STABILITY ANALYSIS MODULE

Transcription

1 SURFAES STABIITY ANAYSIS MOUE User Manual

2 SURFAES - Stability Analysis Module Orientation of Forces and Moments...3 Force and Moment Nomenclature...4 Aerodynamic versus Stability oordinate System...5 Increase in Angle of Attack... 5 Increase in Angle of Yaw... 6 Standard tion of Stability Parameters...7 Stability erivatives omputed by SURFAES...15 ocument Title Page Numbers stab.doc Surfaces - Validation Page of 17

3 Orientation of Forces and Moments Positive F Positive M Y +α Positive M -α Y Aerodynamic S (AS: Note that +α causes F >0, M >0, and M Y<0 STABE M +M STABE M Y +M Y NEUTRA M +M Stability S (SS: Note that +α (is also +α in the AS causes F <0, M <0, and M Y<0 -α +α -α +α -α +α -M -M Y -M Positive M Negative M Positive F Y Y -β +β Aerodynamic S (AS: Note that +β causes F Y>0, M <0, and M >0 STABE M NEUTRA M Y STABE M Stability S (SS: Note that +β (is actually β in the AS causes F Y<0, M >0, and M <0 +M +M Y +M +β +β -β -β -β +β -M -M Y -M ocument Title Page Numbers stab.doc Surfaces - Validation Page 3 of 17

4 Force and Moment Nomenclature Name SURFAES Other names Axial force (along -axis F Side force (along Y-axis FY Y Normal force (along -axis F Rolling moment (about -axis M Pitching moment (about Y-axis MY M Yawing moment (about -axis M N oefficient of axial force (along -axis x x oefficient of side force (along Y-axis y y oefficient of normal force (along -axis z z oefficient of rolling moment (about -axis l l oefficient of pitching moment (about Y-axis m m oefficient of yawing moment (about -axis n n z x y x y Standard right-handed Aerodynamic oordinate System (AS. z Typical right-handed Stability oordinate System (SS. Note 1: Positive rotation about an axis is always in the direction of the thumb of the right hand, as can be seen in the above figure. Note : SURFAES uses a standard right handed Aerodynamic oordinate System (AS, which is conventionally used for other aspects of aircraft aerodynamic analyses. In this coordinate system, the sign of the lift is positive, when pointing upwards (i.e. towards positive, and the sign of the drag is positive, when pointing backwards (i.e. towards positive. The user must be cognizant of the orientation of the axes when interpreting results. Note 3: SURFAES comes with a routine that will convert stability derivatives to a standard body axes Stability oordinate System (SS. This is typically the default for stability and control related tools. ocument Title Page Numbers stab.doc Surfaces - Validation Page 4 of 17

5 Aerodynamic versus Stability oordinate System Increase in Angle of Attack Standard right-handed Aerodynamic oordinate System (AS. Typical right-handed Stability oordinate System (SS. x z y +α +α y z x Increase in a (in Aerodynamic S Values in VM x (drag becomes more positive xa > 0 y 0 (no side force for a symmetric aircraft ya 0 z (lift becomes more positive za > 0 l 0 (no roll for a symmetric aircraft la 0 m (nose pitch down more negative ma < 0 n 0 (no yaw for a symmetric aircraft na 0 a > 0 a > 0 Increase in a (in Stability S Values in STAB x (drag becomes more negative xa < 0 y 0 (no side force for a symmetric aircraft ya 0 z (lift becomes more negative za < 0 l 0 (no roll for a symmetric aircraft la 0 m (nose pitch down more negative ma < 0 n 0 (no yaw for a symmetric aircraft na 0 a > 0 a > 0 ocument Title Page Numbers stab.doc Surfaces - Validation Page 5 of 17

6 Increase in Angle of Yaw Standard right-handed Aerodynamic oordinate System (AS. Typical right-handed Stability oordinate System (SS. x z x y +β y z β Increase in b (in Aerodynamic S Values in VM Increase in b (in Stability S Values in STAB x or (expect a small change y > 0 (if β is positive z or (expect a small change l < 0 (for a restoring dihedral effect m (expect a small change n > 0 (yaw for a symmetric aircraft or or xb small yb > 0 zb small lb < 0 mb small nb > 0 b small b small x or (expect a small change y < 0 (if β is positive z or (expect a small change l < 0 (for a restoring dihedral effect m or (expect a small change n > 0 (yaw for a symmetric aircraft or or xb small yb < 0 zb small lb < 0 mb small nb > 0 b small b small ocument Title Page Numbers stab.doc Surfaces - Validation Page 6 of 17

