Category: Aircraft Performance Objective Questions

Aircraft Performance Multiple Choice Questions on “Fixed-Wing Aircraft – Performance Estimation”.

1. What is meant by performance estimation?
a) Prediction of capabilities of the aircraft
b) Provide validated performance data for performance section
c) Verification of aircraft achievements
d) Certification of performance
Answer: a
Clarification: Performance estimation involves the prediction of the capabilities of the aircraft from the consideration of its aerodynamic design, powerplant and operating environment. It is applied to design, modification and supplement.

2. Which of the following is not applied to performance estimation?
a) Design
b) Modification
c) Supplement
d) Validation of performance data
Answer: d
Clarification: Performance estimation is applied in fields of design of a new type of aircraft, modification of an existing aircraft type in respect to design changes affecting its aerodynamic characteristics and to supplement or extend the full-scale measured performance of an aircraft type for conditions outside those already established.

3. ISA stands for_________
a) International Standard Atmosphere
b) International Standard Altitude
c) International Standard Airlines
d) International Standard Aircraft
Answer: a
Clarification: ISA stands for International Standard Atmosphere International Standard Atmosphere (ISA) is a linearized model of the temperature atmosphere. It represents the mean global atmosphere state with respect to seasonal changes and latitude and is used as the basis for aircraft design.

4. The performance estimation process begins with the proposal of some performance target.
a) True
b) False
Answer: a
Clarification: The performance estimation process begins with the proposal of some performance target. Such as the requirement to carry a specified payload over a given route that forms the mission profile, possibly within time and cost limits.

5. The elimination process will include an assumption of the environmental conditions of the atmosphere in which the aircraft will operate.
a) True
b) False
Answer: a
Clarification: The elimination process will include an assumption of the environmental conditions of the atmosphere in which the aircraft will operate. Since the atmosphere is a very variable medium in that its pressure and temperature vary with height and also with geographical location and time. Performance estimation is based on assumption of International Standard Atmosphere (ISA).

6. International Standard Atmosphere (ISA) is a ____________
a) Linearized Model of the Temperature Atmosphere
b) Horizontal Model of the Temperature Atmosphere
c) Linearized Model of the Pressure Atmosphere
d) Horizontal Model of the Pressure Atmosphere
Answer: a
Clarification: International Standard Atmosphere (ISA) is a linearized model of the temperature atmosphere. It represents the mean global atmosphere state with respect to seasonal changes and latitude and is used as the basis for aircraft design.

7. The performance estimation process is _________
a) optional
b) iterative
c) not required
d) single attempt
Answer: b
Clarification: The performance estimation process is iterative. When the estimations show that the performance targets can be met, the aircraft can proceed to manufacture or modification and next is performance measurement and if the estimation fails then this process repeats.

8. Alternative models of ISA are design atmospheres.
a) True
b) False
Answer: a
Clarification: Alternative models of ISA are design atmospheres. These represent the aircraft performance at hotter or colder climates depending on tropical or arctic regions which help in performance estimation.

9. _________ is the important factor to be satisfied during performance estimation.
a) Temperature
b) Pressure
c) Airworthiness requirement
d) Climate
Answer: c
Clarification: Airworthiness requirement is the important factor to be satisfied during performance estimation. Airworthiness is the measure of an aircraft’s suitability for safe flight. Certification of airworthiness is conferred by a certificate of airworthiness from the state of aircraft registry national aviation authority, and is maintained by performing the required maintenance actions.

10. Performance is the initial design phase.
a) True
b) False
Answer: a
Clarification: Performance is the initial design phase. Performance measurement is the testing phase and operational performance covers the certification of the aircraft and the provision of validated operating data.

Aircraft Performance Multiple Choice Questions on “Drag Force”.

1. Total drag is the sum of ______________
a) lift dependent drag and lift independent drag
b) lift dependent drag, lift independent drag and volume dependent wave drag
c) lift dependent drag and volume dependent wave drag
d) volume dependent wave drag and lift independent drag
Answer: b
Clarification: Total drag is the sum of lift dependent drag, lift independent drag and volume dependent wave drag. Also, in high subsonic mach number a value dependent wave drag is induced.

