International Standard Atmosphere (ISA)
Established in 1976, the International Standard Atmosphere is a mathematical description of a theoretical column of air. The lowest region in the ISA is the troposphere which extends from sea level (0 ft) up to 11km (about 36,000ft). The following table describes the ISA conditions at different altitudes:
|
Altitude
ft
|
Air Press.
hPa ["Hg]
|
Air Temp.
°C [°F]
|
Air Density
kg/m³
|
|
0
1000
2000
3000
4000
5000
6000
7000
8000
9000
10000
11000
12000
13000
14000
15000
16000
17000
18000
19000
20000
21000
22000
23000
24000
25000
26000
27000
28000
29000
30000
31000
32000
33000
34000
35000
36000
|
1013.25 [29.92]
977.18 [28.86]
942.12 [27.82]
908.18 [26.82]
875.14 [25.84]
843.13 [24.90]
812.02 [23.98]
781.93 [23.09]
752.74 [22.23]
724.37 [21.39]
696.91 [20.58]
670.37 [19.80]
644.63 [19.04]
619.60 [18.30]
595.49 [17.58]
572.08 [16.89]
549.38 [16.22]
527.50 [15.58]
506.32 [14.95]
485.85 [14.35]
465.99 [13.76]
446.84 [13.20]
428.30 [12.65]
410.47 [12.12]
393.14 [11.61]
376.52 [11.12]
360.41 [10.64]
344.91 [10.19]
329.91 [9.74]
315.42 [9.31]
301.44 [8.90]
288.07 [8.51]
275.10 [8.12]
262.63 [7.76]
250.68 [7.40]
239.13 [7.06]
227.98 [6.73]
|
15 [59.0]
13 [55.4]
11 [51.8]
9.1 [48.4]
7.1 [44.8]
5.1 [41.2]
3.1 [37.6]
1.1 [34.0]
-0.8 [30.6]
-2.8 [27.0]
-4.8 [23.4]
-6.8 [19.8]
-8.8 [16.2]
-10.8 [12.6]
-12.7 [9.1]
-14.7 [5.5]
-16.6 [2.1]
-18.6 [-1.5]
-20.6 [-5.1]
-22.6 [-8.7]
-24.6 [-12.3]
-26.5 [-15.7]
-28.5 [-19.3]
-30.5 [-22.9]
-32.5 [-26.5]
-34.5 [-30.1]
-36.4 [-33.5]
-38.4 [-37.1]
-40.4 [-40.7]
-42.4 [-44.3]
-44.4 [-47.9]
-46.3 [-51.3]
-48.3 [-54.9]
-50.3 [-58.5]
-52.3 [-62.1]
-54.2 [-65.6]
-56.2 [-69.2]
|
1.225
1.190
1.155
1.121
1.088
1.056
1.024
0.993
0.963
0.934
0.905
0.877
0.849
0.823
0.797
0.771
0.746
0.722
0.698
0.676
0.653
0.631
0.610
0.589
0.569
0.550
0.530
0.512
0.494
0.476
0.459
0.442
0.426
0.411
0.395
0.380
0.366
|
The ISA consists of dry air (=0% relative humidity).
Density Altitude
In reality, this air column has different characteristics than the theoretical ones above. The constant changes create different weather conditions and vice versa. At one moment in time at any given altitude, the air pressure, air temperature and relative humidity can all differ substantially from the theoretical values resulting in a totally different air density. (To calculate air density under any given condition, go to the following website: density altitude )
The definition of density altitude is the altitude at which the density of the 1976 International Standard Atmosphere is the same as the density of the air being evaluated. The height indicated on the altimeter in an aircraft shows the approximate density altitude, when the reference is set to the ISA air pressure at sea level. The altimeter only measures the air pressure and presumes the temperature is equal to the standard temperature at that altitude.
Engine performance in reality
To be able to compare performance, the power/torque curves of aircraft engines are always published under ISA conditions, so the performance graph is a theoretical one. Real engine performance can differ significantly depending on the prevailing atmospheric conditions in which it is operating!
Engine horsepower (and torque) will decrease proportionally with decreasing air density: hp2 = hp1 * (d2/d1)
where :
hp2 = the new horsepower value at density d2
hp1 = the old horsepower value at density d1
An example: An engine operating at a density altitude of 10,000ft (altimeter set to ISA reference: 1013.25hPa) which according to the manufacturer produces 100hp in ISA conditions, would effectively only produce 100hp*0.905/1.225 = 73.9hp !
If the outside temperature at a particular time deviates from the standard temperature corresponding to the density altitude found on the altimeter, then an additional correction should also be made: hp3 = hp2*T2/T3
where :
hp3 = new horsepower value at temperature T3 in Kelvin (=°C+273.15)
hp2 = old horsepower value at temperature T2 in Kelvin (=°C+273.15)
So if the real air T° the engine is taking in (at the throttle/air filter) is 2°C [36°F] instead of the standard -4.8°C [23°F], then the actual horsepower the engine would effectively be producing equals: 73.9hp*(-4.8+273.15)/(2+273.15) = 72.1hp or 2.4% less.
Although ISA specifies that the air is dry (0% humidity) this is never the case. Because of the relatively small effect the relative humidity has on the air density, we won't discuss it any further. Just keep in mind that the power will decrease slightly the more humid it gets.
The effect of a turbo normaliser
The above shows that power diminishes with increasing density altitude. Although the air temperature (usually) drops as the height increases and lower temperatures mean better performance, the positive effect of lower air T° with increasing altitude is more than offset by the decreasing air pressure. Equipping an engine with a turbo which only "normalises" the air pressure at higher altitudes to the sea-level value, can mean a large power gain at high altitudes when compared to a normal aspirated engine. Since the turbo normaliser produces a constant (sea-level) air pressure for the engine's operation inspite of the increasing density altitude, the lower T° of the increasing altitude results in performance better than sea-level power!
The following graph shows the difference in horsepower produced between a normally aspirated 100hp engine and the same engine equipped with a turbo normaliser operating in different density altitudes:
ConclusionThe published/indicated (ISA) power of an engine is the power it theoretically would have at sea level if the atmospheric conditions were equal to those of the theoretical International Standard Atmosphere. In most cases, especially in summer, a normally aspirated engine produces less power. Conversion factors need to be applied to calculate the real power output of the engine or to know how much it is capable of producing in different conditions. A simple approximation of the actual power output of an engine at any given time can be calculated using its' fuel flow. (see "Fuel consumption vs Hp"). |
