a) Its inertia characteristic -) 5arth.s acceleration due to gravity c) 3ropulsive force generated -y power plant d) Aerodynamic forces 067+) and moments created on it due to the reaction -etween airplane and air
8) Why the airplane is considered as a dynamic system in si$ degrees of freedom? What are the conditions to -e satisfied for e9uili-rium along a st raight unaccelerated flight path? Ans: Airplane motion in air can -e completely defined only if si$ velocity components 0linear velocities u,v,w along ,;,< a$es and angular velocities p,9,r a-out ,;,< ,;,< ) are given =ence airplane is considered as a dynamic system in si$ degrees of freedom >or e9uili-rium along a straight unaccelerated flight path, the e9uation of static applied to each degree of freedom must -e satisfied:
) What is plane of symmetry of airplane and define symmetric and asymmetric degrees of freedom? Ans: 3lane of symmetry of airplane is the < plane that divides it into two symmetric halves Symmetric degrees of freedom are t hose components of motion related to airplane/s longitudinal motion 2hey are motions along and < a$es and a-out ;a$is Asymmetric Asymmetric degrees of freedom are those components of motion related to airplane/s lateral motion 2hey are motions along ; a$is and a-out and < a$es
@) What will decide the lateral 0asymmetric) degrees of freedom and define directional sta-ility and dihedral effect Ans: 6ateral degrees of freedom of an airplane is decided -y the direction of relative wind to the plane of symmetry 2his angle is called sideslip 0 ) and the airplane is designed to resist the development of sideslip during all normal flight maneuvers 2he a-ility of the airplane to create yawing moments that tend to eliminate any sideslip is called directional sta-ility 0sometimes called weathercock sta-ility) 2he rolling moment created -ecause of sideslip is
a) Its inertia characteristic -) 5arth.s acceleration due to gravity c) 3ropulsive force generated -y power plant d) Aerodynamic forces 067+) and moments created on it due to the reaction -etween airplane and air
8) Why the airplane is considered as a dynamic system in si$ degrees of freedom? What are the conditions to -e satisfied for e9uili-rium along a st raight unaccelerated flight path? Ans: Airplane motion in air can -e completely defined only if si$ velocity components 0linear velocities u,v,w along ,;,< a$es and angular velocities p,9,r a-out ,;,< ,;,< ) are given =ence airplane is considered as a dynamic system in si$ degrees of freedom >or e9uili-rium along a straight unaccelerated flight path, the e9uation of static applied to each degree of freedom must -e satisfied:
) What is plane of symmetry of airplane and define symmetric and asymmetric degrees of freedom? Ans: 3lane of symmetry of airplane is the < plane that divides it into two symmetric halves Symmetric degrees of freedom are t hose components of motion related to airplane/s longitudinal motion 2hey are motions along and < a$es and a-out ;a$is Asymmetric Asymmetric degrees of freedom are those components of motion related to airplane/s lateral motion 2hey are motions along ; a$is and a-out and < a$es
@) What will decide the lateral 0asymmetric) degrees of freedom and define directional sta-ility and dihedral effect Ans: 6ateral degrees of freedom of an airplane is decided -y the direction of relative wind to the plane of symmetry 2his angle is called sideslip 0 ) and the airplane is designed to resist the development of sideslip during all normal flight maneuvers 2he a-ility of the airplane to create yawing moments that tend to eliminate any sideslip is called directional sta-ility 0sometimes called weathercock sta-ility) 2he rolling moment created -ecause of sideslip is
referred to as dihedral effect 2he second type of static lateral sta-ility is associated with the dihedral effect
1") +efine compressi-ility of fluids and what decides the speed of propagation of small pressure waves in fluids ? Ans: ompressi-ility of fluids 0*) is defined as the reciprocal of -ulk modulus of fluids or it is the volumetric strain 0dv'v) developed per unit change in pressure 0 * ! 0dv'v)'dp ) Speed of propagation of small pressure waves 0sound waves) is dependent on the elastic property 0-ulk modulus) of the fluids Speed of propagation of sound wave is a ! 0dp'd ), where dp 7d are change in pressure and density
11) =ow the sound waves travel in gases and give the e$pression for the speed of sound in gases? Ans: Sound waves travel in gases as a series of adia-atic compressions and rare fractions and hence the e$pression for the speed of sound waves is a ! 0 0dp'd ))"% ! 0 p' ) "% ! 0 gB2)"%
1() What are the different power plants used in airplanes? Which power plant is most efficient for su-sonic airplanes Ans: 6atest power plants used in airplanes include propeller driven -y recipro cating engines as well as tur-ines , tur-oCets ,ramCet and rockets =ere other than rockets all other power plants are using air-reathing engines 2ur-oCet 2ur-oCet power plants are most efficient for su-sonic airplanes compared to 2u 2ur-oprop, r-oprop, ramCet and rockets BamCet and rockets are efficient for short duration supersonic flights whereas tur-o propellers propellers are less efficient and can -e used only at low speed
1#) Write down the maCor differences -etween the tur-oprop and tur-oCet engines in generating the propulsive power Ans: In airplanes using tur-o propeller system, out of total useful work done to propel the airplane , "@%D is derived from the propeller and the reminder only from the e$haust Cet reaction In typical tur-oprop system, power03! 2E) is nearly constant and hence thrust 02) decreases as speed 0E) increases In tur-oCet propulsion system, the total useful work done to propel the airplane is produced -y the e$pansion of the com-ustion gases through e$haust noFFle 2hrust is made nearly constant -y increasing the mass flow rate 0kg's) at high speed 0E)
1G) What are the conditions for minimum drag and minimum power re9uired for an airplane? Hention them in drag coefficients also Ans: Hinimum drag 0+) occurs when 6'+ or 6'+ is a ma$imum It occurs when parasite drag ! induced drag or when +f !6(' Ae Hinimum power 03min) occurs when the parasite power is 1'# of Induced power In the drag coefficient form +f ! 1'#06(' Ae)
1%) What causes induced drag? Ans: Induced drag is an unavoida-le -yproduct of lift and it increases as the angle of attack 0 ) increases Jp to a critical angle of attack 0 c at which 6ma$ occurs) -oth lift and induced drag increases Since there are two types of lift 0dynamic 7 induced lift) , there are two types of drag also dynamic drag and induced drag A-ove cr ,lift will decrease and drag will overcome the thrust causing reduction of speed and altitude
14) +efine skin friction drag and pressure drag Ans: +rag caused -y the shear force 0viscous flow) in the -oundary layer is called skin friction drag 2he drag caused -y the pressure variation over and -elow the surface of the wing is called pressure drag It is caused -y flow of high pressure
air from under the wing to over the wing Sum of the a-ove two drags are called profile drag All drags other than induced drag is called parasite drag
18) What are the conditions re9uired for ma$imum drag and minimum power? Ans: Ha$imum drag occurs when the angle of attack e$ceeds the critical angle of attack and the speed approaches the stalling speed 2he left hand limit of 3B versus Ecurve shows the stalling speed corresponding to ma$imum lift 06ma$) and ma$imum drag Hinimum power occurs at the speed at which total power03B) is minimum 2his occurs when parasite drag is 1'# of induced drag In drag coefficient form, +f ! 1'#06(' Ae)
1) 5$plain the significance of load factor Ans: 6oad factor 0n) is defined as the lift 0 6) divided -y the weight 0W) at the stalling speed corresponding to 6ma$ Any attempt to increase the lift -y further increasing the angle of attack will result in the reduction of 6 and increase of + 2his will result in increase of thrust re9uired to maintain the flight at lower speed =ence a load factor of 1, at 6ma$, only feasi-le provided enough power is availa-le
1@) 3lot the variation of power availa-le 03A) with flight speed 0E) for a propeller powered airplane and indicate the effect of altitude on the curve Ans: >irm line 03AK) on the 3A versus E graph shows the power availa-le at sea level for a propeller powered airplane 2he dotted line 3A shows the power availa-le at an altitude where the density ratio, ! of air at altitude' of air at sea level , 3A ! 3A"
(") =ow load factor 06'W) is related to -ank angle? Ans: +uring turning, the -ank angle 0
) is related to 6ift 06) and weight 0W) as
follows: 6 Sin
! > !
(Wv gB ie, Sin
!
