Design, Analysis and Research Corporation (DARcorporation) ERRATA: Airplane Flight Dynamics and Automatic Flight Controls Part I

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1 Design, Analysis and Research orporation (DARcorporation) ERRATA: Airplane Flight Dynamics and Automatic Flight ontrols Part I opyright 995 by Dr. Jan Roskam Year of Print, 995 (Errata Revised August 7, 08) Please check the website for updated errata page iii, line 3 page x, line 4 page xxii xxviii Topic 3..7 Review of Important Sign onventions should be removed The second word control in the description of the cl should be deleted Add the following symbols and descriptions Symbol Description Unit page xxii X, Y, Z Body-fixed (rotating) axis system -- page xxii X, Y, Z Earth-fixed (non-rotating) axis system -- page xxvi,, 3 Eular rotation sequence (the use of the symbol to denote the first Euler rotation is used only in hapter ) page xxvii P Origin of the XYZ system page xiii, Line 7 X should be Z page xxv, Line 6 page 6, Equation (.7) page 7, Line 4 g should be dimensionless. r p should be r p Should read The transformation formula of both equations (.) and (.). First, for the l.h.s. of Eqn (.): page 4, Line 33 = 90) should be = 90 page 7, Figure.7 The aircraft of the lowest figure should be seen from behind, i.e. a positive bank angle should have right wing down. Errata: Airplane Flight Dynamics and Automatic Flight ontrols Part I, Year of Print: 995

2 page 6, Equation (.6) = k should be = j page 8, Line 9 page 34, Line 5 page 40, Line 6 un should be in Should read Roskam, J.; Airplane Design, Parts I through VIII; Design, Analysis, and Research orporation, 440 Wakarusa Drive Suite #500, Lawrence, KS 66049, USA; 990 Should read apply to cambered (un-symmetrical) airfoils. page 43, Figure.6 S w f should be S w f page 44, Equation (.6) ( o i) ( + ) ( )( ) Sw = S f i + o page 47, Line page 5, Line 0 In variant should be invariant top should be to page 55, Equation (.7) d d d d = M M = ( 0 M ) page 59, Figure.0 Flap hord, c f, should go from hinge line to trailing edge page 63, Line 8 b) should be c) page 66, Figure 3. should be in Note 3 page 67, Line page 7, Equation (3.5) page 77, Equation (3.) page 80, Equation (3.9) page 84, Equation (3.30) loose should be lose D is the value of 0 D for: = i h = e = 0 L is the value of 0 L for: = i h = e = 0 m is the value of 0 m for: = i h = e = 0 Errata: Airplane Flight Dynamics and Automatic Flight ontrols Part I, Year of Print: 995

3 ( ) cos ( ) ( ) cos ( ) M = M + L x x L x x A acwf wf cg acwf h ach cg page 84, Equation (3.3) ( wf ) m = m + ac L + 0 L xcg xac wf wf wf S d ( x x ) + + i + S d h L h ac cg h o h ee h page 84, Line 7 Eqn (3.33) should be Eqn (3.3) page 85, Line 9 page 95, Line 6 page 97, Figure 3.8 page 98, Line page 99, Figure 3.30 page 04, Line page 04, Line 30 page 06, Equation (3.67) page 08, Figure 3.38 as well a positive should be as well as positive Should read shed vortices (at high angles of attack) which Normal velocity vector on left wing should not be present three-vies should be three-views Axis labeled as Z should be labeled as X loose should be lose right wheel deflection are activated should be right wheel deflection) are activated K SW needs to be defined: is the gearing constant between cockpit control wheel or stick and aileron or spoiler deflection The subscripts v should be taken out from the two variables Fa yrudder and N A rudder Sz v v page 08, Equation (3.7) s l = L r v r v Sb page 09, Equation (3.7) A = A = ( l + l a + l r ) L L qsb s a r page, Equation (3.76) F A y L y qs d = = q v S v v v v d Errata: Airplane Flight Dynamics and Automatic Flight ontrols Part I, Year of Print: 995 3

