Addendum : Correlations of VPM-B(), RGBM, and GF Gradients and Tensions Compartment Gradients and Tensions are Tracked Stop-by-Stop for Alternative Ascents from a min dive to ft on Trimix 8/ This addendum tracks and compares gradients for ascents from dive only: min at ft on 8/. Alternative ascent tables for this dive are shown on page 9. VPM-B was at conservatism level (), GAP RGBM and GF were at nominal conservatisms. Page of the original slides notes that "TATs are closely related to comparative surfacing gradients." TATs were therefore used as convenient -point summaries of correlations of VPM-B to GAP RGBM and GF schedules. A more detailed comparison of compartment gradients and tensions requires analysis of many more data points for each ascent. Essentially, the TAT data summarized by the two red-colored points on the two plots on page have been expanded into plots each, with 6 points per plot, shown on pages and 7. Correlation plots for times at each stop and stair-step profiles are shown in the lower righthand charts on pages 8 and 9 for VPM-B() vs. RGBM, and on page, and for VPM- B() vs. GF. Organization Original Slides VPM-B vs GAP RGBM and GF Slides (pages -8) VPM-Bv._vs_GAP_RGBM_and_GF_ft_mix8_Dives.pdf Addendum HSE RGBM vs. GAP RGBM (pages 9-6) HSE_vs_GAP_RGBM_ft_mix8_Dives.pdf Addendum (pages 7-7) TandG_VPMB_vs_GAP_RGBM_and_GF_ft_mix8.pdf 7
Notations and Conventions Gradients and Tensions were calculated as functions of time from ascent schedules generated by V-Planner and GAP decompression models. Profiles The ascent schedules calculated by V-Planner and GAP software, shown on page 9, were used to calculate compartment tensions and gradients in a custom Mathematica program. If you really want details, then review all of the modeling assumptions (such as compartment half-times, partial pressure of H O, etc.) in the open source code of the obsolete Mathematica VPM program at my website: http://www.decompression.org/maiken/vpm/multigas_vpm.htm Plots Both compartment tensions (T) and gradients (G) are considered, even though the information is redundant. Although tensions are conventional, gradients are more closely related to physical and physiological processes. Compartments are labeled according to Buhlmann's ZHL-6 Nitrogen half-times. Conventionally, Helium half-times are scaled by the ratio of the two gas's diffusivities. This is physically inconsistent with the idea that compartments represent time-scales for perfusion. Just another deco model inconsistency! Discussion of Correlation Plots VPM-B() and RGBM Ts and Gs, shown on pages and, are much more nearly correlated than VPM-B() and GF Ts and Gs, shown on pages 6 and 7. VPM-B() and RGBM Gs and Ts are : correlated for compartments ranging from the slowest (6 min), to the controlling compartment (a point near plot's upper left corner). RGBM fast compartment Gs and Ts are lower than VPM-B() for the deepest stops, nonetheless, RGBM Gs and Ts are greater than either VPM-B() and GF from ft up to the surface. Slide discusses the general (ie: applies to all ft dives) operational factors that lead to larger surfacing gradients for RGBM compared to VPM-B() and GF. GF surfacing Gs and Ts are much less than VPM-B() and RGBM, but GF TATs are 8 mins longer than VPM-B() and RGBM (which are virtually identical at ~6 min TAT). 8
Ascent Schedules For reference, the depths, run times, and gas oxygen and nitrogen fractions are tabulated for the three alternative ascent models. Stair-step plots of the ascents are shown in the lower right-hand plots of slides 8 and VPM-B() ft min fo / fn. 8. 8 8 67. 8. 8 7 8 8 8 9 8 8 66 8 7 7 6 8 9. 6. 7. RGBM(N) ft min fo / fn. 8. 8 8 67. 8. 8 6 8 8 8 7 8 9 6 8 8 78 8 7 86 6 97 6 98.. 7. GF(N) ft min fo / fn. 8. 8 8 67. 8. 8 6 8 8 8 8 9 7 8 8 9 8 7 6 9 7 8. 9. 6. 9
