TIME OF CONSCIOUSNESS DURING EXPOSURE TO 
VARIOUS PRESSURE ALTITUDES 
by 
A. P. Webster 
Commander, HS, USNR 
and 
Orr E. Reynolds 
Lieutenant (jg), HS, USNR 
7 August 1946 
Biodynamics Branch 
Research Division 
Bureau of Medicine and Surgery 
Navy Department Table 3 
Time of Useful OOnMOaisness and Time to Unconsciousness at 
Various Altitudes Breathing Air. 
Altitude 
feet 
Time of 
Useful Con- 
sciousness 
sec. 
Time to 
Uncon- 
sciousness 
sec. 
Altitude 
feet 
Time of 
Useful Con- 
sciousness 
sec. 
Time to 
Uncon- 
sciousness 
sec. 
25000 
198 
483 
55000 
17 
27 
26000 
148 
356 
56000 
17 
26 
27000 
118 
281 
57000 
16 
25 
28000 
97 
229 
58000 
16 
24 
29000 
83 
193 
59000 
16 
23 
30000 
73 
167 
60000 
15 
22 
31000 
64 
144 
61000 
15 
21 
32000 
57 
128 
62000 
15 
21 
33000 
52 
114 
63000 
14 
20 
34000 
47 
102 
64000 
14 
19 
35000 
43 
92 
65000 
14 
19 
36000 
40 
84 
66000 
14 
18 
37000 
37 
77 
67000 
14 
18 
38000 
35 
71 
68000 
13 
17 
39000 
33 
65 
69000 
13 
17 
40000 
31 
61 
70000 
13 
16 
41000 
29 
57 
71000 
13 
16 
42000 
27 
53 
72000 
13 
16 
43000 
26 
50 
73000 
13 
15 ’ 
44000 
25 
47 
74000 
12 
15 
45000 
24 
44 
75000 
12 
14 
46000 
23 
41 
76000 
12 
14 
47000 
22 
39 
77000 
12 
14 
48000 
21 
37 
78000 
12 
14 
49000 
20 
35 
79000 
12 
13 
50000 
20 
34 
80000 
12 
13 
51000 
19 
32 
52000 
19 
30 
53000 
18 
29 
54000 
18 
28 CONTENTS 
Page 
I. Introduction 1 
II. Notation 2 
III. Theoretical Derivation of Relationship Between Conscious 
Time and Altitude 3 
IV. Fit of Theoretical Equation (Equation 8) to Experimental 
Data 5 
A. Time of consciousness (time to unconsciousness) 
versus pressure altitude 5 
B. Time of useful consciousness versus pressure 
altitude 9 
V. Applications of Equations 8a and 12a 15 
A. Non-useful consciousness versus pressure altitude . 15 
B. Relation between time of useful consciousness and 
time to unconsciousness • 15 
C. Time to unconsciousness on air and oxygen versus 
altitude in feet 16 
D. Time of useful consciousness on air and oxygen 
versus altitude in feet 16 
E. Time of useful consciousness versus time to 
unconsciousness breathing oxygen 17 
VI. Summary of Equations and Constants 25 
VII. Source of Data 26 I. INTRODUCTION 
For any given set of anoxic conditions, the time of consciousness 
is identical with the measured time to loss of consciousness. The 
words time of consciousness then become synomymous with time to 
unconsciousness. For theoretical and practical reasons the time of 
consciousness may be considered as composed of two separate and 
distinct parts: (1) the time of useful consciousness, and (2) the time 
of non-useful consciousness. The first part represents that conscious 
time when deliberate and purposeful acts can be successfully carried 
out; and the second part represents that conscious time when deliberate 
and purposeful acts cannot be successfully carried out. The sum of 
these two times, then, is the time of consciousness or the time to 
unconsciousness. 