4 page 3, Equation (3.78) page 3, Equation (3.80) page 5, Line 4 page 7, Line 9 page 7, Line 8-9 page 8, Figure 3.46 page 8, Figure 3.46, Note The subscripts v should be taken out from the variables F a yrudder ( ) F = F = + + qs A y A y y a y r s y a r Should read The yawing moment due to the vertical tail may be written as: After Line 9, should read Methods for computing the yawing moment due to aileron control derivative are found in Part VI of Reference 3.. Lines 8-9 should read Methods for computing the yawing moment due to spoiler control derivative are found in Part VI of Reference 3.. Positive rolling moment should be Positive yawing moment induces drag should be induced drag page, Equation (3.9) A = A = ( n + n a + n r ) N N qsb s a r page, Equation (3.9a) i= n LT = L T = Ti ( zt cost sint yt sint ) cos i i i i i + s i = i= n + Ti ( xt cost sint yt cost cos T ) sin i i i i i i i = page, Equation (3.9b) i= n ( cos sin ) F F T = = Ty T i T T y i i i= page, Equation (3.9c) Errata: Airplane Flight Dynamics and Automatic Flight ontrols Part I, Year of Print: 995 4

5 i= n NT = N T = Ti ( xt cost sint yt cost sint ) cos i i i i i i + s i = i= n Ti ( zt cost sint yt sint ) sin i i i i i i = page 4, Equation (3.95b) The summation should say i = page 6, Table 3.4 V should be Q page 7, Line 4 Should read ) partial derivatives in Table 3.4 indicate the slope by which a particular perturbed force or moment is affected by a particular perturbed variable. page 33, Figure 3.5 V should be V p in all cases page 34, Figure 3.5 arctan D 0 should be P M M = M arctan D 0 M M = M page 34, Figure 3.5 aption should read Example of Determination of: D / M at a constant angle of attack page 36, Equation (3.9) Lu = M ( M ) L M u U page 36, Equation (3.) ( m m ) A = + q Sc u page 37, Line 4 Should read... are affected by changes in angle of attack, :... F Az = L + D q S page 39, Equation (3.33) ( ) page 4, Equation (3.4) airplane, caused by should be airplane L, caused by page 43, Line 5 Should read... multiplying by the non-dimensional Errata: Airplane Flight Dynamics and Automatic Flight ontrols Part I, Year of Print: 995 5

6 moment... M A page 45, Equation (3.56) = m qsc = m q qsc qc qc U U page 47, Equation (3.6) Replace the variable L in (,) entry to D c c page 47, Equation (3.6) should be U U page 48, Equation (3.63a) Ay y F = qs page 48, Equation (3.63b) LA = lqsb page 48, Equation (3.63c) NA = nqsb page 48, Line 7 changes in sideslip, should be changes in sideslip rate, page 48, Line 8 sideslip angle, should be sideslip rate, page 57, Equation (3.89) x vs S v yr yr L v v v = b S page 6, Equation (3.97) n p should be n p page 6, Equation (3.97) n r should be n r page 67, Equation (3.4) n p 550 pbhp F Tx = U + u page 68, Line 5 X Tu should be T Xu d page 68, Equation (3.3) T m = T T u Xu c page 73, Line 7 Should read normally sufficiently small that they can Errata: Airplane Flight Dynamics and Automatic Flight ontrols Part I, Year of Print: 995 6

7 be neglected page 74, Equation (3.48) 0 should be page 8, Line Should read Roskam, J.; Airplane Design, Parts I through VIII; Design, Analysis, and Research orporation, 440 Wakarusa Drive, Lawrence, KS 66049, USA; 990 page 8, Line 6 Should read Lan,.E. and Roskam, J.; Airplane Aerodynamics and Performance; Design, Analysis, and Research orporation, 440 Wakarusa Drive, Lawrence, KS 66049, USA; 990 page 86, Equation (4.3) ( Tx Du ) ( Tx D ) MA+ MT page 87, Table 4. Entry (5,5), ( MA+ MT) 0 u + 0 ( ) 0 should be page 89, Equation (4.7) A + T = y y ( y + Ty ) page 89, Line 3 (4.) should be (4.6) F F qs page 90, Line 6 criterion (4.) should be criterion (4.0) page 90, Line Z T L should be T z L page 95, Equation (4.36) ( m m ) ( u T m m T ) page 95, Line 6 Table 5. should be Table 4. page 96, Line Table 5. should be Table 4. page 98, Line (4.) should be (4.4) u page 99, Line 9 Where: which L mg. Note that cos.0, qs Errata: Airplane Flight Dynamics and Automatic Flight ontrols Part I, Year of Print: 995 7

