Exercises Lecture 7

Propulsion

Prof. dr. ir. Jacco Hoekstra

Tim van Leeuwen
Delft University of Technology

R. Ede - CC - BY - NC
 AE1110x - Introduction to Aeronautical Engineering

Exercise 1
What was the main reason that propulsion formed a hurdle initially in the quest to be able to fly?
Around the year 1900:
A) Engines were too heavy
B) Engines were not powerful enough
C) Engines were too big
D) Engines were too unreliable

Exercise 2
What is the main problem that aircraft with very large engines (such as this Gee Bee Model R)
face?

Figure 1: The Bee Gee model R. Image courtesy of Kemon 01, CC - BY - NC - SA

A) The fuel-thirsty engine leads to a very short range.

B) The aircraft can only fly very fast because of its very small wings.
C) Changing the engine throttle leads to stability and control issues.
D) The engine causes a lot of vibration, which means the structure needs to be reinforced.

Exercise 3
A propeller engine for a model airplane is measured to have a jet velocity of 50 kilometres per hour.
When strapped to a fixed support it is measured to produce 10 Newtons of thrust. Determine the
mass flow through this propeller (in kilograms per second).

Exercise 4
Again consider the model propeller of the previous problem. If we assume the jet velocity to be
equal to the velocity of the air through the propeller, then we can say that ṁ = ρAVj , where ρ is
the air density, A is the propeller area and Vj is the speed of the flow through the propeller.
Given that the test was performed with an air density of 1.225 kilograms per cubic metre, determine
the propeller diameter (in metres).

Exercise 5
A general aviation aircraft (m = 1200 kg) flies (under ISA conditions) at 850 metres altitude, with
a constant velocity (true airspeed) of 116.6 knots. Its wing surface area is 22 square metres.
Given that its propeller is able to accelerate 80 kilograms of air to a velocity of 105.56 m/s every
second, determine the plane’s drag coefficient CD .

Exercises Lecture 7 - Propulsion 1

 AE1110x - Introduction to Aeronautical Engineering

Exercise 6
The most powerful variant of the General Electric GE90 engine (the biggest turbofan engine in
the world, see below) is able to produce over 500 kN of thrust in a standstill full power test at sea
level. Its exhaust speed is estimated to be 730.8 kts. Based on this data, determine the volume of
air (in cubic metres) this engines takes in per second for this thrust.

Figure 2: An aircraft equipped with GE90 engines. Image courtesy of Angelo DeSantis, CC - BY

Exercise 7
Which one of the following five names does not specify a type of piston engine?
A) Radial engine
B) Wankel engine
C) In-line engine
D) Four-phase engine
E) Boxer engine

Exercise 8
Which of the following is/are not (an) option(s) to let a combustion engine deliver more net work?
(Multiple answers possible)
A) Expand the air-fuel mixture slower
B) Add more fuel before combustion
C) Compress the air more
D) Expand the air less

2 Exercises Lecture 7 - Propulsion

 AE1110x - Introduction to Aeronautical Engineering

Exercise 9
You are given the following (p,V)-diagram, which depicts one cycle of a combustion engine.

Figure 3: A hypothetical combustion cycle.

Which line segment corresponds to the expansion phase?

A) Pink (1)
B) Green (2)
C) Yellow (3)
D) Blue (4)
E) Red (5)

Exercise 10
Again consider the combustion cycle shown in the previous problem. What is the net work done
(in Joule) by this cylinder during one cycle?

Exercise 11
The tip of a 2.5m diameter propeller turns with a speed of M = 0.8 at sea level, under ISA
conditions. Determine the rotational speed of the propeller (in radians per second).

Exercise 12
Propeller engines are limited in the amount of thrust they can generate. What is the cause of this
limitation?
A) Increasing the propeller diameter leads to reduced ground clearance.
B) A propeller can’t expel air very fast, so Vj is low.
C) When spinning a propeller faster or increasing its diameter, the propeller tips go supersonic.
D) Centrifugal stresses in propeller blades become too high when the propeller spins too fast or
becomes too large.

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 AE1110x - Introduction to Aeronautical Engineering

Exercise 13
The Pilatus PC-12 (shown on the picture below) is a popular private propeller jet.

Figure 4: Image courtesy of Daniel S., CC - BY - NC - ND

From the manufacturer the following data can be obtained:

Engine power = 1200 hp
Propeller diameter = 2.67 m
Propeller RPM = 1700
Cruise: 270kts@20, 000 ft
Propulsive efficiency = 60%
1) Determine the propeller tip speed (in metres per second) in normal operation.
2) Determine the thrust generated by the propeller (in kN).

Exercise 14
A twin-engined propeller aircraft is equipped with two engines, each rated at 98 kW shaft power.
During cruise flight at 72 m/s at an altitude of 3400 metres, the aircraft experiences a lift coefficient
of 0.555. Its wing surface area is 28 square metres, with an average chord length c̄ of 2 metres.
Its zero-lift drag coefficient is 0.01 and its span efficiency (or Oswald) factor is 0.7.

Figure 5: Image courtesy of Airwolfhound, CC - BY - SA

Determine the propulsive efficiency (in percent) in this flight condition.

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 AE1110x - Introduction to Aeronautical Engineering

Exercise 15
What kind of jet engine is shown below?

Exercise 16
What kind of jet engine is shown below?

Exercise 17
What kind of jet engine is shown below?

Figure 6: Image courtesy of Yukun Chen, CC - BY - NC

Exercise 18
Why are modern jet engines so big?
A) To increase their jet efficiency
B) To increase the ratio air/fuel
C) To make them more powerful
D) To provide space for their ever more complex components

Exercise 19
What is a typical value for the bypass ratio of the most modern engines?

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 AE1110x - Introduction to Aeronautical Engineering

Exercise 20
In an earlier problem we considered the GE90 engine, one of the world’s most powerful engines. A
picture of this engine is shown below.

Figure 7: Image courtesy of Patrick Cardinal, CC - BY - NC - ND

It was already determined that the jet velocity of this engine is 376 metres per second. Suppose
that this Boeing 777 flies at 11 kilometres at M=0.82, what is then the jet efficiency of this engine
(in percent)?

Exercise 21
In the previous clips the ETOPS rules were shortly discussed, which prohibit aircraft with only two
engines from making certain Atlantic crossings. An example illustrating the need for this rule is
Air Transat Flight 236, a flight from Toronto to Lisbon. Over the Atlantic ocean the Airbus A330
(shown below) experienced a fuel leak and subsequent double engine failure.

Figure 8: Image courtesy of Abdallahh, CC - BY

Still 120 kilometres removed from the nearest airport (on the Azores), the A330’s second engine
failed at an altitude of 10 kilometres, causing the aircraft to lose electric and hydraulic power as
well.
Eventually the aircraft made it to a military base on the Azores, for this exercise we estimate the
’spare’ altitude to be 500 metres. Assume that there was no wind. What was the glide ratio of
this A330?

6 Exercises Lecture 7 - Propulsion