2. In high subsonic mach number a value dependent wave drag is not induced.
a) True
b) False
Answer: b
Clarification: In high subsonic mach number a value dependent wave drag is induced. The components that act on the aircraft moving at high subsonic mach number are lift dependent drag, lift independent drag and volume dependent wave drag.

3. Which of the following is the correct relation between lift dependent drag, lift independent drag and drag coefficient?
a) C_D=C_Dz+KC_L²
b) C_D=C_Dz-KC_L²
c) C_D=C_Dz*KC_L²
d) C_D=C_Dz/KC_L²
Answer: a
Clarification: The correct relation between lift dependent drag, lift independent drag and drag coefficient is C_D=C_Dz+KC_L² where C_D is drag coefficient, C_Dz is lift independent drag, C_L is lift independent drag and K is a constant.

4. There are three types of drag.
a) True
b) False
Answer: a
Clarification: There are three types of drag. They are parasitic drag which is further divided into form drag and skin friction drag. The second kind of drag is lift-induced drag and third type of drag is wave drag.

5. Which of the following are the two types of lift independent drag?
a) surface friction drag and profile drag
b) induced drag and profile drag
c) surface friction drag and induced drag
d) parasitic drag and induced drag
Answer: a
Clarification: Lift independent drag is divided into two types. They are the surface friction drag and the profile drag. Surface friction drag corresponds to 75% of the lift independent drag whereas the profile drag leads to 25% of the lift independent drag.

6. Surface friction drag corresponds to 35% of the lift independent drag whereas the profile drag leads to 65% of the lift independent drag.
a) True
b) False
Answer: b
Clarification: Lift independent drag is divided into two types. They are the surface friction drag and the profile drag. Surface friction drag corresponds to 75% of the lift independent drag whereas the profile drag leads to 25% of the lift independent drag.

7. The surface friction drag coefficient is not effected by reynold’s number effect.
a) True
b) False
Answer: b
Clarification: The surface friction drag coefficient is effected by reynold’s number effect. This effect results in the variation of surface friction drag coefficient and mach number. Surface friction drag coefficient decreases slightly as the increase in mach number.

8. How is the zero-lift drag force related to atmospheric pressure?
a) The zero-lift drag force is directly proportional to atmospheric pressure
b) The zero-lift drag force is indirectly proportional to atmospheric pressure
c) The zero-lift drag force is twice multiple to atmospheric pressure
d)The zero-lift drag force is half divided to atmospheric pressure
Answer: a
Clarification: The zero-lift drag force is directly proportional to atmospheric pressure i.e. the zero-lift drag force increases as the increase in atmospheric pressure. This is because the drag force is directly proportional to the dynamic pressure.

9. The drag force is directly proportional to the dynamic pressure.
a) True
b) False
Answer: a
Clarification: The drag force is directly proportional to the dynamic pressure. This results in the effect of zero-lift drag force. The zero-lift drag force is directly proportional to atmospheric pressure i.e. the zero-lift drag force increases as the increase in atmospheric pressure.

10. The zero-lift drag force will decrease with decrease respect to altitude.
a) True
b) False
Answer: b
Clarification: The zero-lift drag force will decrease with increase respect to altitude. This is due to atmospheric pressure varying with respect to altitude. Also the zero-lift drag force increases as the increase in atmospheric pressure.

Aircraft Performance Multiple Choice Questions on “Cruising Performance – Aircraft with Mixed Power Plants”.

1. What is a turboprop?
a) It is a combination of turbojet and ramjet
b) It is a combination of turbojet and turbofan
c) It is a combination of turbojet and scramjet
d) It is a combination of turbojet and propeller engine
Answer: d
Clarification: Turbo-prop is a combination of turbojet and propeller engine. The power-plants used in turboprop are mixed power-plants i.e. it is a combination of both thrust producing engine and power producing engine.