There are a number of situations and problems in high velocity, 
high altitude flying where a knowledge of the time of consciousness of 
individuals exposed to reduced atmospheric pressure may play a role 
in aircraft design, methods of escape, placement of controls and 
other mechanisms, etc. For altitudes up to approximately 40,000 
feet, knowledge of the time of consciousness is important in event of 
sudden interruption of oxygen supply, necessitating certain actions 
on the part of the individual in the useful conscious time available to 
him. At higher altitudes where pressurized cabins may be used', 
sudden exposure to the ambient pressure, with or without oxygen 
supply, by explosive decompression due to failure of the pressurized 
cabin, will subject the individual to anoxia giving rise to a certain 
conscious time during which certain acts necessary to his well- 
being must take place. Knowledge of the time of useful consciousness 
and the time to unconsciousness in event that bail-out is necessary at 
high altitude may set the limits beyond which bail-out is impossible-- 
and may be fatal--for’a given type aircraft, cockpit design, and bail- 
out equipment. This paper was written in order to present the avail- 
able data on time of consciousness at various altitudes; to present a 
rational theory on time of consciousness at various altitudes to which 
the rather meager data is fitted; and from which theory tables and 
charts were prepared and presented from which the time of conscious- 
ness at any altitude may be obtained. 
1 II. NOTATION 
= rate of transfer of oxygen into or out of the organism. 
w = quantity of oxygen transferred in time, t, when the altitude is 
unchanged. 
Pa = constant pressure of air which will just maintain the oxygen 
supply to the organism sufficiently to barely maintain conscious 
ness indefinitely, mm.Hg. 
Pa = pressure at various altitudes, mm.Hg. 
U = overall coefficient of oxygen transfer. 
= quantity of oxygen transferred prior to unconsciousness. 
Wg = quantity of oxygen transferred prior to loss of ability to carry 
out.purposeful acts. 
= time to unconsciousness, sec. 
tx = onset of “physiological time”, sec. 
t2 = time of useful consciousness, sec. 
tg = time of non-useful consciousness, sec. 
2 III. THEORETICAL DERIVATION OF RELATIONSHIP BETWEEN 
CONSCIOUS TIME AND ALTITUDE 
It is tacitly assumed that consciousness depends on the main- 
tenance of a given rate of oxygen supplied to the organism. Whether 
consciousness depends upon supplying this oxygen to the organism 
as a whole, or to the cerebral cortex, or to any other tissue, is not 
important to this derivation. The mechanism by which oxygen is 
transferred and transported within the organism, from the air 
breathed, is also of no importance in this development. 
The major premise is that there is a constant pressure of 
air (or tension of oxygen) which (when this air is breathed) will just 
maintain the oxygen supply to the organism sufficiently to barely 
maintain consciousness at a near threshold level for an indefinite 
period of time. Let this constant pressure of air be represented by 
pa. It follows, axiomatically, that when the individual is exposed to 
(breathing) air at a pressure of pa or greater, consciousness will 
be maintained indefinitely. 
For any other air pressure, p , less than p/", the rate of trans- 
fer of oxygen (out of the organism, probably) is given by: 
3f -U(p'-pa) (1) 
where dw/dt is the rate of transfer of oxygen, and U is the overall 
coefficient of transfer. The quantity - pa) represents the 
“driving force”. Integration of Equation 1 will give the quantity of 
oxygen, w, transferred in time, t. 
Jdw = U(pa - pa)/dt (2) 
Note that the “driving force”, (pa; - pa), is a constant for a given 
altitude. Then 
w = U(p a - pa)t + C (3) 
To evaluate the constant of integration, C, it is necessary to assume 
that the starting chronological time does not necessarily correspond 
with the onset of “physiological time” for this situation. That is, 
3 when t = 0; chronologically, t = physiologically. It follows that 
when t = t/, w = 0, and 
C =-U(p/-pa)t' (4) 
Whence 
w = U(pa — pa)(t +t/) (5) 
Equation 5 represents the quantity of oxygen, w, transferred in 
time, t, at a constant altitude pressure, pa. If the organism be- 
comes unconscious when a given quantity of oxygen, Wp is trans 
ferred, we have 
Wi = U(pa - PaHti + t/), (6) 
where represents the time to unconsciousness at the constant 
altitude, pa. If we assume the organism will go unconscious when- 
ever the quantity of oxygen transferred is Wp regardless of altitude 
we obtain the relation between the time to unconsciousness, tp, at 
any pressure altitude, pa: 
<Pa - Pa% +ti) (V) 
or 
(Pa - PaKti + 11> = K4 (8) 
and 
Ki / 
11 = ~ (8a) 
where 
K-, (9) 
1 U 
4 IV. FIT OF THEORETICAL EQUATION (EQUATION 8) TO EX- 
PERIMENTAL DATA 
A. Time of Consciousness (Time.to Unconsciousness) Versus 
Pressure Altitude. 