((1vWv gB 6 gB 6oadfactor
! =ence -ank angle 0
) decreases when load factor 06'W) increases
(1) +efine service and a-solute ceiling Ans: 2he system of 3B and 3A versus E curves, -oth at sea level 0o) and altitude 0 ) are fundamental in determining clim- and decent performance of airplane Hinimum and ma$imum speeds 0a-solute ceilings) are determined -y the intersection of the two curves 03B and 3A) taken for the same altitude Any speed -etween the ma$imum and minimum ceiling speeds can -e the service speed Sometimes in altitude flight, the minimum speed will -e higher than the stalling speed and hence the stalling speed cannot -e achieved in level continuous flight
(() What is the compressi-ility speed correction of airplane and how Ecorr is related to true speed E? Ans: At or near the critical mach num-er 0Hcr) of the air plane , the drag increases at a greater rate than the para-olic variation Speed correction curves 0thrust constant ) at different altitudes are availa-le A correction speed Ecorr is o-tained from the chart for any incompressi-le speed ,E Ly the assumption of constant thrust for tur-oCet -etween E and Ecorr ,the E can -e related to
Ecorr as follows: 2 ! + ie + 9 S ! +corr9 corrS =ence E ! Ecorr 0 +corr'+)
(#) =ow the speed correction 0Ecorr) due to compressi-ility effect is related to incompressi-le speed 0E) when speed, altitude, t'c ratio and 6 increases Ans: >or a specific E, Ecorr will -e lesser than E and the deviation increases with the speed , increase in t'c ratio and 6 >or each case Hcr is the upper limit A-ove specified deviations -etween E and Ecorr are further enhanced in higher altitude >rom constant power curves , Ecorr is related to E as follows : E ! Ecorr0+corr'+)"###
(G) +efine range and endurance of an airplane Ans: >or an airplaneengine com-ination, the range 0B km ) may -e determined Ly multiplying the total fuel 0>kg) availa-le -y the average km traveled per kg of fuel consumed ie B 0km) ! >0kg) 0km'kg ) Similarly for an airplane engine com-ination, the endurance 05hrs) may -e computed -y dividing the total fuel 0kg) availa-le -y the average consumption of fuel in kg'hr ie 5 0hrs) ! > 0kg) '0kg'hr)
(%) >or tur-oCet driven airplane at what E'E6'+ma$ min or ma$ occurs Also for the tur-opropeller driven airplane at what E'E6'+ma$, B'ma$ or B'Smin occurs Ans: >or tur-oCet driven airplane , from the 2A'26'+ma$ versus E'E6'+ma$ curve , it is found that at min or ma$, the value of E'E6'+HA !1 Similarly for the tur-opropeller driven airplane from the 3A'36'+ma$ versus
E'E6'+ma$ curve, it is found that at B' ma$ or B'Smin , the value of E'E6'+ma$ is e9ual to "84
(4) +raw 2B versus E graph of tur-oCet airplane and indicate Ema$5 and Ema$Binit Ans: Ema$5 is the minimum 2B point on the graph Ema$B is the tangent point on the graph
(8) +raw 3B versus E graph of tur-o propeller airplane and indicate Ema$5 and Ema$B in it Ans: Ema$5 is the minimum 3B point on the graph Ema$B is the tangent point on the graph
() What are the conditions for ma$imum endurance of a Cet powered airplane? Ans: 59uation for ma$imum endurance 05ma$) for Cet powered airplane is: 5ma$ ! 01'c)06'+)ma$ ln 0Wo'W1) >or ma$imum endurance: 1) c01'hr) should -e small () 06'+) ma$ should -e high #) 0Wo'W1) mass ratio should -e high
(@) What is the condition for Bmin for turning an airplane in level flight? Also give the time 0t) for #4"" turn in terms of E and tanM 0Mturning or yawing angle) Ans: onsidering the turning -anking angle as M, tan M! E('Bg , ie B ! E('g tan M >or Bmin 1) E should -e small, approaching to Estall () tan M should -e high 2ime for #4"" turn 0t) ! ( B'E !( E'g tan M
#") What is the impact of acceleration in B' as compared to nonaccelerating clim-? Ans: Angle of clim- 0 ) is related to B' as Sin ! 0B' ) 'E Also Sin !02+>1)'W 0where 2 is thrust , + drag and >1 inertia for acceleration), then B' 0m's) ! E02+>1)'W 01) And B' without acceleration !E02+)'W 0() If acceleration is not considered 0(), the B' will -e higher than B' with acceleration 01) 2hat is the time to clim- to a particular altitude will -e higher -y (% #"D than that of without acceleration
#1) Show -y graphical solution of range 0B), what is the additional fuel0d>) re9uired to get the same range when empty weight is increased -y 0 W) Ans: >or keeping the range 0B) same, the additional fuel 0d>) re9uired when empty weight of airplane is increased -y W , can -e find out -y e9uating area A1! A( , ie 1d> !( W 0where 1 and ( are the range per kg at the start and end of flight ( will -e higher than 1 2hen d> ! W ('1 , ie d> is greater than W Short 9uestions and answers0HoduleIII)
#() What is meant -y control of an airplane, how longitudinal, roll and directional controls are provided in airplane Ans: When an airplane is sta-le, it is necessary for the pilot to -e a-le to control it, so that he can maneuver it into any desired position 6ongitudinal control is provided -y the elevator, ie flaps hinged -ehind the tail plane Boll control is provided -y the ailerons, ie flaps hinged at the rear of the Aero foils near each wing tip +irectional control is provided -y the rudder, ie a vertical tail hinged to the stern post
##) What is meant -y sta-ility of an airplane and what way it is different from Lalance? Ans: 2he sta-ility of an airplane means its a-ility to return to some particular condition of flight , after having distur-ed from that condition ,without any effort -y the pilot 2he sta-ility is often confused with the -alance or e9uili-rium of an aircraft >or eg: when an airplane flies with one wing lower than the other may often ,when distur-ed from that attitude ,return to it Such an airplane is out of its -alance or trim, -ut it is sta-le Sta-ility is sometimes called inherent sta-ility
#G) +efine the three conditions of sta-ility Ans: 2here is a halfway condition -etween sta-ility and insta-ility If the airplane on distur-ance tends to move father away from its original position, it is unsta-le If it comes -ack to its original position, then it is in sta-le condition Lut sometimes the airplane may tend to do neither of the two and prefer to remain in its new position 2his condition of airplane is called neutral sta-ility
#%) With the help of m vs 6 curve of an airplane, state the sta-le, neutral and unsta-le conditions of it Ans: +raw a graph with m on ; a$is and 6 on a$is In ; a$is, represent m !" a-ove origin to indicate -oth positive and negative m values 6ine 01)70() in which dm'd6 " shows unsta-ility or neutral sta-ility 6ine 0#) in which dm'd6 " sta-ility When m ! ", the airplane is in e9uili-rium
#4) What are the two methods for predicting fuselage contri-ution to longitudinal sta-ility of airplane? Write down the formulae for simpler method and e$plain the terms in it
Ans: Hethods for predicting fuselage contri-ution to longitudinal sta-ility are 0a) omputational method -y dividing the fuselage ito many sections 0-) A Shorter method for which the following formulae is used 0 dm'd 6 ) fus ! 0*f Wf( 6f)'Sw c aw 0where 6f is the over all fuselage length ,Wf is its ma$imum width and *f is an empirical factor developed f rom e$perimental evidence It depends entirely on the wing root chord/s position on the fuselage
#8) +efine neutral point Ans: It is the limit of the centre of gravity of the airplane at which the static longitudinal sta-ility -ecomes neutral 0dm'd6) !" 2his sta-ility criterion of the airplane 0ie neutral point) will -e different at different operating conditions like, stickfi$ed with and without power ,stick f ree with power Also there is aft cg limit as well as forward cg limit Letween these limits of neutral points only the airplane cg can -e allowed to shift during all maneuvering conditions of airplane in order to maintain longitudinal sta-ility
#) What is the criterion for static longitudinal sta-ility? Ans: >or static longitudinal sta-ility of the airplane 0A3) the over all value of 0dm'd6)A3 " 2his rate of change of coefficient of moment a-out ;a$is 0dm) with respect to the change in lift coefficient 0d6) is the summation of similar values contri-uted -y different parts of airplane , like ,wing ,fuselage , engine power, tail'elevator etc Some of them are positive and others are negative 2he cumulative effect should -e such that over all value should -e negative 0ie 0dm'd6)total " )
#@) State two contri-utions for static longitudinal sta-ility and indicate them with a plot Ans: In m versus 6 plot indicate the longitudinal sta-ility contri-utions of wing
And fuselage, tail alone and the total for airplane If the total longitudinal sta-ility which is the sum of individual contri-utions is negative 0dm'd6 ) " then the airplane will -e sta-le
