The WeatherDatabase doesn't need the voronoi code anymore but uses
Dave Eberly's spherical interpolation code (found in the Lib/Math directory). So it would be great if you could give him also a place in the thanks file. Changing the WeatherDatabse made actually a heavy internal redesign necessary but no code outside the database is affected (isn't code hiding great?).
This commit is contained in:
curt
parent
1963e006c3
commit
210e87ec3a
14 changed files with 517 additions and 330 deletions
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@ -37,6 +37,10 @@ HISTORY
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suggestion
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19.10.1999 Christian Mayer change to use PLIB's sg instead of Point[2/3]D
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and lots of wee code cleaning
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15.12.1999 Christian Mayer changed the air pressure calculation to a much
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more realistic formula. But as I need for that
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the temperature I moved the code to
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FGPhysicalProperties
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*****************************************************************************/
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/****************************************************************************/
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@ -62,25 +66,23 @@ FGAirPressureItem operator-(const FGAirPressureItem& arg);
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/* CLASS DECLARATION */
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/* NOTE: The value stored in 'value' is the air preasure that we'd have at */
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/* an altitude of 0.0 The correct airpreasure at the stored altitude */
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/* gets calulated when getValue() is called. */
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/* gets calulated in FGPhyiscalProperties as I need to know the */
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/* temperatures at the different altitudes for that. */
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/****************************************************************************/
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class FGAirPressureItem
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{
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private:
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WeatherPrecision value;
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WeatherPrecision value; //that's the airpressure at 0 metres
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protected:
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public:
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FGAirPressureItem(const WeatherPrecision v) {value = v;}
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FGAirPressureItem(const WeatherPrecision v) {value = v; }
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FGAirPressureItem() {value = FG_WEATHER_DEFAULT_AIRPRESSURE;}
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WeatherPrecision getValue(const WeatherPrecision& alt) const
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WeatherPrecision getValue(void) const
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{
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return (WeatherPrecision)((value / 101325.0) *
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(
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1.01325e5 + alt * (-1.19459535223623e1 + alt * (5.50461110007561e-4 + alt * (-1.13574703113648e-8 + alt * 8.61601726143988e-14)))
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));
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return value;
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};
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FGAirPressureItem& operator*=(const WeatherPrecision arg);
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@ -38,6 +38,10 @@ HISTORY
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suggestion
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19.10.1999 Christian Mayer change to use PLIB's sg instead of Point[2/3]D
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and lots of wee code cleaning
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14.12.1999 Christian Mayer Changed the internal structure to use Dave
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Eberly's spherical interpolation code. This
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stops our dependancy on the (ugly) voronoi
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code and simplyfies the code structure a lot.
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*****************************************************************************/
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/****************************************************************************/
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@ -49,7 +53,6 @@ HISTORY
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#include <Aircraft/aircraft.hxx>
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#include "FGLocalWeatherDatabase.h"
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#include "FGVoronoi.h"
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#include "FGWeatherParse.h"
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@ -57,37 +60,6 @@ HISTORY
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/********************************** CODE ************************************/
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/****************************************************************************/
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/****************************************************************************/
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/* return the index (better: ID) of the area with point p */
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/****************************************************************************/
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unsigned int FGLocalWeatherDatabase::AreaWith(const sgVec2& p) const
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{
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for (FGMicroWeatherList::size_type i = 0; i != WeatherAreas.size(); i++)
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{
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if (WeatherAreas[i].hasPoint(p) == true)
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return i+1;
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}
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return 0; //nothing found
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}
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/****************************************************************************/
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/* make tiles out of points on a 2D plane */
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/****************************************************************************/
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void FGLocalWeatherDatabase::tileLocalWeather(const FGPhysicalProperties2DVector& EntryList)
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{
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FGVoronoiInputList input;
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for (FGPhysicalProperties2DVectorConstIt it1 = EntryList.begin(); it1 != EntryList.end(); it1++)
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input.push_back(FGVoronoiInput(it1->p, *it1));
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FGVoronoiOutputList output = Voronoiate(input);
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for (FGVoronoiOutputList::iterator it2 = output.begin(); it2 != output.end(); it2++)
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WeatherAreas.push_back(FGMicroWeather(it2->value, it2->boundary));
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}
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FGLocalWeatherDatabase* FGLocalWeatherDatabase::theFGLocalWeatherDatabase = 0;
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FGLocalWeatherDatabase *WeatherDatabase;
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@ -98,7 +70,6 @@ void FGLocalWeatherDatabase::init(const WeatherPrecision visibility, const Datab
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if (theFGLocalWeatherDatabase)
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{
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//FG_LOG( FG_GENERAL, FG_ALERT, "Error: only one local weather allowed" );
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cerr << "Error: only one local weather allowed";
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exit(-1);
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}
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@ -106,7 +77,7 @@ void FGLocalWeatherDatabase::init(const WeatherPrecision visibility, const Datab
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setWeatherVisibility(visibility);
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DatabaseStatus = type;
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global = 0; //just get sure...
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database = 0; //just get sure...
