ADVANCES in DYNAMICAL SYSTEMS and CONTROL The Density Altitude. Influence Factors and Evaluation TEODOR LUCIAN GRIGORIE Avionics Department University of Craiova 107 Decebal Street, 200440 Craiova ROMANIA [email protected] http://www.elth.ucv.ro LIVIU DINCA Avionics Department University of Craiova 107 Decebal Street, 200440 Craiova ROMANIA [email protected] http://www.elth.ucv.ro JENICA-ILEANA CORCAU Avionics Department University of Craiova 107 Decebal Street, 200440 Craiova ROMANIA [email protected] http://www.elth.ucv.ro OTILIA GRIGORIE Carol I, High School 2 Ioan Maiorescu Street, 200418 Craiova ROMANIA [email protected] Abstract: - The paper presents a method to determinate the density altitude with an electronic flight instrument system. A brief review of the flight altitudes is performed, and the calculus relations of the density altitude are developed. The first two atmospheric layers (0÷11 Km and 11÷20 Km) are considered. For different indicated barometric altitudes an evaluation of the density altitude, as a function of non-standards temperature variations and of dew point value, is realized. Key-Words: - standard atmosphere; atmospheric layers; barometric formula; density-altitude; evaluation 1 Introduction altitude information on board can be made directly by Regarded as one of the most important parameters that the measuring system or through an Electronic Flight must known by the pilot during the flight, the altitude is Instrument System (EFIS). If it is determined using a defined as the distance between the centre of mass of the GPS than it can be defined as the aircraft elevation from aircraft and the corresponding point on the surface of the the reference geoid WGS 84 surface (World Geodetic Earth, considered by the vertical ground [1]. In general, System) [2]. at the board, the altitude is measured directly using the Relative to the position of the ground point taken as a altimeter, but can be also calculated by means of reference or to the corrections introduced in the complementary systems, such as, for example, the Air measuring system, the flight altitude behaves different Data Computer (ADC), the Inertial Navigation System names [3]: (INS) or Global Positioning System (GPS). Showing • true altitude (Hnm): is real altitude of aircraft above ISSN: 1790-5117 44 ISBN: 978-960-474-185-4 ADVANCES in DYNAMICAL SYSTEMS and CONTROL mean sea level (MSL); • decreasing of the aircraft maximum flight altitude, • relative altitude (Hr): is the altitude reported at an affecting their capacity to fly above the higher airfield level on which the aircraft performs take off obstacles. or landing manoeuvres; its value depends on the altimeter adjustment. • absolute altitude (Ha): in this case the reference point 2 Vapor Pressure Determination is considered at the intersection of the local vertical The density of the atmospheric air, considered dry, can and the Earth surface, so its calculation takes into be calculated with the relation account the overflowed forms of relief. This altitude is considered to have the greatest importance for ρ = µ RTp ),/( (1) flight safety. the static pressure p being measured directly. In relation • barometric altitude (pressure altitude) (Hb): this is the (1) T is the air temperature, µ - molecular mass of the air altitude indicated by the altimeter when this is tuned (µ=0.0289644 kg/mol), and R is the gas universal on a basic pressure, so the reference point is constant (R=8.31432 N·m/(mol·K)). In real conditions, positioned on a baric surface. If the reference pressure this density is affected by the humidity in the air, which is 760 mmHg it corresponds to the mean sea level in is considered to be a mixture of dry air molecules and the International Standard Atmosphere (ISA) [4]. water vapor. So, the measured barometric pressure is in • density altitude (Hρ): is the barometric altitude fact the mixture pressure not the dry air pressure. Thus, corrected for non-standard temperature variations. to determinate the density of the dry air the Dalton This corresponds to the altitude at which the density partial pressures law must be used. In this way, the of air is equal to ISA air density evaluated for the mixture pressure is expressed as the sum of the dry air current flight conditions. and water vapor pv pressures • indicated altitude (H): is the altitude displayed on the = + ppp . (2) dashboard. am v One of the altitudes of great importance, calculated from It results the barometric altitude, is the density altitude (Hρ). Strongly influenced by changes in temperature and to a = − ppp vam (3) lesser extent by changes in air humidity, the real air density can provides to the pilot vital information for the and the relation (1) for the density calculation becomes flight safety. It is known that the