inclusive), with each stop of approximately equal duration
(d) spend the second half of the calculated deco time at the 6m “shallow stop”
(e) ascend to surface at 1m/min

These steps are annotated in Figures 1 and 2. Figure 1 is the profile calculated using Ratio Deco as outlined by Team Foxturd for a 30min bottom time at 45m using 21/35 trimix bottom gas and 50% nitrox deco gas, while Figure 2 is a VPM-B +2 decompression profile calculated in Subsurface for the same bottom time and depth. The VPM-B +2 ceiling is plotted in green in both figures. The Ratio Deco profile spends slightly longer in the “intermediate stops” and slightly less time in the “shallow stop”, but the profiles are quite similar, and importantly the ratio deco profile does not break the ceiling +2. In both instances, the ceiling clears by the end of the 6m stop (end of deco time as defined above), so ascending to the surface over 6 minutes provides an extra buffer.

Figures 3 and 4 compare the bottom time to the deco time for VPM-B +2 dives to 45m and 51m, respectively, using 21/35 or 18/45 trimix bottom gas and 50% nitrox decompression gas. As described above, deco time is taken as the time from the first stop until leaving the 6m stop. It does not include the time to ascend from the bottom to the first stop, or the 6 minutes to ascend at 1m/min from the 6m stop to the surface. For comparison, the 1:1 ratio line is plotted on the 45m plot, and the 1:1 ratio plus 10 minutes (5 minutes per 3m increments beyond 45m) line is plotted on the 51m plot. So to is a line at 1:1 (or 1:1 + 10 minutes) ratio plus 6 minutes, representing the surfacing time, which is when the ceiling must have cleared so as not to be broken.

Figure 3 shows that for a 45m dive, the 1:1 bottom time to deco time ratio provides a good approximation when using 21/35 trimix bottom gas, up to about 35 minute bottom time. Beyond this the decompression time increases, diverging away from the 1:1 ratio. However, the 6 minutes taken to surface from the last stop provides some buffer, so for dives using 21/35 trimix, the ratio might be used up to about 50 minute bottom time without breaking the VPM-B +2 ceiling. Compared to 21/35, 18/45 trimix includes a greater portion of inert gas, so it is not surprising that decompression time is increased when using 18/45 trimix bottom gas. But for dives with bottom time up to 30 minutes, the 6 minutes surfacing time provides enough of a buffer that the VPM-B +2 ceiling might not be broken.

Figure 4 shows that for a 51m dive, the 1:1 + 10 minutes bottom time to deco time ratio is a poor fit. To be clear, this is beyond the specified depth range (maximum 48m) in the Team Foxturd post. It is more conservative than VPM-B for shorter bottom times and more aggressive for longer bottom times. However, up to 30 minute bottom time, the 6 minutes surfacing time provides enough of a buffer that the VPM-B +2 ceiling might not be broken when using either 21/35 or 18/45 trimix bottom gas.

Another way to compare ratio deco ascent schedule to the VPM-B model is to enter the ratio deco profile into Subsurface as a dive and see if the VPM-B +2 ceiling is broken at any point. If the ceiling is not broken, the profile is acceptable according to the model, and if the ceiling is broken the profile does not comply with the model. Where the ceiling is broken is also relevant. Some divers would excuse spending a minute or two just above a deep stop ceiling calculated with a bubble model like VPM-B (which calculate much deeper ceilings early in the ascent than a conventional Buhlmann model), so long as the time was minimal. Such a case is illustrated in Figure 5, which shows a 51m dive with 35 minute bottom time using 18/45 trimix bottom gas and 50% nitrox for decompression. Surfacing before the ceiling had cleared, such as illustrated by Figure 6 for a 45m dive with 60 minute bottom time, would be considered more risky.

Figures 7 and 8 plot the total runtime for profiles calculated using the ratio deco method outlined by Team Foxturd according to bottom time for 45m and 51m dives (noting that 51m exceeds the depth limit given), respectively. Also plotted are the runtimes when the VPM-B +2 ceiling clears, calculated by entering the ratio deco profile into Subsurface. For instances when it took longer than the total dive time for the ceiling to clear, the time to clear was determined by extending the final stop as long as necessary.

These figures show that for 45m and 51m dives with bottom time up to 35 minutes, the VPM-B +2 ceiling clears before surfacing in accordance with the ratio deco profile, when either 21/35 or 18/45 trimix bottom gas is used. However, brief breaches of the deep stop ceiling occurred when using 18/45 for 30 or 35 minute bottom time. For 40-45 minute bottom time, the ceiling clears just before or just after calculated ratio deco surface time and the deep stop ceiling is also breached. For bottom times exceeding 45 minutes, the ratio becomes increasingly unsatisfactory and risky.

Summary
The above examples demonstrate that it is possible to develop a approximation of a decompression model that provides a reasonable fit over a limited range of depths, bottom times and breathing gasses. Going beyond these limits the approximation starts to fall apart. Undoubtedly there exists, or could be created, approximations that are reasonable for greater depths, longer bottom times, different breathing gasses, altitude diving, and non-square profiles. But with more variations, modifications and adjustments to deal with different situations and contingencies, what started out as a reasonably simple approximation rapidly becomes complicated. Each adjustment introduces its own inaccuracies, not to mention the opportunity for human error.

Understanding trends and the effect of changes to depth, time and gas selection on a decompression model and plan is very powerful. This is the basis for any ratio deco “rules”. Even when the primary means of planning relies on software, and even when a dive computer is used to determine “revisions” to a planned dive, ratio deco can be used as an efficient cross-check. It is very easy to enter an incorrect depth in Subsurface or any other planning software, and it is very easy to select an incorrect gasmix (or neglect to select one at all) when using a dive computer.

Anyone using ratio deco methods for diving needs appropriate training and must understand the limits of the approximation. Not only that, they need to understand the limits of their own ability. This is especially true if they intend to use the technique for on-the-fly planning. Am I really up to calculating my decompression schedule during the dive? Will I have enough gas for the new plan? What about my buddy? How would I deal with lost gas? The ratio deco examples above approximate a VPM-B +2 profile. Many divers and experts disagree on whether VPM-B or Buhlmann (or Thalmann or RGBM) are better models, and many would regard +2 conservatism as not conservative enough.

A little knowledge is a dangerous thing, and this is certainly true of ratio deco. Training in ratio deco should cover not just the principle, and not just a set of rules of thumb, but must also reinforce the limitations of the technique and the need for dive planning to consider more than just developing a decompression schedule.