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Thunderstorm = false;
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//I don't need to set theThunderstorm as Thunderstorm == false
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@ -115,33 +86,42 @@ void FGLocalWeatherDatabase::init(const WeatherPrecision visibility, const Datab
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{
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case use_global:
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{
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global = new FGGlobalWeatherDatabase; //initialize GlobalDatabase
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global->setDatabaseStatus(FGGlobalWeatherDatabase_working);
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tileLocalWeather(global->getAll(last_known_position, WeatherVisibility, 3));
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cerr << "Error: there's no global database anymore!\n";
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exit(-1);
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}
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break;
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case use_internet:
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{
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FGWeatherParse parsed_data;
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FGWeatherParse *parsed_data = new FGWeatherParse();
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parsed_data.input( "weather/current.gz" );
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global = new FGGlobalWeatherDatabase; //initialize GlobalDatabase
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global->setDatabaseStatus(FGGlobalWeatherDatabase_working);
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parsed_data->input( "weather/current.gz" );
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unsigned int n = parsed_data->stored_stations();
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sgVec2 *p = new sgVec2 [n];
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FGPhysicalProperties *f = new FGPhysicalProperties[n];
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// fill the database
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for (unsigned int i = 0; i != parsed_data.stored_stations(); i++)
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for (unsigned int i = 0; i < n; i++)
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{
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global->add( parsed_data.getFGPhysicalProperties2D(i) );
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//cerr << parsed_data.getFGPhysicalProperties2D(i);
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f[i] = parsed_data->getFGPhysicalProperties(i);
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parsed_data->getPosition(i, p[i]);
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if ( (i%100) == 0)
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cerr << ".";
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}
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cerr << "\n";
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//and finally tile it
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tileLocalWeather(global->getAll(last_known_position, WeatherVisibility, 3));
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// free the memory of the parsed data to ease the required memory
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// for the very memory consuming spherical interpolation
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delete parsed_data;
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//and finally init the interpolation
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cerr << "\nInitialiating Interpolation. (2-3 minutes on a PII-350)\n";
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database = new SphereInterpolate<FGPhysicalProperties>(n, p, f);
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//and free my allocations:
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delete[] p;
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delete[] f;
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cerr << "Finished weather init.\n";
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}
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@ -154,9 +134,11 @@ void FGLocalWeatherDatabase::init(const WeatherPrecision visibility, const Datab
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case manual:
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case default_mode:
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{
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vector<sgVec2Wrap> emptyList;
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WeatherAreas.push_back(FGMicroWeather(FGPhysicalProperties2D(), emptyList)); //in these cases I've only got one tile
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double x[2] = {0.0, 0.0}; //make an standard weather that's the same at the whole world
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double y[2] = {0.0, 0.0}; //make an standard weather that's the same at the whole world
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double z[2] = {1.0, -1.0}; //make an standard weather that's the same at the whole world
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FGPhysicalProperties f[2]; //make an standard weather that's the same at the whole world
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database = new SphereInterpolate<FGPhysicalProperties>(2,x,y,z,f);
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}
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break;
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@ -168,13 +150,7 @@ void FGLocalWeatherDatabase::init(const WeatherPrecision visibility, const Datab
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FGLocalWeatherDatabase::~FGLocalWeatherDatabase()
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{
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//Tidying up:
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//delete every stored area
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WeatherAreas.erase(WeatherAreas.begin(), WeatherAreas.end());
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//delete global database if necessary
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if (DatabaseStatus == use_global)
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delete global;
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delete database;
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}
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/****************************************************************************/
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@ -182,16 +158,7 @@ FGLocalWeatherDatabase::~FGLocalWeatherDatabase()
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/****************************************************************************/
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void FGLocalWeatherDatabase::reset(const DatabaseWorkingType type)
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{
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//delete global database if necessary
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if ((DatabaseStatus == use_global) && (type != use_global))
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delete global;
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DatabaseStatus = type;
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if (DatabaseStatus == use_global)
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tileLocalWeather(global->getAll(last_known_position, WeatherVisibility, 3));
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//delete every stored area
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WeatherAreas.erase(WeatherAreas.begin(), WeatherAreas.end());
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cerr << "FGLocalWeatherDatabase::reset isn't supported yet\n";
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}
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/****************************************************************************/
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@ -199,45 +166,29 @@ void FGLocalWeatherDatabase::reset(const DatabaseWorkingType type)
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/****************************************************************************/
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void FGLocalWeatherDatabase::update(const WeatherPrecision dt)
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{
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if (DatabaseStatus==use_global)
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global->update(dt);
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//if (DatabaseStatus==use_global)
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// global->update(dt);
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}
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void FGLocalWeatherDatabase::update(const sgVec3& p) //position has changed
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{
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sgCopyVec3(last_known_position, p);
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if ( AreaWith(p) == 0 )
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{ //I have moved out of my local area...
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//now I should erase all my areas and get the new ones
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//but that takes too long :-( I have to take care about that soon
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}
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//uncomment this when you are using the GlobalDatabase
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/*
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cerr << "****\nupdate(p) inside\n";
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cerr << "Parameter: " << p[0] << "/" << p[1] << "/" << p[2] << "\n";
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sgVec2 p2d;
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sgSetVec2( p2d, p[0], p[1] );
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cerr << FGPhysicalProperties2D(global->get(p2d), p2d);
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cerr << FGPhysicalProperties2D(get(p2d), p2d);
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cerr << "****\n";
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*/
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}
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void FGLocalWeatherDatabase::update(const sgVec3& p, const WeatherPrecision dt) //time and/or position has changed
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{
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sgCopyVec3(last_known_position, p);
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if ( AreaWith(p) == 0 )
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{ //I have moved out of my local area...
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//now I should erase all my areas and get the new ones
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//but that takes too long :-( I have to take care about that soon
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}
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if (DatabaseStatus==use_global)
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global->update(dt);
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}
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/****************************************************************************/
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@ -245,154 +196,46 @@ void FGLocalWeatherDatabase::update(const sgVec3& p, const WeatherPrecision dt)
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/****************************************************************************/
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FGPhysicalProperty FGLocalWeatherDatabase::get(const sgVec3& p) const
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{
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unsigned int a = AreaWith(p);
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if (a != 0)
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return WeatherAreas[a-1].get(p[3]);
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else //point is outside => ask GlobalWeatherDatabase
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return global->get(p);
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return FGPhysicalProperty(database->Evaluate(p), p[3]);
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}
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FGPhysicalProperties FGLocalWeatherDatabase::get(const sgVec2& p) const
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{
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sgVec3 temp;
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sgSetVec3(temp, p[0], p[1], 0.0);
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unsigned int a = AreaWith(temp);
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if (a != 0)
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return WeatherAreas[a-1].get();
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else //point is outside => ask GlobalWeatherDatabase
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return global->get(p);
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return database->Evaluate(p);
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}
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WeatherPrecision FGLocalWeatherDatabase::getAirDensity(const sgVec3& p) const
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{
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FGPhysicalProperty dummy;
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unsigned int a = AreaWith(p);
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if (a != 0)
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dummy = WeatherAreas[a-1].get(p[3]);
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else //point is outside => ask GlobalWeatherDatabase
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dummy = global->get(p);
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FGPhysicalProperty dummy(database->Evaluate(p), p[3]);
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return
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(dummy.AirPressure*FG_WEATHER_DEFAULT_AIRDENSITY*FG_WEATHER_DEFAULT_TEMPERATURE) /
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(dummy.Temperature*FG_WEATHER_DEFAULT_AIRPRESSURE);
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}
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/****************************************************************************/
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/* Add a weather feature at the point p and surrounding area */
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/****************************************************************************/
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void FGLocalWeatherDatabase::addWind(const WeatherPrecision alt, const sgVec3& x, const sgVec2& p)
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{
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unsigned int a = AreaWith(p);
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if (a != 0)
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WeatherAreas[a-1].addWind(alt, x);
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}
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void FGLocalWeatherDatabase::addTurbulence(const WeatherPrecision alt, const sgVec3& x, const sgVec2& p)
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{
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unsigned int a = AreaWith(p);
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if (a != 0)
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WeatherAreas[a-1].addTurbulence(alt, x);
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}
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void FGLocalWeatherDatabase::addTemperature(const WeatherPrecision alt, const WeatherPrecision x, const sgVec2& p)
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{
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unsigned int a = AreaWith(p);
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if (a != 0)
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WeatherAreas[a-1].addTemperature(alt, x);
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}
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void FGLocalWeatherDatabase::addAirPressure(const WeatherPrecision alt, const WeatherPrecision x, const sgVec2& p)
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{
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unsigned int a = AreaWith(p);
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if (a != 0)
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WeatherAreas[a-1].addAirPressure(alt, x);
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}
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void FGLocalWeatherDatabase::addVaporPressure(const WeatherPrecision alt, const WeatherPrecision x, const sgVec2& p)
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{
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unsigned int a = AreaWith(p);
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if (a != 0)
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WeatherAreas[a-1].addVaporPressure(alt, x);
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}
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void FGLocalWeatherDatabase::addCloud(const WeatherPrecision alt, const FGCloudItem& x, const sgVec2& p)
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{
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unsigned int a = AreaWith(p);
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if (a != 0)
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WeatherAreas[a-1].addCloud(alt, x);
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}
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void FGLocalWeatherDatabase::setSnowRainIntensity(const WeatherPrecision x, const sgVec2& p)
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{
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unsigned int a = AreaWith(p);
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if (a != 0)
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WeatherAreas[a-1].setSnowRainIntensity(x);
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/* not supported yet */
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}
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void FGLocalWeatherDatabase::setSnowRainType(const SnowRainType x, const sgVec2& p)
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{
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unsigned int a = AreaWith(p);
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if (a != 0)
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WeatherAreas[a-1].setSnowRainType(x);
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/* not supported yet */
|
||||
}
|
||||
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void FGLocalWeatherDatabase::setLightningProbability(const WeatherPrecision x, const sgVec2& p)
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{
|
||||
unsigned int a = AreaWith(p);
|
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if (a != 0)
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WeatherAreas[a-1].setLightningProbability(x);
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}
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void FGLocalWeatherDatabase::addProperties(const FGPhysicalProperties2D& x)
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{
|
||||
if (DatabaseStatus==use_global)
|
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{
|
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global->add(x);
|
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|
||||
//BAD, BAD, BAD thing I'm doing here: I'm adding to the global database a point that
|
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//changes my voronoi diagram but I don't update it! instead I'm changing one local value
|
||||
//that could be anywhere!!
