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Imece2008-66518 Proceedings of IMECE2008 2008 ASME International Mechanical Engineering Congress and Exposition October 31-November 6, 2008, Boston, Massachusetts, USA IMECE2008-66518 APPLICATION OF THE RAPID UPDATE CYCLE (RUC) TO AIRCRAFT FLIGHT SIMULATION Yan Zhang Seamus McGovern EG&G Technical Services U.S. DOT National Transportation Systems Center Cambridge, Massachusetts, USA Cambridge, Massachusetts, USA ABSTRACT ters for Environmental Prediction (NCEP), the National Oceanic An aircraft flight simulation model under development aims and Atmospheric Administration (NOAA), and produces numer- to provide a computer simulation tool to investigate aircraft flight ical weather prediction data hourly with horizontal spatial reso- performance during en route flight and landing under various lution of 20 km or 13 km, and vertical pressure resolution of 25 atmospherical conditions [1]. Within this model, the air pres- mb [4]. The RUC provides a broad range of environmental pa- sure and temperature serve as important parameters for deriv- rameters including, as a function of 37 constant pressure levels, ing the true airspeed (TAS). Also important are the wind speed the geopotential height, temperature, relative humidity, horizon- and direction, which will be direct inputs for the flight simulation tal wind velocity, and pressure vertical velocity. However, the model. air pressure is not provided in RUC data in terms of the geodetic In this paper, the Rapid Update Cycle (RUC) data, pro- location, rather it is used as the reference to specify other param- vided hourly by the National Centers for Environmental Predic- eters such as the geopotential height, temperature, wind veloc- tion (NCEP) and the National Oceanic and Atmospheric Admin- ity, etc., preventing the RUC data to be directly used for a given istration (NOAA) are used to derive the atmospherical param- geodetic location of an aircraft. eters. We relate the pressure to the geodetic altitude by using In the paper, the pressure is retrieved for a given geodetic the geopotential height from the RUC data and the theoretical location by using the geopotential height from the RUC data and model. Then the resultant pressure as a function of the geodetic a theoretical gravity model [5]. Then the resultant pressure is altitude is used to retrieve other parameters such as the temper- used to extract other RUC data, hence they can be represented as ature and wind velocity by multi-dimensional interpolation. Air- a function of a geodetic location. In addition, formulations and plane flights simulated by the X-Plane°R simulator with the input procedures of retrieving/processing the RUC data for the need of of the RUC data are demonstrated. aircraft flight simulation are presented, including the coordinate transformation, geopotential height modeling, data interpolation, and time averaging. We will also demonstrate airplane’s flight performance by using the existing aircraft flight simulator, the INTRODUCTION X-Plane°R V8.40 with the input of the RUC data. An aircraft flight simulation model takes atmospherical data as part of the input for its flight dynamics and cockpit display modeling. Among these data, the air pressure serves as an im- portant parameter for deriving the true airspeed (TAS) [and ulti- DESCRIPTION OF THE SIMULATION ALGORITHMS mately the ground speed (GS)] from the indicated airspeed (IAS). The functionality of the aircraft simulation with the input The wind speed and direction are also important factors that di- of environmental data from RUC is illustrated by the informa- rectly affect the airplane’s flight dynamics. tion flowchart shown in Fig. 1. The outputs from the aircraft The Rapid Update Cycle (RUC) data is adopted in this flight model are the flight time t and the aircraft’s “true” location paper to obtain the most accurate and realistic atmospherical (geodetic latitude f, longitude l, and altitude h). The RUC data data [2, 3]. The RUC runs operationally at the National Cen- are available hourly, therefore we need to read the RUC data at 1 Copyright °c 2008 by ASME The geopotential height, temperature, and easterly and northerly wind velocities have, respectively, 37 records at dif- ferent pressure levels from 1;000 mb to 100 mb with decreasing step of 25 mb. These data for a particular location in the airspace are projected to the Lambert conformal surface, the cone tangent to the spherical Earth with the apex over the North Pole. The pa- rameters for the Lambert conformal projection, such as the grid 0 length dx and dy, longitude of the reference meridian l0, latitude 0 0 0 of the tangent point