WOLFRAM SYSTEM MODELER
Saab2000High-speed turboprop airliner: Saab 2000 |
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Diagram
Wolfram Language
In[1]:=
SystemModel["Aircraft.Physical.FixedWing.Saab2000"]
Out[1]:=
Information
This model extends the AircraftBase model and contains the parameters of the Saab 2000.
The moments of inertia from Reference [2] are from a comparable airliner, ATR-72 due to the lack of sources for moments of inertia values for the Saab 2000.
References for Aircraft Parameter Values
[1] Wikipedia. (2022). "Saab 2000". [online]
Available at: https://en.wikipedia.org/wiki/Saab_2000#Specifications [Accessed 24 Oct. 2022].
[2] Aviation Safety Council Taipei, Taiwan. GE 791 Occurrence Investigation Report. (2002). [online]
Available at: https://www.smartcockpit.com/docs/OTHERPROPS_ATR72-Inflight_Icing_and_Crash.pdf [Accessed 24 Oct. 2022].
Parameters (145)
| mDry |
Value: 14380 Type: Mass (kg) Description: Aircraft dry mass (total mass for electric aircraft and gliders) |
|---|---|
| initialMfuel |
Value: 5000 Type: Mass (kg) Description: Initial fuel mass |
| xCMdry |
Value: 1.36 Type: Length (m) Description: Aircraft center of mass x coordinate w.r.t. fuselage reference point (with total mass for electric aircraft and gliders, positive x axis toward nose) |
| yCMdry |
Value: 0 Type: Length (m) Description: Aircraft center of mass y coordinate w.r.t. fuselage reference point (with total mass for electric aircraft and gliders, positive y axis toward right) |
| zCMdry |
Value: 0.5 Type: Length (m) Description: Aircraft center of mass z coordinate w.r.t. fuselage reference point (with total mass for electric aircraft and gliders, positive z axis toward ground) |
| IxxDry |
Value: 289900 Type: MomentOfInertia (kg⋅m²) Description: Aircraft dry moment of inertia about x axis |
| IyyDry |
Value: 298400 Type: MomentOfInertia (kg⋅m²) Description: Aircraft dry moment of inertia about y axis |
| IzzDry |
Value: 573600 Type: MomentOfInertia (kg⋅m²) Description: Aircraft dry moment of inertia about z axis |
| IxyDry |
Value: 0 Type: MomentOfInertia (kg⋅m²) Description: Aircraft xy product of dry moment of inertia |
| IxzDry |
Value: 0 Type: MomentOfInertia (kg⋅m²) Description: Aircraft xz product of dry moment of inertia |
| IyzDry |
Value: 0 Type: MomentOfInertia (kg⋅m²) Description: Aircraft yz product of dry moment of inertia |
| MTOMdes |
Value: 22800 Type: Mass (kg) Description: Design maximum takeoff mass |
| nPax |
Value: 56 Type: Integer Description: Design number of passengers |
| mPLdes |
Value: 4716.8 Type: Mass (kg) Description: Design payload mass |
| machDes |
Value: 0.6 Type: Real Description: Design Mach number |
| compMat |
Value: false Type: Boolean Description: true, if composite materials are used in structures |
| qMax |
Value: 15000 Type: Pressure (Pa) Description: Maximum dynamic pressure |
| nMax |
Value: 2.5 Type: Real Description: Maximum load factor |
| nEng |
Value: 2 Type: Integer Description: Number of engines |
| wingMounted |
Value: true Type: Boolean Description: true, if engines are mounted on the main wing |
| engineType |
Value: 1 Type: Integer Description: Type of engine (0 = piston, 1 = turboprop, 2 = turbojet, 3 = turbofan, 4 = electric) |
| bWing |
Value: 24.76 Type: Length (m) Description: Main wing span |
| cWingRoot |
Value: 3.18 Type: Length (m) Description: Main wing root chord (where wing intersects with fuselage) |
