This set of Aircraft Design Questions and Answers focuses on “Conceptual Sketch Sizing – Fuel-Fraction Estimation-2”.

1. What does the following diagram represents?

a) Simple cruise mission profile

b) Accelerated cruise

c) Bomber mission

d) Penetration strike

View Answer

Explanation: The diagram is representing altitude vs time relation. It is also called ‘mission profile’ of an aircraft. This mission profile consist only basic phases of flight. Hence, it can be termed as simple cruise mission profile.

2. For given mission leg ‘n’, mission leg weight fraction is _____

a) Wn / Wn+1

b) Wn / Wn-2

c) Wn-1 / Wn+1

d) Wn / Wn-1

View Answer

Explanation: For any mission leg or mission phase, mission fuel fraction is ratio of fuel weight at the end and at beginning of each phase. Hence, if it is mission phase n then, (n-1) will be the phase before nth phase. Hence, correct answer is Wn / Wn-1.

3. Which of the following is part of the fuel-fraction method?

a) Developing lofting

b) Empty weight fraction

c) Calculating individual mission segment weight fraction

d) Finding volume ratio

View Answer

Explanation: Lofting is a vital part of preliminary design phase. The fuel fraction method is very simple and basic approximation method. Here, mission profile is divided and then for every individual phase we calculate mission segment weight fraction.

4. An Aircraft has gross weight of 10000lb. At the end of the mission segment it has weight fraction as 0.985. Determine fuel consumed for this mission.

a) 150kg

b) 150lb

c) 60kg

d) 60lb

View Answer

Explanation: Given,

Aircraft gross weight W

_{0}= 10000lb

Fuel weight fraction at the end of mission = W

_{x}/W

_{0}= 0.985

Here, there is no provision of reserved fuel is mentioned. So, we are neglecting reserve fuel fraction.

Now, from fuel fraction method,

Used fuel weight fraction is W

_{f}/ W

_{0}= 1 – (W

_{x}/ W

_{0})

= 1 – 0.985 = 0.015

Hence, fuel consumed during this mission = W

_{f}= W

_{0}* 0.015 = 10000 * 0.015 = 150lb.

5. Choose appropriate option for cruise mission leg weight fraction.

a) Breguet endurance formula

b) Breguet range formula

c) Cruise invert method

d) Breguet approximation

View Answer

Explanation: Breguet range formula is used to calculate range for respective mission. In simple sizing method we consider that the cruise is ending with descent. Also, we assume that cruise range has accounted for descent as well. Hence, we use range formula to determine fuel fraction.

6. A jet aircraft is cruising at 12000ft. What will be the cruise leg (mission phase ‘n’) weight fraction?

a) Wn/Wn-1 = \(e^{\left(-\frac{R*C}{V*\frac{L}{D}}\right)}\)

b) Wn/Wn+1 = \(e^{\left(-\frac{R*C}{V*\frac{L}{D}}\right)}\)

c) Wn/Wn-2 = \(e^{\left(-\frac{R*C}{V*\frac{L}{D}}\right)}\)

d) Wn/Wn-1 = \(e^{\left(-\frac{R*C}{V*\frac{L}{D}}\right)}\)

View Answer

Explanation: Aircraft is cruising at 12000ft and the cruise mission leg is nth mission phase of whole mission profile. Here, we will use Breguet range formula to find Weight fraction. Breguet range formula,

R = (V/C) * (L/D) * ln (Wn-1/ Wn)

Now by re-arranging, cruise mission leg weight fraction is,

Wn/Wn-1 = \(e^{\left(-\frac{R*C}{V*\frac{L}{D}}\right)}\)

7. What will be the total fuel weight fraction for x-number of mission phases?

a) W_{f} / W_{0} = 1 / (W_{x} / W_{0})

b) W_{f} / W_{0} = 1 + (W_{x} / W_{0})

c) W_{f} / W_{0} = 1 – (W_{x} / W_{0})

d) W_{f} / W_{0} = 1 + (W_{x} / W_{0})

View Answer

Explanation: The fuel-fraction method is used to determine total fuel weight fraction.

According to which if there are x – number of mission phases in mission profile then the total fuel weight fraction is given by,

W

_{f}/ W

_{0}= 1 – (W

_{x}/ W

_{0})

Since, reserved fuel is not mentioned we can neglect it.

