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4.4 Secondary psychrometric calculations for aircraft ventilation
4.4.1 Consignment “flags”
A group of parameters discussed in this section were considered as “flags” for allowable consignment conditions. These parameters included Effective Temperature ET, Upper Critical
Temperature UCT and Wet Bulb Temperature WBT. The results of the various calculations for these parameters are included in the ESC results for each hold. However, the validity of
using various parameters as black and white decision factors for what is considered short haul transportation is questionable. In particular, high ET values for flights of eight to ten hours do not
present a significant issue unless those conditions were present before the flight and continue for a considerable time after the flight i.e. days not hours. Of all the parameters, WBT was chosen
as the primary go no-go decision factor in Version 2 of LATSA primarily because of its acceptance in the HotStuff software used in assessment of sea freight of livestock shipments.
While parameters such as Temperature Humidity Index THI and UCT remain in the ECS results they are provided as guidance only and should not be considered as primary decision factors
regarding consignments. Many of the preceding computations rely on known or calculated values for various
psychrometric or environmental variables. The standard equations used to calculate the specific heat of air, mixing ratio, and air density are detailed below as well as the most appropriate
methodologies for other parameters found in the literature review process see Section 3.2.
4.4.2 Specific heat of air
The specific heat of moist air c
p
is given by:
r c
c
pd p
3
10 84
. 1
1
Equation 29
Where: c
pd
= specific heat of dry air Jkg°K; =
1004.67 Jkg°K;
and r = mixing ratio of water vapour gkg.
4.4.3 Mixing humidity ratio
The mixing ratio of water vapour in the hold atmosphere can be determined with reasonable accuracy on the basis:
100 or
100
s s
r RH
r r
r RH
Equation 30
Where: RH
= relative humidity ; and r
s
= mixing ratio at saturation gkg.
s s
s
e P
e r
622
.
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Equation 31
Where: e
s
= saturation vapour pressure kPa.
T
K K
e
s
1 273
1 5423
exp 611
.
Equation 32
Where: T =
temperature °K.
4.4.4 Air density
In level flight, the atmospheric pressure in the cabin and pressurised holds of a modern aircraft are less than at sea level. The density of air in an aircraft hold under cruise conditions can
therefore be determined as:
sl sl
P P
Equation 33
Where: ρ
= density of air in the aircraft hold kgm³; P
= atmospheric pressure in the aircraft hold kPa; P
sl
= atmospheric pressure at sea level kPa; and ρ
sl
= density of air at sea level kgm³. The density of air at sea level is normally assumed to be 1.225 kgm³, and the atmospheric
pressure is similarly assumed to be 101.325 kPa. Typically the atmospheric pressure in an aircraft hold is held at around 85 of sea level pressure, although the precise operational
atmospheric pressure in the aircraft cabin and holds varies with aircraft make and model, and can be further regulated, within certain parameters, by aircraft engineers and the flight crew.
4.4.5 Ventilation rates
In the many older industry publications, as well as IATA standards, the ventilation rates in aircraft are expressed in terms of the number of times the entire volume of air in the passenger cabin or
cargo hold is being notionally replaced each hour n.b. this assumes an empty cabin or hold,
with a completely mixed, non-stratified atmosphere in that space. The ventilation rate units applied in these publications and standards are typically air changes per hour ACH.
In version 2 of LATSA, the ventilation rates in the calculations rely on the use of SI volumetric
e.g. m³hr or mass e.g. kgs units, rather than ACH units. Thus it was necessary to convert the published ACH values to SI volumetric units. This was done using the following equation.
3600 ACH
V F
v
Equation 34
Where: F
v
= ventilation rate m³s; V
h
= empty hold volume m³; and ACH
= air changes per hour ACH.
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As well as ACH values, the IATA standards list the empty cargo hold volumes for Boeing aircraft. Unfortunately this volumetric flow data level is not available in the IATA standards for Airbus
aircraft, and in most cases it was not possible to obtain SI unit values to verify those derived from version 1 of LATSA. Other sources of spatial hold data consulted in this process included MAC
1984, Mikolajczak Moore 2001, Boeing 2003 and Airbus 2004. To derive ventilation rates expressed in terms of unit mass, the SI unit volumetric rates were
adjusted for the nominal operational air pressure in the cabin or hold under cruise conditions. While typically around 85 kPa, these values do vary slightly for different makes and models of
aircraft, and so the representative values used in version 2 of LATSA were generally derived from manufacturer’s specifications or the like see Section 9.2 Appendix 2 – Aircraft Data
Tables. For calculations that require the velocity of air movement within the hold
e.g. the lower critical temperature for the consigned species, that velocity was estimated using the volumetric flow
rate and the cross sectional area of the hold at the loading positions for ULDs. Cross-sectional areas for different makes and models of aircraft were obtained by digitising cross-sectional
drawings of main and lower holds provided in manufacturer’s airport planning publications e.g.
Boeing’s 2002 747-400 Airplane Characteristics for Airport Planning or Airbus’ 2009 A380
Airplane Characteristics. In the digitising process the US unit dimensions were converted to SI units, prior to the area of a polygon the same shape as the hold perimeter being calculated.
Error Reference source not found. provides an example of the process applied; in this case for the main hold in an Airbus A330-200F.