Table 1 gives the data obtained from the various references 
noted in Section VII of this paper for the time of consciousness (time 
to unconsciousness) at various pressure altitudes. 
TABLE 1. 
Pressure 
Altitude, 
Pa mm.Hg. 
Time to Con- 
sciousness, 
t]_, min. 
Source 
No. 
34.4 
0.25 
1 
41.4 
0.28 
1 
48.5 
0.33 
1 
56.5 
0.38 
1 
66.2 
0.45 
1 
77.5 
0.53 
1 
123.7 
0.83 
1 
140.0 
1.15 
2 
140.0 
0.75 
3 
168.0 
1.33 
1 
178.7 
1.50 
3 
198.2 
2.00 
1 
225.6 
3.00 
3 
267.4 
7.00 
6 
281.9 
5.00 
3 
281.9 
7.30 • 
7 
281.9 
10.00 
6 
Figure 1 is a plot of the experimental data from Table 1. on 
time of consciousness versus pressure altitude. The smooth curve 
in Figure 1 represents Equation 8 as fitted to the data by an ob- 
jective, semi-least-squares, method as follows: Equation 8 was 
expanded, then three simultaneous equations were set up and solved 
for the three constants: t'*, and K. 
5 Figure 1. 
7 A2 17 /17 
3- Pal-ll - ZPa1! “ t iSZPa + 4(pat i - Ki) = 0. 
14 14 14 
The equation of the smooth curve thus obtained is 
(322 - pa)(tx + 0.98) = 361 (10) 
and 
•> -drbr ' 
B. Time of Useful Consciousness Versus Pressure Altitude 
For practical applications in the design of controls, release 
mechanisms, and the like, it is convenient to separate the time to 
unconsciousness, tj_, into two components: to, the time of useful 
consciousness, i.e., that time after the onset of anoxia when 
deliberate and purposeful acts can be successfully carried out; 
and tg, the time of non-useful consciousness when deliberate and 
purposeful acts cannot be successfully carried out. It follows that 
the time to unconsciousness is given by 
tl=t2+t3 (ID 
Assuming that the point of demarkation between tg and to is 
reached when the quantity of oxygen transferred is wo, the equation 
relating time of useful consciousness and pressure altitude may be 
derived in the same manner as that for the time to unconsciousness 
versus pressure altitude. Hence 
(Pa - PaHt2 - tg) = K2 C12) 
Theory demands that the pressure altitude at which consciousness 
would be maintained indefinitely, p a, be the same for the two 
equations, 8 and 12. It will subsequently be shown that the data 
substantiate this argument. 
Table 2 gives the data obtained from the various references 
for the time of useful consciousness at various pressure altitudes. 
9 TABLE 2. 
Pressure 
Altitude, 
pa mm.Hg. 
Time of Useful 
Consciousness 
t2, min. 
Source 
No. 
140.0 
0.50 
2 
144.8 
0.25 
4 
154.9 
0.58 
5 
178.7 
0.77 
5 
225.6 
1.22 
5 
230.8 
1.00 
4 
267.4 
2.00 
4 
246.9 
1.83 
5 
246.9 
2.00 
2 
281.9 
5.00 
8 
307.4 
5.00 
4 
Figure 2 is a plot of the experimental data of Table 2 on time of 
useful consciousness versus pressure altitude. The smooth curve 
of Figure 2 represents Equation 12 fitted in the same manner as 
the smooth curve of Figure 1. The three simultaneous equations 
are: 
The resulting equation for the smooth curve thus obtained is 
(322 - pa)(t2 + 0.28) = 143 (13) 
and 
'2 = ~ °'28 (13a) 
10 Note that pain equations 10 and 13 for time 
and time of useful consciousness is given as 322 millimeters of 
mercury. Actually, in the solution of the three simultaneous equa- 
tions for the two situations, we obtained 321.84 and 321.63. Thus, 
the theory which demands that be a constant is substantiated by 
the data. 