8. What will be the weight fraction of the aircraft at final mission segment w.r.t. W_{0}?

a) Subtraction of individual weight fraction

b) Division of individual weight fraction

c) Addition of individual weight fraction

d) Multiplication of individual weight fraction

View Answer

Explanation: We can divide whole mission profile of aircraft into number of mission phases or legs. Fuel fraction at each mission segment will be fuel weight at end of phase to that of beginning. Hence, if there are z – number of mission phase then, final mission phase fraction will be multiplication of individual weight fraction which will give weight fraction w.r.t. take-off gross weight W

_{0}

9. How will you determine climb mission weight fraction?

a) Climb Endurance

b) Loiter

c) Always constant

d) Cruise Speed

View Answer

Explanation: Climb phase usually measured by rate of climb. Climb endurance formula is used to determine the endurance of aircraft at climb phase. Typically we can find climb weight fraction from historic time line however in some cases we can also use climb endurance formula to determine fuel fraction.

10. If all the other factors remain unchanged and only aerodynamic efficiency of the aircraft is doubled then, what will be the cruise segment fuel weight fraction?

a) Will decrease

b) Will increase

c) Will remain same

d) Will be independent of aerodynamic efficiency

View Answer

Explanation: Cruise phase fuel fraction is determined by using range formula as follows:

Wn/Wn-1 = \(e^{\left(-\frac{R*C}{V*\frac{L}{D}}\right)}\)

Now if we double the value of aerodynamic efficiency the denominator will increase which in turn increases fuel fraction during cruise.

11. Fuel consumption during cruise is affected by wetted area.

a) True

b) False

View Answer

Explanation: Fuel conception or fuel fraction during cruise segment will be affected by the overall aerodynamic efficiency. The aerodynamic efficiency is ratio of lift and drag. Lift is directly affected by the wetted area, which affects L/D. As a result, it will affect fuel fraction during cruise mission phase.

12. A prop-driven aircraft is cruising with 90% propeller efficiency. If, range of aircraft is 7*10^{6} ft, C=1.38*10^{-7} s^{-1} and L/D = 14 then what will be the fuel weight fraction for the cruise?

a) 0.9216

b) 0.9261

c) 0.9289

d) 0.9365

View Answer

Explanation: Given, a prop-driven aircraft,

Range R = 7*10

^{6}ft, C = 1.38*10

^{-7}s

^{-1}, L/D =14

Here, propeller efficiency is 90% hence, η = 0.9

Now cruise weight fraction is given by range formula. For, prop-driven aircraft it is given by,

W

_{cruise}/ W

_{0}= \(e^{\left(-\frac{R*C}{\eta*\frac{L}{D}}\right)}\) = \(e^{-(\frac{7 * 10^ 6* 1.38 * 10^ {-7}}{0.9*14})}\) = 0.9261.

13. An Aircraft has following mission profiles with their respective mission weight fraction. There is 10% allowance of reserved fuel. Now, due to some reason loiter weight fraction has changed to 0.90. Now, with same amount of fuel as initial, will aircraft be able to perform loiter?

Mission | Weight fraction |
---|---|

Engine start-up | 0.975 |

Taxi | 0.98 |

Climb | 0.970 |

Cruise | 0.989 |

Loiter | 0.96 |

Landing | 0.975 |

a) Yes, loiter can be performed

b) Will not depend on change

c) No, loiter cannot be performed

d) 12% less fuel will require

View Answer

Explanation: Here, individual weight fraction is given for aircraft.

First, let’s find what would be the total fuel fraction of this aircraft with 10% reserved fuel.

Total fuel fraction without reserved fuel is W

_{f}/ W

_{0 }= 1 – (W

_{x}/ W

_{0}), x = final mission phase

Now 10% of total fuel is reserved fuel hence, the actual total fuel fraction is given by,

W

_{f}/ W

_{0}= 1 – (W

_{x}/ W

_{0}) + 10% of W

_{f}/ W

_{0}

= 1.1 * [1 – (W

_{x}/ W

_{0})]

Now from fuel fraction method,

W

_{x}/ W

_{0}= multiplication of each phase fraction

= 0.975*0.98*0.970*0.989*0.96*0.975

= 0.8579

Now,

W

_{f}/ W

_{0}= 1.1 * [1 – (W

_{x}/ W

_{0})]

= 1.1*[1-0.8579] = 1.1*[0.1420] W

_{f}/ W

_{0}= 0.1562 – Actual total fuel weight fraction

Now, if loiter weight fraction is changed to 0.90. Now to check whether aircraft will be able to loiter or not we need to compare new total fuel fraction with actual. If it is less then aircraft will have enough fuel to loiter otherwise it won’t be able to loiter for same amount of fuel storage.

New, W

_{x}/ W

_{0}= 0.975*0.98*0.970*0.989*0.90*0.975 = 0.8043

New, W

_{f}/ W

_{0}= 1.1 * [1 – (W

_{x}/ W

_{0})] = 1.1*[1-0.8043] = 0.2152 which is more. Hence, answer is no, pilot will not be able to perform loiter.

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