atmospheres and decompression - umd · between caisson disease and air embolisms • suggested...

Pulmonary Physiology and Decompression ENAE 697 - Space Human Factors and Life Support

U N I V E R S I T Y O FMARYLAND

Atmospheres and Decompression• Emergency and explosive decompression• Denitrogenation and decompression sickness• Tissue models• Physics of bubble formation• Atmosphere constituent analysis

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© 2019 David L. Akin - All rights reserved http://spacecraft.ssl.umd.edu

http://spacecraft.ssl.umd.edu



Effective Performance Time at Altitude

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Altitude, m Altitude, ft Effective Performance Time5500 18,000 20-30 minutes6700 22,000 10 minutes7600 25,000 3-5 minutes8500 28,000 2.5-3 minutes9100 30,000 1-2 minutes

10,700 35,000 0.5-1 minute12,200 40,000 15-20 seconds13,100 43,000 9-12 seconds15,200 50,000 9-12 seconds



Cabin Depressurization Rates• Fliegner’s Equation

– t=time of decompression (seconds)– A=cross-sectional area of opening (square inches)– V=cabin volume (cubic feet)– P=initial cabin pressure (psia)– B=external ambient pressure (psia)

• Decent approximation for aircraft cabins

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t = 0.22VA

P − BB



Cabin Depressurization Rates• Haber-Clamann Model

– tc=time constant for cabin (sec)– V=cabin volume (cubic feet)– A=area of opening (square feet)– C=speed of sound (1100 ft/sec)– t=time of depressurization (sec)– P=initial cabin pressure (psia)– B=external ambient pressure (psia)

– 4

tc =V

ACt = tc [1.68 ln ( PB ) + 0.27]



Cabin Depressurization Rates• Violette’s Equation

– t=time of depressurization (sec)– V=cabin volume (cubic meters)– A=area of opening (square meters)– P=initial cabin pressure– B=external ambient pressure

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t =V

220Acosh−1 ( PB )



S/C Depressurization (Sonic Orifice)• External environment at zero pressure• Any hole is a sonic orifice• Mass flow rate

• Switch to pressure (ideal gas, isentropic)

vflow = γRT

·m =dmdt

= ρvflowAorifice

dmdt

= APoγ

RTo (2

γ + 1 )γ + 1γ − 1



Sonic Orifice Analysis (2)

dm

dt= 0.04042

APop

To

For air, � = 1.4; R = 287J

kg K

Isothermal: t =0.086

To

VA

ln ( PoPf )

Solve for time to reach final pressure Pf

Adiabatic: t =0.43

To

VA ( PoPf )

0.143

− 1



S/C Depressurization (Bernoulli)• Bernoulli’s Law

• g=0• Interior and exterior to spacecraft

• Inside vo~0, outside Pe=0

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P +1

2⇢v

2 + ⇢gh = constant

Po

+1

2⇢v2

o

= Pe

+1

2⇢v2

e

Po

=1

2⇢v2

e



Bernoulli Analysis (2)

ve

=

s2P

o

⇢

dm

dt= ⇢Av

e

= A⇢

s2P

o

⇢= A

p2⇢P

o

⇢ = m/V

dmpm

= A

r2P

o

Vdt



Cabin Leak Pressure Loss

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0"

2"

4"

6"

8"

10"

12"

14"

16"

0" 50" 100" 150" 200" 250" 300" 350"

Cabin&Pressure&(p

si)&

Depressuriza1on&Time&(sec)&

Bernoulli" Sonic"Nozzle"

10 m3 cabin volume 1 cm2 leak area



Lung Overpressure Following Decompression

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From Nicogossian and Gazenko, Space Biology and Medicine - Volume II: Life Support and Habitability, AIAA 1994



Violette’s Explosive Decompression Limits

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Caissons• Pressurized chambers

for digging tunnels and bridge foundations

• Late 1800’s - caisson workers exhibited severe symptoms– joint pain– arched back– blindness– death

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Brooklyn Bridge• Designed by John Roebling, who

died from tetanus contracted while surveying it

• Continued by son Washington Roebling, who came down with Caisson Disease in 1872