Notes on Reading Tension Plots Total CompartmentTensions vs. Time Slow compartments out-gas after surfacing Ascent to st stop T ension H A t m L Switch to O at ft rapidly reduces tensions in fast compartments (to for the fastest ) Ascent to surface Sea level pressure Saturation Tension at Surface T = ( (pph O + ppco )) x () Switch to Nitrox % at 7 ft rapidly reduces tensions in fast compartments min TAT 9 min T Fastest Compartments In-gas 78% N + % Ar at surface after desatuation by O at and ft stops Slowest Compartment 6 min Fastest Compartment min
Notes on Reading Gradient Plots Negative surface saturation gradient G radient H A t m L - - - - - -6 Fastest compartments control deepest stops CompartmentGradients vs. Time Ascent to st stop Switch to O at ft rapidly reduces gradients in fast compartments Switch to Nitrox % at 7 ft rapidly reduces gradients in fast compartments Slowest compartments drive bubble growth after surfacing Ascent to surface +G supports bubble growth -G drives bubble dissolution min TAT 9 min Slowest Compartment 6 min Fastest Compartment min
Plots of Tensions and Gradients vs. Run Time VPM-B () Total CompartmentTensions vs. Time CompartmentGradients vs. Time T ension H A t m L G radient H A t m L - - - - - RGBM -6 Total CompartmentTensions vs. Time CompartmentGradients vs. Time - T ension H A t m L G radient H A t m L - - - - Gradient Factor Total CompartmentTensions vs. Time Note horizontal scale change -6 - CompartmentGradients vs. Time T ension H A t m L G radient H A t m L - - - 6 min 6 - -6 6 min
Construction of Tension and Gradient Correlation Plots Example: Comparative Tensions at end of ft stop -to- correlation line. Points above the line have larger RGBM Tensions. Points below the line have larger VPM tensions RGBM Tension Time Plot RGBM tensions as Y components for end of ft Stop ft Stop (x,y) End of Dive Finish ft stop Run time = min example points corresponding to total tensions (Ttotal=TN + THe) in compartments representing 6 min, 8. min, and min N Bhulmann ZHL-6 compartments. Plot VPM tensions, just like the RGBM illustration, as X components for end of ft Stop N Compartments 6 min 8. min min
Stop-by-Stop Correlation Plots of RGBM vs. VPM-B() Tensions RGBM vs. VPM-B Compartment Tensions at End of Each Decompression Stop on Ascent from min Dive to feet ftstop ft Stop ft Stop 9 ft Stop 8 ft Stop 7 ft Stop 6 ft Stop ft Stop ft Stop ft Stop ft Stop ft Stop N Compartments 6 min min
Stop-by-Stop Correlation Plots of RGBM vs. VPM-B() Gradients RGBM vs. VPM-B Compartment Gradients at End of Each Decompression Stop on Ascent from min Dive to feet - - -. - -. ft Stop - --.--.-- - - -. - ft Stop -. -.--.-- - - -. - ft Stop - -. - - 9 ft Stop 8 ft Stop 7 ft Stop - - -. -. - - - - -. -. - - - - -. -. - - - - -7 - -. -. -. 6 ft Stop - - - - -7 - -. ft Stop - - - - -6-8 - -. ft Stop - - - - -6-8 - - ft Stop - - - -. ft Stop -. - - - - -7 - -. ft Stop - - N Compartments min 6 min
Stop-by-Stop Correlation Plots of GF vs. VPM-B() Tensions GF vs. VPM-B Compartment Tensions at End of Each Decompression Stop on Ascent from min Dive to feet ft Stop ft Stop ft Stop 9 ft Stop 8 ft Stop 7 ft Stop TG F H A t a L TG F H A t a L TG F H A t a L 6 ft Stop ft Stop ft Stop ft Stop ft Stop ft Stop N Compartments 6 min 6 min
Stop-by-Stop Correlation Plots of GF vs. VPM-B() Gradients GF vs. VPM-B Compartment Gradients at End of Each Decompression Stop on Ascent from min Dive to feet - - -. - -. ft Stop - --.--.-- - - -. - ft Stop -. -.--.-- - - -. - ft Stop - -. - - 9 ft Stop 8 ft Stop 7 ft Stop - - -. -. - - - - -. -. - - - - -. -. - - - - -7 - -. -. -. 6 ft Stop - - - - -7 - -. ft Stop - - - - -6-8 - -. ft Stop - - - - -6-8 - - ft Stop - - - -. ft Stop -. - - - - -7 - -. ft Stop - - N Compartments min 7 6 min