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| /*----==== FLIGHTMODEL.H ====---- | |
| Author: Jeffrey Kiah | |
| Date: 2/2/2009 | |
| -------------------------------*/ | |
| #pragma once | |
| #include "Math/IMath.h" | |
| /*============================================================================= | |
| class FlightModel | |
| =============================================================================*/ | |
| class FlightModel { | |
| private: | |
| public://TEMP | |
| ///// Flight Force Coefficients ///// | |
| // -------------------------------------------------------------------- | |
| // Returns: Slope per radian (dCL/dAlpha = CLalpha) of the linear portion | |
| // of the Coefficient of Lift (CL) curve for a 3d lifting surface | |
| // Parameters: span (b), ft. | |
| // rootChord (Croot), ft. | |
| // tipChord (Ctip), ft. | |
| // leadingEdgeSweep (Lambda_le), radians | |
| // mach (M) | |
| // zeroMachSlope (a0) - use 2*pi if unknown | |
| // Description: CLalpha = (2*pi*AR)/[2 + sqrt([AR^2*B^2/k^2]*[1+(tan^2(Lambda_c2)/B^2)]+4)] | |
| // where: AR = aspect Ratio | |
| // B = compressibility correction | |
| // k = a0/(2*pi) | |
| // Lambda_c2 = half-chord sweep angle | |
| // -------------------------------------------------------------------- | |
| static float calcCLalpha(float span, float rootChord, float tipChord, float leadingEdgeSweep, | |
| float mach, float zeroMachSlope) | |
| { | |
| float S = calcPlanformArea(rootChord, tipChord, span); | |
| float AR = calcAspectRatio(span, S); | |
| float B = calcCompressibilityCorrection(mach); | |
| if (B == 0.0f) { B = 0.0000001f; } | |
| float k = zeroMachSlope / (TWO_PIf); | |
| if (k == 0.0f) { k = 1.0f; } | |
| float tanLambda_c2 = calcTanHalfChordSweep(leadingEdgeSweep, rootChord, tipChord, span); | |
| float tSlope = (mach < 1.0f) ? TWO_PIf : 4.0f; // subsonic theoretical slope is 2pi, supersonic is 4 | |
| return (tSlope * AR) / | |
| (2.0f + sqrtf((AR*AR*B*B)/(k*k) * (1.0f + ((tanLambda_c2*tanLambda_c2)/(B*B))) + 4.0f)); | |
| } | |
| // -------------------------------------------------------------------- | |
| // Returns: Compressibility Correction (B) | |
| // Parameters: mach (M) | |
| // Description: B = sqrt(M^2 - 1) or B = sqrt(1 - M^2) | |
| // -------------------------------------------------------------------- | |
| static float calcCompressibilityCorrection(float mach) | |
| { | |
| return ((mach >= 1.0f) ? (sqrtf(mach*mach-1.0f)) : (sqrtf(1.0f-mach*mach))); | |
| } | |
| // -------------------------------------------------------------------- | |
| // Returns: Coefficient of Drag Induced by Lift (CDi) | |
| // Parameters: Coefficient of Lift (CL) | |
| // aspectRatio (AR) | |
| // spanEfficiency (e) = 1.0 for eliptically loaded wing | |
| // Description: CDi = CL^2 / (pi * AR * e) | |
| // -------------------------------------------------------------------- | |
| static float calcCDInduced(float CL, float aspectRatio, float spanEfficiency) | |
| { | |
| return (CL*CL) / (PIf * aspectRatio * spanEfficiency); | |
| } | |
| ///// Pitch Stability Derivatives ///// | |
| ///// Directional Stability Derivatives ///// | |
| // -------------------------------------------------------------------- | |
| // Returns: Slope per radian (dCN/dBeta = CNbeta) of the dihedral | |
| // effect of the wing on directional stability | |