8 page 0, Line 6 L mg = should be qs L mg qs page 06, Line 8 in Example. should be in Example ). page 08, Fig. 4.0 In the graph on the left, x cg = 0.5 should be x cg = 0.30 and vice versa page 09, Figure 4.b page, Line page, Line page, Line page 6, Line 5 page 8, Line 3 The negative tail stall locus as shown in the diagram is wrong. The trim diagram should have a positive tail stall locus at = 5 and a negative tail stall locus at = -. Both of these lines are out of the range of the diagram so none of them should be shown. The corresponding values for tail stall should be and 5, respectively. The sentence that reads, Figure 4.b shows only the negative tail stall locus because the positive locus is outside of the diagram should be removed degespectively should be deg respectively Appendix A.. should be Appendix A. F S TO should be V S TO page 9, Equation (4.76) should be ( NT + N ) page 0, Equation (4.8) D a r Vmc = n r r Sb max page, Figure 4.5 = 5 should be = 0 page, Figure 4.6a page, Figure 4.6a The lateral axis should be the Y-axis. Should read as shown is negative page 5, Equation (4.86b) Rb mur mg sin = y + y + r y a + y r q S U a r Errata: Airplane Flight Dynamics and Automatic Flight ontrols Part I, Year of Print: 995 8

9 page 5, Line 0 three of these should be four of these page 6, Equation (4.89) Rt = U g tan page 6, Equation (4.90) = g tan U page 6, Line 8 Should read By combining Eqns (4.85b) and (4.85c) with page 6, Equation (4.95) mur = mg sin page 7, Equation (4.96) Rb 0 = y + y + r y a + y r q S U a r page 7, Equation (4.97) should be page 7, Equation (4.03b) should be page 7, Equation (4.03c) should be page 7, Line 6 The first sentence should be removed. page 8, Equation (4.98) Variables a, b and c should be a, b and c page 8, Equation (4.99) Variables a, b and c should be a, b, and c page 8, Equation (4.00) Variables a, b and c should be a, b, and c page 8, Equation (4.00) should be page 8, Equation (4.0a) should be page 8, Equation (4.0b) should be page 8, Equation (4.0c) should be a r Errata: Airplane Flight Dynamics and Automatic Flight ontrols Part I, Year of Print: 995 9

10 page 8, Equation (4.0a) a should be a page 8, Equation (4.0b) b should be b page 8, Equation (4.0c) c should be c page 3, Equation (4.3b) should be page 3, Equation (4.4a) should be page 33, Line forward should be aft page 34, Figure 4. Arrow for M ac wf should act on the A.. of the wing-fuselage not the.g. page 35, Line 4 Should read M ( ) ac L wf wf x cg x ac wf page 35, Line 4 conventional should be canard is satisfied. page 36, Line 3 Should read M ( ) ac L wf wf x cg x ac wf is satisfied. page 37, Equation (4.3) ( ) ( ) + ( ) = 0 L x x L x x M L x x c cg acc wf acwf cg acwf h ach cg page 37, Line 7 in Eqn (4.0) should be in Eqn (4.3) page 37, Lines 0- Should read From Eqn (4.33) it may be concluded that as long as L h is positive (i.e. up) and ( xac xcg ) wf is positive the canard load to trim, L c, will also be positive (i.e. up). page 4, Equation (4.36) HM = hqhsece page 44, Line 7 q q h = should be h h = qh q page 50, Equation (4.47) Errata: Airplane Flight Dynamics and Automatic Flight ontrols Part I, Year of Print: 995 0

11 d = + ( i ) + d h m h m e d e L ( L m m L e e ) ho h 0 h h o h e trim L = d e L = 0 page 5, Line Should read... differentiating Eqn (4.48) with respect to the angle of attack. page 5, Equation (4.50) = ( x x )... m L cg ac stick free wf wf page 5, Equation (4.54) page 53, Equation (4.58) page 53, Line 3 m h e d NPfree xac + NPfix NPfix + wf L d h e m e d h SM fix SM free NPfix NPfree = = L d h e found by by should be found by page 55, Line 0 from Eqn 4.69) should be from Eqn (4.69) page 56, Equation (4.7) page 56, Line Scg MP x NP h e free = cg = free m Fs / n = 0. 4 q h W e stick-force-per- g should be stick-force page 59, Figure 4.36a e = should be = t e df page 59, Figure 4.36b e dv should be s df dv page 63, Line page 67, Line 0 Should read Next, recall the stick-force equation positive should be negative Errata: Airplane Flight Dynamics and Automatic Flight ontrols Part I, Year of Print: 995

