Ground Speed Calculation Using Wind Component Information for Trajectory Prediction

Volume 4, Number 3, September 2013 Journal of Convergence

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]

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. This equation basically describes the ground distance. This occurs at the speed for which the existence of the jet stream, a westerly current of air with

maximum wind speeds close to the tropopause which is (even Given the coordinates of the two points (φ1, λ1) and (φ2, λ2) though other factors are also important) the result of the Vincenty’s inverse method finds the azimuths α1, α2 and the temperature contrast between the equator and the poles. ellipsoidal distance s by calculating the reduced latitude U1 arctan[(1 - f ) tanj ] arctan[(1 - f ) tanj ] ( 1 , U2( 2 , and L, and setting the initial value of λ= L, then iteratively evaluating the following III. PROPOSED GROUND SPEED CALCULATION ALGORITHM equations until λ converges. This section describes the method of computing the various parameters used to compute the flight plan and our GS 2 2 sins = (cosU 2 sin l) + (cosU1 sinU 2 - sinU1 cosU 2 cosl) (7) calculation algorithm. First of all, we need coordinates of the waypoint and to coss = sinU sinU + cosU cosU cosl (8) create the aircraft’s path and then the wind components and 1 2 1 2 the aircraft’s airspeed used to calculate the GS of the actual s = arctan(sins / coss ) (9) aircraft.

2 cos(2s m ) = coss - (sinU1 sinU 2 / cos a) (10)

sina = [(cosU1 cosU 2sin l)/(sins )] (11)

cos 2 a = 1- sin 2 a (12)

C = (1/16)cos 2 a[4 + f (4 - 3cos 2 a)] (13)

2 l = L + (1 - C) f sin a{s + C sin s [cos(2sm) + C cos s (-1 + 2 cos (2sm)]} (14)

When λ has converged to the desired accuracy, the following are evaluated:

Fig. 2. GS calculation methods 2 2 U = COS a[(a2 - a1 ) / b2 ] (15) Waypoints consist of latitude and longitude. Accordingly, to measure the distance between waypoints over a flight A = 1+ (u 2 /16384){4096 + u 2 [-768 + u2(320 -175u 2 )]} (16) information region, the curvature of the Earth must be taken into consideration. B = (u 2 /1024){256 + u 2 [-128 + u 2 (74 - 47U 2 )]} (17) As a rough estimate, we could assume the Earth is a sphere.

Ds = B sins{cos(2sm) + 0.25B[coss (-1+ 2cos 2 (2sm) (18) dN = Rqf (5)

(-3 + 4sin 2s )(-3 + 4cos 2(2sm))]} dE = R cosqfl (6)

s = bA(s - Ds ) (19) where R is the radius of the Earth (average of 6378.1 km) and the differences in latitude and longitude are in radians, the a1 = arctan[(cosU 2 sin l) /(cosU 2 sinU 2 - sinU 2 cosU 2 cos l) (20) distance is 447.47 km. This method is a valid assumption over very small distances; however, over large distances we need to a = arctan[(cosU sin l) /(- sinU cosU + sinU cosU cos l) (21) account for the non-uniformity of the Earth. The Earth is not 2 2 2 2 2 2 actually a sphere; it is an ellipsoid of revolution, 21 km shorter in the north–south direction than the east–west direction. Then the azimuths (α1, α2) and distance s can be computed.

The flattening at the poles is caused by the centrifugal force of the spinning Earth. Because of this flattening, the radius if IV. EXPERIMENTAL RESULTS OF PROPOSED SCHEME the Earth is not a constant value as we assume for Spherical The performance of the GS calculation algorithm is Earth coordinates. measured using wind components and the aircraft’s airspeed. A more accurate method of measuring the distance between two points on the surface of the Earth is Vincenty’s Formula. It is accurate to 0.5 mm over a distance of a few centimeters to TABLE 1. SIMULATION DATA nearly 20,000 km. Aircraft’s Airspeed (TAS) 100 [Knot] Wind Component Speed: 15 [Knot] Direction: 320 [Degree]

Start Fix Location SEL(N372449, E1265542) End Fix Location BELMI(N371249, E1265929)

First of all, the start position and airspeed are needed. The start position consists of the latitude and longitude. To use the GS algorithm, the predicted GS and estimates time are as shown in Figure 3.