f0, location of the first grid point (f1 and l1), the radius of the spherical Earth, as listed in Tab. 1, are defined in the RUC data and are useful for coordinate transformations as shown later in the paper. Lambert Coordinate Transformation. The RUC pro- vides the data in the Lambert conformal projection with a uni- form grid (I;J). In order to achieve fast data interpolation by adopting the integers I and J as the indices of the memory ad- dresses that contain the data, we convert airplane’s geodetic po- sition (latitude, longitude, and altitude), output from the aircraft simulation model, to the Lambert coordinates. First, we convert the aircraft’s geodetic location to the geo- centric location. Given the geodetic latitude (f), longitude (l) and geodetic height (h), the geocentric latitude (f0), longitude (l0) and radius (R) can be solved in closed form. By considering the Earth as an ellipsoid with semi-major axis a and flattening f [thus the semi-minor axis can be computed by b = a(1 ¡ f )], and defining the first eccentricity squared as e2 = 2 f ¡ f 2, the Cartesian coordinates of a point (X;Y;Z) in the Earth-Centered Figure 1. THE INFORMATION FLOWCHART OF THE AIRCRAFT Earth-Fixed (ECEF) frame can be expressed both geocentrically FLIGHT SIMULATION WITH THE INPUT OF THE RUC DATA. THE and geodetically as DESCRIPTION OF THE SYMBOLS AND THE FUNCTIONS CAN BE FOUND IN THE NOMENCLATURE AND IN THE TEXT. 8 µ ¶ > 0 0 a > X = Rcosf cosl = + h cosfcosl > µ c ¶ two adjacent hours tn and tn+1, where tn < t < tn+1, then process <> 0 0 a the RUC data for the time t by data interpolation/averaging. The Y = Rcosf sinl = + h cosfsinl (1) > à ¡ c ¢ ! details of the algorithms are described in the following. > 2 > a 1 ¡ e > Z = Rsinf0 = + h sinf : c RUC Data Retrieval The RUC data, archived in the GRIB format [6] in q the NOAA National Operational Model Archive and Dis- where c = 1 ¡ e2 sin2 f. Eliminating R and l0 (which is equal tribution System (NOMADS) [7], can be downloaded for 0 a particular RUC Time specified by the year, month, day, to l), we get the equation that can be used to solve f by provid- and UTC hour, and decoded by using the modified C/C++ ing f and h: code originally developed by Ebisuzaki [8]. For exam- ·µ ¶ ¸ ple, for the UTC time 16:00, May 1st, 2007, the RUC a f0 = tan¡1 1 ¡ e2 tanf (2) data with the file name ruc2_252_20070501_1600_000.grb a + hc (where the number ‘252’ specifies the particular grid with 20 km resolution [7]) can be found and downloaded from the directory 200705/20070501/ in the web site Next, we convert the geocentric latitude and longitude to the http://nomads.ncdc.noaa.gov/data/ruc/. In the RUC coordinates in the Lambert conformal projection. Consider n¤ = 0 data which contains 315 data records, the geopotential height H sinf0 to be the constant of the cone for the Lambert conformal (record # 1–37), temperature (record # 38–74), and wind (record projection where H = 1 or ¡1 when the apex is over the North #112–185) will be used in this paper. or South Pole, respectively. In terms of the pixel index number 2 Copyright °c 2008 by ASME (i; j) of the image, the local coordinates (x;y) is expressed by Table 1. PARAMETERS IN RUC FOR LAMBERT CONFORMAL PRO- JECTION ½ Parameter Notation Value x = (i ¡ 1)dx + x1 (3) 6 y = ¡( j ¡ 1)dy + y1 Radius of the R0 6:36747 £ 10 m Spherical Earth where dx and dy are grid lengths in x and y-direction, respec- 0 ± Latitude of First f1 16:281000 tively, and the indices (i; j) do not have to be integers. The local Grid Point coordinates of the left lower pixel (x ;y ) are calculated from 1 1 0 ± Longitude of First l1 233:862000 8 0 Grid Point > s1R0 cosf £ ¡ ¢¤ < x = 1 sin n¤ l0 ¡ l0 1 n¤ 1 0 Latitude of the Point 0 (4) 0 ± > s1R0 cosf £ ¡ ¢¤ at Which the Secant f 25 : y = 1 cos n¤ l0 ¡ l0 0 1 n¤ 1 0 Cone Tangent to the Spherical Earth In addition, the image scale of the Lambert conformal projection, Longitude of the l0 265± s , is defined by, 0 1 Reference Meridian µ ¶ ¤ µ ¶ ¤ X-direction Grid Length dx 20,318.000 m cosf0 1¡n 1 + n n s = 0 (5) 1 0 0 Y-direction Grid Length dy 20,318.000 m cosf1 1 + H sinf1 0 0 where (f1;l1) depicts the geocentric coordinates of the left lower and J < j < J + 1, are used for the 2-D data interpolation. We pixel. The detail derivation for Eqns. (4) and (5) can be found first determine whether the point (i; j) is in the triangle ‘A’ with 0 0 in [9]. Given the geocentric coordinates (f ;l ), we define the vertices (I;J), (I + 1;J), and (I + 1;J + 1) or in the triangle ‘B’ polar angle, with vertices (I + 1;J + 1), (I;J + 1), and (I;J) by checking the ratio r = ( j ¡ J)=(i ¡ I).
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