12 page 67, Line page 67, Line 4 positive should be negative negative should be positive page 68, Line 4 page 68, Figure 4.43 Include in r definition: r negative Note should be: h > 0 v h < 0 r = and is normally r page 69, Equation (4.97) page 69, Equation (4.98) Svx v h Svxv n = L v r L v v free v Sb h v Sb r s v s Sx v v h s v n = n L v r Sb free fix v h r h v page 69, Equation (4.99) n = n + n free fix r h r page 69 Equation (4.03) F G q S c r = r v r r h r n r n free page 73, Line 4 Should read or, with Eqn (4.08) as: page 77, Line 3 D o should be D o page 78, Line 6 page 78, Line page 78, Line 6 Should read HM is the elevator hinge moment as expressed by Eqn (4.36) Should read, The hingemoment coefficient equation Equation 4.5 should be 4.5a Errata: Airplane Flight Dynamics and Automatic Flight ontrols Part I, Year of Print: 995

13 page 80, Line 6 e n F should be s n page 8, Line 0 Should read moment and stick-force trim. This represents page 8, Line List is inconsistent with Figure 4.49 page 86, Equation (4.4) h should be h r v page 88, Line 3 page 88, Line 5 Should read Exceptions to this are airplanes like the B-5. Should read at the instant of rotation: no load on the nose-gear. D = q S page 88, Equation (4.45) g Dg rotate page 88, Line 7 D ground should be D g page 90, Equation (4.46) L wf = L q rotate S page 90, Line 3 L should be wfground L wfg g wf g page 90, Equation (4.47) Lh = L h qrotate Sh g hg g page 90, Line 6 L should be hground L hg M = q Sc page 90, Equation (4.48) acwf mac rotate g wf g page 90, Line 8 m acwfground should be m acwfg page 9, Line 4 page 9, Equation (4.50) are should be area should be mg page 9, Equation (4.50) L maxhground should be L maxhg Errata: Airplane Flight Dynamics and Automatic Flight ontrols Part I, Year of Print: 995 3

14 page 9, Table 4.0 D ground should be D g page 9, Table 4.0 L should be wfground L wfg page 9, Table 4.0 L maxhground should be L maxhg page 9, Table 4.0 m acwfground should be m acwfg page 9, Figure 4.5b xcg g = 38 ft should be xcg g = 39 ft and vice versa page 99, Line 0 Eqn (4.55) should be Eqn (4.59) page 305, Figure 5. t should be t 0 in all cases page 307, Equation (5.a) page 307, Equation (5.b) page 307, Equation (5.c) page 34, Figure 5.6 page 36, Line 9 u u mu = mgcos + qs ( D + D ) + ( T + u x T U x ) + u U ( D L ) D e e u ( ) sin ( L L ) ( L D ) m w Uq = mg + qs u U c qc L L L e U q U e u ( ) ( ) u I yyq = qsc m + m + u m + T m + T m + m + U u U T c qc + m + m + m e U q U e Solid black line should be removed the system is zero should be the system are zero page 38, Line 5 Should read First, by using the substitution q = and w= U Errata: Airplane Flight Dynamics and Automatic Flight ontrols Part I, Year of Print: 995 4

15 qsc m page 39, Table 5. M = I U should be qsc m M = I U page 3, Equation (5.34) Equation for should read: = ( X ) u + X Tu Mq( U Z ) + Z + M ( U+ Zq) + yy + MqZ Zu X + M g sin ( M + MT )( U+ Zq ) page 3, Equation (5.35) Equation for B u should read: yy ( ) ( ) B u = X e U Z M q + Z + M U + Z q + Z e X page 34, Line 6 Should read Response of the airplane to control page 38, Equation (5.48) m m u + + L D Lu L m page 38, Equation (5.49) ( xcg x ) m = u ac A L L + u L page 33, Equation (5.53) page 333, Equation (5.54) s,, n j, n,, s = or sp = spn jn sp sp sp s 3,4 3,4n j 3,4 n3,4 3,4 s = or ph = phn jn ph ph ph page 333, Line 8 Should read T = 0.35sec and T = 0.8 sec page 333, Equation (5.56) 3,4 3,4n j 3,4 n3,4 3,4 s = or s 3 rd = 3 rd n jn 3 rd 3 rd 3 rd Errata: Airplane Flight Dynamics and Automatic Flight ontrols Part I, Year of Print: 995 5

16 () s ( Z s XuZ e + X e Z e u) page 338, Equation (5.69) = () s e gz U s Xus U u page 340, Line 3 ration should be ratio page 340, Equation (5.76) u( t) page 340, Equation (5.77) ( ) page 340, Equation (5.78) ( t) lim lim e Nu = s =... t s 0 s D lim lim e N t s = =... t s 0 s D lim lim e N s = =... t s 0 s D page 34, Equation (5.8a) page 34, Equation (5.8b) ps n sp ps n sp should be ps np should be ps np page 34, Equation (5.8b) n should be s n page 34, Equation (5.8c) ps n sp should be ps np page 346, Equation (5.94) In the (3,3) element of the transformation matrix, cos should be cos page 350, Line 6 ( s) / ( s) should be ( s) / ( s) e page 357, Line (pitching moment of inertia) should be (lat.-dir. inertias) page 364, Line 8 Eqn (5.0) should be Eqn (5.) Errata: Airplane Flight Dynamics and Automatic Flight ontrols Part I, Year of Print: 995 6

