Introduction to Flight Testing. James W. Gregory
altitude is defined, in aviation terms, as the pressure altitude corrected for non‐standard temperature. If the temperature on a given day at a particular altitude is hotter than the standard temperature, then the density altitude will be higher. In engineering terms, density altitude is defined as the altitude corresponding to a given density in the standard atmosphere. Aircraft performance depends significantly on local air density, so density altitude is a direct indication of aircraft performance. Higher density altitude (corresponding to lower density) will lead to longer takeoff ground roll, slower rates of climb, higher true airspeed for stall, etc.
Finally, pilots are also concerned with the height of the aircraft above the local terrain, which is termed absolute altitude. In the aviation realm, absolute altitude is often also termed height above ground level, so the acronym AGL is often used. On aviation charts, both true altitude (MSL) and absolute altitude (AGL) are reported for various obstacles. For example, the top of a 500‐ft tall radio tower mounted on ground that is 1500 ft above sea level will have a maximum height of 2000 ft MSL or 500 ft AGL. Thus, pilots pay close attention to the absolute altitude (also referred to as QFE) as well as the true altitude (QNH). Note that absolute altitude (AGL) in an aviation context is not the same as absolute altitude (hA) in an engineering context. The engineering definition of absolute altitude is seldom used in aerospace or aviation, outside of discussions of the standard atmosphere.
A selection of the most significant of these altitudes is illustrated in Figure 2.8. The aircraft depicted in this figure is cruising at a true altitude of 5000 ft (MSL), but because its flight is over mountains rising 2000 ft above sea level, the aircraft is at an absolute altitude of only 3000 ft AGL. On this given day, the local barometric pressure reading is lower than standard, causing the pressure altitude to be higher than the true altitude. And, if the temperature on this day is higher than standard, then the density altitude will be even higher than pressure altitude or true altitude. Thus, we could easily have a situation where absolute altitude, true altitude, pressure altitude, and density altitude are all different. In Chapter 3, as we move into instrumentation used for flight testing, we will discuss the operation of the altimeter in greater detail.
Figure 2.8 Illustration of different altitudes used in aviation.
Nomenclature
atemperature lapse rate, dT/dhcchordggravitational accelerationggravitational acceleration at sea levelhgeopotential altitudehAabsolute altitude (height relative to the center of the Earth)hGgeometric altitude (height above mean sea level)kconstant, a/TSLmmass of air in the control volumenconstant, −g/aRppressureRgas constant for airrEarthEarth's mean radiusRecReynolds number based on chordSviscSutherland's constantTtemperatureU∞freestream velocityWweight of air in the control volumexlength of control volume elementywidth of control volume elementβconstant used in Sutherland's Lawδpressure ratio, p/pSLμdynamic viscosityνkinematic viscosityρdensityσdensity ratio, ρ/ρSLθtemperature ratio, T/TSL
Subscripts
refreference conditions at the base of a given atmospheric layerSLsea leveltroptropopause1beginning of an atmospheric layer2end of an atmospheric layer
Acronyms and Abbreviations
AGLheight above ground levelICAOInternational Civil Aviation OrganizationMSLheight above mean sea levelNOAANational Oceanic and Atmospheric Administration
References
1 Anderson, J.D. Jr. (2016). Introduction to Flight, 8e. New York: McGraw‐Hill.
2 Carmichael, R. (2018). Public domain aeronautical software for the aeronautical engineer. http://www.pdas.com/atmos.html (accessed 28 December 2020).
3 ICAO (1993). Manual of the ICAO Standard Atmosphere (Extended to 80 Kilometres (262 500 Feet)), 3e, ICAO Document 7488. Montréal, QC: International Civil Aviation Organization.
4 NOAA, NASA, and USAF (1976). U.S. Standard Atmosphere, 1976, NOAA‐S/T‐76‐1562, NASA‐TM‐X‐74335. Washington, DC: U.S. Government Printing Office. http://hdl.handle.net/2060/19770009539.
5 Sartorius, S. (2018). Standard Atmosphere Functions, v. 2.1.0.0. MathWorks File Exchange. https://www.mathworks.com/matlabcentral/fileexchange/28135-standard-atmosphere-functions.
6 Sutherland, W. (1893). LII. The viscosity of gases and molecular force. The London, Edinburgh, and Dublin Philosophical Magazine and Journal of Science, Series 5 36 (223): 507–531. https://doi.org/10.1080/14786449308620508.
Notes
1 1 There have been many iterations of the U.S. Standard Atmosphere over the years. The original version was published in 1958, and as scientific understanding of the atmosphere advanced, was updated in 1962, 1966, and finally 1976. Some older versions of the standard atmosphere persist today – for example, Anderson (2016) continues to refer to a 1959 definition of the standard atmosphere from the U.S. Air Force. However, the 1976 U.S. Standard Atmosphere and the 1993 ICAO standard atmosphere are widely accepted as the appropriate standards to use today.
2 2 There are two different definitions of absolute altitude that we will use in this chapter. The first one, considered here, is for development of the standard atmosphere. The second definition is widely used in aviation as the height above ground level. We will clarify these distinctions at the end of this chapter.
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