2. The residual energy is converted into __________
a) power
b) thrust
c) lift
d) drag
Answer: b
Clarification: The residual energy in the exhaust is converted into thrust by the exhaust nozzle. The shaft power is converted into thrust through the propeller. This way the cruise performance characteristics of an aircraft wiith mixed power-plants lies between that of aircraft with pure thrust or pure power-producing plants.

3. What is the range of thrust producing engine?
a) R_T=(big[frac{V_{mdi}}{C_T}E_{max}big]big{frac{2u^4}{u^4+1}big})lnω
b) R_T=(big[frac{V_{mdi}}{C_T}big]big{frac{2u^3}{u^4+1}big})lnω
c) R_T=(big[frac{V_{mdi}}{C_T}E_{max}big]big{frac{2u^3}{u^4+1}big})lnω
d) R_T=(big[frac{V_{mdi}}{C_T}E_{max}big]big{frac{u^3}{u^4+1}big})lnω
Answer: c
Clarification: The correct equation for range of thrust producing engine is given by the equation R_T=(big[frac{V_{mdi}}{C_T}E_{max}big]big{frac{2u^3}{u^4+1}big})lnω where V is true airspeed, C is specific fuel consumption, E_max is endurance and ω is fuel ratio.

4. What is the range of the power producing engine?
a) R_P=(big[frac{eta}{C_P}E_{max}big]big{frac{2u^2}{u^4+1}big})lnω
b) R_P=(big[frac{eta}{C_P}E_{max}big]big{frac{2u^3}{u^4+1}big})lnω
c) R_P=(big[frac{eta}{C_P}big]big{frac{2u^2}{u^4+1}big})lnω
d) R_P=(big[frac{V_{mdi}}{C_P}E_{max}big]big{frac{2u^3}{u^4+1}big})lnω
Answer: a
Clarification: The correct equation for range of thrust producing engine is given by the equation R_P=(big[frac{eta}{C_P}E_{max}big]big{frac{2u^2}{u^4+1}big})lnω where V is true airspeed, C is specific fuel consumption, E_max is endurance, η is propeller efficiency and ω is fuel ratio.

5. What is the range formula for mixed power-plant?
a) R=E_max(big[Πfrac{eta}{C_P}+(1+Π)frac{uV_{md}}{C_T}big]big{frac{2u^2}{u^4-1}big})lnω
b) R=E_max(big[Πfrac{eta}{C_P}+(1-Π)frac{uV_{md}}{C_T}big]big{frac{2u^2}{u^4-1}big})lnω
c) R=E_max(big[Πfrac{eta}{C_P}+(1-Π)frac{uV_{md}}{C_T}big]big{frac{2u^2}{u^4+1}big})lnω
d) R=E_max(big[Πfrac{eta}{C_P}+(1+Π)frac{uV_{md}}{C_T}big]big{frac{2u^2}{u^4+1}big})lnω
Answer: c
Clarification: The range formula for mixed power-plant is given by the equation R=E_max(big[Πfrac{eta}{C_P}+(1-Π)frac{uV_{md}}{C_T}big]big{frac{2u^2}{u^4+1}big})lnω where Π is the proportion of thrust derived from the shaft power in the overall thrust of the power-plant, C_T, C_P are the specific fuel consumption of thrust producing and power producing engines, E_max is endurance and V is true airspeed.

6. What is the full form of ESHP?
a) Equivalent shaft horsepower
b) Equal shaft horsepower
c) Engine shaft horsepower
d) Endurance shaft horsepower
Answer: a
Clarification: ESPH stands for Equivalent shaft horsepower. It is the combination of thrust output with the shaft power output to give the total output in power form as if the engine was a pure power producing engine.

7. ESPH is the combination of thrust output and shaft power output.
a) True
b) False
Answer: a
Clarification: ESPH stands for Equivalent shaft horsepower. It is the combination of thrust output with the shaft power output to give the total output in power form as if the engine was a pure power producing engine.

8. The proportions of thrust and power are independent of speed and engine output.
a) True
b) False
Answer: a
Clarification: The proportions of thrust and power are independent of speed and engine output. So there is a need for the calculations of each combination of engine power setting and aircraft speed.