| cWingTip |
Value: 1.25 Type: Length (m) Description: Main wing tip chord |
| tWingRoot |
Value: 0.57 Type: Length (m) Description: Main wing root thickness |
| tWingTip |
Value: 0.23 Type: Length (m) Description: Main wing tip thickness |
| xWingRootLE |
Value: 2.46 Type: Length (m) Description: Main wing root leading edge x coordinate w.r.t. fuselage reference point (positive x axis toward nose) |
| zWingRootLE |
Value: 0.9 Type: Length (m) Description: Main wing root leading edge z coordinate w.r.t. fuselage reference point (positive z axis toward ground) |
| lambdaWing |
Value: 0.0610865238198015 Type: Angle (rad) Description: Main wing sweep angle at 1/4 chord |
| gammaWing |
Value: 0.11693705988362 Type: Angle (rad) Description: Main wing dihedral angle |
| iWing |
Value: 0.0523598775598299 Type: Angle (rad) Description: Main wing incidence angle |
| bHT |
Value: 9.8 Type: Length (m) Description: Horizontal tail span |
| cHTroot |
Value: 2.34 Type: Length (m) Description: Horizontal tail root chord |
| cHTtip |
Value: 0.92 Type: Length (m) Description: Horizontal tail tip chord |
| tHTroot |
Value: 0.35 Type: Length (m) Description: Horizontal tail root thickness |
| tHTtip |
Value: 0.15 Type: Length (m) Description: Horizontal tail tip thickness |
| xHTrootLE |
Value: -9.74 Type: Length (m) Description: Horizontal tail root leading edge x coordinate w.r.t. fuselage reference point (positive x axis toward nose) |
| zHTrootLE |
Value: -0.5 Type: Length (m) Description: Horizontal tail root leading edge z coordinate w.r.t. fuselage reference point (positive z axis toward ground) |
| lambdaHT |
Value: 0.0610865238198015 Type: Angle (rad) Description: Horizontal tail sweep angle at 1/4 chord |
| iHT |
Value: 0 Type: Angle (rad) Description: Horizontal tail incidence angle |
| bVT |
Value: 4.30 Type: Length (m) Description: Vertical tail span |
| cVTroot |
Value: 3.55 Type: Length (m) Description: Vertical tail root chord |
| cVTtip |
Value: 1.42 Type: Length (m) Description: Vertical tail tip chord |
| tVTroot |
Value: 0.35 Type: Length (m) Description: Vertical tail root thickness |
| tVTtip |
Value: 0.25 Type: Length (m) Description: Vertical tail tip thickness |
| xVTrootLE |
Value: -8.87 Type: Length (m) Description: Vertical tail root leading edge x coordinate w.r.t. fuselage reference point (positive x axis toward nose) |
| zVTroot |
Value: -1.04 Type: Length (m) Description: Vertical tail root z coordinate w.r.t fuselage reference point |
| lambdaVT |
Value: 0.523598775598299 Type: Angle (rad) Description: Vertical tail sweep angle at 1/4 chord |
| lFus |
Value: 27.03 Type: Length (m) Description: Fuselage length |
| wFus |
Value: 2.31 Type: Length (m) Description: Fuselage maximum width |
| hFus |
Value: 2.31 Type: Length (m) Description: Fuselage maximum height |
| dFusHT |
Value: 1.80 Type: Length (m) Description: Fuselage diameter at horizontal tail 1/4 chord |
| kSkinAC |
Value: 6.35e-06 Type: Length (m) Description: Surface roughness height (same value to be used for all components) |
| kSkinWing |
Value: kSkinAC Type: Length (m) Description: Main wing surface roughness height |
| ClAlphaWing2D |
Value: 4 Type: CurveSlope (rad⁻¹) Description: Change in the section lift coefficient of the main wing airfoil (2D) due to alpha |
| alpha0Wing2D |
Value: -0.0349065850398866 Type: Angle (rad) Description: Zero-lift angle of attack of the main wing airfoil (2D) |