G") Lriefly define wingNs vorte$ system with figure Ans: WingNs vorte$ system can -e represented as shown in figure, consisting of N-ound vorte$ N located at the wing 9uarter chord 0"(% c) and a vorte$ sheet streaming from the wing trailing edge, which will roll up to form the familiar two trailing vortices 2he wing wake center line which is in the vorte$ sheet is displaced downward and deformed -y the influence of the -ound vorte$ and the powerful trailing vortices 2he strength of the vorte$ system is prop ortional to the 6 therefore the downwash 0O) at any particular point will -e proportional to 6 ie O ! f0 6)
G1) What is &eutral point 0&") of an airplane at stick fi$ed and poweroff condition Show the new position of .&"/ at poweron condition relative to the earlier &" Ans: 2he aft position of cg of the airplane o-tained -y e9uating the static longitu dinal sta-ility e9uation 0dm'd6)total to Fero , with the contri-ution for sta-ility at stickfi$ed and power off condition added to it 2his cg limit at aft end with stickfi$ed and poweroff gives the limit for the sta-ility 2he new position of the airplane neutral point &oN at poweron condition will -e towards the forward side of the &o, since the contri-ution to sta-ility -y the power effect is slightly desta-iliFing
G() What are the two maCor effects of the running propeller that contri-ute to the 6ongitudinal sta-ility and define them Ans: 2wo maCor effects are 01) +irect propeller contri-ution arising as a result of the forces created -y the propeller itself 0() Indirect effects which arises as the result of the slip stream from the propeller and its interaction with the
wing and tail surfaces 3ropeller forces ,-oth thrust 02) and normal force0&p) create moments a-out cg of the airplane and hence they have sta-ility contri -ution 0dmp'd6) which influence the over all static longitudinal sta-ility
G#) What are the maCor contri-utions of the indirect effects of the running propellers on the static longitudinal sta-ility ? Ans: 2here are G maCor contri-utions making up the indirect effects of the running propellers on static longitudinal sta-ility 2hey are the effects of slip stream created -y propeller on the following : a effect of slipstream on wingfuselage moments - effect of slipstream on wing lift coefficient 06) c effect of slipstream downwash at the horiFontal tail d effect of increased slipstream dynamic pressure 09) on the tail
GG) +efine elevator power and write down the elevator power criterion e9uation Ans: 2he magnitude of pitching moment coefficient, m, o-tained per degree deflection of the elevator is termed as the elevator power It is the derivative of m wrt elevator deflection 0dm'd e !m ) 2he elevator power criterion is mentioned -elow dm'd e !m
G%) What are the direct propeller contri-utions to S6S arising due to the forces created -y propeller and write their simple forms in terms of 0h'c) and 0lp'c) Ans: +irect propeller contri-ution to S6S arising due to forces 0 2 and &p) created -y propeller are thrust 02) contri-ution 0dmp'd6)2 and the normal >orce 0&p) contri-ution 0dmp'd6)&3 0dmp'd6)2 ! "(% h'c if cg of airplane is a-ove thrust line 0h'c is Pve ), 0dmp'd6) is positive and hence desta-iliFing If thrust line is a-ove cg 0h'c is ve),0dmp'd6) is negative and hence sta-iliFing Simlarly 0dmp'd6)&3 ! ""(lp'c
G4) Lriefly e$plain the cg limits with the help of a figure and what decides the anticipated cg travel of the airplane Ans: Letween stickfi$ed poweron condition neutral point 0&o) and forward cg limit at 6ma$ landing condition ,the cg of airplane can travel Hore cg range re9uired , the more powerful will -e the elevator It can -e seen that anticipated cg travel of the airplane is decided -y the elevator and the horiFontal tail
G8) =ow the most forward cg limit of the airplane is fi$ed? Ans: An indication of the most forward cg permissi-le comes from t he elevator theory 2hat is from the re9uirement that the elevator must always -e capa-le of -ringing the airplane into e9uili-rium at 6ma$ attaina-le -y it As the cg moves forward ,the airplane -ecomes more sta-le and more upelevator is re9uired to trimout 6ma$ K-viously some forward cg , the elevator will -e Cust powerful enough to attain e9uili-rium at 6ma$
G) Write down the e$pression for the ma$imum sta-ility attaina-le -y the elevator using its ma$imum upelevation Ans: 2he e$pression for the limiting sta-ility can -e o-tained -y su-stituting ema$ and 6ma$ in the e9ation given -elow : 5levator up deflection e ! eo 0dm'd6) 6'm and solving for 0dm'd6)ma$ ! 0 eo ema$ ) m ' 6ma$ 0where eo is the elevator angle at Fero lift and m is the elevator power )
G@) =ow the forward cg limit is restricted -y the ground effect or for landing maneuvers Ans: 2he forward cg location is limited -y the influence of the ground on the
downwash during landing 2he varia-les that will -e altered -y the ground effect are wingNs angle of attack 0 w) ,elevator power 0m ) due to increase in at ! d6t 'd t and d ' d t ! , the elevator effectiveness
%") Write the total elevator hinge moment coefficient e9uation and define the components it Ans: 5levator total hinge moment coefficient 0h) e9uation can -e written as: h ! Ph P h ho is the hinge moment coefficient term at Fero angle of attack h the partial derivative of hinge moment coefficient wrt angle of attack of the tail ! h' h the partial derivative of hinge moment coefficient wrt control surface 0elevator ) deflection ! h ' Since most control surfaces 0elevator) are symmetric airfoil sections the 2erm ho will not -e included unless specifically asked for
%1) What is meant -y aerodynamic -alancing control surface and how it is most fre9uently done? Ans: Hethods for controlling the parameters h and h 0partial derivatives of hinge moment coefficients with respect to and ) are called aerodynamic -alancing control surfaces Kne of the most fre9uently used methods is the set-ack hinge In this ,-y suita-le mechanism the hinge line is moved aft such that the sum of moments a-out the hinge line will -ecome smaller
%() What is a ta- and how it is effective? Ans: 2a- is a control surface and is an au$illary flap usually -uilt into the trailing edge of the main control surface Lecause of its location, it can create very powerful moments a-out the control surface hinge line It is used as a trimming device,a -alancing device and in some cases as a primary control
surface
%#) et a relation for the control surface floating angle of an elevator fitted with ta- also Ans: Assuming linearity for the hinge moment coefficients, the total control surface hinge moment coefficient 0h) can -e written : h ! h Ph e e Ph t t At the floating -alanced condition, h ! ", and e ! float Ie float ! 0h ' h e ) 0h t ' h e ) t which indicates that deflecting the ta- can change the control surface floating angle
%G) =ow the effect of freeing the elevator changes the tail contri-ution to the longitudinal sta-ility ? Ans: 2he effect of freeing the elevator enters the tail term of the longitudinal sta-ility as a multiplying factor 0 1 0h ' h e)) If an elevator has a large floating angle , 0h ' h e) will -e large and positive 2hen the sta-ility contri-ution of the horiFontal tail can -e reduced sufficiently >or eg: if 0h ' h e) ! ( and ! "%, the floating of the elevator can make the whole tail contri-ution of sta-ility Fero 2his shows the importance of careful elevator -alance design to ensure proper hinge moment characteristics and there-y good stickfree sta-ility can -e readily appreciated
%%) What is the effect of gradient of stickforce with velocity on the sta-ility of the airplane ? Ans: 2he gradient of stickforce 0>s) with velocity is e$tremely important, as it plays a maCor role in determining the pilotNs feel of airplane sta-ility A large gradient 0d>s'dE) will tend to keep the airplane flying at constant E and will resist the influence of distur-ance towards changing E It also ena-le the
pilot to -ring the airplane to trim easily and will not re9uire a lot of pilot attention to hold the given Etrim
%4) What are the two methods in determining the stickfree neutral point 0&oN) and define them Ans: Loth methods are through flight test data evaluation In 1st method , the non dimensional stick force e9uation 0>s'9) is differentiated wrt to 6 and e9uate to Fero 2he cg position for d0>s'9)'d6 ! " will give the neutral point It can -e seen that 0&oN) will decrease with increase of 6 In the second for getting neutral point 0&oN) is to o-tain flight curves of ta- angle 0 e) to trim 0>s!") versus speed for different cg positions 2he slope of t vs 6 is a function of stickfree longitudinal sta-ility criterion and the neutral point 0&oN) is the cg position when d t 'd6 !"