| // Parameters: gamma (G), radians | |
| // coefficient of lift (CL) | |
| // Description: (CNbeta)G,wing = -0.75*G*CL | |
| // -------------------------------------------------------------------- | |
| static float calcCNbetaWingDihedral(float gamma, float CL) | |
| { | |
| return -0.75f * gamma * CL; | |
| } | |
| // -------------------------------------------------------------------- | |
| // Returns: Slope per radian (dCN/dBeta = CNbeta) of the sweep | |
| // effect of the wing on directional stability | |
| // Parameters: coefficient of lift (CL) | |
| // span (b), ft. | |
| // rootChord (Croot), ft. | |
| // tipChord (Ctip), ft. | |
| // leadingEdgeSweep (Lambda_le), radians | |
| // Description: (CNbeta)L,wing = (CL^2)[(1/(4*pi*AR)) - (tanLambda_c4/(pi*AR*(AR+(4*cosLambda_c4)))) | |
| // * (cosLambda_c4 - AR/2 - AR^2/(8*cosLambda_c4) - (6*Xa_bar*sinLambda_c4/AR))] | |
| // where: AR = aspect Ratio | |
| // Lambda_c4 = quarter-chord sweep angle | |
| // Xa_bar = (Xcg - Xac) / MAC | |
| // -------------------------------------------------------------------- | |
| static float calcCNbetaWingSweep(float CL, float span, float rootChord, float tipChord, float leadingEdgeSweep) | |
| { | |
| float S = calcPlanformArea(rootChord, tipChord, span); | |
| float AR = calcAspectRatio(span, S); | |
| float tanLambda_c4 = calcTanQuarterChordSweep(leadingEdgeSweep, rootChord, tipChord, span); | |
| float Lambda_c4 = atanf(tanLambda_c4); | |
| float cosLambda_c4 = cosf(Lambda_c4); | |
| float Xa_bar = 0.0f; // TEMP | |
| return (CL*CL) * ( (1.0f/(4.0f*PIf*AR)) - (tanLambda_c4/(PIf*AR*(AR+4.0f*cosLambda_c4))) * | |
| (cosLambda_c4 - (0.5f*AR) - ((AR*AR)/(8.0f*cosLambda_c4)) - (6.0f * Xa_bar * sinf(Lambda_c4) / AR)) ); | |
| } | |
| // -------------------------------------------------------------------- | |
| // Returns: Slope per radian (dCN/dBeta = CNbeta) of the fuselage | |
| // with wing contribution to directional stability | |
| // Parameters: Wing-body interference factor (KN) | |
| // Reynolds number factor (KRl) | |
| // bodySideArea (Sbs), ft.^2 | |
| // planformArea (S), ft.^2 | |
| // lengthFuselage (lf), ft. | |
| // span (b), ft. | |
| // Description: (CNbeta)B(w) = (-KN)(KRl)(Sbs/S)(lf/b) | |
| // -------------------------------------------------------------------- | |
| static float calcCNbetaBody(float KN, float KRl, float bodySideArea, float planformArea, | |
| float lengthFuselage, float span) | |
| { | |
| if (planformArea == 0.0f) { planformArea = 0.0000001f; } | |
| if (span == 0.0f) { span = 0.0000001f; } | |
| return -KN * KRl * (bodySideArea / planformArea) * (lengthFuselage / span); | |
| } | |
| // -------------------------------------------------------------------- | |
| // Returns: Slope per radian (dCN/dBeta = CNbeta) of the vertical | |
| // stabilizer contribution to directional stability | |
| // Parameters: | |
| // Description: | |
| // -------------------------------------------------------------------- | |
| static float calcCNbetaTail(float k) | |
| { | |
| return 0.0f; | |
| } | |
| ///// Geometry Functions ///// | |
| // -------------------------------------------------------------------- | |
| // Returns: Planform Area (S), ft.^2 | |
| // Parameters: rootChord (Croot), ft. | |
| // tipChord (Ctip), ft. | |
| // span (b), ft. | |
| // Description: S = b[(Croot + Ctip)/2] | |