|
||||
//This only *might* work when the plane moves so far so fast that the diagram gets newly
|
||||
//calculated soon...
|
||||
unsigned int a = AreaWith(x.p);
|
||||
if (a != 0)
|
||||
WeatherAreas[a-1].setStoredWeather(x);
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||||
}
|
||||
else
|
||||
{
|
||||
unsigned int a = AreaWith(x.p);
|
||||
if (a != 0)
|
||||
WeatherAreas[a-1].setStoredWeather(x);
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||||
}
|
||||
/* not supported yet */
|
||||
}
|
||||
|
||||
void FGLocalWeatherDatabase::setProperties(const FGPhysicalProperties2D& x)
|
||||
{
|
||||
if (DatabaseStatus==use_global)
|
||||
{
|
||||
global->change(x);
|
||||
|
||||
//BAD, BAD, BAD thing I'm doing here: I'm adding to the global database a point that
|
||||
//changes my voronoi diagram but I don't update it! Instead I'm changing one local value
|
||||
//that could be anywhere!!
|
||||
//This only *might* work when the plane moves so far so fast that the diagram gets newly
|
||||
//calculated soon...
|
||||
unsigned int a = AreaWith(x.p);
|
||||
if (a != 0)
|
||||
WeatherAreas[a-1].setStoredWeather(x);
|
||||
}
|
||||
else
|
||||
{
|
||||
unsigned int a = AreaWith(x.p);
|
||||
if (a != 0)
|
||||
WeatherAreas[a-1].setStoredWeather(x);
|
||||
}
|
||||
/* not supported yet */
|
||||
}
|
||||
|
||||
void fgUpdateWeatherDatabase(void)
|
||||
{
|
||||
//cerr << "FGLocalWeatherDatabase::update()\n";
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||||
sgVec3 position;
|
||||
sgSetVec3(position,
|
||||
current_aircraft.fdm_state->get_Latitude(),
|
||||
|
|
|
|||
|
|
@ -38,6 +38,10 @@ HISTORY
|
|||
suggestion
|
||||
19.10.1999 Christian Mayer change to use PLIB's sg instead of Point[2/3]D
|
||||
and lots of wee code cleaning
|
||||
14.12.1999 Christian Mayer Changed the internal structure to use Dave
|
||||
Eberly's spherical interpolation code. This
|
||||
stops our dependancy on the (ugly) voronoi
|
||||
code and simplyfies the code structure a lot.
|
||||
*****************************************************************************/
|
||||
|
||||
/****************************************************************************/
|
||||
|
|
@ -49,21 +53,16 @@ HISTORY
|
|||
/****************************************************************************/
|
||||
/* INCLUDES */
|
||||
/****************************************************************************/
|
||||
//This is only here for smoother code change. In the end the WD should be clean
|
||||
//of *any* OpenGL:
|
||||
#ifdef HAVE_WINDOWS_H
|
||||
# include <windows.h>
|
||||
#endif
|
||||
#include <GL/glut.h>
|
||||
#include <XGL/xgl.h>
|
||||
|
||||
#include <vector>
|
||||
|
||||
#include "sg.h"
|
||||
#include <sg.h>
|
||||
|
||||
#include <Math/sphrintp.h>
|
||||
|
||||
#include "FGPhysicalProperties.h"
|
||||
#include "FGGlobalWeatherDatabase.h"
|
||||
#include "FGMicroWeather.h"
|
||||
#include "FGPhysicalProperty.h"
|
||||
|
||||
|
||||
#include "FGWeatherFeature.h"
|
||||
#include "FGWeatherDefs.h"
|
||||
#include "FGThunderstorm.h"
|
||||
|
|
@ -81,10 +80,7 @@ class FGLocalWeatherDatabase
|
|||
{
|
||||
private:
|
||||
protected:
|
||||
FGGlobalWeatherDatabase *global; //point to the global database
|
||||
|
||||
typedef vector<FGMicroWeather> FGMicroWeatherList;
|
||||
typedef FGMicroWeatherList::iterator FGMicroWeatherListIt;
|
||||
SphereInterpolate<FGPhysicalProperties> *database;
|
||||
|
||||
typedef vector<sgVec2> pointVector;
|
||||
typedef vector<pointVector> tileVector;
|
||||
|
|
@ -92,10 +88,6 @@ protected:
|
|||
/************************************************************************/
|
||||
/* make tiles out of points on a 2D plane */
|
||||
/************************************************************************/
|
||||
void tileLocalWeather(const FGPhysicalProperties2DVector& EntryList);
|
||||
|
||||
FGMicroWeatherList WeatherAreas;
|
||||
|
||||
WeatherPrecision WeatherVisibility; //how far do I need to simulate the
|
||||
//local weather? Unit: metres
|
||||
sgVec3 last_known_position;
|
||||
|
|
@ -103,23 +95,11 @@ protected:
|
|||
bool Thunderstorm; //is there a thunderstorm near by?
|
||||
FGThunderstorm *theThunderstorm; //pointer to the thunderstorm.
|
||||
|
||||
/************************************************************************/
|
||||
/* return the index of the area with point p */
|
||||
/************************************************************************/
|
||||
unsigned int AreaWith(const sgVec2& p) const;
|
||||
unsigned int AreaWith(const sgVec3& p) const
|
||||
{
|
||||
sgVec2 temp;
|
||||
sgSetVec2(temp, p[0], p[1]);
|
||||
|
||||
return AreaWith(temp);
|
||||
}
|
||||
|
||||
public:
|
||||
static FGLocalWeatherDatabase *theFGLocalWeatherDatabase;
|
||||
|
||||
enum DatabaseWorkingType {
|
||||
use_global, //use global database for data
|
||||
use_global, //use global database for data !!obsolete!!
