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Ground Speed Calculation Using Wind Component Information for Trajectory Prediction

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Ground Speed Calculation Using Wind Component Information for Trajectory Prediction Volume 4, Number 3, September 2013 Journal of Convergence Ground Speed Calculation Using Wind Component Information for Trajectory Prediction 1 1 1 Yong-Kyun Kim , Deok Gyu Lee †, Jong Wook Han Hyodal Park2 1 Electronics & Telecommunications Research Institute 2 Electronic and Electrical Engineering, Inha University, Software Research Laboratory Dept. of Cyber Security #100, Inharo, Nam-gu, Incheon, Rep. of Korea Daejeon, Rep. of Korea [email protected] {Ykkim1, deokgyulee, hanjw}@etri.re.kr ` Abstract—Ground speed calculation is basic work for trajectory an arrival airport. The following simplifications are made. The prediction, conflict detection and air traffic flow management. airspace is considered as an Euclidean space, where all airports This paper proposes a novel algorithm based on Vincenty’s formulas for ground speed calculation. Our experiments used are at altitude 0. Latitudes and longitudes on the ellipsoidal simulations with wind components and our experimental results Earth’s surface are converted into (x, y) coordinates by a show that our ground speed calculation exhibits much better stereographic projection, and the altitude in feet shall be our z accuracy performance. coordinate [5]. Keywords—Ground speed, True Airspeed, Trajectory Prediction, ATFM I. INTRODUCTION The air traffic control (ATC) system improves the safety and efficiency of air traffic by preventing collisions against other aircraft and obstacles and managing an aircraft’s navigation status [1]. Air traffic demand is expected to more Fig. 1. Basic design of trajectory than double over the next 20 years [2]. The accuracy of trajectory predictions in en-route airspace impacts ATM All aircraft fly with identical performances and follow linear conflict predictions and estimated times of arrival (ETA) to slopes of climb and descent. control fixes. For the airspace user, inaccurate trajectory B. PARAMETERS FOR GROUND SPEED CALCULATION predictions may result in less-than-optimal maneuver advice in response to a given traffic management problem [3][4]. These For ground speed calculation, we must consider the concept include missed advice and false advice. Missed advice refers to of speed, speed variation due to changes in altitude and wind the lost opportunity of resolving a traffic management problem parameters. in a manner most efficient to the airspace user. False advice First, airspeed is the ground speed calculation relative to the refers to the suggestion of an unnecessary maneuver that may air. Among the common conventions for qualifying airspeed cause an aircraft to depart from its most efficient or user- are: indicated airspeed (IAS), calibrated airspeed (CAS), true preferred trajectory. In this paper, we propose a ground speed airspeed (TAS), and ground speed (GS). calculation using wind component information. The remainder of this paper is organized as follows. In the next section, IAS is the airspeed indicator reading (ASIR) uncorrected ground speed calculation techniques and the theoretical for instrument, position, and other errors. From current background about ground speed calculations are presented. We EASA(European Aviation Safety Agency) definitions, IAS describe our ground speed calculation algorithm in Section 3. means the speed of an aircraft as shown on its pitot static In Section 4 we present some experimental results of our airspeed indicator, calibrated to reflect standard atmosphere proposed scheme, and finally give our conclusions in Section 5. adiabatic compressible flow at sea level uncorrected for airspeed system errors. Most airspeed indicators show the speed in knots (i.e. II. GROUND SPEED CALCULATION TECHNIQUES nautical miles per hour). Some light aircraft have airspeed indicators showing speed in miles per hour A. GROUND SPEED CALCULATION THEORY CAS is IAS corrected for instrument errors, position error Let us first consider a fairly simplified model for our trajectory and installation errors. CAS values of less than the speed of design problem. The set of flows shall be arbitrarily chosen. A sound at standard sea level (661.4788 knots) are calculated as flow is defined as a set of flights between a departure airport and follows: 1 This research was supported by a grant (code# 07aviation-navigation-03) from the Aviation Improvement Program funded by the Ministry of Construction & Transportation of the Korean government. † Deok Gyu Lee, Corresponding Author, [email protected] Copyright ⓒ 2010 Future Technology Research Association International 1 Journal of Convergence Volume 4, Number 3, September 2013 difference between thrust and drag is the greatest (maximum é 2 ù æ Q ö 7 excess thrust). In a jet airplane, this is approximately the V = A 5êç c +1÷ -1ú (1) c 0 êç ÷ ú minimum drag speed, or the bottom of the curve of drag vs. è