=0.312 kg/m3
Cabin Altitude
Cabin altitude is a term used to express cabin pressure in terms of equivalent altitude above sea level. For example, a cabin altitude of 6,000 feet means that the pressure inside the aircraft cabin is the same as the atmospheric pressure at an altitude of 6,000 feet. Looking at the Standard Atmosphere Table (table 2.6), the pressure is found to be 1,696 Ibs/ft2 which upon division by 144 gives the pressure in Ib/in2 to be 11.78 Ibs/in2
At a cabin altitude of 8,000 feet, the passengers and crew can ride in relative comfort without any special oxygen supply. Planes which fly at much higher altitudes than 8,000 feet must be furnished with a special atmosphere control system. It is highly advantageous to fly at high altitudes both for economy of fuel consumption, and the smooth air high above the level of turbulent weather systems. At these high altitudes, the pressure outside the plane can be significantly lower than the cabin pressure.
At 8,000 ft., the Standard Atmosphere Table tells us that the air pressure is 1,572 Ibs/ft2 or 10.92 Ibs/in2 This is the pressure that is normally maintained in the cabin even though the plane is flying at a higher altitude.
Suppose the plane is flying at an altitude of 40,000 ft. At this altitude the pressure (from the table 5-1) is 393 Ibs/ft2 or 2.73 Ibs/in2 This means that for a cabin altitude of 8,000 ft. for a plane flying at 40,000 ft., there is a net outward pressure of 8.19 Ibs/in2 This number was obtained by subtracting 2.73 Ibs/in2 from 10.92. For a Learjet with a pressurized area of 45,000 in2, we are dealing with a bursting force of over 368,000 Ibs. (8.19 x 45 thousand), in addition to being able to withstand this much force, a safety factor of 1.33 is generally used by design engineers. Therefore, the pressurized portion of the fuselage must be constructed to have an ultimate strength of over 460 thousand pounds or about 230 tons. The challenge of finding lightweight materials which can withstand these large forces is great.
In the description of an aircraft's air conditioning and pressurization system, a differential pressure is given.
The differential pressure is the maximum difference between cabin pressure and atmospheric pressure which the pressurization system can sustain. For example, the air-cycle air-conditioning system of a Boeing 747 can maintain a pressure differential of 8.9 Ibs/in2 This means that the system can maintain a cabin pressure 8.9 Ibs/in2 greater than the atmospheric pressure surrounding the plane. This also means that there is an upper limit imposed by the pressurization system on the altitude at which the plane can fly.
Standard Atmosphere — English Units
Altitude (ft.) Temperature (°R) Pressure (Ib./Ft2) Density (Slug/Ft3)
0 519 2,116 0.002377
500 517 2,078 0.002342
1,000 515 2,041 0.002308
2,000 512 1,968 0.002241
3,000 508 1,897 0.002175
4,000 504 1,828 0.002111
5,000 501 1,761 0.002048
6,000 497 1,696 0.001987
7,000 494 1,633 0.001927
8,000 490 1,572 0.001869
9,000 487 1,513 0.001811
10,000 484 1,456 0.001756
15,000 465 1,195 0.001496
20,000 447 973 0.001267
25,000 430 786 0.001066
30,000 412 630 0.000891
35,000 394 499 0.000738
40,000 390 393 0.000585
45,000 390 309 0.000462
50,000 390 244 0.000364
55,000 390 192 0.000287
60,000 390 151 0.000226
65,000 390 119 0.000178
Table 2.6: Quantities within the Standard Atmosphere (English Units)
Standard Atmosphere — Metric Units
Altitude Temperature Pressure Density
(M) (K) (kPa) (kg/m3)
0 288 101.3 1.225
100 288 100.1 1.213
200 287 98.9 1.202
300 286 97.8 1.190
400 286 96.6 1.179
500 285 95.5 1.167
600 284 94.3 1.156
700 284 93.2 1.145
800 283 92.1 1.134
900 282 91.0 1.123
1,000 282 89.9 1.112
1,500 278 84.6 1.058
2,000 275 79.5 1.007
2,500 272 74.7 0.957
3,000 269 70.1 0.909
3,500 265 65.8 0.863
4000 262 61 7 0819
4,500 259 57.8 0.777
5,000 256 54.0 0.736
5,500 252 50.5 0.697
6,000 249 47.2 0.660
6,500 246 44.1 0.624
7,000 243 41.1 0.590
7,500 239 38.3 0.557
8,000 236 35.7 0.526
8,500 233 33.2 0.496
9,000 230 30.8 0.467
9,500 227 28.6 0.439
10,000 223 26.5 0.414
12,000 217 19.4 0.312
14,000 217 14.2 0.228
16,000 217 10.4 0.166
18,000 217 7.57 0.122
20,000 217 5.53 0.0889
22,000 217 4.04 0.0650
Table 2.7: Quantities within the Standard Atmosphere (Metric Units)
Humidity
Some water in the form of invisible vapour is intermixed with the air throughout the atmosphere. It is the condensation of this vapour which gives rise to most weather phenomena: clouds, rain, snow, dew, frost and fog. There is a limit to how much water vapour the air can hold and this limit varies with temperature. When the air contains the maximum amount of vapour possible for a particular temperature, the air is said to be saturated. Warm air can hold more vapour than cold air. In general the air is not saturated, containing only a fraction of the possible water vapour.