|
||||
use_internet, //use the weather data that came from the internet
|
||||
manual, //use only user inputs
|
||||
distant, //use distant information, e.g. like LAN when used in
|
||||
|
|
@ -186,19 +166,12 @@ public:
|
|||
/************************************************************************/
|
||||
/* Add a weather feature at the point p and surrounding area */
|
||||
/************************************************************************/
|
||||
|
||||
void addWind (const WeatherPrecision alt, const sgVec3& x, const sgVec2& p);
|
||||
void addTurbulence (const WeatherPrecision alt, const sgVec3& x, const sgVec2& p);
|
||||
void addTemperature (const WeatherPrecision alt, const WeatherPrecision x, const sgVec2& p);
|
||||
void addAirPressure (const WeatherPrecision alt, const WeatherPrecision x, const sgVec2& p);
|
||||
void addVaporPressure(const WeatherPrecision alt, const WeatherPrecision x, const sgVec2& p);
|
||||
void addCloud (const WeatherPrecision alt, const FGCloudItem& x, const sgVec2& p);
|
||||
// !! Adds aren't supported anymore !!
|
||||
|
||||
void setSnowRainIntensity (const WeatherPrecision x, const sgVec2& p);
|
||||
void setSnowRainType (const SnowRainType x, const sgVec2& p);
|
||||
void setLightningProbability(const WeatherPrecision x, const sgVec2& p);
|
||||
|
||||
void addProperties(const FGPhysicalProperties2D& x); //add a property
|
||||
void setProperties(const FGPhysicalProperties2D& x); //change a property
|
||||
|
||||
/************************************************************************/
|
||||
|
|
@ -231,34 +204,10 @@ void inline FGLocalWeatherDatabase::setWeatherVisibility(const WeatherPrecision
|
|||
WeatherVisibility = visibility;
|
||||
else
|
||||
WeatherVisibility = MINIMUM_WEATHER_VISIBILITY;
|
||||
|
||||
#if 0
|
||||
//This code doesn't belong here as this is the optical visibility and not
|
||||
//the visibility of the weather database (that should be bigger...). The
|
||||
//optical visibility should be calculated from the vapor pressure e.g.
|
||||
//But for the sake of a smoother change from the old way to the new one...
|
||||
|
||||
GLfloat fog_exp_density;
|
||||
GLfloat fog_exp2_density;
|
||||
|
||||
// for GL_FOG_EXP
|
||||
fog_exp_density = -log(0.01 / WeatherVisibility);
|
||||
|
||||
// for GL_FOG_EXP2
|
||||
fog_exp2_density = sqrt( -log(0.01) ) / WeatherVisibility;
|
||||
|
||||
// Set correct opengl fog density
|
||||
xglFogf (GL_FOG_DENSITY, fog_exp2_density);
|
||||
|
||||
// FG_LOG( FG_INPUT, FG_DEBUG, "Fog density = " << w->fog_density );
|
||||
//cerr << "FGLocalWeatherDatabase::setWeatherVisibility(" << visibility << "):\n";
|
||||
//cerr << "Fog density = " << fog_exp_density << "\n";
|
||||
#endif
|
||||
}
|
||||
|
||||
WeatherPrecision inline FGLocalWeatherDatabase::getWeatherVisibility(void) const
|
||||
{
|
||||
//cerr << "FGLocalWeatherDatabase::getWeatherVisibility() = " << WeatherVisibility << "\n";
|
||||
return WeatherVisibility;
|
||||
}
|
||||
|
||||
|
|
|
|||
|
|
@ -71,7 +71,7 @@ FGPhysicalProperties::FGPhysicalProperties()
|
|||
|
||||
AirPressure = FGAirPressureItem(101325.0);
|
||||
|
||||
VaporPressure[ 0.0] = FG_WEATHER_DEFAULT_VAPORPRESSURE; //in Pa (I *only* accept SI!)
|
||||
VaporPressure[-1000.0] = FG_WEATHER_DEFAULT_VAPORPRESSURE; //in Pa (I *only* accept SI!)
|
||||
VaporPressure[10000.0] = FG_WEATHER_DEFAULT_VAPORPRESSURE; //in Pa (I *only* accept SI!)
|
||||
|
||||
//Clouds.insert(FGCloudItem()) => none
|
||||
|
|
@ -126,7 +126,7 @@ ostream& operator<< ( ostream& out, const FGPhysicalProperties2D& p )
|
|||
out << "\n";
|
||||
|
||||
out << "Stored AirPressure: ";
|
||||
out << p.AirPressure.getValue(0)/100.0 << " hPa at " << 0.0 << "m; ";
|
||||
out << p.AirPressure.getValue()/100.0 << " hPa at " << 0.0 << "m; ";
|
||||
out << "\n";
|
||||
|
||||
out << "Stored VaporPressure: ";
|
||||
|
|
@ -140,4 +140,154 @@ ostream& operator<< ( ostream& out, const FGPhysicalProperties2D& p )
|
|||
}
|
||||
|
||||
|
||||
inline double F(const WeatherPrecision factor, const WeatherPrecision a, const WeatherPrecision b, const WeatherPrecision r, const WeatherPrecision x)
|
||||
{
|
||||
const double c = 1.0 / (-b + a * r);
|
||||
return factor * c * ( 1.0 / (r + x) + a * c * log(abs((r + x) * (b + a * x))) );
|
||||
}
|
||||
|
||||
WeatherPrecision FGPhysicalProperties::AirPressureAt(const WeatherPrecision x) const
|
||||
{
|
||||
const double rho0 = (AirPressure.getValue()*FG_WEATHER_DEFAULT_AIRDENSITY*FG_WEATHER_DEFAULT_TEMPERATURE)/(TemperatureAt(0)*FG_WEATHER_DEFAULT_AIRPRESSURE);
|
||||
const double G = 6.673e-11; //Gravity; in m^3 kg^-1 s^-2
|
||||
const double m = 5.977e24; //mass of the earth in kg
|
||||
const double r = 6368e3; //radius of the earth in metres
|
||||
const double factor = -(rho0 * TemperatureAt(0) * G * m) / AirPressure.getValue();
|
||||
|
||||
double a, b, FF = 0.0;
|
||||
|
||||
//ok, integrate from 0 to a now.
|
||||
if (Temperature.size() < 2)
|
||||
{ //take care of the case that there aren't enough points
|
||||
//actually this should be impossible...
|
||||
|
||||
if (Temperature.size() == 0)
|
||||
{
|
||||
cerr << "ERROR in FGPhysicalProperties: Air pressure at " << x << " metres altiude requested,\n";
|
||||
cerr << " but there isn't enough data stored! No temperature is aviable!\n";
|
||||
return FG_WEATHER_DEFAULT_AIRPRESSURE;
|
||||
}
|
||||
|
||||
//ok, I've got only one point. So I'm assuming that that temperature is
|
||||
//the same for all altitudes.