| ClMaxWing2D |
Value: 1.5 Type: Real Description: Maximum section lift coefficient of the main wing airfoil (2D) |
| kSkinHT |
Value: kSkinAC Type: Length (m) Description: Horizontal tail surface roughness height |
| ClAlphaHT2D |
Value: 4 Type: CurveSlope (rad⁻¹) Description: Change in the section lift coefficient of the horizontal tail airfoil (2D) due to alpha |
| alpha0HT2D |
Value: 0 Type: Angle (rad) Description: Zero-lift angle of attack of the horizontal tail airfoil (2D) |
| ClMaxHT2D |
Value: 1.5 Type: Real Description: Maximum section lift coefficient of the horizontal tail airfoil (2D) |
| kSkinVT |
Value: kSkinAC Type: Length (m) Description: Vertical tail surface roughness height |
| ClAlphaVT2D |
Value: 4 Type: CurveSlope (rad⁻¹) Description: Change in the section lift coefficient of the vertical tail airfoil (2D) due to alpha |
| kSkinFus |
Value: kSkinAC Type: Length (m) Description: Fuselage surface roughness height |
| deltaElvMax |
Value: 0.392699081698724 Type: Angle (rad) Description: Maximum elevator deflection |
| deltaAilMax |
Value: 0.392699081698724 Type: Angle (rad) Description: Maximum aileron deflection |
| deltaRdrMax |
Value: 0.785398163397449 Type: Angle (rad) Description: Maximum rudder deflection |
| cAil |
Value: 0.58 Type: Length (m) Description: Aileron average chord |
| yAilRoot |
Value: 8.54 Type: Length (m) Description: Aileron root y-coordinate w.r.t. fuselage centerline |
| yAilTip |
Value: 12.10 Type: Length (m) Description: Aileron tip y-coordinate w.r.t. fuselage centerline |
| Selv |
Value: 7.48 Type: Area (m²) Description: Elevator area |
| Srdr |
Value: 4.26 Type: Area (m²) Description: Rudder area |
| sigmaBeta |
Value: max(3.06 * (SrefVT / SrefWing) / (1 + cos(lambdaWing)) + 0.4 * (-tan(gammaWing) * (yWingAC - wFus / 2) + zWingRootLE) / wFus + 0.009 * (bWing ^ 2 / SrefWing) - 0.276, 0) Type: Real Description: Change in sidewash due to beta |
| rACcm |
Value: if weightEst then {xWingRootLE - lambdaWingLE * (yWingAC - wFus / 2) - 0.15 * cWingMean, 0, 0} else {xCMdry, yCMdry, zCMdry} Type: Length[3] (m) Description: Aircraft dry center of mass w.r.t. fuselage reference point (estimated to be at 15% of MAC if weight estimation method is used) |
| Cfus |
Value: Modelica.Constants.pi * (3 * (hFus / 2 + wFus / 2) - sqrt(10 * hFus / 2 * wFus / 2 + 3 * ((hFus / 2) ^ 2 + (wFus / 2) ^ 2))) Type: Length (m) Description: Fuselage circumference |
| SwetFus |
Value: Cfus * lFus * (1 - 2 / (lFus / (Cfus / Modelica.Constants.pi))) ^ (2 / 3) * (1 + 1 / (lFus / (Cfus / Modelica.Constants.pi)) ^ 2) Type: Area (m²) Description: Fuselage wetted area |
| FFfus |
Value: 1 + 0.0025 * (lFus / hFus) + 60 * (hFus / lFus) ^ 3 Type: Real Description: Fuselage form factor |
| CDmaxFus |
Value: 0.8 * lFus * hFus / SrefWing Type: Real Description: Maximum drag coefficient of the fuselage |
| nSeatAbs |
Value: if nPax > 180 then floor(0.9 * wFus / 0.5588) - 1 else floor(0.9 * wFus / 0.5588) Type: Real Description: Number of seats abreast |
| cWingMean |
Value: 2.45 Type: Length (m) Description: Main wing mean chord length |
| xWingAC |
Value: -0.25 * cWingMean Type: Length (m) Description: Main wing aerodynamic center from wing leading edge at mean chord (positive x-axis towards nose) |
| yWingAC |
Value: 5.96 Type: Length (m) Description: Main wing aerodynamic center from fuselage centerline (y-coordinate w.r.t. fuselage centerline of mean chord) |