%8) What are the commonly used gadgetries for improving stick force gradient? Ans: 2here are a few new devices now availa-le for giving constant pull force on the stick 2he most common of them are the down spring and -o- weight, vee ta- or spring ta- 2he down spring and -o- weight are not very effective in ground operation where as the spring ta-s are more efficient in giving a constant tor9ue a-out the hinge line of the elevator
%) What is the restriction on the aft cg imposed -y the stickfree neutral point 0&oN) ? Ans: 2he concept of stickfree neutral point 0&oN) is that cg location where 0dm'd6)free ! " or where d>s'dE ! " through trim speed where >s!" 2his -rings a new restriction on the aft limit of the allowa-le cg range At present the Army and &avy call only for the most aft cg to -e ahead Kf the stickfree neutral point 0&oN) 0Show the new aft limit of cg 0&oN) and usa-le cg range in a figure usually
used )
%@) What are the two important maneuvering flights and their essential re9uirements? Ans: >light in curved paths are called maneuvering flight 2wo important maneuvering flights 0a) that taking place in vertical plane passing through the plane symmetry of air plane called pullup maneuvering 0-) that taking place in horiFontal plane called normal turn In 0a) , the net upward force 06W ) act as the pullup force perpendicular to the curved path In 0-) the resultant of lift vector in the horiFontal plane perpendicular to the flight path act as the centripetal force
4") +efine stickfi$ed maneuvering point 0&m) and stick free maneuvering point 0&mN) Ans: If the cg is moved aft -ehind 0&o) and 0&oN), the sta-ility in accelerated flight will -e reduced until at some cg position the change in elevator angle 0d e ) and the stick force 0>s) re9uired to accelerate flight will -e Fero 2hese cgNs are termed as the maneuvering points 2he cg where the elevator angle 0 e) re9uired to accelerate the airplane vanishes is the stickfi$ed maneuvering point 0&m) and the cg where >s re9uired to accelerate the airplane vanishes is the stick free maneuvering point 0&mN)
41) What is the criterion for longitudinal sta-ility and control in maneuvering flight? Ans: 2he increment of elevator angle 0 e) and stick f orce 0 >s) to produce an increment in normal acceleration e9ual to 1g at constant speed ,-oth in pull ups and in steady turn is the criterion for longitudinal sta-ility and control in maneuvering flight 2hat is 0d e 'dn ) and 0d>s'dn) are criterion
4() +efine stick fi$ed maneuvering point 0&m) and where it is located with reference to neutral point at stickfi$ed 0&o) Ans:As the airplane cg is moved aft of 0&o) , the gradient 0d e 'dn ) continues to reduce until at some cg position it vanishes 2his cg position at which d e'dn !" is termed as the stick fi$ed maneuver point 0&m) Since &m &o! 0dm'd6)fi$ , the &m is aft of &o 2he difference -etween &m and &o is the greatest at sea level and for light wing loads 0W'S)min
4#) +efine stick free maneuver point 0&mN) and where it is located with reference to neutral point at stick free 0&oN) Ans: 2he gradient of the stick force 0d>s 'dn) do not vanish at stick free neutral point 0at 0dm'd6)free !" ) -ut shows that , if cg is moved sufficiently aft of &oN , a position will reach where d>s'dn !" 2his cg position is termed as stickfree maneuver point 0&mN)
4G) What are the restrictions on the cg travel imposed -y t he gradient of stick force per g in modern airplane ? Ans: 2he upper limit or lower limit of stickforce per g 0d>s'dn) re9uired for modern airplanes imposed further restriction on the cg travel of the airplane for maintaining S,6,S 2he forward cg is limited to ma$: gradient d>s'dn and the aft cg is limited -y the min: gradient of the same =owever it is found that the stickfree neutral point 0&oN) comes -etween these two
4%) What is the final cg travel limit of the airplane for S6S considering the flight upto stickfree conditions ? Ans: 2he critical limits on airplaneNs cg are : 1) Kn the forward cg,
0a) Ha$imum gradient ,stick force per g 0d>s'dn) ma$ 0-) 5levator re9uired to land at 6ma$ ()Kn the aft c,g : 0a) 3ower on stickfree neutral point 0&oN) 0-) Hinimum gradient, stick force per g 0d>s'dn) min 2he usa-le cg range is -etween 0d>s'dn)ma$ point and poweron stickfree &eutral point 0&oN) Short 9uestions and answers0HG 7 H%)
44) What is meant -y dihedral effect? Ans: 2he angle that the relative wind makes with longitudinal a$is of airplane is called sideslip 2his sideslip 0 ) alters the wing/s span wise lift distri-ution to create a net rolling moment 2his rolling moment due to sideslip is termed as dihedral effect It is the measure of change in rolling moment coefficient 0dl) per degree change in sideslip 0 ! for straight flight path ) ie dihedral effect ! dl'd or l 0 Pve for sta-le )
48) +efine power of lateral or aileron control Ans: 2he power of lateral or aileron control will -e e$pressed as the change in rolling moment coefficient per degree deflection of the ailerons It is e$pressed as dl 'd a and it acts in such a way that to counter -alance the dihedral effect so that the wings can -e held level from straight flight or maintained at some e9uili-rium angle of -ank 0 ) during turn
4) What are the -asic re9uirements that are to -e fulfilled -y the lateral control system? Ans: 2he -asic re9uirements that determine the siFe of the control and amount of aerodynamic -alance are 0a) it should -e large enough to provide sufficient rolling moment at low speeds to counteract the un-alance tending to roll the
airplane 0-) the second re9uirement is that it roll the airplane at a sufficiently high rate at highspeed for a given stick force
4@) What is meant -y aileron reversal speed? Ans: 2he deflection of the aileron will create a pitching moment tending to twist the wing When the wing twists it rotates in a direction tending to reduce the rolling moment created -y the aileron When the speed is high enough, a point can -e reached where the wing twist will Cust counter t he aileron rolling moment and lateral control will -e lost 2his speed is known as the aileron reversal speed =ence designer should ensure that wings are sufficiently rigid in torsion so that the aileron reversal speed is higher than the ma$imum speed anticipated -y the airplane
8") What are the advantages of sideslip? Ans: Sideslip can -e used 0a) to increase the airplane drag and there-y its flight path angle during an approach for landing, 0-) useful in getting smooth aero-atics such as slow rolls and 0c ) finally it can help during flight with asymmetric power
81) =ow the total directional sta-ility contri-utions of parts of airplane is made more sta-iliFing ? Ans: Sum of the directional sta-ility contri-utions of wings, fuselage and propeller and that of their interference effects will usually give an unsta-le effect =ence an additional sta-iliFing surface must -e incorporated not only to overcome the insta-ility -ut also to give the desired level of directional sta-ility 2his sta-iliFing surface is the normal vertical tail placed as far aft of the cg of airplane as practica-le
8() What is the re9uirement of directional control rudder? Ans: Although the airplane will normally -e in e9uili-rium at Fero sideslip 0 !"), there are many maneuvers that introduce yawing moments which are to -e opposed -y some yawing moment control 0directional control) to achieve Fero sideslip 2his yawing moment control is supplied -y pilot -y means of a rudder, normally a plane flap attached to the aft portion of the vertical tail
8#) What are the flight conditions or maneuvers that produce un-alance yawing moments those are to -e overcome -y rudder? Ans: Kne is 0a) the adverse yaw moment, which happens due to turn during normal flight 0-) slipstream rotation the slip stream -ehind the propeller has rotational components which changes the angle of attack on the vertical tail 0 v ) and create sideslip 2his is critical at high power low speed flight Q ross wind during takeoff and landing 0d) spinning recovery -y rudder 0e) antisymmetric power flight ,when one of the multiengines of airplane fails
8G) +efine rudder power and how it is related to directional sta-ility of airplane Ans: 2he rate of change of yawing moment coefficient 0dn) per degree change in rudder angle 0d r) is called the rudder power 2hat is e9ual to dn' d r or n r 2he directional sta-ility of airplane is dn'd ! n If n r ! """1 and n ! """1, it can -e seen that 1" of rudder will produce 1" of yaw
8%) What is adverse yaw effects and how it is controlled -y rudder? Ans: Budder power re9uired to overcome the adverse yaw during rolling maneuver is usually not very high and not usually used for rudder design Adverse yaw is created -y the normal action of the aileron together with the yawing moment created -y the twisting of wing itself 2hese adverse moments are always critical at low speeds and rudder must -e capa-le of overcoming them at speeds very close to stall
84) =ow rudder power is estimated? Ans: Budder power to overcome the adverse yawing moment 0n)tail is estimated using windtunnel model test data 2he adverse yawing moment coefficient due to rolling of the wing 0n)roll can -e estimated theoretically So the rudder power re9uired to overcome adverse yaw can -e e$pressed as follows: dn'd r !n r ! 00n)roll P0n)tail )' rudder throw 0!#"")
88) Why the rudder is designed to suit oneengine inoperative condition? Ans: 2he yawing moment coefficient due to the asymmetric thrust 0nth ) is proportional to 1'E# 2he rudder at full deflection gives a constant corrective yaw moment coefficient 0nr) 2he intersection of these two nth and nr gives the critical speed of airplane -elow which nth is more than nr =ence -elow the critical speed 0near stalling at full power ) the full rudder will not -alance out the moment due to antisymmetric power Since other types of yawing moments are not critical , most rudder are designed only to fulfill the antisymmetric power flight condition
8) =ow the floating rudder 0stickfree) affects the directional sta-ility? Ans: When rudder is left free to float in response to its hinge moment, it can have large effects on the directional sta-ility It is in the similar way, the floating elevator affects the longitudinal sta-ility When the airplane sideslips, the restoring moment due to the tail will -e decreased if the rudder floats with the wind and will -e increased if it floats against the wind 2he floating rudder changes the effective angle of attack of the total vertical tail
8@) What is the criterion to keep the directional sta-ility with stickfree a-ove certain limit or not to lose much?