|
||||
a = 1;
|
||||
b = TemperatureAt(0);
|
||||
FF += F(factor, a, b, r, x );
|
||||
FF -= F(factor, a, b, r, 0.0);
|
||||
}
|
||||
else
|
||||
{ //I've got at least two entries now
|
||||
|
||||
//integrate 'backwards' by integrating the strip ]n,x] first, then ]n-1,n] ... to [0,n-m]
|
||||
|
||||
if (x>=0.0)
|
||||
{
|
||||
map<WeatherPrecision, WeatherPrecision>::const_iterator temp2 = Temperature.upper_bound(x);
|
||||
map<WeatherPrecision, WeatherPrecision>::const_iterator temp1 = temp2; temp1--;
|
||||
|
||||
if (temp1->first == x)
|
||||
{ //ignore that interval
|
||||
temp1--; temp2--;
|
||||
}
|
||||
|
||||
bool first_pass = true;
|
||||
while(true)
|
||||
{
|
||||
if (temp2 == Temperature.end())
|
||||
{
|
||||
//temp2 doesn't exist. So cheat by assuming that the slope is the
|
||||
//same as between the two earlier temperatures
|
||||
temp1--; temp2--;
|
||||
a = (temp2->second - temp1->second)/(temp2->first - temp1->first);
|
||||
b = temp1->second - a * temp1->first;
|
||||
temp1++; temp2++;
|
||||
}
|
||||
else
|
||||
{
|
||||
a = (temp2->second - temp1->second)/(temp2->first - temp1->first);
|
||||
b = temp1->second - a * temp1->first;
|
||||
}
|
||||
|
||||
if (first_pass)
|
||||
{
|
||||
|
||||
FF += F(factor, a, b, r, x);
|
||||
first_pass = false;
|
||||
}
|
||||
else
|
||||
{
|
||||
FF += F(factor, a, b, r, temp2->first);
|
||||
}
|
||||
|
||||
if (temp1->first>0.0)
|
||||
{
|
||||
FF -= F(factor, a, b, r, temp1->first);
|
||||
temp1--; temp2--;
|
||||
}
|
||||
else
|
||||
{
|
||||
FF -= F(factor, a, b, r, 0.0);
|
||||
return AirPressure.getValue() * exp(FF);
|
||||
}
|
||||
}
|
||||
}
|
||||
else
|
||||
{ //ok x is smaller than 0.0, so do everything in reverse
|
||||
map<WeatherPrecision, WeatherPrecision>::const_iterator temp2 = Temperature.upper_bound(x);
|
||||
map<WeatherPrecision, WeatherPrecision>::const_iterator temp1 = temp2; temp1--;
|
||||
|
||||
bool first_pass = true;
|
||||
while(true)
|
||||
{
|
||||
if (temp2 == Temperature.begin())
|
||||
{
|
||||
//temp1 doesn't exist. So cheat by assuming that the slope is the
|
||||
//same as between the two earlier temperatures
|
||||
temp1 = Temperature.begin(); temp2++;
|
||||
a = (temp2->second - temp1->second)/(temp2->first - temp1->first);
|
||||
b = temp1->second - a * temp1->first;
|
||||
temp2--;
|
||||
}
|
||||
else
|
||||
{
|
||||
a = (temp2->second - temp1->second)/(temp2->first - temp1->first);
|
||||
b = temp1->second - a * temp1->first;
|
||||
}
|
||||
|
||||
if (first_pass)
|
||||
{
|
||||
|
||||
FF += F(factor, a, b, r, x);
|
||||
first_pass = false;
|
||||
}
|
||||
else
|
||||
{
|
||||
FF += F(factor, a, b, r, temp2->first);
|
||||
}
|
||||
|
||||
if (temp2->first<0.0)
|
||||
{
|
||||
FF -= F(factor, a, b, r, temp1->first);
|
||||
|
||||
if (temp2 == Temperature.begin())
|
||||
{
|
||||
temp1 = Temperature.begin(); temp2++;
|
||||
}
|
||||
else
|
||||
{
|
||||
temp1++; temp2++;
|
||||
}
|
||||
}
|
||||
else
|
||||
{
|
||||
FF -= F(factor, a, b, r, 0.0);
|
||||
return AirPressure.getValue() * exp(FF);
|
||||
}
|
||||
}
|
||||
}
|
||||
}
|
||||
|
||||
return AirPressure.getValue() * exp(FF);
|
||||
}
|
||||
|
||||
|
||||
|
|
|
|||
|
|
@ -38,6 +38,10 @@ HISTORY
|
|||
suggestion
|
||||
19.10.1999 Christian Mayer change to use PLIB's sg instead of Point[2/3]D
|
||||
and lots of wee code cleaning
|
||||
15.12.1999 Christian Mayer changed the air pressure calculation to a much
|
||||
more realistic formula. But as I need for that
|
||||
the temperature I moved the code to
|
||||
FGPhysicalProperties
|
||||
*****************************************************************************/
|
||||
|
||||
/****************************************************************************/
|
||||
|
|
@ -63,7 +67,7 @@ HISTORY
|
|||
#include <vector>
|
||||
#include <map>
|
||||
|
||||
#include "sg.h"
|
||||
#include <sg.h>
|
||||
|
||||
#include "FGWeatherDefs.h"
|
||||
|
||||
|
|
@ -107,7 +111,7 @@ public:
|
|||
void WindAt (sgVec3 ret, const WeatherPrecision a) const;
|
||||
void TurbulenceAt (sgVec3 ret, const WeatherPrecision a) const;
|
||||
WeatherPrecision TemperatureAt (const WeatherPrecision a) const;
|
||||
WeatherPrecision AirPressureAt (const WeatherPrecision a) const;
|
||||
WeatherPrecision AirPressureAt (const WeatherPrecision x) const; //x is used here instead of a on purpose
|
||||
WeatherPrecision VaporPressureAt(const WeatherPrecision a) const;
|
||||
|
||||
//for easier access to the cloud stuff:
|
||||
|
|
@ -214,7 +218,7 @@ inline FGPhysicalProperties& FGPhysicalProperties::operator += (const FGPhysical
|
|||
if (!Temperature.insert(*TemperatureIt).second)
|
||||
Temperature[TemperatureIt->first] += TemperatureIt->second;
|
||||
|
||||
AirPressure += p.AirPressure.getValue(0.0);
|
||||
AirPressure += p.AirPressure.getValue();
|
||||
|
||||
for (scalar_iterator VaporPressureIt = p.VaporPressure.begin();
|
||||
VaporPressureIt != p.VaporPressure.end();
|
||||
|
|
@ -249,7 +253,7 @@ inline FGPhysicalProperties& FGPhysicalProperties::operator -= (const FGPhysical
|
|||
if (!Temperature.insert( make_pair(TemperatureIt->first, -TemperatureIt->second) ).second)
|
||||
Temperature[TemperatureIt->first] -= TemperatureIt->second;
|
||||
|
||||
AirPressure -= p.AirPressure.getValue(0.0);
|
||||
AirPressure -= p.AirPressure.getValue();
|
||||
|
||||
for (scalar_iterator VaporPressureIt = p.VaporPressure.begin();
|
||||
VaporPressureIt != p.VaporPressure.end();