| SwetWing |
Value: 2 * (SrefWing / cos(gammaWing) - cWingRoot * wFus) * (1 + 0.25 * (tWingRoot / cWingRoot) * (1 + tWingTip / cWingTip / (tWingRoot / cWingRoot) * TRwing) / (1 + TRwing)) Type: Area (m²) Description: Main wing wetted area |
| CLmaxWing3D |
Value: 0.9 * ClMaxWing2D * cos(lambdaWing) Type: Real Description: Maximum lift coefficient of the main wing (3D) |
| CDmaxWing3D |
Value: 1.98 - 0.81 * (1 - Modelica.Constants.e ^ (-20 / ARwing)) Type: Real Description: Maximum drag coefficient of the main wing (3D) |
| FFwing |
Value: 0.421 * (2 + 4 * tWingMean / cWingMean + 240 * (tWingMean / cWingMean) ^ 4) Type: Real Description: Main wing form factor |
| sdWing |
Value: 0.9998 + 0.0421 * (wFus / bWing) - 2.6286 * (wFus / bWing) ^ 2 + 2 * (wFus / bWing) ^ 3 Type: Real Description: Fuselage drag factor for main wing |
| kdWing |
Value: -3.333 * 10 ^ (-4) * lambdaWing ^ 2 + 6.667 * 10 ^ (-5) * lambdaWing + 0.38 Type: Real Description: Empirical constant for Oswald efficiency factor for main wing |
| kCnDeltaAil |
Value: -0.350894 - 0.066355 * (yAilRoot / (bWing / 2)) ^ 4.15179 + 0.029308 * (bWing ^ 2 / SrefWing) Type: Real Description: Empirical factor for the yaw moment derivative due to ailerons |
| tauAil |
Value: 1.129 * (Sail / SrefWing) ^ 0.4044 - 0.1772 Type: Real Description: Aileron effectiveness coefficient |
| SrefHT |
Value: 18.7 Type: Area (m²) Description: Horizontal tail reference area |
| cHTmean |
Value: 2 / 3 * cHTroot * (1 + TRht + TRht ^ 2) / (1 + TRht) Type: Length (m) Description: Horizontal tail mean chord |
| SwetHT |
Value: 2 * (SrefHT - cHTroot * dFusHT) * (1 + 0.25 * (tHTroot / cHTroot) * (1 + tHTtip / cHTtip / (tHTroot / cHTroot) * TRht) / (1 + TRht)) Type: Area (m²) Description: Horizontal tail wetted area |
| CLmaxHT3D |
Value: 0.9 * ClMaxHT2D * cos(lambdaHT) Type: Real Description: Maximum lift coefficient of the horizontal tail (3D) |
| CDmaxHT3D |
Value: 1.98 - 0.81 * (1 - Modelica.Constants.e ^ (-20 / ARht)) Type: Real Description: Maximum drag coefficient of the horizontal tail (3D)*(SrefHT/SrefWing) |
| FFht |
Value: 1 + 0.1 * (1 - 0.893 * abs(zHTrootLE / hFus)) * (2 + 4 * tHTmean / cHTmean + 240 * (tHTmean / cHTmean) ^ 4) Type: Real Description: Horizontal tail form factor |
| sdHT |
Value: 0.9998 + 0.0421 * (dFusHT / bHT) - 2.6286 * (dFusHT / bHT) ^ 2 + 2 * (dFusHT / bHT) ^ 3 Type: Real Description: Fuselage drag factor for horizontal tail |
| kdHT |
Value: -3.333 * 10 ^ (-4) * lambdaHT ^ 2 + 6.667 * 10 ^ (-5) * lambdaHT + 0.38 Type: Real Description: Empirical constant for Oswald efficiency factor for horizontal tail |
| tauElv |
Value: 1.129 * (Selv / SrefHT) ^ 0.4044 - 0.1772 Type: Real Description: Elevator effectiveness coefficient |
| cVTmean |
Value: 2 / 3 * cVTroot * (1 + TRvt + TRvt ^ 2) / (1 + TRvt) Type: Length (m) Description: Vertical tail mean chord |
| SwetVT |
Value: 2 * SrefVT * (1 + 0.25 * (tVTroot / cVTroot) * (1 + tVTtip / cVTtip / (tVTroot / cVTroot) * TRvt) / (1 + TRvt)) Type: Area (m²) Description: Vertical tail wetted area |
| FFvt |
Value: 0.5 * (2 + 4 * tVTmean / cVTmean + 240 * (tVTmean / cVTmean) ^ 4) Type: Real Description: Vertical tail form factor |
| sdVT |
Value: 0.9998 Type: Real Description: Fuselage drag factor for vertical tail |
| kdVT |
Value: -3.333 * 10 ^ (-4) * lambdaVT ^ 2 + 6.667 * 10 ^ (-5) * lambdaVT + 0.38 Type: Real Description: Empirical constant for Oswald efficiency factor for vertical tail |