Two points (reference 9) representing the time of con 
sciousness after arrest of cerebral circulation are shown 
the graphs, but were not used in fitting the experimental 
data to the theory. 
11  
13 V. APPLICATIONS OF EQUATIONS 8a AND 12a 
A. Non-Useful Consciousness Versus Pressure Altitude. 
The time of non-useful consciousness, tg, is given by Equation 
11 as the difference between the time to unconsciousness, ti, and the 
time of useful consciousness, t2- Subtracting Equation 12a irom 
Equation 8a, we have 
t3 = ti - t2 =SL-J£2,) _ (tl' _ t2'), (14) 
Pa 
from which 
*3 = r3- - ■ - t3/, (15) 
Pa - Pa 13 
where 
Kg = Ki - K2 , (16) 
and 
t3 = ti - t2/ (17) 
Equation 15 for non-useful consciousness is the same form as 
Equations 8a and 12a, all three equations being hyperbolas having 
the common asymptote, indicating the constant pressure altitude 
at which consciousness is maintained indefinitely; and three separate 
time asymptotes, tg'', and tcf, indicating the physiological onset of 
the particular phenomena. The equation for non-useful consciousness 
versus pressure altitude with the numerical constants inserted is 
then 
(322 - pa)(tg - 0.70) = 218, (18) 
and 
(16a) 
B. Relation Between Time of Useful Consciousness and Time 
to Unconsciousness. 
Eliminating the pressure altitude, p , between Equations 10a 
and 13a, we obtain 
15 t2 = 0.396 tx 4- 0.108 (19) 
as the- relation between time of useful consciousness and time to 
unconsciousness. Note that this expression is linear and that the 
time of useful consciousness is approximately four tenths the time 
to unconsciousness for all pressure altitudes. Equation 19 is plotted 
in Figure 3. 
C. Time to. Unconsciousness on..Air-ami Oxygen Versus.. 
Altitude in Feet. 
Equation 10a is plotted in Figure 4, replacing the pressure 
altitude, p«, by the appropriate altitude in feet as obtained from the 
National Advisory Committee for Aeronautics, Report No. 218, 
“Standard Atmosphere - Tables and Data”, by Walter S. Diehl. 
Also, in Figure 4, the time to unconsciousness is plotted in seconds. 
Figure 4 then gives the time to unconsciousness in seconds versus 
the altitude in feet. 
In order to obtain the curve for exposure to one hundred per 
cent oxygen, rather than air, it was necessary to obtain a relationship 
between altitudes breathing air and altitudes breathing oxygen. This 
relationship was obtained from the curve for equivalent altitudes, 
Chart A-2, “Handbook of Respiratory Data in Aviation”, CAM and 
CMR, 1944. The equation derived from this chart is 
hi qqq = 0.6h 209 + 33,800 feet, (20) 
where hi qQO Is the altitude breathing oxygen which is equivalent to 
the altitude breathing air, h#2Q9* By plotting the time to unconscious- 
ness corresponding to h>2Q9* against hi.000 as obtained from Equation 
20, the curve for time to unconsciousness against altitude when 
breathing oxygen was obtained in Figure 4. 
D. Time of Useful Consciousness on Air and Oxygen Versus 
Altitude in Feet. 
Equation 13a is plotted in Figure 5 replacing the pressure 
altitude, pa, by the appropriate altitude in feet, the time in seconds, 
and the appropriate altitude breathing oxygen in the same manner as 
the curves of Figure 4 were prepared. 