Ans: >or high speed airplanes which re9uire close aerodynamic -alance of rudder and hence the rudder pedal force to -e applied -y the pilot should -e within practica-le limit So it is essential that the ratio of derivative of =H coefficient with tail angle of attack 0 v )and rudder power 0h r) should -e kept low so as not to lose too much directional sta-ility with stickfree
") What is the relation for the greatest of pedal force 03>) with respect to sideslip 0 ) and give its accepted value Ans: 2he greatest of pedal force 03>) wrt to sideslip 0 ) can -e derived as d3>'d ! 0 9 v Sr r h r 'n r ) 0n )free ,where 0n )free ! 0n )fi$ 0 h v n r) ' h r It shows that d3>'d varies with E( for normal aerodynamic -alance A criterion of ((% kgf'deg of sideslip at (G" km'hr speed has -een taken as the minimum for this gradient
1) What is meant -y rudder lock? Ans: A typical curve of floating angle 0 float) vs sideslip 0 ) can -e made for a closely -alanced rudder 2he rudder angle 0 r) re9uired to produce the sideslip varies some what linearly upto high 0 ) 2he pedal force re9uired is a function of the difference -etween rre9d and float At high , the float may catch up to rre9d, at which point the 3> -ecomes Fero 2his point of intersection is called rudder lock onsidera-le force is re9uired afterwards, to -reak the lock and restore the airplane to Fero sideslip
() =ow to avoid rudder lock? Ans: Budder lock can -e avoided -y two ways 1) 2o cut down the rudder effectiveness 0d v 'd r ) , there-y increasing the rre9d at a given sideslip 0 ) 0()Another way is to provide a dorsal fin which increases the fuselage sta-ility at high 0 ) as well as reduces the tendency of the vertical tail to stall
#) What is the concern of the designer to keep the pedal force re9uired within suita-le practica-le values? Ans: A fighter airplane clim-ing at full throttle 0power) at ( km'hr may push over to a dive up to 8(" km'hr speed If the airplane is trimmed out directionally at clim-, the pilot may have to e$ert a 3> as high as @( kgf to maintain Fero sideslip in the dive =ence it is essential for the designer to keep the pedal force changes with speed as low as possi-le -y suita-le aerodynamic -alance
G) Why the study on dynamic characteristics of the airplane is necessary ? Ans: In order to understand the re9uirements for static sta-ility and control, it is necessary to study the dynamic characteristics of the airplane It is done -y investigating the types of motions of the airplane in response to a distur-ance from some e9uili-rium flight condition and the nature of transient motions of the airplane in response to the movement of its controls
%) What way the dynamic sta-ility analysis of the airplane help the design of control systems and the pilot who operates it ? Ans: If the motion of the airplane in response to some distur-ance is very slow divergence, the control re9uirements are different from those needed if the divergence is e$tremely rapid 2he a-ility of the pilot to react and apply the controls is a factor which must -e kept in mind for all studies of airplane dynamics 2he design of controls and t he a-ility of the pilot to apply controls in time , re9uires some knowledge of the transient response of the airplane to a distur-ance or to controls
4) What are the G different modes of motion of a dynamic system when responding to a distur-ance from an e9uili-rium position?
Ans: +ynamic system in general have G different modes of motion when responding to a distur-ance from its e9uili-rium position 2hey are aperiodic and oscillatory modes with and without damping 2hat is aperiodic can -e pure convergence if the motion is damped 0sta-le) and divergence if undamped 0unsta-le) Similarly oscillatory motions 0periodic ) can -e damped oscillation 0sta-le) or undamped oscillation 0unsta-le)
8) What are the si$ degrees of motion of a dynamic system and how it is formed for the airplane ? Ans: According to the &ewtonian laws of motion which states that 0a) the sum of all e$ternal forces in any direction must -e e9ual to the time rate of change of momentum, and 0-) the sum of all e$ternal moments of forces must -e e9ual to the time rate of change of moment of momentum, all measured w,r,t a$es fi$ed in space 2he si$ e9uations of motion are: >$ ! m a$ , >y ! m ay , >F ! m aF , 6 ! d=$ 'dt , H ! d=y'dt , & ! d=F 'dt 0where NmN is the mass , a$ ,ay ,aF are linear accelerations and >$ , >y , >F are e$ternal forces and 6, H, & are e$ternal moments of forces and =$ ,=y , =F are moments of momentum a-out , ;, < a$es respectively )
) =ow the true acceleration and moment of momentum of airplane w r t fi$ed a$es in space are generated ? Ans: Accelerations w r t moving a$es 0, ;, < ) as well as moments of momentum are generated 1st w r t moving a$es Lut they will not -e the true values -ecause as per &ewtonian laws they are to -e w orked with reference to fi$ed a$es in space 2o overcome this difficulty use is made of moving a$es which coincide in some particular manner from instant to instant with a definite set of a$es fi$ed in the airplane
@) What are the different ways the moving airplane a$is system can -e fi$ed with reference to the airplane? Ans: 2he moving airplane a$is system can -e fi$ed with reference to the airplane in two different ways : 01) Kne is to consider the a$es fi$ed to airplane under all conditions ,and are called -ody a$es in which a$is is along the thrust a$is 0() Kther possi-ility is to consider the a$is always pointing to the direction of motion or into the relative wind , called wind a$es 2he wind a$es are usually convenient
@") What are the e9uations of longitudinal motion with free control ? Ans: It involves # symmetric e9uations in the plane of symmetry of airplane 0< plane) and e9uation of motion of the elevator control a-out its own hinge 2hey are: >$ ! m , >F ! mE , H ! I; 9N and =He !Ie eNNHaCor varia-les to -e considered for dynamic analysis are the change in forward speed E, ,change in altitude0 ) and change in elevator angle e
@1) What are the different modes and sta-ility criterion of dynamic longitudinal motion whose governing e9uation is a Gth degree 9uartic ? Ans: If all the G roots 0 Ns) come out as real num-ers , the dynamic motion is aperiodic , damped or convergent if the real root is negative and undamped or divergent if the real root is positive If any of the roots 0 Ns) form a comple$ pair , the motion is oscillatory it will -e damped oscillation if the real part of the comple$ root is negative and undamped oscillation if the real part is positive
@() =ow the sta-ility of dynamic motion can -e Cudged using the coefficients of the Gth order 9uartic which govern the motion ? Ans: If all coefficients 0A to 5 ) are positive , there can -e no positive real root and no possi-ility of pure divergence If the BouthNs discriminant0B+)! 0L+
A+( L(5) is positive , then there is no possi-ility of comple$ root with positive real part and hence no undamped oscillation If B+ is Fero, there will -e neutrally damped oscillation and if B+ is negative, one root will -e comple$ pair with positive real part, representing undamped oscillation etc
@#) Lriefly e$plain the sta-ility derivatives, lp and nr Ans: 2he derivatives lp and nr are the damping derivatives in roll and yaw respectively where as the derivatives lr and np are usually referred to as the rotary or cross derivative 2hey are the rolling moment 0l) due to yawing velocity 0r) and yawing moment 0n) due to rolling velocity 0p)
@G) What are the characteristic modes of stickfi$ed longitudinal motion of airplane? Ans: haracteristic modes of stickfi$ed longitudinal motion for nearly all airplanes are two oscillations 01) 6ong period with poor damping called phugoid mode 0() Short period with heavy damping is referred to as the short period mode or second mode 0&ote: give figures also) 2he damping of the phugoid motion is therefore a direct function of + 2he cleaner the designer makes the airplane, the more difficult will -e to ensure damping of phugoid mode
@%) What is proposing mode of dynamic motion? Ans: 2he damping of long period mode 0phugoid mode) can -ecome very weak under certain design conditions and can -ecome neutrally damped or even unsta-le 2his mode when neutrally damped is usually called proposing Such modes have occurred in high speed airplanes, in which the oscillations of normal acceleration -ecome so severe that the pilot was inCured seriously and airplane damaged -efore the pilot could stop the oscillation -y slowing down