| // -------------------------------------------------------------------- | |
| static float calcPlanformArea(float rootChord, float tipChord, float span) | |
| { | |
| return span * ((rootChord + tipChord) * 0.5f); | |
| } | |
| // -------------------------------------------------------------------- | |
| // Returns: Mean Aerodynamic Chord Length (MAC or C), ft. | |
| // Parameters: rootChord (Croot), ft. | |
| // tipChord (Ctip), ft. | |
| // Description: MAC = (2/3)[(Croot+Ctip) - ([Croot*Ctip]/[Croot+Ctip])] | |
| // -------------------------------------------------------------------- | |
| static float calcMACLength(float rootChord, float tipChord) | |
| { | |
| float c = rootChord + tipChord; | |
| return (2.0f / 3.0f) * (c - ((rootChord * tipChord) / c)); | |
| } | |
| // -------------------------------------------------------------------- | |
| // Returns: Aspect Ratio (A) | |
| // Parameters: span (b), ft. | |
| // planformArea (S), ft.^2 | |
| // Description: A = b^2 / S | |
| // -------------------------------------------------------------------- | |
| static float calcAspectRatio(float span, float planformArea) | |
| { | |
| if (planformArea == 0.0f) return 0.0f; | |
| return (span * span) / planformArea; | |
| } | |
| // -------------------------------------------------------------------- | |
| // Returns: Tangent of Half-Chord Sweep (Lambda_c/2) | |
| // Parameters: leadingEdgeSweep (Lambda_le), radians | |
| // rootChord (Croot), ft. | |
| // tipChord (Ctip), ft. | |
| // span (b), ft. | |
| // Description: tan(Lambda_c/2) = tan(Lambda_le) - ((Croot - Ctip) / b) | |
| // -------------------------------------------------------------------- | |
| static float calcTanHalfChordSweep(float leadingEdgeSweep, float rootChord, float tipChord, float span) | |
| { | |
| if (span == 0.0f) return tanf(leadingEdgeSweep); | |
| return tanf(leadingEdgeSweep) - ((rootChord - tipChord) / span); | |
| } | |
| // -------------------------------------------------------------------- | |
| // Returns: Tangent of Quarter-Chord Sweep (Lambda_c/4) | |
| // Parameters: leadingEdgeSweep (Lambda_le), radians | |
| // rootChord (Croot), ft. | |
| // tipChord (Ctip), ft. | |
| // span (b), ft. | |
| // Description: tan(Lambda_c/4) = tan(Lambda_le) - ((Croot - Ctip) / 2b) | |
| // -------------------------------------------------------------------- | |
| static float calcTanQuarterChordSweep(float leadingEdgeSweep, float rootChord, float tipChord, float span) | |
| { | |
| if (span == 0.0f) return tanf(leadingEdgeSweep); | |
| return tanf(leadingEdgeSweep) - ((rootChord - tipChord) / (2.0f * span)); | |
| } | |
| // -------------------------------------------------------------------- | |
| // Returns: Leading Edge Sweep (Lambda_le), radians | |
| // Parameters: quarterChordSweep (Lambda_c/4), radians | |
| // rootChord (Croot), ft. | |
| // tipChord (Ctip), ft. | |
| // span (b), ft. | |
| // Description: Lambda_le = arctan(tan(Lambda_c/4) + ((Croot - Ctip) / 2b)) | |
| // -------------------------------------------------------------------- | |
| static float calcLeadingEdgeSweep(float quarterChordSweep, float rootChord, float tipChord, float span) | |
| { | |
| if (span == 0.0f) return 0.0f; | |
| return atanf(tanf(quarterChordSweep) + ((rootChord - tipChord) / (2.0f * span))); | |
| } | |
| public: | |
| explicit FlightModel() {} | |
| ~FlightModel() {} | |
| }; |