density of air is the vam µ−=ρ RTpp )./()( (4) most important factor influencing the performances of aircraft both at the lift forces level, and at the thrust As a consequence, the dry air density calculation forces level generated by the propulsion systems. supposes to know the actual air pressure (the mixture Density altitude is such a simple way to give the pilot pressure pam), the water vapor pressure pv and the local information on air density, this parameter being temperature T of the atmospheric air. The Mixture calculated such as the pilot can make a coarse pressure and the temperature of local atmospheric air is assessment of aircraft performance in the current flight determined relatively easily by placing the sensors conditions [5]. For example, the increase of the outside the aircraft. Instead, the vapor pressure temperature or of the humidity of the outdoor determination involves the performing of numerical environment in which is operated aircraft lead to lower calculations using information on relative humidity and air density [5], [6], which are as a consequence (as dew point [8]. defined by the density altitude) the indication of a According to [8], two relations often used in the density altitude higher than the current indicated calculation of vapor pressure from the dew point: barometric altitude. a) The first relation shows a high accuracy and is based Therefore, the pilot should expect the following effects on a polynomial development on the aircraft [5], [6], [7]: C (5) pv = 8 , • lift decreasing and the need to increase the flight 0 1 2 3 4 5 6 7 ((((((((( 8 ⋅+++++++++ ctctctctctctctctctc 9 ))))))))) speed to maintain the desired lift; o where t is the dew point expressed in C, C=610.78, c0= • decreasing of the propulsion systems power, and, -2 -4 =0.99999683, c1=-0.90826951·10 , c2=0.78736169·10 , thus, decreasing of the thrust forces; -6 -8 c3=-0.61117958·10 ,c4=0.4388418·10 ,c5=-0.29883885 • runway acceleration decreasing because of the low -10 -12 -14 ·10 ,c6=0.2187442·10 , c7=-0.1789232·10 , c8=0.111 thrust; 1201·10-16, c = -0.30994571·10-19. 9 • increasing of the take off distance and decreasing of b) The second relation, much easier, is generally used in the climb speed; applications that require a lower accuracy ISSN: 1790-5117 45 ISBN: 978-960-474-185-4 ADVANCES in DYNAMICAL SYSTEMS and CONTROL c t/( c t ) 1⋅ 2 + layer 0). In this situation, the barometric formula, that pv = C ⋅10 , (6) gives the dependence of the static pressure p by the with C=610.78, c1=7.5 and c2=237.3. For both relations altitude Hb, is expressed under the form [1] the pressure pv measure unity is Pascal. −µg/( R τ0 ) In Fig. 1 are represented graphically the dependences p= p0(1 + τ 0 ( Hb − H b0 )/ T 0 ) , (8) p =f(t) between vapor pressure and dew point, given by v p =101325N/m2=760mmHg is the static pressure for the the relation (5), respectively the difference ε between the 0 altitude Hb0. So, for the atmospheric layer 0, the pressure pv values calculated with relations (5) and (6). To be more suggestive the characteristics were designed following equations system is obtained for pressures represented in mmHg. ρ = pµ /, RT Dependence pv=f(t) analysis combined with the equation TTHH= + τ( − ), (9) (4) confirming earlier observations that the most 0 0 b b0 −µg/( R τ0 ) disadvantageous circumstances for flying are those with p= p0(1 + τ 0 ( Hb − H b0 )/ T 0 ) . high humidity (positive dew point). For these cases the Successively eliminating the temperature and the vapor pressure can reach up to 42 mmHg, the growth pressure between the three equations is obtained the being exponential. On the other hand, on observes that formula for calculating the density altitude in the form the differences between the two methods of calculation (H becomes H ) are very small (up to 0.012 mmHg). Analyzing both b ρ R/( g R ) graphs shows that for positive dew points can be used HHT= −( / τ )[1 −( ρRT /( p µ ))− τ0 µ + τ0 ], (10) without problems relation (6) in high accuracy ρ b0 0 0 0 0 applications. Instead, in such applications, for negative which, numerically, is values of dew point, especially for those below -20oC, it H =4.433076 ⋅ 104 ⋅ [1 − 0.953434 ⋅ρ0.234969 .] (11) is necessary to use formula (5) because the relative error ρ caused by the simplified formula is high, reaching up to In previous relation the density values are entered in 4%. kg/m3, and the resulting density altitude values are in m. 50 0.015 Representing graphically the density altitude for the 40 0.01 change ∆t of environmental temperature outside the aircraft (in the range -30oC÷30oC from the standard 30 0.005 values in ISA) and for different values of dew point t [mmHg] [mmHg] v 20 0 o o ε p (between -50 C÷35 C), the three-dimensional character- 10 -0.005 ristics in Fig.