|
||||
|
|
@ -261,7 +265,6 @@ inline FGPhysicalProperties& FGPhysicalProperties::operator -= (const FGPhysical
|
|||
return *this;
|
||||
}
|
||||
|
||||
|
||||
inline void FGPhysicalProperties::WindAt(sgVec3 ret, const WeatherPrecision a) const
|
||||
{
|
||||
typedef map<FGPhysicalProperties::Altitude, FGWindItem>::const_iterator vector_iterator;
|
||||
|
|
@ -302,10 +305,8 @@ inline WeatherPrecision FGPhysicalProperties::TemperatureAt(const WeatherPrecisi
|
|||
return ( (it2->second - it->second)/(it2->first - it->first) ) * (a - it2->first) + it2->second;
|
||||
}
|
||||
|
||||
inline WeatherPrecision FGPhysicalProperties::AirPressureAt(const WeatherPrecision a) const
|
||||
{
|
||||
return AirPressure.getValue(a);
|
||||
}
|
||||
//inline WeatherPrecision FGPhysicalProperties::AirPressureAt(const WeatherPrecision x) const
|
||||
//moved to FGPhysicalProperties.cpp as it got too complex to inline
|
||||
|
||||
inline WeatherPrecision FGPhysicalProperties::VaporPressureAt(const WeatherPrecision a) const
|
||||
{
|
||||
|
|
|
|||
|
|
@ -62,7 +62,7 @@ HISTORY
|
|||
|
||||
#include <vector>
|
||||
|
||||
#include "sg.h"
|
||||
#include <sg.h>
|
||||
|
||||
#include "FGWeatherDefs.h"
|
||||
#include "FGPhysicalProperties.h"
|
||||
|
|
|
|||
|
|
@ -58,7 +58,7 @@ HISTORY
|
|||
# include <windows.h>
|
||||
#endif
|
||||
|
||||
#include "sg.h"
|
||||
#include <sg.h>
|
||||
|
||||
#include "FGWeatherDefs.h"
|
||||
|
||||
|
|
|
|||
|
|
@ -51,7 +51,7 @@ HISTORY
|
|||
/****************************************************************************/
|
||||
#include <Include/compiler.h>
|
||||
|
||||
#include "sg.h"
|
||||
#include <sg.h>
|
||||
|
||||
#include "FGWeatherDefs.h"
|
||||
|
||||
|
|
@ -86,4 +86,4 @@ public:
|
|||
};
|
||||
|
||||
/****************************************************************************/
|
||||
#endif /*FGWeatherFeature_H*/
|
||||
#endif /*FGWeatherFeature_H*/
|
||||
|
|
|
|||
|
|
@ -50,12 +50,13 @@ You can also visit his homepage at http://www.wetterzentrale.de
|
|||
HISTORY
|
||||
------------------------------------------------------------------------------
|
||||
18.10.1999 Christian Mayer Created
|
||||
14.12.1999 Christian Mayer minor internal changes
|
||||
*****************************************************************************/
|
||||
|
||||
/****************************************************************************/
|
||||
/* INCLUDES */
|
||||
/****************************************************************************/
|
||||
#include "Include/fg_constants.h"
|
||||
#include <Include/fg_constants.h>
|
||||
|
||||
#include "FGWeatherParse.h"
|
||||
#include "FGWeatherUtils.h"
|
||||
|
|
@ -81,48 +82,75 @@ void FGWeatherParse::input(const char *file)
|
|||
cerr << "Parsing \"" << file << "\" for weather datas:\n";
|
||||
|
||||
in.open( file );
|
||||
|
||||
while ( in )
|
||||
|
||||
if (! in.is_open() )
|
||||
{
|
||||
entry temp;
|
||||
|
||||
in >> temp.year;
|
||||
in >> temp.month;
|
||||
in >> temp.day;
|
||||
in >> temp.hour;
|
||||
in >> temp.station_number;
|
||||
in >> temp.lat;
|
||||
in >> temp.lon;
|
||||
in >> temp.x_wind;
|
||||
in >> temp.y_wind;
|
||||
in >> temp.temperature;
|
||||
in >> temp.dewpoint;
|
||||
in >> temp.airpressure;
|
||||
in >> temp.airpressure_history[0];
|
||||
in >> temp.airpressure_history[1];
|
||||
in >> temp.airpressure_history[2];
|
||||
in >> temp.airpressure_history[3];
|
||||
|
||||
weather_station.push_back( temp );
|
||||
|
||||
// output a point to ease the waiting
|
||||
if ( ((nr++)%100) == 0 )
|
||||
cerr << ".";
|
||||
cerr << "Couldn't find that file!\nExiting...\n";
|
||||
exit(-1);
|
||||
}
|
||||
else
|
||||
{
|
||||
bool skip = false;
|
||||
while ( in )
|
||||
{
|
||||
entry temp;
|
||||
|
||||
in >> temp.year;
|
||||
in >> temp.month;
|
||||
in >> temp.day;
|
||||
in >> temp.hour;
|
||||
in >> temp.station_number;
|
||||
in >> temp.lat;
|
||||
in >> temp.lon;
|
||||
in >> temp.x_wind;
|
||||
in >> temp.y_wind;
|
||||
in >> temp.temperature;
|
||||
in >> temp.dewpoint;
|
||||
in >> temp.airpressure;
|
||||
in >> temp.airpressure_history[0];
|
||||
in >> temp.airpressure_history[1];
|
||||
in >> temp.airpressure_history[2];
|
||||
in >> temp.airpressure_history[3];
|
||||
|
||||
for (int i = 0; i < weather_station.size(); i++)
|
||||
{
|
||||
if ((weather_station[i].lat == temp.lat) && (weather_station[i].lon == temp.lon))
|
||||
{
|
||||
// Two weatherstations are at the same positon
|
||||
// => averageing both
|
||||
|
||||
cerr << "\n" << nr << " stations read\n";
|
||||
// just taking care of the stuff that metters for us
|
||||
weather_station[i].x_wind += temp.x_wind; weather_station[i].x_wind *= 0.5;
|
||||
weather_station[i].y_wind += temp.y_wind; weather_station[i].y_wind *= 0.5;
|
||||
weather_station[i].temperature += temp.temperature; weather_station[i].temperature *= 0.5;
|
||||
weather_station[i].dewpoint += temp.dewpoint; weather_station[i].dewpoint *= 0.5;
|
||||
weather_station[i].airpressure += temp.airpressure; weather_station[i].airpressure *= 0.5;
|
||||
|
||||
skip = true;
|
||||
}
|
||||
}
|
||||
|
||||
if (skip == false)
|
||||
weather_station.push_back( temp );
|
||||
|
||||
skip = false;
|
||||
|
||||
// output a point to ease the waiting
|
||||
if ( ((nr++)%100) == 0 )
|
||||
cerr << ".";
|
||||
}
|
||||
|
||||
cerr << "\n" << nr << " stations read\n";
|
||||
}
|
||||
}
|
||||
|
||||