| tauRdr |
Value: 1.129 * (Srdr / SrefVT) ^ 0.4044 - 0.1772 Type: Real Description: Rudder effectiveness coefficient |
| initialAltitude |
Value: Type: Altitude (m) Description: Initial altitude |
| initialLatPosition |
Value: {0, 0} Type: Position[2] (m) Description: Initial lateral position of the aircraft (x and y coordinates in world frame) |
| initialVelocity |
Value: Type: Velocity (m/s) Description: Initial velocity |
| initialTrack |
Value: 0 Type: Angle (rad) Description: Initial track angle |
| initialGamma |
Value: 0 Type: Angle (rad) Description: Initial flight path angle |
| initialPhi |
Value: 0 Type: Angle (rad) Description: Initial roll angle |
| initialTheta |
Value: 0 Type: Angle (rad) Description: Initial pitch angle |
| initialPsi |
Value: 0 Type: Angle (rad) Description: Initial yaw angle (heading) |
| initialAngularVelocity |
Value: {0, 0, 0} Type: AngularVelocity[3] (rad/s) Description: Initial {roll [p], pitch [q], yaw [r]} |
| CADshapes |
Value: false Type: Boolean Description: True, if external CAD files are used for animation |
| CADpath |
Value: "modelica://Aircraft/Resources/CAD/PathName.obj" Type: String Description: Path for CAD file |
| SrefWing |
Value: 55.74 Type: Area (m²) Description: Main wing reference area |
| SrefVT |
Value: 10.65 Type: Area (m²) Description: Vertical tail reference area |
| weightEst |
Value: false Type: Boolean Description: True, if weight estimation method is used for masses, center of mass location and inertia tensor |
| ARwing |
Value: bWing ^ 2 / SrefWing Type: Real Description: Main wing aspect ratio |
| TRwing |
Value: cWingTip / cWingRoot Type: Real Description: Main wing taper ratio |
| tWingMean |
Value: (yWingAC - wFus / 2) * (tWingTip - tWingRoot) / (bWing / 2 - wFus / 2) + tWingRoot Type: Length (m) Description: Main wing mean thickness |
| lambdaWingLE |
Value: atan((cWingRoot / 4 - cWingTip / 4 + tan(lambdaWing) * bWing / 2) / (bWing / 2)) Type: Angle (rad) Description: Main wing leading edge sweep angle |
| lambdaWingHC |
Value: atan((cWingTip / 4 - cWingRoot / 4 + tan(lambdaWing) * bWing / 2) / (bWing / 2)) Type: Angle (rad) Description: Main wing half-chord sweep angle |
| lambdaWingTE |
Value: atan((lambdaWingLE * ((bWing - wFus) / 2) + cWingTip - cWingRoot) / ((bWing - wFus) / 2)) Type: Angle (rad) Description: Main wing trailing edge sweep angle (at ailerons location) |
| ARht |
Value: bHT ^ 2 / SrefHT Type: Real Description: Aspect ratio of horizontal tail |
| TRht |
Value: cHTtip / cHTroot Type: Real Description: Taper ratio of horizontal tail |
| tHTmean |
Value: bHT / 2 * (1 + 2 * TRht) / (3 + 3 * TRht) * (tHTtip - tHTroot) / (bHT / 2 - dFusHT / 2) + tHTroot Type: Length (m) Description: Horizontal tail mean thickness |
| lHTcm |
Value: abs(xHTrootLE - xCMdry - tan(lambdaHTle) * (bHT / 2 - dFusHT / 2) * (1 + 2 * TRht) / (3 + 3 * TRht) - 0.25 * cHTmean) Type: Length (m) Description: Horizontal tail arm length (from aircraft center of mass to horizontal tail 1/4 chord) |
| lHTwingAC |
Value: abs(xHTrootLE - (xWingRootLE - lambdaWingLE * (yWingAC - wFus / 2))) + tan(lambdaHTle) * (bHT / 2 - dFusHT / 2) * (1 + 2 * TRht) / (3 + 3 * TRht) + 0.25 * cHTmean - abs(xWingAC) Type: Length (m) Description: Horizontal tail arm length (from wing aerodynamic center to horizontal tail 1/4 chord) |
| vHT |
Value: SrefHT / SrefWing * (lHTcm / cWingMean) Type: Real Description: Horizontal tail volume coefficient |