0.5 1
1.5 2
2.5 3
3.5 4
4.5 5
5.5 Metres
0.5 1
1.5 2
2.5
Me tr
es
0.5 1
1.5 2
2.5 3
3.5 4
4.5 5
0.5 1
1.5 2
Boundary 1: length: 13.6804, area: 11.1424, vertices: 25
Figure 7: Cross-sectional area of a A330-200F main hold
In an aircraft cargo hold, the effective ventilation rate will be affected by the volume of air in the hold that is displaced by the cargo. Consequently it is the headspace air, or the free air volume
in the hold that is actually being changed by the ventilation system. In version 2 of LATSA the headspace volume is therefore considered to be the difference between the empty hold volume,
and the combined volume of the volumetrically-largest of the ULDs able to be held at each available loading position in the hold.
4.4.6 Wet bulb
temperature
By themselves temperature and humidity do not provide a reliable indicator of thermal comfort or the relative risk of heat stress in animals. Concepts such as web bulb temperature and effective
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temperature
16
have been developed to provide a better indication of their combined effects in humans.
Since the latent heat used for evaporation comes from the sensible heat associated with the cooling, then:
w v
w d
p
r r
L T
T c
Equation 35
Where: c
p
= specific heat of moist air Jkg.°K; T
d
= dry bulb temperature °C or °K; T
w
= wet bulb temperature °C or °K; L
v
= latent heat of vaporisation Jkg; and r
w
= wet bulb mixing ratio water:air as gkg. If the temperatures in
Error Reference source not found. have units of °C, the ambient mixing
ratio is given by:
w d
w
T T
r r
4
10 0224
. 4
Equation 36
The wet bulb mixing ratio is further given by:
1 5
. 243
67 .
17 exp
631 .
1 622
.
w w
w
T T
P r
Equation 37
Where: P
= atmospheric pressure kPa. While the above equations are useful for estimating the mixing ratio humidity from the wet bulb
temperature, the converse is not true, and Normand’s Rule or Theorem needs to be applied to provide an estimate of
T
w
when the mixing ratio is known. This method of estimating, using Normand’s Rule, is computationally complex, involving the further estimation of the lifting
condensation level or more simply a parcel of air’s saturation point as a result of cooling and the dew point temperature. Consequently a number of authors have provided regression
equations that allow estimation of T
w
using simpler regression equations, as well as using more readily quantifiable variables. Martinez 1994 provides a polynomial regression equation that
provides one such approximation of T
w
. This method uses the following equations:
16
The effective temperature is numerically equal to the temperature of still, saturated air which induces an identical sensation
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97 .
23 .
662 966
. 100
45 .
1480 65
. 8264
1 27
4 2
27 4
2
3 1
2 1
3 2
3 1
2 1
3 2
S T
e RH
Q S
Q Q
S Q
Q T
d s
w
Equation 38
Where: RH
= relative humidity ; e
s
= saturation vapour pressure kPa; and ρ
= air density kgm³.
Error Reference source not found. has been used in the calculation of WBT in version 2 of LATSA and its use as a primary decision factor “Consignment Flag” is discussed in Section 4.9.
4.4.7 Effective temperature
To date the most utilitarian, non-specific approach available in livestock is provided by the Temperature Humidity Index THI, which was originally developed by Thom in 1959.
2 .
41 36
.
p d
T T
THI
Equation 39
Where: T
p
= dewpoint temperature °C; THI values derived from the above equation serve as the basis for the Livestock Weather Safety
Index LWSI; LCI, 1970 and have been used by the U.S National Weather Service for advisories USDC-ESSA, 1970. Widely recognised thresholds for the LWSI LCI 1970 are
listed in Table 6 below. These thresholds have been principally applied to dairy and beef cattle held under intensive conditions in the US.
Table 6: THI category thresholds
Safety index THI
Normal 74
Alert 75 to 78
Danger 79 to 83
Emergency 84
While these thresholds have been considered appropriate over a number of years, there has been considerable ongoing analysis and development Mader et al, 2006. As an example “
THI- hrs analysis of the 1995 heat wave and others have reinforced the LWSI thresholds for
categories of risk, and support an environmental profile for single heat wave events that create conditions likely to result in deaths of Bos-taurus cattle in feedlots: 15 or more THI-hrs per day for
three or more successive days at or above a base level of 84 Emergency category of the LWSI with minimal or no night time recovery opportunity. Death losses can be expected if shade,
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precautionary wetting, or other relief measures are not provided during such conditions.” Hahn et al, 2006.
It is therefore important to note that the emergency level recommended in LWSI can be exceeded for lengthy periods during the “day” if respite is available at “night”. In the case of
livestock transportation by air, both the limited length of the flight and in-flight environmental control systems may provide sufficient respite to overcome significant “short term” heat stress.
Heat tolerance will also vary between species and the values in Table 6 should be considered against the period of exposure. It may be more effective to consider the accumulated heat load
over time as exposure to higher THI may occur for relatively short periods of time without any noticeable impact. The impact of high exposure could be more noticeable during loading, take-
off and landing were ESC systems are generally curtailed. A modified form of Equation 39 generates similar index values based on dry bulb temperature
T
d
and relative humidity RH
17
are provided by the following equation Hahn et al., 2009:
4 .
46 4
. 14
8 .
d d
T RH
T THI
Equation 40
This latter method, Equation 40, is used in version 2.0 of LATSA to provide an estimate of the effective temperature however the calculations rely only on the temperature of the hold and its
relative humidity. In addition to an expansion to the notion of accumulated heat load, it has been previously stated
that the exit temperatures and moisture loads calculated using the above methods may over state the actual conditions in the hold which may place doubt on any firm reliance on THI as an
environmental indicator. It should also be noted that the use of THI was developed for the external impact of weather systems and not for enclosed, controlled environments.
17
Identical THI values can be obtained using dry bulb temperature in combination with either dew-point and wet bulb temperatures both alternative measures of humidity in analogous equations
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4.5 Validation of animal factor algorithms
Kategori