The amount of vapour in the air can be measured in a number of ways. The humidity of a packet of air is usually denoted by the mass of vapour contained within it, or the pressure that the water vapour exerts. This is the absolute humidity of air. Relative humidity is measured by comparing the actual mass of vapour in the air to the mass of vapour in saturated air at the same temperature. For example, air at 10°C contains 9.4 g/m3 (grams per cubic metre) of water vapour when saturated. If air at this temperature contains only 4.7 g/m3 of water vapour, then the relative humidity is 50%.
When unsaturated air is cooled, relative humidity increases. Eventually it reaches a temperature at which it is saturated. Relative humidity is 100%. Further cooling leads to condensation of the excess water vapour. The temperature at which condensation sets in is called the dew point. The dew point, and other measures of humidity can be calculated from readings taken by a hygrometer. A hygrometer has two thermometers, one dry bulb or standard air temperature thermometer, and one wet bulb thermometer. The wet bulb thermometer is an ordinary thermometer which has the bulb covered with a muslin bag, kept moist via an absorbent wick dipped into water. Evaporation of water from the muslin lowers the temperature of the thermometer. The difference between wet and dry bulb temperatures is used to calculate the various measures of humidity.
Definitions
Absolute humidity: The mass of water vapour in a given volume of air (i.e., density of water vapour in a given parcel), usually expressed in grams per cubic meter
Actual vapour pressure: The partial pressure exerted by the water vapour present in a parcel. Water in a gaseous state (i.e. water vapour) exerts a pressure just like the atmospheric air. Vapour pressure is also measured in Millibars.
Condensation: The phase change of a gas to a liquid. In the atmosphere, the change of water vapour to liquid water.
Dewpoint: the temperature air would have to be cooled to in order for saturation to occur. The dewpoint temperature assumes there is no change in air pressure or moisture content of the air.
Dry bulb temperature: The actual air temperature. See wet bulb temperature below. Freezing: The phase change of liquid water into ice. Evaporation: The phase change of liquid water into water vapour. Melting:
The phase change of ice into liquid water.
Mixing ratio: The mass of water vapour in a parcel divided by the mass of the dry air in the parcel (not including water vapour).
Relative humidity: The amount of water vapour actually in the air divided by the amount of water vapour the air can hold. Relative humidity is expressed as a percentage and can be computed in a variety of ways. One way is to divide the actual vapour pressure by the saturation vapour pressure and then multiply by 100 to convert to a percent.
Saturation of air: The condition under which the amount of water vapour in the air is the maximum possible at the existing temperature and pressure. Condensation or sublimation will begin if the temperature falls or water vapour is added to the air.
Saturation vapour pressure: The maximum partial pressure that water vapour molecules would exert if the air were saturated with vapour at a given temperature. Saturation vapour pressure is directly proportional to the temperature.
Specific humidity: The mass of water vapour in a parcel divided by the total mass of the air in the parcel (including water vapour).
Sublimation: In meteorology, the phase change of water vapour in the air directly into ice or the change of ice directly into water vapour. Chemists, and sometimes meteorologists, refer to the vapour to solid phase change as "deposition."
Wet bulb temperature: The lowest temperature that can be obtained by evaporating water into the air at constant pressure. The name comes from the technique of putting a wet cloth over the bulb of a mercury thermometer and then blowing air over the cloth until the water evaporates. Since evaporation takes up heat, the thermometer will cool to a lower temperature than a thermometer with a dry bulb at the same time and place. Wet bulb temperatures can be used along with the dry bulb temperature to calculate dew point or relative humidity.
Problems
1. Verify, that using the Gas Law (p = P/RT) and the temperature and pressure from the Standard Atmosphere Table, at an altitude of 65,000 ft., the density of air is 0.000178 slug/ft.3
2. A pressurized Cessna Centurion II has a cabin pressurization system which can maintain a pressure differential of 3.45 Ibs/in2 What is the maximum altitude at which the plane can fly and still maintain a cabin altitude of 8,000 feet?
3. (Hint: convert the of 3.45 Ibs/in2 to Ibs/ft2 and compare with the Standard Atmosphere table) What is the maximum altitude at which this same Cessna plane can fly and maintain a cabin altitude of 6,000 ft?
Answers
2. About 18,000 ft 3. About 14,000 ft