FGPhysicalProperties2D FGWeatherParse::getFGPhysicalProperties2D(const unsigned int nr) const
|
||||
FGPhysicalProperties FGWeatherParse::getFGPhysicalProperties(const unsigned int nr) const
|
||||
{
|
||||
FGPhysicalProperties2D ret_val;
|
||||
FGPhysicalProperties ret_val;
|
||||
|
||||
//chache this entry
|
||||
entry this_entry = weather_station[nr];
|
||||
|
||||
//set the position of the station
|
||||
sgSetVec2( ret_val.p, this_entry.lat * DEG_TO_RAD, this_entry.lon * DEG_TO_RAD );
|
||||
|
||||
ret_val.Wind[-1000.0] = FGWindItem(this_entry.x_wind, this_entry.y_wind, 0.0);
|
||||
ret_val.Wind[10000.0] = FGWindItem(this_entry.x_wind, this_entry.y_wind, 0.0);
|
||||
ret_val.Temperature[0.0] = Celsius( this_entry.temperature );
|
||||
|
|
@ -138,6 +166,9 @@ FGPhysicalProperties2D FGWeatherParse::getFGPhysicalProperties2D(const unsigned
|
|||
return ret_val;
|
||||
}
|
||||
|
||||
|
||||
|
||||
void FGWeatherParse::getPosition(const unsigned int nr, sgVec2 pos) const
|
||||
{
|
||||
//set the position of the station
|
||||
sgSetVec2( pos, weather_station[nr].lat * DEG_TO_RAD, weather_station[nr].lon * DEG_TO_RAD );
|
||||
}
|
||||
|
||||
|
|
|
|||
|
|
@ -49,6 +49,7 @@ You can also visit his homepage at http://www.wetterzentrale.de
|
|||
HISTORY
|
||||
------------------------------------------------------------------------------
|
||||
18.10.1999 Christian Mayer Created
|
||||
14.12.1999 Christian Mayer minor internal changes
|
||||
*****************************************************************************/
|
||||
|
||||
/****************************************************************************/
|
||||
|
|
@ -121,7 +122,8 @@ public:
|
|||
return weather_station[nr];
|
||||
}
|
||||
|
||||
FGPhysicalProperties2D getFGPhysicalProperties2D(const unsigned int nr) const;
|
||||
FGPhysicalProperties getFGPhysicalProperties(const unsigned int nr) const;
|
||||
void getPosition(const unsigned int nr, sgVec2 pos) const;
|
||||
};
|
||||
|
||||
/****************************************************************************/
|
||||
|
|
|
|||
|
|
@ -43,7 +43,7 @@ HISTORY
|
|||
/****************************************************************************/
|
||||
/* INCLUDES */
|
||||
/****************************************************************************/
|
||||
#include "sg.h"
|
||||
#include <sg.h>
|
||||
|
||||
/****************************************************************************/
|
||||
/* DEFINES */
|
||||
|
|
|
|||
|
|
@ -58,7 +58,7 @@ HISTORY
|
|||
# include <windows.h>
|
||||
#endif
|
||||
|
||||
#include "sg.h"
|
||||
#include <sg.h>
|
||||
|
||||
#include "FGWeatherDefs.h"
|
||||
|
||||
|
|
|
|||
|
|
@ -3,9 +3,7 @@ noinst_LIBRARIES = libWeatherCM.a
|
|||
libWeatherCM_a_SOURCES = \
|
||||
FGAirPressureItem.cpp FGAirPressureItem.h \
|
||||
FGCloud.h FGCloudItem.cpp FGCloudItem.h \
|
||||
FGGlobalWeatherDatabase.cpp FGGlobalWeatherDatabase.h \
|
||||
FGLocalWeatherDatabase.cpp FGLocalWeatherDatabase.h \
|
||||
FGMicroWeather.cpp FGMicroWeather.h \
|
||||
FGPhysicalProperties.cpp FGPhysicalProperties.h \
|
||||
FGPhysicalProperty.cpp FGPhysicalProperty.h \
|
||||
FGSnowRain.h \
|
||||
|
|
@ -13,7 +11,6 @@ libWeatherCM_a_SOURCES = \
|
|||
FGThunderstorm.cpp FGThunderstorm.h \
|
||||
FGTurbulenceItem.cpp FGTurbulenceItem.h \
|
||||
FGVaporPressureItem.cpp FGVaporPressureItem.h \
|
||||
FGVoronoi.cpp FGVoronoi.h \
|
||||
FGWeatherDefs.h FGWeatherFeature.h FGWeatherUtils.h \
|
||||
FGWeatherParse.cpp FGWeatherParse.h \
|
||||
FGWeatherVectorWrap.h \
|
||||
|
|
|
|||
212
src/WeatherCM/air-pressure-explanation.txt
Normal file
212
src/WeatherCM/air-pressure-explanation.txt
Normal file
|
|
@ -0,0 +1,212 @@
|
|||
The formula p(x) for calculating the air pressure at a given altitude
|
||||
---------------------------------------------------------------------
|
||||
|
||||
Well known is the baromertic(?) formula
|
||||
|
||||
rho0
|
||||
------ * g * x
|
||||
p0
|
||||
p(x) = p0 * e
|
||||
|
||||
with p0 being the airpressure and rho0 being the air density at an altitude of
|
||||
0 metres above sea level and g being the gravity constant of 9.81 m/sq. sec
|
||||
|
||||
This formula can easily be derivated when you know, that:
|
||||
|
||||
* the pressure difference is
|
||||
|
||||
dp = - rho * g * dx
|
||||
|
||||
* Boyle-Mariotte says:
|
||||
|
||||
p0 : p = rho0 : rho
|
||||
|
||||
Combinig the terms and changing them around I get:
|
||||
|
||||
dp [ rho0 ]
|
||||
-- = - rho * g = - [ ------ * p(x) ] * g
|
||||
dx [ p0 ]
|
||||
|
||||
rho0
|
||||
p'(x) = - ------ * p(x) * g
|
||||
p0
|
||||
|
||||
Solving that differential equation and knowing that p(0) = p0 I get:
|
||||
|
||||
rho0
|
||||
- ------ * g * x
|
||||
p0
|
||||
p(x) = p0 * e
|
||||
|
||||
q.e.d.
|
||||
|
||||
-------------------------------------------------------------------------------
|
||||
|
||||
The problem with that equation is that it doesn't take different temperatures
|
||||
at different altitudes into account. And the inaccuracies due to it are huge.
|
||||
That's why this formula is only used in very low altitudes.
|
||||
|
||||
So to get a usefull formula for FlightGear I need to extend it. And as I'm
|
||||
already 'recreating' that formula I'm taking the change in g into account, too.
|
||||
This doesn't make such a dramatic difference to the result as the inclusion of
|
||||
temperature change does, but it doesn't complicate the final formula too much.