@4) =ow many degrees of freedom are there for lateral dynamic motion and what are they ? Ans: 2here are % degrees of freedom for the lateral dynamic motion, -ecause there are two lateral controls the rudder and aileron 2he five degrees of freedom are : a) Eelocity along the ; a$is 0-) rotation a-out a$is 0c) rotation a-out <a$is 0d) rotation of rudder a-out its hinge 0e) rotation of aileron a-out its hinge
@8) +efine spiral divergence in dynamic sta-ility? Ans: 2his is a characteristics associated with lateral dynamic sta-ility of modern airplane 2he divergent mode 0undamped) motion is known as spiral divergence It can -e easily demonstrated in e9uili-rium flight -y giving a kick to rudder or aileron and watching the response If it is uncontrolled, steep high speed spiral divergence develops Inspection of lateral dynamic sta-ility 9uartic e9uation gives an idea a-out spiral divergence If 5 in 9uartic is Fero, it is spiral -oundary and when 5 is negative it is unsta-le and positive, sta-le Jsually with 6 more than "(1#, the airplane will -e spirally unsta-le
@) +efine +utch roll and its effects Ans: 6ateral short period oscillation with weak damping are o-Cectiona-le and such oscillations are called +utch roll In most airplane designs the short period oscillation with control locked is not o-Cectiona-le as the damping is normally heavy Lut with control free the +utch roll can have very weak damping which is 9uite o-Cectiona-le &eutrally damped +utch roll can -e investigated -y e9uating the BouthNs discriminant to Fero ,ie0L+A+(L(5) ! ", which is oscillation -oundary -etween sta-le and unsta-le
@@) What is meant -y snaking? Ans: In most cases with inade9uate damping of lateral oscillation, it is tied in with the floating characteristic of the rudder 0 rfloat ) 2his characteristic under certain conditions of aerodynamic -alance can introduce a poorly damped lateral oscillation known as snaking
1"") Lriefly e$plain autorotation 0&ote: give figure, vs 6 and show the cause of autorotation) Ans: When the wing/s are stalled ie -eyond the critical angle of attack 0 cr ) , the rising wing will have higher 6 than the falling wing 2his creates an un-alanced couple a-out a$is to rotate 0roll) further which is called autorotation Bolling occurring in the almost horiFontal plane is also a form of autorotation
1"1) Lriefly e$plain the spinning of an aircraft Ans: Spinning is caused -y the autorotation developed -y the une9ual lift in the wings In a spin the airplane follows a steep spiral path which is composed of varying degrees of yaw, pitch and roll A flat spin is chiefly yaw and spinning nosedive is chiefly roll 2he amount of pitch depends on how much the wings are -anked from the horiFontal Area and disposition of the fin , rudder and tail plane e$ert considera-le influence on the airplane to spinning
1"()=ow to get out of the spin smoothly ? Ans: In order to get out of a spin we must get out of the stalled 06ma$ ) state -y putting the nose down 0reduce ) and also we must stop rotation -y applying Nopposite rudder N In practice the roll is stopped first, -ecause it is found the elevators are not effective 0to change ) until the rotation is stopped
1"#) State two -asic re9uirements of aircraft control surface Ans: A3 control surfaces are mainly ailerons, canard0forward tail), elevator, rudder and spoilers0special ailerons) Host of the control surfaces are used to produce additional forces when it is re9uired at different locations of A3 Also they produce counter-alancing a-out three maCor a$es of the A3 to improve sta-ility It aids the pilot to produce control forces to come out of maneuring flights
1"G) +istinguish -etween sta-ility and controlla-ility Ans: Sta-ility and control characteristics of an A3 are called flying 9ualities Sta-ility is the property of an e9uili-rium state and it is divided into static and dynamic sta-ility Static sta-ility is the tendency of the A3 to return to its e9uili-rium after a distur-ance In dynamic sta-ility, the vehicle/s motion with the time after it is distur-ed from its e9uili-rium point is considered ontrolla-ility of a system is related to its a-ility to transfer control re9uirements A system is controlla-le if it transfers any initial state i0t) to any final state f0t) in finite time
1"%) What is the need for aerodynamic -alancing? Ans: ontrol surfaces like elevators, ailerons and rudders are used for generating forces and moments in different directions for controlling the A3 When using, the methods of controlling parameters0=H coefficients) h and h are of prime interest and are referred to as methods of aerodynamic -alancing If these coefficients are not suita-ly controlled, the sta-ility and control will -e in danger and it will do harm 0eg, In 0dm ' d6)free e9n, the effect of elevator freeing comes as 1 h ' h and if h ' h ! 1, the whole tail contri-ution to S6S will -ecome Fero
1"4) What is meant -y weather cocking effect? Ans: See Ans to the short 9uestion@ a-ove
1"8) 5$plain the term sta-ility derivatives Ans: >or the analysis of dynamic characteristics0Hodes of motion) of A3 either in longitudinal or lateral direction, respective simultaneous homogenous differential e9uations are to -e developed 2he constant coefficients of these e9uations are made up of A3 mass and inert parameters and so called sta-ility derivatives, like 6 , + and m 6 ! d6 ' d which is the slope of the lift curve with respect to angle of attack m ! 0dm ' d6)0d6 ' d ) ! 0d6 ' d ) 0S6S) criteria
3AB2 L 0RJ5S2IK&S7 =I&2S 'A&S) 1) 0i) Lriefly e$plain with the temperaturealtitude plot , the structure of the standard atmosphere upto a 1"% km altitude 01") =int: +raw the graph, temperature 0*) ES altitude 0km) up to 1"% km and e$plain different temp: gradient as well as isothermal layers upto 1"% km0see p(7# of ISA notes in module1) 0ii) >ind out the geopotential altitude corresponding to (%km geometric altitude 02ake radius of earth ! 4#""km) 04) =int: 0See p% of ISA &ote given in Hodule1) Belation -etween geopotential altitude0h) and geometric altitude 0hg) is h ! 0r'0rP hg))hg ,where NrN is the radius of earth ie h ! 04#""'4#(%) (% ! km () 0i) +erive the relation for the pressure variation in the gradient layers of the ISA 01") =int: Jse the relation dp'p ! 0go'Ba) 0d2'2) and integrate -etween the -ase of the gradient layer 0p1) and to some point in it 0p72) and get the result , p'p1! 02'21)0 go'Ba) 0where NaN is the lapse rate) 0ii) >ind the density at @km altitude from earth/s surface which is on a gradient layer having lapse rate e9ual 4%*'km 2ake standard sea level as the -ase and B of air ! (8m('s(* 04)
=int: +ensity variation in the gradient layer 0 ' 1) is o-tained from the relation ' 1 ! 0p'p1)021'2) ! 02'21)00go'Ba) 1) ' 1 ! 0((@%'()00@1'( 8" 4%)1) ! rp , hence at @ km ! 1 rp 0 1 at stdsea level ! 1((4 kg'm#) #) 0i) +erive the relation for pressure variation in the isothermal layers of the ISA >ind out the pressure in the isothermal layer of 14%* and at a height of %km from the -ase, given the -ase pressure as #"&'m( 0B of air ! (8m('s(*) 01") =int: >or derivation use dp'p ! 0go'B2)dh ive the -ase value at h1 as p1, 217 1 and at altitude 0h) a-ove -ase as p, 27 2hen integrate dp'p -etween p17p and righthandside -etween h17 h , the derivation is o-tained as p'p1 !e 0go'B2)0hh1) and ' 1 ! p'p1 , since 2!21 0for isothermal layer) 3ro-lem :2!21 ! 14%* , 0hh1) ! % km , p1 ! #" &'m(, B! (8 m('s( * 0go'B2) 0hh1) ! 0@1'(814%)%""" ! rp p ! p10e0rp)) ! #" e0rp)) 0ii) >ind out the density at the isothermal layers of 14%* at a height 1"km from the -ase, given the -ase density as 1($1"G*g'm# 0B of air ! (8m('s(*) 04) =int: ' 1 ! p'p1 ! e0rp ), then ! 1 e0rp ) , where 1 !1(1"G kg'm# G) 0i) +erive the relations for ma$imum 6'+ as well as E 6'+ma$ and Emin3B 0) =int: >or ma$: 6'+ , + '6 should -e minimum get + ! +f P 6( ' Ae +ifferentiate 0+ '6) function wrt 6 and e9uate to Fero 2hen 0+ '6)min or 06 '+)ma$ at +f ! +i ! 6(' Ae 2hen get 06 '+)ma$ ! 06'+)ma$ ! "4 0Ae' +f)"% >rom 6! W , get E06'+)ma$ ! 0(W ' S 6) "% ! Eo >or E06'+)ma$ at altitude use at altitude or ! Eo'0 ) "% Emin 3B occurs when +f ! +i '# or +! G +i '# 2his can -e o-tained -y differentiating 0+'6 #'() function wrt 6 and e9uate to Fero 2hen repeating the a-ove process 0 from 6!W ) get Emin 3B !