9. The calculations in turboprop aircraft are done in a continuous function.
a) True
b) False
Answer: b
Clarification: The calculations in turboprop aircraft are done in a point to point manner and not in a continuous function. This is because the proportions of thrust and power are independent of speed and engine output. So there is a need for the calculations of each combination of engine power setting and aircraft speed.

10. The expression of range and endurance is written in terms of endurance factor and relative speed function.
a) True
b) False
Answer: a
Clarification: The expression of range and endurance is written in terms of endurance factor and relative speed function. This helps in easy calculations and understanding of cruising performance. This also helps in analyzing the effects of drag characteristics and specific fuel consumption.

Aircraft Performance Multiple Choice Questions on “Fixed-Wing Aircraft – Performance Measurement”.

1. WAT stands for _______
a) Weight, Altitude, Temperature
b) Weather,Altitude, Temperature
c) Weight, Atmosphere, Temperature
d) Weather,Atmosphere, Temperature
Answer: a
Clarification: WAT stands for Weight, Altitude, Temperature. Data measured in flight are measured under the arbitrary WAT conditions existing at the time. The flight –measured data will need to be processed to conform to specific combinations of WAT for the construction of the performance manual.

2. Operating Data Manual (ODM) contains the information on the performance of the aircraft needed by the operator for flight planning.
a) True
b) False
Answer: a
Clarification: ODM stands for Operating Data Manual. Operating Data Manual (ODM) contains the information on the performance of the aircraft needed by the operator for flight planning above the ground.

3. ODM stands for _________
a) Operation Data Manual
b) Operating Data Manual
c) Operation Data Management
d) Operating Digital Manual
Answer: b
Clarification: ODM stands for Operating Data Manual. Operating Data Manual (ODM) contains the information on the performance of the aircraft needed by the operator for flight planning above the ground.

4. What is meant by performance measurement?
a) Verification of aircraft achievements
b) Design new type of aircraft
c) Modification of existing aircraft type
d) Supplementor extent the full-scale measured performance of an aircraft
Answer: a
Clarification: Performance measurement is the process of verification of aircraft estimations in design performance, to demonstrate that the aircraft can satisfy the safety criteria set down in the airworthiness requirements, to provide validated performance data for the performance section of the flight manual.

5. Which of the following is applied to performance measurement?
a) Design
b) Modification
c) Supplement
d) Validation of performance data
Answer: d
Clarification: Performance measurement is the process of verification of aircraft estimations in design performance, to demonstrate that the aircraft can satisfy the safety criteria set down in the airworthiness requirements, to provide validated performance data for the performance section of the flight manual.

6. APMS stands for _________
a) Aviation Performance Measurement System
b) Aviation Performance Measuring System
c) Aircraft Performance Measuring System
d) Aircraft Performance Measurement System
Answer: b
Clarification: APMS stands for Aviation Performance Measuring System. APMS is an advanced software analysis tool used in flight-data analyses. It is mostly preferred for safety and to increase fight reliability.

7. FAA stands for ________
a) Fundamental Aviation Administration
b) Federal Aircraft Administration
c) Federal Aviation Administration
d) Fundamental Aircraft Administration
Answer: c
Clarification: FAA stands for Federal Aviation Administration. FAA is a national aviation agency of the US. This was formed after the formation of ICAO in the early 1970’s. The functions of FAA is to look after the safety, air traffic and follow the five degrees of freedom.

8. AFM stands for ______
a) Authority of Flight Manual
b) Aircraft Flight Manual
c) Aircraft Flight Management
d) Authority of Flight Management
Answer: b
Clarification: AFM stands for Aircraft Flight Manual. It is also known as Pilot’s Operating Handbook (POH). It contains the operating data such as climb, take-off and range data of the aircraft. Few changes had to be done by the user or check for those variations to make the data useful.

9. POH stands for __________
a) Pilot’s Operational Handbook
b) Pilot’s Operating Handbook
c) Performance Operating Handbook
d) Performance Operational Handbook
Answer: b
Clarification: POH stands for Pilot’s Operating Handbook. It contains the operating data such as climb, take-off and range data of the aircraft. Few changes had to be done by the user or check for those variations to make the data useful.