|
||||
|
||||
So I get three formulas that I'm combining in the end:
|
||||
|
||||
* the change of g with the altitude:
|
||||
|
||||
G * m
|
||||
g(x) = -----------
|
||||
(x + r)^2
|
||||
G is the universal gravity constant(?) and is 6.673e-11 m^3 kg^-1 s^-2
|
||||
m is the mass of the earth and is 5.977e24 kg
|
||||
r is the radius of the earth and is 6368 km
|
||||
|
||||
* The pressure difference stays the same:
|
||||
|
||||
dp = - rho * g(x) * dx
|
||||
|
||||
* If I combine Boyle-Mariotte with Gay-Lussac I get:
|
||||
|
||||
rho0 * T0 p
|
||||
rho = ----------- * ---
|
||||
p0 T
|
||||
|
||||
Combining the terms again I get this time:
|
||||
|
||||
dp [ rho0 * T0 p(x) ]
|
||||
-- = - rho * g(x) = - [ ----------- * ------ ] * g(x)
|
||||
dx [ p0 T(x) ]
|
||||
|
||||
rho0 * T0 p(x) * g(x)
|
||||
p'(x) = - ----------- * -------------
|
||||
p0 T(x)
|
||||
|
||||
This DE isn't that easy to solve as the one above, it by looking into the right
|
||||
books you'll see the general solution for:
|
||||
|
||||
y' + f(x)*y = 0
|
||||
|
||||
is
|
||||
x
|
||||
/\
|
||||
- | f(x) dx
|
||||
\/
|
||||
n
|
||||
y = m * e
|
||||
|
||||
and P(m,n) will be a point on the graph.
|
||||
|
||||
For q = n = 0 metres altitude we get y = m. As y is p(x) we know that m has to
|
||||
be p0.
|
||||
|
||||
So our final formuala is
|
||||
|
||||
ho0 * T0 g(x)
|
||||
f1(x) = ----------- * ------
|
||||
p0 T(x)
|
||||
|
||||
|
||||
x x
|
||||
/\ /\
|
||||
- | f1(x) dx | f(x) dx
|
||||
\/ \/
|
||||
0 0 F(x) - F(0)
|
||||
p(x) = p0 * e = p0 * e = p0 * e
|
||||
|
||||
The only disturbing thing we've got left is the integral. Luckily there is a
|
||||
great service at http://integrals.wolfram.com/ that helps me doing it :-)
|
||||
|
||||
But the f(x) is still too general so I'm substituting:
|
||||
|
||||
rho0 * T0 * G * m
|
||||
f(x) = - -----------------------
|
||||
p0 * (x + r)^2 * T(x)
|
||||
|
||||
but even that isn't good enough. But as I'm linearily interpolating between
|
||||
two different temperatures I can say that T(x) = a*x + b for the x inbetween
|
||||
two different stored temperatures. So I just need to integrate every pice
|
||||
independandly. But anyway, I get:
|
||||
|
||||
rho0 * T0 * G * m
|
||||
f(x) = - ------------------------------
|
||||
p0 * (x + r)^2 * (a * x + b)
|
||||
|
||||
Integrating that I get:
|
||||
|
||||
rho0 * T0 * G * m [ 1
|
||||
F(x) = - ------------------- * [ ------------------------ -
|
||||
p0 [ (-b + a * r) * (r + x)
|
||||
|
||||
|
||||
a * log|r + x| a * log|b + a * x| ]
|
||||
---------------- + -------------------- ]
|
||||
(b - a * r)^2 (b - a * r)^2 ]
|
||||
|
||||
To lower the computional cost I can transfere the equation.
|
||||
|
||||
* I'm defining
|
||||
|
||||
rho0 * T0 * G * m
|
||||
factor = - -------------------
|
||||
p0
|
||||
1
|
||||
c = --------------
|
||||
(-b + a * r)
|
||||
|
||||
* now I can write
|
||||
|
||||
[ c ]
|
||||
F(x) = factor * [ --------- - a * c * c * [log|r + x| + log|b + a * x|] ]
|
||||
[ (r + x) ]
|
||||
|
||||
* and simplyfy it to
|
||||
|
||||
[ 1 ]
|
||||
F(x) = factor * c * [ --------- - a * c * log|(r + x) * (b + a * x)| ]
|
||||
[ (r + x) ]
|
||||
|
||||
-------------------------------------------------------------------------------
|
||||
The following table shows quite nicely how accurate my formula is:
|
||||
|
||||
Altitude[m] | Airpressure [hPa] | Error [%]
|
||||
| Official | My formula |
|
||||
------------+---------------+---------------+---------------
|
||||
-200 | 1037.51 | 1037.24 | 0.0260
|
||||
-100 | 1025.32 | 1025.19 | 0.0127
|
||||
0 | 1013.25 | 1013.25 | 0.0
|
||||
500 | 954.59 | 955.224 | 0.0664
|
||||
1000 | 898.70 | 899.912 | 0.1349
|
||||
2000 | 794.88 | 797.042 | 0.2720
|
||||
3000 | 700.99 | 703.885 | 0.4130
|
||||
4000 | 616.28 | 619.727 | 0.5593
|
||||
5000 | 540.07 | 543.89 | 0.7073
|
||||
6000 | 471.67 | 475.731 | 0.8610
|
||||
7000 | 410.46 | 414.643 | 1.0191
|
||||
8000 | 355.84 | 360.054 | 1.1842
|
||||
9000 | 307.27 | 311.422 | 1.3513
|
||||
10000 | 264.21 | 268.238 | 1.5245
|
||||
20000 | 54.670/55.3 | 55.7971 | 2.0616/0.8989
|
||||
30000 | 11.8 | 11.3149 | 1.5441
|
||||
40000 | 3.0 | 2.74665 | 18.9703
|
||||
50000 | 0.88 | 0.753043 | 41.9183
|
||||
60000 | 0.257 | 0.221907 | 57.9802
|
||||
70000 | 0.0602 | 0.0530785 | 61.9153
|
||||
80000 | 0.0101 | 0.00905461 | 51.5725
|
||||
100000 | 2.14e-4 | 2.03984e-4 | 5.5131
|
||||
|
||||
The official values are from the CINA atmosphere which assumes a air pressure
|
||||
of 1013.25 hPa and a temperature of 15 degC at sea level and a temperature
|
||||
gradient of -6.5 deg/km. The CINA atmosphere gives only values for altiudes
|
||||
up to 20 km. The values for 20 km and above are from the 1959 ARDC atmosphere.
|
||||
That's why I've got two values at 20000 metres.
|
||||
The temperature changes dramtically in the altitudes over 20 km which I didn't
|
||||
take care of in my calculations which explains the huge errors at that altitude
|
||||
range. But you can see nicely that the values are at least quite close to the
|
||||
official values.
|
||||
Using a better temperature model for the altitudes above 20 km should
|
||||
dramatically increase the accuracy there.
|
||||
|
||||
|
||||
|
||||
|
||||
Loading…
Reference in a new issue