7 Standard tion of Stability Parameters The following expressions can be used when other method fail to yield results. Note that selected formulation is obtained from hapter 4 in Reference 1. The user must understand limitations of each for proper use. escription Total force in the -direction of a plane-fixed global coordinate system. General Forces and Moments SURFAES 1 F F df Surface Total force in the Y-direction of a plane-fixed global coordinate system. FY F Y df Y Surface Total force in the -direction of a plane-fixed global coordinate system. F F df Surface Total moment about the -axis of a plane-fixed global coordinate system. M r l M ( df Surface r Total moment about the Y-axis of a plane-fixed global coordinate system. MY r m M Y ( df Surface r Y Total moment about the -axis of a plane-fixed global coordinate system. M r n M ( df Surface r escription Steady State oefficients SURFAES rag coefficient + i 0 ρ V S 1 The symbols are recommended as some of them are recognized internally by SURFAES. ocument Title Page Numbers stab.doc Surfaces - Validation Page 7 of 17

8 Induced drag i i π AR e ift coefficient + α 0 α ρ V S M Rolling moment coefficient l l M ρ V S b M Pitching moment coefficient m 3 m M Y ρ V S Y M ρ Yawing moment coefficient n 4 n M V S b Force in the -direction. x 5 General form: Small angle relation: sin α cosα T T α Force in the Y-direction. (Main contributions made are by and the fuselage y 6 Tail contribution: Y ( ( α S β σ S Force in the -direction. z 7 General form: ( cosα sin α Small angle relation: ( α Thrust coefficient. t T T ρ V S Note that l derivatives are referred to as la, lb, lta, lu, lp, lq, lr. 3 Note that m derivatives are referred to as ma, mb, mta, mu, mp, mq, mr. 4 Note that n derivatives are referred to as na, nb, nta, nu, np, nq, nr. 5 Note that x derivatives are referred to as xa, xb, xta, xu, xp, xq, xr. 6 Note that y derivatives are referred to as ya, yb, yta, yu, yp, yq, yr. 7 Note that z derivatives are referred to as za, zb, zta, zu, zp, zq, zr. ocument Title Page Numbers stab.doc Surfaces - Validation Page 8 of 17

9 irectional stability contribution of vertical tail nvt ( n V ( V V V escription SURFAES AOA erivatives ift curve slope a α + AR β κ π AR tan Λ 1+ β / + 4 rag curve slope a α π AR e α General form: α T + + α Since T is typically not dependent on α, this becomes: F variation with AOA. xa α π AR e α as shown in Reference 1. Note that the subscript 0 in the reference document is omitted here, but this refers to a reference condition. SURFAES always uses and where Reference 1 uses o and o. Should be zero for a symmetric airplane. FY variation with AOA. ya Yα Y F variation with AOA. za + + α ( + α α α Should be zero for a symmetric airplane: Rolling moment variation with AOA. la M α M l ocument Title Page Numbers stab.doc Surfaces - Validation Page 9 of 17

10 M Static stability derivative Y ma ( Mα α neu cg Should be zero for a symmetric airplane. Yawing moment variation with AOA. na M α M n escription SURFAES AOY erivatives ift curve variation with AOY b rag curve variation with AOY b rag force derivative xb Should be a symmetric curve, with a zero when AOY0. Side force derivative yb Tail contribution: ( ( Yβ α σ S 1 β S ift force derivative zb Should be a symmetric curve, with a zero when AOY0. ihedral effect (rolling moment lb Use USAF ATOM ontribution of vertical tail to dihedral effect σ S z 1 β S b V V lb ( l ( β β Pitching moment variation with AOY. mb Should be a symmetric curve, with a zero when AOY0. irectional stability nb nβ n β ontribution of vertical tail to directional stability V V V nbvt ( n V ( β β ocument Title Page Numbers stab.doc Surfaces - Validation Page 10 of 17

11 escription Rolling moment derivative Pitching moment derivative Yawing moment derivative rag force derivative Side force derivative ift force derivative d(aoa/dt erivatives SURFAES TA YTA TA TA YTA TA escription SURFAES U erivatives General form: u V V u u T ρ V S u T T u M M Speed damping xu Gliders: Jets/rockets: u u onstant speed propellers: u M M 3 3 T T M M ( + tan θ M M ( + tan θ M M M M ift damping yu Usually zero. Variation of vertical force by change in airspeed. By definition this is: u V u V u M M ift damping zu Get by a first or a second order curvefit of versus U in radians. This tends to be small, except at transonic speeds. Per Reference 1, theoretical values are easily calculated for high AR straight wings from: M 1 M u α The derivative impacts phugoid mode by changing the damping. ocument Title Page Numbers stab.doc Surfaces - Validation Page 11 of 17