"84E06'+)ma$ at sea level Emin 3B at altitude ! "84 Eo'0 ) "% 0ii) >ind out 06'+)ma$, E6'+ ma$, 26'+ ma$ and Emin 3B of an airplane with the following features: W ! 1(""kgf, S ! ("m(, A ! %, e ! ", f ! Gm( and ! "%kg'm# 0) =int: +f ! f'S ! Gm('(" m( ! "( 06'+)ma$ at sea level ! "40Ae' +f)"% !"4 (" E06'+)ma$ ! 0W' S 6) ,at 06'+)ma$ , +f ! 6(' Ae , 6 !0" )"% 206'+)ma$ ! + 06'+)ma$ ! W'06'+)ma$ !1(""@1'006'+)ma$ Emin 3B !"84E06'+)ma$ %) 0i) 5$plain with the help of a simple pendulum, the characteristics of static and dynamic e9uili-rium and how its sta-ility can -e evaluated 0) =int: +raw the figure given in the note and at position A 0top ) it is statically unsta-le and at position L 0-ottom) it is statically sta-le +ynamic sta-ility at -ottom 0position L ) can -e analyFed -y response analysis In dynamic sense it will -e neutrally sta-le at L 0ii) +erive the e9uili-rium e9uations for the longitudinal degrees of freedom along a straight path and get the e$pressions for uniform flight velocity and velocity of clim- 0) =int: >or longitudinal degrees of freedom along a straight line 6 ! W cos r ! "% 6E( S Jniform velocity E !0(Wcos r ' 6 S )"% Bate of clim- !Ec ! B' ! 02+)E'W 4) 0i) +erive from the fundamental e9uation for B', the non dimensional form of thrust availa-le 02A) vs velocity relation and plot 2A'26'+ma$ vs E'E6'+ma$ curves Also prove that angle of clim- is a ma$imum 0 ma$) at E'E6'+ma$ ! 1 0) =int: B' ! 02A 2B )E'W Hultiply 7 divide B' e9uation -y 26'+ ma$ E6'+ma$ and put ( 2A'26'+ma$ !y1 , (2B'26'+ma$ ! ; and E'E6'+ma$ ! $ also we know that 2B ! AE( P L'E( and 26'+ma$ !A E( 6'+ma$ P L 'E( 6'+ma$
( 2B '26'+ma$ ! 0 E'E6'+ma$) ( P 1'0 E'E6'+ma$) ( ie y ! $( P 1'$( 2he ma$: B' or B'S occurs at ma$imum 2 E or ma$imum $ y ! $ 0y1 y) ! $0y1 $( 1'$( ) d0$ y)'d$ !" ! y1#$(P 1'$( ! #$Gy1 $( 1 !" $( !0y1P' 0y1(P1())'4 or $ ! 00y1 P' 0y1(P1())'4)"% Also Sin r !0B')'E !02+)'W ie r ! Sin 102+)'W ! onstant 02A2B)' 26'+ma$ , ie r ! constant 0y1y) ! constant 0y1$(1'$( ) >or ma$: r , dr'd$ !" ! ($ P ('$# , ($ G P (!" , ie $ ! 1 ! E'E6'+ma$ 0ii) >ind out the velocity ratio 0$) for ma$: B', when y1 ! 0(2A'26'+ma$) is ( and Gand also o-tain the flight velocity of air plane if its E6'+ma$ ! %""km'hr 0) =int: $! ?, ( 2A' 26'+ma$ !;1 ! ( 7 G , 0a) $ ! 0(P'0GP1()"%)'4) !1 , ie E ! $ E6'+ma$ !%"" km'hr 0-) $! 00GP'014P1()"%)'4)"% ! a , ie E ! a E6'+ma$ 8) 0i) +erive the e$pression for drag polar and e$plain it with a neat plot 04) =int: See page 1(1# of &ote of Hodule1 0after ISA note) 0ii) +raw the thrust ' power re9uired 02B ' 3B) and thrust ' power availa-le 02A ' 3A) curve for a Cet engine and piston engine and state your o-servations =int: 3age (1 for Cet engine 7 p(# for tur-opropeller engine Show -oth sea level and altitude curves 01") ) 0i) +erive the two e9uations given -elow and represent it graphically + ! A E( P L'E( 3 ! A E# P L ' E , 04) =int : +! +3f P +i or + ! +f P +i 0!6 ( ' Ae) ! f E( P 0W'-)('0 e E() ie +! A E(PL 'E( 01) 3 ! +E !A E# P L' E 0() 0ii) An aircraft weighing (% k & has a wing area 1""m( and its drag coefficient is + ! ","14 P ""G 6 ( , calculate the minimum thrust re9uired for straight and
level flight ,and the corresponding true air speed at sea level and at 1"km 0 !"%)alculate also the minimum power re9uired and the corresponding true air speeds at the a-ove conditions 01") =int: iven + !""14 P ""G6 ( ie +f ! ""14, >or min: drag +f !+i ie ""14 !6 (' Ae ,or 1' Ae !""G or Ae ! (%' , 06'+)ma$ ! 06'+)ma$ ! 0 "G)'(+f ! (" E6'+ma$ ! 0W' S 6) !0(%""'###)"% ! EK , 2hen E !Eo' !EK'"% 2min ! W'06'+)ma$ ! (%"""'(" , 3min ! 2min Emin3B Lut Emin3B !"84 E6'+ma$ Emin3B ! "84EK , And Emin3B at altitude ! Emin3B' @) 0i) Assuming para-olic polar variation for + vs 6, write down the thrust re9uired 02B) and power re9uired 03B) e9uations of an airplane ive the conditions of speed for minimum 3B and minimum 2B in terms of drag coefficients also 0) =int : Jse 2B ! 2B3 P 2Bi ! f E( P 0W'-)('0 e E( ) Also 3B ! 3B3 P 3Bi ! f E# P 0W'-)('0 e E ) Speed at minimum 2B is when 06'+) ma$ or 0+'6)min >orm + ! +f P 6 (' Ae 2o get the 0+'6)min , differentiate the e9uation + ' 6 , wrt 6 and e9uate to Fero 2hen , the condition +f ! 6 (' Ae is o-tained 2hen 06'+)ma$ !06'+)ma$ ! 6'( +f ! "4 0Ae'+f) &e$t using relation , 6 ! W , E ! 0W' S 6)"% ! E6'+ma$ >or 3Bmin ! 2 min Emin3B , Lut Emin3B ! ",84 E6'+ma$ , 2min ! W'06'+)ma$ 0ii) >or the ma$imum 6'+ as well as minimum 3B conditions of an airplane, find out 06'+)ma$, E6'+ma$, 26'+ma$ and Emin 3B with the following features: W! 1%""kgf, S! ("m(, A! %, e! ", f ! Gm( , ! "%kg'm# 0) =int: Jse the a-ove method given for 0i) and solve pro-lem 1") 0i) +erive from the fundamental e9uation for B', the generaliFed form of thrust vs velocity curves and show that 2B'26'+ma$ !1 when E'E6'+ma$ ! 1Also
indicate in the 2A'26'+ma$ vs E'E6'+ma$ graph, the regions of ma$ B' and min B'S and speed for min or ma$ 0) =int: 0See page 11 of &ote of Hodule () Also draw fig 4 given in page 11 0ii) >ind out the velocity ratio 0$) for ma$: B', when y1! 0(2A'26'+ma$) is ( and % and also o-tain the flight velocity of air plane if its E6'+ma$ ! 4""km'hr 0) =int: $ for ma$imum B' ! 00y1P'0y1 (P1( )"%)'4)"% When y1 ! ( , $ ! 00(P'0GP 1( )"%)'4)"% ! 1 ,hence E ! E6'+ma$ When y1 ! % , find out $ -y the a-ove e9uation , let it -e e9ual to NaN 2hen E ! a E6'+ma$ 11) 0i) +erive the relation for the ma$imum range of a tur-oCet airplane 01") =int: 0See 3age (# of &ote of Hodule ( ) Bma$ ! 0('cN)061'('+)ma$0WK' S)"% 01 0W1'WK)"% ) 0ii) alculate the ma$imum endurance of a tur-oCet airplane having the following flying characteristic c/!(%hr 1 , W"'W1 !1(, A! 1", S! G"m(, e!" and f!(m( 04) =int: >or ma$imum endurance, flight E !E6'+ma$ 5ma$ ! 01'cN)06'+)ma$ ln 0WK 'WI ) where 6'+ ma$ !"4 -0e'f)"% and - ! 0A S )"% !(" m, then get 6'+ma$ and 5ma$ -y su-stitution 1() 0i) +erive the relation for the ma$imum range of a tur-opropeller airplane 1") =int: See page 1418 of &ote of Hodule (, Bma$ !k106'+)ma$0 'c) ln0Wo'W1) 0ii) alculate the ma$imum endurance of a tur-opropeller airplane having the following flying characteristic ! "%, /!"G%hr 1 , W"'W1 !1(, k!1%m's, 6!1( , +! ""# , Wo' S !1""m('s( 04) =int: 5ma$ ! k 0 'c) 06 1%'+) 0 S 'WK)"%00W"'W1)"% 1) 1#) 0i)+erive the relation for the takeoff ground run distance 0S) for an airplane in terms of weight 0W), takeoff velocity 0E2K), effective thrust 02e) "8 E2K 0) =int: See page #1#( of &ote of Hodule (
Sg ! W E( 2K'0(g2e "8 E2K ) 0ii ) >ind out the takeoff ground run distance for an airplane having W!1%""kgf, E2K!#4"km'hr and 25 at "8E2K!#k& and then find the horiFontal distance to clim- an vertical o-stacle of 1%m, if the ground run distance is " times of total distance 0) =int: Sg ! 1%""@11"G'0(@1#""") ! (%"" m Sg ! " Stot , ie Stot ! Sg ' " ! #1(% m Sc !4(% m 1G)0i) +erive the relation for the total landing distance from over a 1%m height o-stacle consideringE1%!1#ES and E6!11%ES,whereES is stalling speed 01") =int: SA ! 0W'>)00E( 1% E( 6)'(g P1% ES !1"" m's Sg ! E( 6' (0a) , Stot !SA P Sg 0ii) >ind out the total landing distance re9uired for an airplane having W'> 0average resistance coefficient) 1", and stalling speed #4"km'hr 2ake average deceleration during ground run as (#m's 04) =int: Jse the a-ove method given in =int 1G0i) and solve 1%) +erive from fundamentals that the relation for the ma$imum rate of clim-, "% ma$ ma$ 11%% 0') 0 ' ) +f 3*W B Ws6+ h s
!