Fig. 5. Simulation results (climb rate [degree])

V. CONCLUSION

In this paper we proposed a GS calculation using wind component information.

Experimental results show that our GS calculation exhibits Fig. 3. Simulation result much better accuracy performance. The applicability of the proposed algorithm is manifold during trajectory prediction and modeling, such as in aeronautical traffic flow management TABLE 2. SIMULATION DATA WITH CLIMB RATE (ATFM) systems and vehicle trajectory prediction. Aircraft’s Airspeed 100 [Knot] (TAS) From now on, it is further suggested that the proposed Wind Component Speed: 50 [Knot] algorithm may be extended to trajectory modeling, which may Direction: 300 [Degree] further improve the 4D trajectory prediction. Start Fix Location N372449, E1265542 End Fix Location N371249, E1265929 ACKNOWLEDGMENT Climb Rate 7160.771 [ft/min], This research was supported by a grant (code# 07aviation- 45 [Degree] navigation-03) from the Aviation Improvement Program funded by the Ministry of Construction & Transportation of The following experiments were tested by adding the climb the Korean government. rate. To use the GS algorithm with the climb rate, the predicted GS and estimated time are as shown in Figures 4 and 5 REFERENCES

[1] RTCA, Inc, “VHF Air-Ground Communications System Improvements Alternative Study and Selection of Proposals for Future Action.” RTCA/DO-255, 1994. [2] David P. Thipphavong, Charles A. Schultz, Alan G. Lee, Steven H. Chan, “Adaptive algorithm to improve trajectory prediction accuracy of climbing aircraft”, Journal of Guidance, Control, and dynamics, Vol. 36, No. 1, January-February 2013 [3] Nicolas Barnier, Cyril Allignol, “4D-Trajectory deconfliction through departure time adjustment”, Eighth USA/Europe Air Traffic Management Research and Development Seminar (ATM2009) [4] Geraud Granger, Nicolas Durand, Jean-Marc Alliot, “Optimal resolution of en route conflicts”, http://atm-seminar-97.eurocontrol.fr/durand.pdf. [5] C.M. Thomas, W.E. Featherstone, “Validation of Vincenty’s formulas for the geodesic using a new fourth-order extension of Kivioja’s Fig. 4. Simulation results (climb rate[ft/min]) formula”, Journal of Surveying Engineering, pp.20–26,Feb., 2005

BIOGRAPHIES

Yong-kyun Kim 2007: MS from the Dept. of Electronic Engineering, Inha

University

2010~: Researcher in the software research laboratory, ETRI Research interests: Air traffic management systems, 4D trajectory modeling

Deok Gyu Lee Dr. D. G. Lee received his PhD degree from the Graduate School of Computer Science from Soonchunhyang University, Korea. He is now a post-graduate doctor of the R&D Institute, ETRI (Electronics and Telecommunication Research Institute), Korea. Dr. Lee has published many research papers in international journals and conferences. Dr. Lee has served as the chairs and on the program committees for many international conferences and workshops. Dr. Lee’ s research interests include key management, signature schemes, broadcast encryption, content security, wireless security, ubiquitous computing, home networks, etc. He is a member of the KICS, KMMS, KIPS, and IEEE, ACM.

Jong Wook Han

1991: MS from the Dept. of Electronic Engineering, Kwangwoon University 2001: PhD from the Dept. of Electronic Engineering, Kwangwoon University 1991~: Researcher in the Software Research Laboratory Research interests: Home network security, convergence service security, optical security

Hyodal Park 1987: PhD from the Dept. of Electronics Engineering, ENSEA(École nationale supérieure de l'aéronautique et de l'espace), France

1992~: professor at Inga University

Research interests: Avionics and microwave systems, radar systems, antennae. Member of Air Traffic Control Assiociation(ATCA)