12 Rolling moment derivative lu Usually zero. hange in pitching moment with airspeed. May be due to compressibility or aeroelastic reasons, but primarily due to shift in center of pressure at transonic speeds. Theoretically, this is given by: Pitching moment derivative mu m u M M MY + ρ V MY 1 ( ρ V Yawing moment derivative nu Usually zero. The derivative impacts phugoid mode by changing the frequency of oscillation (i.e. period. P (Roll Rate erivatives escription SURFAES rag force derivative xp Negligible. amping in roll derivative (mostly a wing contribution yp FY variation with P. (Often negligible, but mostly impacted by wing and. ypvt contribution: ( ( yp α S S z b σ P b V ift force derivative zp amping in roll derivative lp No simple formula. Pitching moment derivative mp Negligible. ross derivative due to roll np Negligible. contribution: ontribution of the to the ross derivative due to roll npvt ( ( np HT α z VV b HT σ P b V Q (Pitch Rate erivatives escription SURFAES rag force derivative xq Negligible, unless wing is swept or of low aspect ratio. Side force derivative yq Negligible, unless wing is swept or of low aspect ratio. F variation with Q. zq Negligible, unless wing is swept or of low aspect ratio. ontribution of the horizontal tail to the F variation with Q. zqht ( zq ( H HT α HT V Rolling moment derivative lq Negligible, unless wing is swept or of low aspect ratio. MY variation with Q, etc. mq Negligible, unless wing is swept or of low aspect ratio. ontribution of the horizontal tail to the MY variation with Q. mqht ocument Title Page Numbers stab.doc Surfaces - Validation Page 1 of 17

13 HT ( ( V mq HT α HT H Yawing moment derivative nq Negligible, unless wing is swept or of low aspect ratio. R (Yaw Rate erivatives escription SURFAES rag force derivative xr Negligible. amping in roll derivative (mostly a contribution yr Most important contribution is normally from the. Vertical tail contribution. yrvt contribution: ( ( yr α S S b σ + P b V ift force derivative zr Negligible. ross derivative due to yaw lr No simple formula. aused by increase in lift on one wing and decrease in the other. Additionally, large may contribute. argest at low speeds. ontribution of the vertical tail to the ross derivative due to yaw lrvt contribution: ( ( lr α S S z b + b σ + P b V Pitching moment derivative amping-in-yaw derivative mr nr No simple formula. Always negative. Fuselage effects are usually negligible. Mostly affected by wing and. ontribution of the vertical tail to the amping-in-yaw derivative nrvt contribution: ( ( nr α VV b σ + P b V escription Horizontal Tail Volume Miscellaneous oefficients SURFAES Vht V H HT S S HT ocument Title Page Numbers stab.doc Surfaces - Validation Page 13 of 17

14 Horizontal Tail Volume Vvt V V S b S ocument Title Page Numbers stab.doc Surfaces - Validation Page 14 of 17

15 Stability erivatives omputed by SURFAES escription STEAY STATE OEFFIIENTS Basic lift coefficient ift curve slope ift coefficient Basic drag coefficient (user input Skin friction drag coefficient (user input Induced drag coefficient rag coefficient rag coefficient slope o a o f i a F variation with AOA FY variation with AOA F variation with AOA Rolling Moment wrt AOA Pitching Moment wrt AOA Yawing Moment wrt AOA Variation of thrust with AOA ocation of neutral point as % of MA ongitudinal Static Margin F variation with AOY Side force derivative F variation with AOY ihedral Effect Pitching Moment wrt AOY irectional Stability AOA ERIVATIVES AOY ERIVATIVES xa ya za la ma na Ta hn SM xb yb zb lb mb nb U ERIVATIVES rag variation with airspeed (Mach Number Thrust variation with airspeed Speed amping Side force damping ift force damping Rolling moment with U Pitching moment with U Yawing moment with U M Tu xu yu zu lu mu nu ift variation with P rag variation with P F variation with P Side force due to roll derivative F variation with P amping-in-roll derivative P ERIVATIVES(RO p p xp yp zp lp ocument Title Page Numbers stab.doc Surfaces - Validation Page 15 of 17

16 Pitching moment variation with P ross derivative due to roll ift variation with Q rag variation with Q F variation with Q FY variation with Q F variation with Q Rolling moment with Q Pitching moment with Q Yawing moment with Q ift variation with R rag variation with R F variation with R FY variation with R F variation with R ross derivative due to yaw Pitching moment with R amping-in-yaw derivative Q ERIVATIVES(PITH R ERIVATIVES(YAW mp np q q xq yq zq lq mq nq r r xr yr zr lr mr nr ift variation with roll rag variation with roll F variation in roll FY variation in roll F variation in roll M variation in roll MY variation in roll M variation in roll ift variation with pitch rag variation with pitch F variation in pitch FY variation in pitch F variation in pitch M variation in pitch MY variation in pitch M variation in pitch ift variation with yaw rag variation with yaw F variation in yaw FY variation in yaw F variation in yaw M variation in yaw AIERON EFETION ERIVATIVES(RO EEVATOR EFETION ERIVATIVES(PITH RUER EFETION ERIVATIVES(YAW da da xda yda zda lda mda nda de de xde yde zde lde mde nde dr dr xdr ydr zdr ldr ocument Title Page Numbers stab.doc Surfaces - Validation Page 16 of 17

17 MY variation in yaw M variation in yaw ift variation with flap rag variation with flap F variation in flap FY variation in flap F variation in flap M variation in flap MY variation in flap M variation in flap HIGH IFT EFETION ERIVATIVES mdr ndr df df xdf ydf zdf ldf mdf ndf ocument Title Page Numbers stab.doc Surfaces - Validation Page 17 of 17