P0 ø ëê ûú speed. The climb angle is proportional to the excess thrust. where Climbing at Vy allows pilots to maximize the altitude gain per unit of time. That is, Vy allows pilots to maximize their VC is the calibrated speed. climb while sacrificing the least amount of time. This occurs at Q is the impact pressure sensed by the pitot tube. the speed for which the difference between engine power and C the power required to overcome the aircraft’s drag is the P0 is 29.92126 inches Hg; static air pressure at greatest (maximum excess power). Climb rate is proportional standard sea level to excess power. A0 is 661.4788 knots; speed of sound at standard sea Vx increases with altitude and Vy decreases with altitude. level Vx = Vy at the airplane’s absolute ceiling, the altitude above which it cannot climb using just its own lift. This expression is based on the form of Bernoulli’s equation applicable to a perfect, compressible gas. The values Last, we consider wind parameters. Wind parameters can P0 and A0 are consistent with the International Standard be divided into two components (weather fronts and thermal Atmosphere (ISA). wind) on a large scale. TAS is the physical speed of the aircraft relative to the air Weather fronts are boundaries between two masses of air of surrounding the aircraft. The TAS is a vector quantity. The different densities, or different temperature and moisture relationship between the TAS (Vt) and the speed with respect to properties, which are normally convergence zones in the wind the ground (Vg) is field and are the principal cause of significant weather. Within surface weather analyses, they are depicted using various V = v -V (2) t g w colored lines and symbols. where The air masses usually differ in temperature and may also differ in humidity. Wind shear in the horizontal occurs near V is the windspeed vector. w these boundaries. Cold fronts feature narrow bands of Aircraft flight instruments, however, do not compute TAS thunderstorms and severe weather, and may be preceded by as a function of groundspeed and windspeed. They use impact squall lines and dry lines. and static pressures as well as a temperature input. Basically, Cold fronts are sharper surface boundaries with more TAS is CAS that is corrected for pressure, altitude and significant horizontal wind shear than warm fronts. When a temperature. The result is the true physical speed of the aircraft front becomes stationary, it can degenerate into a line which plus or minus the wind component. TAS is equal to CAS at separates regions of differing wind speed, known as a shear standard sea level conditions. line, though the wind direction across the feature normally The simplest way to compute TAS is to use a function of remains constant. Directional and speed shear can occur across the Mach number the axis of stronger tropical waves, as northerly winds precede the wave axis and southeast winds are seen behind the wave T axis. Vt = A0 × M (3) Tc Horizontal wind shear can also occur along local land breeze and sea breeze boundaries. where M is the Mach number, T is temperature (kelvins) and T0 is standard sea level temperature (288.15 kelvins) Thermal wind is a meteorological term not referring to an actual wind, but a difference in the geostrophic wind between Second, speed variation due to changes in altitude means two pressure levels p1 and p0, with p1 < p0; in essence, wind when the aircraft climbs or descends. shear. It is only present in an atmosphere with horizontal The rate of climb (RoC) is the speed at which an aircraft changes in temperature. increases its altitude. This is most often expressed in feet per In a barotropic atmosphere, where temperature is uniform, minute and can be abbreviated as ft/min. Elsewhere, it is the geostrophic wind is independent of height. The name stems commonly expressed in meters per second, abbreviated as m/s. from the fact that this wind flows around areas of low (and The RoC of an aircraft is measured with a vertical speed high) temperature in the same manner as the geostrophic wind indicator (VSI) or instantaneous vertical speed indicator (IVSI). flows around areas of low (and high) pressure. The rate of decrease in altitude is referred to as the rate of descent or sink rate. A decrease in altitude corresponds with a ftt = K ´Ñ(f2 -f0 ) (4) negative RoC. There are two airspeeds relating to optimum rates of ascent, where φx are geopotential height fields with f2 > f0 , f is the referred to as Vx and Vy. Vx is the IAS for best angle of climb. Coriolis parameter, and k is the upward-pointing unit vector in Vy is the IAS for best RoC. Vx is slower than Vy. the vertical direction. The thermal wind equation does not determine the wind in the tropics. Since f is small or zero, such Climbing at Vx allows pilots to maximize the altitude gain as near the equator, the equation reduces to stating that per unit of ground distance. That is, Vx allows pilots to maximize their climb while sacrificing the least amount of Ñ(f2 > f0 ) is small.
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