• Competed by wife Emily Warren Roebling

• 110 instances of caisson disease from 600 workers

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Decompression Sickness (DCS)• 1872 - Dr. Alphonse Jaminet noted similarity

between caisson disease and air embolisms• Suggested procedural modifications

– Slow compression and decompression– Limiting work to 4 hours, no more than 4 atm– Restricting to young, healthy workers

• 1908 - J.B.S. Haldane linked to dissolved gases in blood and published first decompression tables

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Supersaturation of Blood Gases• Early observation that “factor of two” (50% drop in

pressure) tended to be safe• Definition of tissue ratio R as ratio between

saturated pressure of gas compared to ambient pressure   

• 50% drop in pressure corresponds to R=1.58  (R values of ~1.6 considered to be “safe”)

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R =PN2

Pambient= 0.79 (nominal Earth value)



Tissue Models of Dissolved Gases• Issue is dissolved inert gases (not involved in

metabolic processes, like N2 or He)• Diffusion rate is driven by the gradient of the

partial pressure for the dissolved gas

where k=time constant for specific tissue (min-1)P refers to partial pressure of dissolved gas

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dPtissue(t)dt

= k [Palveoli(t)� Ptissue(t)]



Solution of Dissolved Gas Diff. Eq.• Assume ambient pressure is piecewise constant

(response to step input of ambient pressure)• Result is the Haldane equation:

• Need to consider value of Palveoli

where Q=fraction of dissolved gas in atmosphere ΔPO2=change in ppO2 due to metabolism

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Ptissue(t) = Ptissue(0) + [Palveoli(0)� Ptissue(0)]�1� e�kt

⇥

Palveoli =�

Pambient � PH2O +1�RQ

RQPCO2

⇥Q

Palveoli = (Pambient � PH2O � PCO2 + �PO2)Q



Linearly Varying Pressure Solution• Assume R is the (constant) rate of change of

pressure - solution of dissolved gases PDE is

• This is known as the Schreiner equation • For R=0 this simplifies to Haldane equation• Produces better time-varying solutions than

Haldane equation• Easily implements in computer models

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Pt(t) = Palv0 + R�

t� 1k

⇥�

�Palv0 � Pt0 �

R

k

⇥e�kt



Tissue Saturation following Descent

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Tissue Saturation after Ascent

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Effect of Multiple Tissue Times

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Haldane Tissue Models• Rate coefficient frequently given as time to evolve

half of dissolved gases:

• Example: for 5-min tissue, k=0.1386 min-1• Haldane suggested five tissue “compartments”: 5,

10, 20, 40, and 75 minutes• Basis of U. S. Navy tables used through 1960’s• Three tissue model (5 and 10 min dropped) • 1950’s: Six tissue model (5, 10, 20, 40, 75, 120)

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T1/2 =ln (2)

kk =

ln (2)T1/2



Workman Tissue Models• Dr./Capt. Robert D. Workman of Navy

Experimental Diving Unit in 1960’s• Added 160, 200, 240 min tissue groups• Recognized that each type of tissue has a differing

amount of overpressure it can tolerate, and this changes with depth

• Defined the overpressure limits as “M values”

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Workman M Values• Discovered linear relationship between partial

pressure where DCS occurs and depth

M=partial pressure limit (for each tissue compartment)M0=tissue limit at sea level (zero depth)ΔM=change of limit with depth (constant)d=depth of dive

• Can use to calculate decompression stop depth

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M = M0 + �Md

dmin =Pt �M0

�M



PADUA (Univ of Penn.) Tissue ModelTissue T1/2 (minutes) M0 (bar)

1 5 3.042 10 2.5543 20 2.0674 40 1.6115 80 1.5816 120 1.557 160 1.528 240 1.499 320 1.4910 480 1.459

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Bühlmann Tissue Models• Laboratory of Hyperbaric Physiology at University

Hospital, Zurich, Switzerland• Developed techniques for mixed-gas diving,

including switching gas mixtures during decompression

• Showed role of ambient pressure on decompression (diving at altitude)

• Independently developed M-values, based on absolute pressure rather than SL depth