and give discussion on it Ans: Befer page 1(a of Hodule( &ote 14) >or a straight and level flight, velocity for minimum power is "84 times velocity for minimum drag Ans: ive the derivations for the velocity 0E06'+)ma$) for minimum drag0+!2B) and minimum power re9uired0Emin3B) 0+etails given in page G 7 G- of Hodule( &ote) +escriptive Ruestions and hints0H#) 18)0a)With the help of a figure, write down the moment e9uation a-out the cg of an airplane flying in poweroff and stick fi$ed condition 2hen show the conditions for e9uili-rium and longitudinal sta-ility 014) =int: See page G4 of &ote of Hodule # 1)0i) +erive the relation for &eutral point 0&") of an airplane at stickfi$ed 3oweroff condition 01") =int: See the page 1@(" of &ote of Hodule # 0ii) >ind out the type of sta-ility of an airplane at the stickfi$ed, power off condition which is having neutral point at %%D of chord and cg located at G% cm aft of ac Also state the sta-ility condition if cg is at 4%cm aft of ac 02ake .c/ of airfoil ! 1m) 04) =int : &eutral point at the stickfi$ed poweroff condition 0&o)! %%D of NcN 0c !1m ), which is aft of aerodynamic centre 0ac) of the wing 01) Sta-ility when cg is at G% cm aft of ac ! G%D of NcN, Ie dm'+c6 ! $cg &o ! 1"D of NcN , 0sta-le) 0() Sta-ility when cg is at 4% cm aft of ac ! 4%D of NcN, Ie dm'+c6 ! $cg &o ! P 1"D of NcN , 0unsta-le) 1@) 0a) >rom fundamental, write down the e9uation for the Wing contri-ution to Static 6ongitudinal Sta-ility 0S6S) and from the simplified form e$plain how the location of cg of airplane with respect to ac of wing decides the S6S of the airplane 014) =int:See page 8@ of &ote of Hodule #
(")0i) +erive the e9uili-rium and S6S e9uation of a tur-opropeller airplane taking the direct thrust alone of the propeller 0) =int: See page (((# of &ote of Hodule # 0ii) Jsing the simplified terms of 0dmp'd6)2 show graphically 0in m vs 6 graph), the positions of, a) dm'd6 for h'c!"(, -) dm'd6 for h'c! "(, c) if dm'd6 ! "1 for h'c! " =int: dm'd6 ! "1 for h'c ! " And 0dmp' d6)2 ! "(% h'c dm'd6 for h'c ! "( , 0dmp' d6)2 ! ""%, dm'd6 ! "1P""% ! ""% 0sta-le ) dm'd6 for h'c ! "( , 0dmp' d6)2 ! ""%, dm'd6 ! "1 ""% ! "1% 0more sta-le) (1)0a)+iscuss in detail the power effects on static longitudinal sta-ility for a Cet powered airplane 014) =int: +etails given in pages #( #G of &ote of Hodule # (( 0a) 0i) =ow most forward cg for free flight of an A3 is fi$ed and write the relation for 0dm'd6)ma$ in terms of elevator deflection, its power0m ) and 6ma$ 04) =int: +etails given in page G1 of &ote of Hodule # 0ii) +erive the relation for $ cg forward from fundamental mcg e9uation at poweroff e9uili-rium with elevator deflection 01") =int: +etails given in page GG of &ote of Hodule # (( 0-) Write short notes on: 0i) Kne engine inoperative condition 0ii) Aileron reversal and adverse yaw =int: Befer noteHoduleIE (#0a) 0i) Show that elevator angle for trim is given -y etrim ! 0mo 6o P m 6trim) ' 0m e 6 m 6 e) Ans: An A3 is said to -e trimmed if t he forces and moments acting on the A3 are in e9uili-rium Setting the pitching moment e9uation e9ual to Fero, we can solve for the elevator angle re9uired to trim as follows
m ! " ! mo P m P m e ee9n01) Kr, etrim ! 0mo P m trim ) ' m ee9n0() 2he lift coefficient to trim is 6trim ! 6 trim P 6 e etrim e9n0#) We can use this e9uation to o-tain the trim angle of attack0 trim) trim ! 6trim 6 e etrim ' 6 e9n0G) If we su-stitute this e9n0G) -ack into e9n0() we get the following e9n for elevator angle to trim: etrim ! 0mo 6o P m 6trim) ' 0m e 6 m 6 e) 0ii) +iscuss the advantages and disadvantages of A&AB+ configuration Ans: A canard is a tail surface located ahead of the wing It has several attractive features 2he canard, if properly positioned, can -e relatively free from wing or propulsive flow interference anard control is more attractive for trimming the large nosedown moments produced -y high lift devices 2o counteract the nosedown pitching moment, canard must produce lift that will add to the lift produced -y the wing An aft tail must produce a download to counteract the pitching moment and thus reduce the airplane/s overall lift 2he maCor disadvantages of the canard is desta-iliFing contri-ution to the aircraft/s static sta-ility =owever, it is not a severe limitation Ly the proper location of the g, one can ensure the A3 is statically sta-le (G0a) Jsing the floating angle of elevator 0 e) and its =H coefficient, derive the relation for the sta-ility criteria at stickfree condition Also get the relation for &o&o/0difference -etween stickfi$ed0&o) and stick free0&o/) neutral points) 014) =int: +etails given in pages 4(4% of &ote of Hodule # (% 0a) 0i) +efine stickfi$ed maneuver point 0&m) and stickfree maneuver point0&m/) Write down the e$pression for &m and &m/ in terms of &o and &o/ respectively 0) =int: +etails given in page 1 and pages # 7 % of &ote of Hodule # 0ii) Lriefly e$plain the limits on A3/s cg with the help of a figure 0) =int: +etails given in page 8 of &ote of Hodule # (4) 0a) +iscuss in detail the contri-ution of various components of the airplane on its static directional sta-ility 014)
=int: See pages 1"1# -riefly of &ote of Hodule G) (8) 0a) +iscuss -riefly the following : 01) +irectional control and the -asic re9uirements of the rudder 0) =int: See page 1418 of &ote of Hodule G 0() Budder lock and how to avoid it 0) =int: See page (G (% of &ote of Hodule G () +iscuss -riefly the following : 01) Lasic re9uirements of the rudder 04) =int: See page 1418 of &ote of Hodule G 0() Aileron reversal 0=int: See page 8 of &ote of Hodule G ) 0%) 0#) Adverse yaw 0=int: See page 11@ of &ote of HoduleG) 0%) (@) 0a)0i) A statically sta-le aircraft can -e dynamically sta-le or unsta-le ive the dynamic conditions under which it happens 0 4) =int:A statically sta-le aircraft can -e dynamically sta-le if its dynamic modes of motion are damped 0Loth aperiodic and periodic motions 2otal G types of modes can -e possi-le) Similarly a statically sta-le aircraft can -e dynamically unsta-le if its dynamic modes of motion are undamped 0Loth aperiodic and periodic motions 2otal G types of modes can -e possi-le) 0ii)+iscuss various sta-ility derivatives relevant to longitudinal dynamics 01") =int: See page 1418 of &ote of Hodule % 05$plain aerodynamic coefficients like , + ,6 , + , 6 etc given in a-ove pages)
#")0a) Write short notes on the following : 01)Autorotation 0=int: page GG@ of Hodule % ) 04) 0() +utch roll 0=int: page G# of Hodule % ) 0%) 0#) Spiral divergence 0=int: page G# 7 G% of Hodule% ) 0%)
#1) +iscuss -riefly the following: 0i) 3hugoid motion 0) 0=int: 3age (#(G of &ote of Hodule % )