10. AIAA stands for ________
a) Australian Institute of Aeronautics and Astronautics
b) Alberta Institute of Aeronautics and Astronautics
c) Andaman Institute of Aeronautics and Astronautics
d) American Institute of Aeronautics and Astronautics
Answer: d
Clarification: AIAA is the acronym for American Institute of Aeronautics and Astronautics. AIAA follows the National Defense Authorization act. AIAA is made up of 85 countries and 95 corporate members. It is associated with the US nation.

Aircraft Performance Multiple Choice Questions on “Minimum Drag Speed”

1. What is the correct expression for induced drag?
a) (frac{ZW^2}{V^2_e})
b) YV_e²
c) (frac{ZW^2}{V_e})
d) YV_e
Answer: a
Clarification: The correct expression for induced drag is (frac{ZW^2}{V^2_e}) where W is weight, V is velocity, Z is constant. Induced drag is the function of lift and caused when an aircraft is moving in the air.

2. What is the correct expression for pressure drag?
a) (frac{ZW^2}{V^2_e})
b) YV_e²
c) (frac{ZW^2}{V_e})
d) YV_e
Answer: b
Clarification: The correct expression for pressure drag is YV_e² where Y is a constant and V is velocity. Pressure drag is caused due to the resultant pressure distribution over a surface of the body. It is generally occurred in turbulent flow.

3. Which of the following is correct equation?
a) D=YV_e^e+(frac{ZW^2}{V^2_e})
b) C_D=C_Dz-KC_L²
c) D=D_z-D_i
d) V_emd=(sqrt[3]{frac{ZW^2}{Y}})
Answer: a
Clarification: The correct equation is D=YV_e^e+(frac{ZW^2}{V^2_e}) where Y is a constant, V is velocity, W is weight, V is velocity, Z is constant and D is total drag. The total drag is the sum of pressure drag and induced drag.

4. Which of the following is the correct equation for minimum speed drag?
a) V_emd=(sqrt[3]{frac{ZW^2}{Y}})
b) V_emd=(sqrt[4]{frac{ZW^2}{Y}})
c) V_emd=(sqrt[4]{frac{ZW^2}{Y^2}})
d) V_emd=(sqrt[3]{frac{ZW^2}{Y^2}})
Answer: b
Clarification: The correct equation for minimum speed drag is V_emd=(sqrt[4]{frac{ZW^2}{Y}}) where Y is a constant, V is velocity, W is weight, Y is a constant and V_emd is minimum speed drag. Induced drag is the function of lift and caused when an aircraft is moving in the air.

5. The minimum drag speed determines the best operating speeds of aircraft with thrust producing engines.
a) True
b) False
Answer: a
Clarification: The minimum drag speed determines the best operating speeds of aircraft with thrust producing engines. The correct equation for minimum speed drag is V_emd=(sqrt[4]{frac{ZW^2}{Y}}) where Y is a constant, V is velocity, W is weight, Y is a constant and V_emd is minimum speed drag. Induced drag is the function of lift and caused when an aircraft is moving in the air.

6. The lift-dependent drag is reduced with the reduction in total drag.
a) True
b) False
Answer: a
Clarification: The lift-dependent drag is reduced with the reduction in total drag. Along with this the minimum air drag speed is also reduced. The total drag is the sum of pressure drag and induced drag.

7. The total drag is the sum of pressure drag and induced drag.
a) True
b) False
Answer: a
Clarification: The total drag is the sum of pressure drag and induced drag. The correct equation is D=YV_e^e+(frac{ZW^2}{V^2_e}) where where Y is a constant, V is velocity, W is weight, V is velocity, Z is constant and D is total drag. The total drag is the sum of pressure drag and induced drag.

8. What is overall drag force?
a) The sum of drag force, zero-lift drag, lift-dependent drag and volume dependent wave drag
b) The sum of lift-dependent drag and volume dependent wave drag
c) The sum of drag force, lift-dependent drag and volume dependent wave drag
d) The sum of drag force, zero-lift drag and lift-dependent drag
Answer: a
Clarification: Overall drag force is the sum of drag force, zero-lift drag, lift-dependent drag and volume dependent wave drag. It is given that the mach number is a function of all the mentioned factors.