Note that in the equations for time to unconsciousness and time 
of useful consciousness, the pressure altitude at which consciousness 
may be expected to last indefinitely (in the average individual) 
16 breathing air is 322 millimeters of mercury, corresponding to 
21,913 feet, and the altitude at which consciousness may be expected 
to last indefinitely breathing oxygen is 46,948 feet, corresponding to 
a pressure altitude of 101 millimeters of mercury. 
E. Time of Useful Consciousness Versus Time to Unconscious 
mss Breathing Oxygen. 
This relationship is given by Equation 19 in which the times 
are those breathing oxygen. 
17 figure 3. 
Time to Unconsciousness 
(Minutes) 
Time of Useful Consciousness 
(Minutes) 
19 Figure 
Altitude (Thousands of feet) 
TIME TO UNCONSCIOUSNESS 
21 
Time (Seconds) Figure 5 
TIME OF USEFUL CONSCIOUSNESS 
Time (Seconds) 
23 VL SUMMARY OF EQUATIONS AND CONSTANTS 
1. Time of Useful Consciousness Breathing Air: 
to = 3-43 - .28 minutes. 
z 322 - pa 
2. Time of Non-Useful Consciousness Breathing Air: 
to = —218 _ .70 minutes. 
6 322 - pa 
3. Time to Unconsciousness Breathing Air: 
ti = — - .98 minutes. 
1 322 - pa 
4. Pressure Altitude Where Consciousness may be Just Maintained 
Indefinitely Breathing Air: 322 mm.Hg. 
5. Altitude in Feet Where Consciousness may be Just Maintained 
Indefinitely Breathing Air: 21,913 feet. 
6. Pressure Altitude Where Consciousness may be Just Maintained 
Indefinitely Breathing Oxygen: 101 mm.Hg. 
7. Altitude in Feet Where Consciousness may be Just Maintained 
Indefinitely Breathing Oxygen: 46,948 feet. 
8. Relation Between Time of Useful Consciousness and Time to 
Unconsciousness Breathing Air or Oxygen: 
tg = 0.396t]_ + .108 minutes. 
9. Times of Useful Consciousness, Non-Useful Consciousness, and 
Time to Unconsciousness Breathing Oxygen: Replace pa in air 
equations by the air equivalent pressure breathing oxygen. 
25 VII. SOURCE OF DATA 
1. Rasher, S. Experiments at Dachau. Communication to Medical 
Liaison Officer, Military Requirements Division, BuAer, Navy 
Department, from Lieutenant Commander A. H. Andrews, Jr., 
17 October 1945. 
2. Barry, Alexander. Emergency Descent from Altitude. U.S. AAF, 
Materiel Command, Engineering Division, Memorandum Report, 
5 February 1946. 
3. Evelyn, Kenneth. The Effects of Low Barometric Pressure on the 
Health of the Adult Male in the Age Group 19 - 32. National 
Research Council, Division of Medical Science, Committee on 
Aviation Medicine, Report No. 19, 3 July 1941. 
4. Aero Medical Exploitation by AAF, Germany, 1945. Studies by 
Tavel. 
5. Hoffman, C. E., Clark, R. T., Jr., and Brown, E. B., Jr. The Rates 
of Fall of Blood Oxygen Saturations at Simulated Altitudes 
Following Mask Removal: Period of Useful Consciousness and 
Time to Imminent Unconsciousness Following Change from 100% 
Oxygen to Ambient Air at Altitudes Above 28.000 Feet. BuMed 
Research Project No. X-572, 1 December 1945. 
6. Commoner, Barry. Voluntary Pressure Breathing of Ambient 
Atmosphere as a Means of Increasing the Oxygen Saturation of 
the Blood. BuMed Research Project No. X-198, 19 October 1943 
7. Houston, Charles S. U.S. Naval Air Station, Miami, Florida. 
Communication to Research Division, BuMed, Navy Department, 
22 September 1944. 
8. Bachrach, William H. Communication to Research Division, 
BuMed, Navy Department, February 1946. 
9. Rossen, R., Kabot, H. and Anderson, J. Acute Arrest of Cerebral 
Circulation in Man. Arch. Neurol, and Psychiat. 50:510-528, 
November 1943. 
26