• “Zurich” 12 and 16-tissue models widely used

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Bühlmann M-Value Models• Modifies Workman model by not assuming sea

level pressure at water’s surface

Pamb=pressure of breathing gasb=ratio of change in ambient pressure to change in tissue pressure limit (dimensionless)a=limiting tissue limit at zero absolute pressure

• ZH-L16 model values for a and b

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M =Pamb

b+ a

a = 2 T�13

1/2 < bar > b = 1.005� T� 121/2



Physics of Bubbles• Pressure inside a bubble is balanced by exterior

pressure and surface tension

where γ=surface tension in J/m2 or N/m (=0.073 for water at 273°K)

• Dissolve gas partial pressure Pg=Pamb in equilibrium

• Gas pressure in bubble Pint>Pamb due to γ• All bubbles will eventually diffuse and collapse

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Pinternal = Pambient + Psurface = Pambient +2�r



Critical Bubble Size• Minimum bubble size is defined by point at which

interior pressure Pint = gas pressure Pg

• rrmin - bubble will grow • r=rmin - unstable equilibrium

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rmin =2�

Pg � pambient



Bubble Formation and Growth• In equilibrium, external pressure balanced by internal

gas pressure and surface tension• Surface tension forces inversely proportional to radius

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“Clinical” Discussion of DCS• Tissue models are predictive, not definitive• Every individual is different

– Overweight people more susceptible to DCS– Tables and models are predictive limits - there will be

“outliers” who develop DCS while adhering to tables

• Doppler velocimetry reveals prevalence of bubbles in bloodstream without presence of DCS symptoms - “asymptomatic DCS”

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Implications of DCS in Space Flight• Drop from sea level pressure to ~4 psi, 100% O2

pressure– Equivalent to ascent from fully saturated 120 ft dive – Launch in early space flight– Extravehicular activity from shuttle or ISS

• To have “safe” (R=1.4) EVA from shuttle requires suit pressure of 8.2 psi

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R =PN2Pamb

=14.7(0.78)

4= 2.87



Current Denitrogenation Approaches• Depress to 10.2 psi for 12-24 hours prior to EVA

– Full cabin depress in shuttle– “Campout” in air lock module of ISS

• Exercise while breathing 100% O2• In-suit decompression on 100% O2 (3.5-4 hours)

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Historical Data on Cabin Atmospheres

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from Scheuring et. al., “Risk Assessment of Physiological Effects of Atmospheric Composition and Pressure in Constellation Vehicles” 16th Annual Humans in Space, Beijing, China, May 2007



Spacecraft Atmosphere Design Space

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Effect of Pressure and %O2 on Flammability

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from Hirsch, Williams, and Beeson, “Pressure Effects on Oxygen Concentration Flammability Thresholds of Materials for Aerospace Applications” J. Testing and Evaluation, Oct. 2006



Atmosphere Design Space with Constraints

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Decompression/Neurovestibular Physiology ENAE 697 - Space Human Factors and Life Support


0.0#

2.0#

4.0#

6.0#

8.0#

10.0#

12.0#

14.0#

0# 200# 400# 600# 800# 1000# 1200#

Tissue

&Nitrogen

&Pressure&(psi)&

Time&(min)&

5*min#.ssue# 80*min#.ssue# 240*min#.ssue#

EVA Denitrogenation - 14.7 psi Cabin

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Suit Pressure 4.3 psi 100% O2

Cabin Atmosphere 14.7 psi 21% O2

R Value = 1.4

Decompression/Neurovestibular Physiology ENAE 697 - Space Human Factors and Life Support


0.0#

1.0#

2.0#

3.0#

4.0#

5.0#

6.0#

0# 200# 400# 600# 800# 1000# 1200#

Tissue

&Nitrogen

&Pressure&(psi)&

Time&(min)&

5+min#/ssue# 80+min#/ssue# 240+min#/ssue#

EVA Denitrogenation - 8.3 psi Cabin

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Suit Pressure 4.3 psi 100% O2

Cabin Atmosphere 8.3 psi 32% O2

R Value = 1.4



Constellation Spacecraft Atmospheres

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atmospheres and decompression - umd · between caisson disease and air embolisms • suggested...

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