9. The drag polar curve is parabolic in shape for subsonic performance aircrafts.
a) True
b) False
Answer: a
Clarification: The drag polar curve is parabolic in shape for subsonic performance aircrafts. The drag polar curve is the graph plotted between the lift coefficient of the aircraft and the drag coefficient of the aircraft.

10. Which of the following is the correct equation for the Prandtl-Glauert factor?
a) β=(sqrt{1-M^2})
b) β=(sqrt{1-M})
c) β=(sqrt{M^2-1})
d) β=(sqrt{1+M^2})
Answer: a
Clarification: The correct equation for the Prandtl-Glauert factor is β=(sqrt{1-M^2}) where β is Prandtl-Glauert factor and M is mach number. This Prandtl-Glauert factor equation is applicable only in cases of subsonic airflow i.e. M<1.

Aircraft Performance Multiple Choice Questions on “Climb and Descent Performance with Thrust-Producing Engines”.

1. Which of the following is the correct thrust balancing equation for thrust producing engines?
a) F_N+D=Wsinγ₂+mV̇
b) F_N-D=Wsinγ₂+mV̇
c) F_N-D=Wsinγ₂-mV̇
d) F_N+D=Wsinγ₂-mV̇
Answer: b
Clarification: The correct thrust balancing equation for thrust producing engines is given by the equation F_N-D=Wsinγ₂+mV̇ where F_N is the normal force acting on the aircraft, γ is the angle at which the force is acting on the aircraft, D is drag produced, W is weight of the aircraft, m is mass and V̇ is velocity.

2. Which of the following is the correct lift balancing equation for thrust producing engines?
a) L=Wcosγ₂
b) L=Wsinγ₂
c) L=(frac{cosgamma _2}{W})
d) L=(frac{singamma_2}{W})
Answer: a
Clarification: The correct lift balancing equation for thrust producing engines is given by the equation L=Wcosγ₂ where L is lift, W is weight and γ is the angle at which the force is acting on the aircraft.

3. What should be the value of thrust- to-weight ratio for a normal take-off so that the acceleration associated with the rate of climb is neglected?
a) 0.1
b) 0.2
c) 0.3
d) 0.4
Answer: c
Clarification: 0.3 must be the value of thrust- to-weight ratio for a normal take-off so that the acceleration associated with the rate of climb is neglected. This way the climb can be assumed with constant airspeed and mach number.

4. The best gradient of climb is attained at the time of maximum drag speed of the aircraft.
a) True
b) False
Answer: b
Clarification: The best gradient of climb is attained at the time of minimum drag speed of the aircraft. The best gradient of climb is attained generally at the airspeed ‘u’ of 1. The gradient of climb is given by E_maxsinγ₂=τ-(frac{1}{2})[u²+u^-2].

5. The best rate of climb occurs when the excess thrust power is minimum than drag power.
a) True
b) False
Answer: b
Clarification: The best rate of climb occurs when the excess thrust power (F_NV) is maximum than the drag power (DV). As the ideal power increases linearly with true airspeed the best gradient of climb is predicted to be at an airspeed greater than minimum drag speed.

6. The best gradient of climb is predicted to be at an airspeed greater than minimum drag speed.
a) True
b) False
Answer: a
Clarification: The best rate of climb occurs when the excess thrust power (F_NV) is maximum than the drag power (DV). As the ideal power increases linearly with true airspeed the best gradient of climb is predicted to be at an airspeed greater than minimum drag speed.

7. What is the relation between thrust power and true airspeed?
a) Thrust power increases with increase in true airspeed
b) Thrust power decreases with increase in true airspeed
c) Thrust power increases with decrease in true airspeed
d) Thrust power is independent of true airspeed
Answer: a
Clarification: Thrust power increases with increase in true airspeed.The best rate of climb occurs when the excess thrust power (F_NV) is maximum than the drag power (DV). As the ideal power increases linearly with true airspeed the best gradient of climb is predicted to be at an airspeed greater than minimum drag speed.