17 page 37, Equation (5.36) ( t) page 37, Equation (5.37) ( t) page 37, Equation (5.38) ( t) page 37, Line 35 ( ) should be ( t) lim lim a N = s =... t s 0 s D lim lim a N = s =... t s 0 s D lim lim a N = s =... t s 0 s D page 38, Figure 5.4 page 38, Figure 5.5 page 38, Figure 5.6 page 38, Figure 5.7 page 383 Remove the two lines before Section page 384, Figure 5.8 page 384, Figure 5.9 page 385, Figure 5.30 page 385, Figure 5.3 page 387, Figure 5.3 page 387, Figure 5.33 page 388, Figure 5.34 page 388, Figure 5.35 page 390, Figure 5.36 page 390, Figure 5.37 page 39, Figure 5.38a page 39, Figure 5.38b Errata: Airplane Flight Dynamics and Automatic Flight ontrols Part I, Year of Print: 995 7

18 page 393, Figure 5.39 page 393, Figure 5.40 page 394, Figure 5.4 page 394, Figure 5.4 page 396, Line 5 page 398, Line page 398, Equation (5.6) page 398, Line 0 page 398, Line 5 page 399, Line 8 page 399, Line 9 Should read say 0 deg/deg/sec, a 3 deg/s pitch rate elevator deflection should be rudder deflection K r ( n n ) n b b rsas rsas on rinherent = = U U n n r pitch should be yaw Should read come out very high, say 0 deg/deg/sec. In that case a 3 deg/sec yaw rate perturbation would /56x.688=.4 deg should be x57.3/(.688x56)=.4 deg -0.8 degrees should be -.6 degrees r page 400, Line Eqns (5.76) should be Eqns (.76) page 40, Figure 5.44 On the Y B vector, the smaller vector should be labeled q page 403, Line 8 ( P ) should be ( ) 4 P page 405, Lines 4-8 Remove paragraph contained by lines 4-8 page 407, Line 4 cos = 0 should be cos = page 4, Line 7 page 44, Table 6.4 Should read How well do these results agree with your conclusions from problem 5.? The ivilian Requirements FAR-3 are updated to the following: Errata: Airplane Flight Dynamics and Automatic Flight ontrols Part I, Year of Print: 995 8

19 For wheel controllers: ( ) F s W TO and n n n limit limit limit 50.0 but not more than: n For stick controllers: Fs n W 5.0 TO and 40 n limit 35.0 but not more than: n limit page 47, Line 6 page 47, Line 7 Remove the return so be and written are on the same line. time to double should be time-to-double page 434, Line Reference 6.5 should be Reference 6.6 page 453, Table 6. ell (,5) should read Number on Root Locus of Figure 6.6 page 456, Equation (6.6) egust ( S ) = 0.03S h h gust page 457, Figure 6.8 Note Add a gust =.8 degrees page 460, Line page 46, Lines 0-3 page 466, Line 6 page 466, Line 9 Should read Roskam, J.; Airplane Design, Parts I through VIII; Design, Analysis, and Research orporation, 440 Wakarusa Drive Suite #500, Lawrence, KS 66049, USA; 990 Should read 440 Wakarusa Drive Suite #500, Lawrence, KS 66049, USA Tel Should read Design, Analysis, and Research orporation, 440 Wakarusa Drive Suite #500, Lawrence, KS 66049, USA Should read Design, Analysis and Research orporation, 440 Wakarusa Drive, Suite #500, Lawrence, KS 66049, Errata: Airplane Flight Dynamics and Automatic Flight ontrols Part I, Year of Print: 995 9

20 USA Tel Appendix B h should be h r v for all examples page 480, Table B page 487, Table B page 50, Table B4 page 560, Line 8.G. location should be 0.64 c.g. location should be 0.33 c.g. location should be 0.7 c Should read Roskam, J.; Airplane Design, Parts I through VIII; Design, Analysis, and Research orporation, 440 Wakarusa Drive Suite #500, Lawrence, KS 66049, USA; 990 Errata: Airplane Flight Dynamics and Automatic Flight ontrols Part I, Year of Print: 995 0