| lambdaHTle |
Value: atan((cHTroot / 4 - cHTtip / 4 + tan(lambdaHT) * bHT / 2) / (bHT / 2)) Type: Angle (rad) Description: Horizontal tail leading edge sweep angle |
| ARvt |
Value: bVT ^ 2 / SrefVT Type: Real Description: Aspect ratio of vertical tail |
| TRvt |
Value: cVTtip / cVTroot Type: Real Description: Taper ratio of vertical tail |
| tVTmean |
Value: bVT * (1 + 2 * TRvt) / (3 + 3 * TRvt) * (tVTtip - tVTroot) / bVT + tVTroot Type: Length (m) Description: Vertical tail mean thickness |
| lVTcm |
Value: abs(xVTrootLE - xCMdry - tan(lambdaVTle) * bVT * (1 + 2 * TRvt) / (3 + 3 * TRvt) - 0.25 * cVTmean) Type: Length (m) Description: Vertical tail arm length (from aircraft center of mass to vertical tail 1/4 chord) |
| lVTwingAC |
Value: abs(xVTrootLE - (xWingRootLE - lambdaWingLE * (yWingAC - wFus / 2))) + tan(lambdaVTle) * bVT * (1 + 2 * TRvt) / (3 + 3 * TRvt) + 0.25 * cVTmean - abs(xWingAC) Type: Length (m) Description: Vertical tail arm length (from wing aerodynamic center to vertical tail aerodynamic center) |
| zVTac |
Value: zVTroot - bVT * (1 + 2 * TRvt) / (3 + 3 * TRvt) Type: Length (m) Description: Vertical tail center of pressure z-coordinate w.r.t. fuselage reference point |
| vVT |
Value: SrefVT / SrefWing * (lVTcm / bWing) Type: Real Description: Vertical tail volume coefficient |
| lambdaVTle |
Value: atan((tan(lambdaVT) * bVT - cVTtip / 4 + cVTroot / 4) / bVT) Type: Angle (rad) Description: Vertical tail leading edge sweep angle |
| T0 |
Value: atmos.T0 Type: Temperature (K) Description: Temperature at sea level |
| rho0 |
Value: atmos.mAir * p0 / (atmos.R0 * T0) Type: Density (kg/m³) Description: Air density at sea level |
| a0 |
Value: sqrt(atmos.gammaAir * atmos.R0 / atmos.mAir * T0) Type: Velocity (m/s) Description: Speed of sound at sea level |
| gammaAir |
Value: atmos.gammaAir Type: Real Description: Adiabatic index for air |
| tauWing |
Value: tWingTip / cWingTip / (tWingRoot / cWingRoot) Type: Real Description: Ratio of thickness-to-chord ratios at the main wing tip and root |
Outputs (1)
| xEtot |
Type: Real Description: State of aircraft total energy |
|---|
Connectors (6)
 |
deltaAilCmd |
Type: RealInput Description: Ailerons deflection command |
|---|---|---|
|
deltaElvCmd |
Type: RealInput Description: Elevator deflection command |
|
deltaRdrCmd |
Type: RealInput Description: Rudder deflection command |
 |
aircraftRP |
Type: Frame_b Description: Connector to aircraft reference point |
 |
flightDataOut |
Type: FlightDataOut Description: Flight data output |
|
deltaThrotCmd |
Type: RealInput[nEng] Description: Engine throttle commands when custom propulsion is used |
Components (5)
 |
atmos |
Type: AtmosphericProperties Description: Property parameters for the U.S. Standard Atmosphere |
|---|---|---|
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flightData |
Type: FlightData Description: Global flight data variables (measured at the aircraft center of mass location) |
 |
body |
Type: Body Description: Model for the mass properties of entire aircraft or only fuselage, landing gear and payload if weight estimation method is used |
 |
propulsion |
Type: TurbopropPropulsion Description: Propulsion model |
 |
controlSurfaces |
Type: Conventional Description: Model of system of surfaces in conventional wing configuration |
Used in Examples (1)
 |
Aircraft.Examples Model for testing stall recovery and stall effects for Saab 2000 |