8. In which of the following the maximum rate of climb occurs?
a) It occurs when difference in thrust power and drag power is minimum
b) It occurs when difference in thrust power and drag power is maximum
c) It occurs when difference in thrust power is minimum
d) It occurs when difference in drag power is minimum
Answer: b
Clarification: The maximum rate of climb occurs when the difference in thrust power and drag power is maximum. The rate of climb is a function of excess thrust power.The best rate of climb occurs when the excess thrust power (F_NV) is maximum than the drag power (DV).

9. Which of the following is the correct climb gradient equation?
a) τ-(frac{1}{2})[u²+u^-2]=E_maxsinγ₂
b) τ+(frac{1}{2})[u²+u^-2]=E_maxsinγ₂
c) τ+(frac{1}{2})[u²+u^-2]=E_max
d) τ-(frac{1}{2})[u²+u^-2]=E_max
Answer: a
Clarification: The correct climb gradient equation is given by the equation τ-(frac{1}{2})[u²+u^-2]=E_maxsinγ₂ where τ is dimensionless thrust, u is airspeed, E_max is endurance and γ is the angle at which the force is acting on the aircraft.

10. At what airspeed does maximum gradient of climb occurs?
a) 1
b) 2
c) 3
d) 4
Answer: a
Clarification: The maximum gradient of climb occurs at airspeed (u) =1. There occurs negative values for sinγ₂ of τ and u when the flight is descending. The climb gradient equation is given by the equation τ-(frac{1}{2})[u²+u^-2]=E_maxsinγ₂.

11. Which of the following is the correct rate of climb equation?
a) τu-(frac{1}{2})[u³+u^-1]=E_maxv
b) τ-(frac{1}{2})[u²+u^-2]=E_maxsinγ₂
c) τ+(frac{1}{2})[u²+u^-2]=E_maxsinγ₂
d) τu-(frac{1}{2})[u³+u^-1]=E_maxv
Answer: d
Clarification: The correct rate of climb equation is given by τu-(frac{1}{2})[u³+u^-1]=E_maxv where τ is dimensionless thrust, u is airspeed, E_max is endurance and γ is the angle at which the force is acting on the aircraft.

12. What is the correct formula for dimensionless rate of climb?
a) ν=(frac{dH/dt}{V_{md}})
b) v=(frac{V_{md}}{dH/dt})
c) v=(frac{-V_{md}}{dH/dt})
d) v=(frac{-dH/dt}{V_{md}})
Answer: a
Clarification: The correct formula for dimensionless rate of climb is given by the formula v=(frac{dH/dt}{V_{md}}) where v the dimensionless rate of climb is and dH/dt is vertical velocity and V_md is velocity. The vertical velocity dH/dt is given in feet/min.

13. The minimum sink rate is attained by flying at a relative airspeed of u/(sqrt[4]{3}).
a) True
b) False
Answer: a
Clarification: The minimum sink rate is attained by flying at a relative airspeed of u/(sqrt[4]{3}). At this airspeed the minimum power speed of aircraft is attained. Flying at this speed will maximize the time of gliding flight.

14. What is the benefit of flying at minimum power speed?
a) Increases gliding flight time
b) Decreases gliding flight time
c) Does not change the gliding flight time
d) Decreases the aircraft performance
Answer: a
Clarification: The benefit of flying at minimum power speed is increase in gliding flight time. The minimum sink rate is attained by flying at a relative airspeed of u/(sqrt[4]{3}). At this airspeed the minimum power speed of aircraft is attained. Flying at this speed will maximize the time of gliding flight.

15. What is the value that maintains minimum power speed of the aircraft?
a) u/(sqrt[4]{3})
b) u/(sqrt[3]{3})
c) u²/(sqrt[4]{3})
d) u²/(sqrt[3]{3})
Answer: a
Clarification: The minimum sink rate is attained by flying at a relative airspeed of u/(sqrt[4]{3}). At this airspeed the minimum power speed of aircraft is attained. Flying at this speed will maximize the time of gliding flight.