联系我们： 手动添加方式: 微信>添加朋友>企业微信联系人>13262280223 或者 QQ: 1483266981

FEEG1050W1
Introduction
The Strenuis Ardua is an aircraft in its final design stages. Several
engineering problems have arisen during the design process, and
C. E. Dunt, the project’s Chief Engineer, would like your help to solve
them.
Page 2 of 10
FEEG1050W1
Page 3 of 10
Please answer each question in a separate document
1. As part of a flight demonstrator test platform for the development
of a hydrogen powered jet engine the Strenuis Ardua will be
fitted with a number of vacuum-insulated liquid hydrogen storage
tanks. To evaluate their safety under different loading scenarios,
the storage tanks can be modelled as a thin-walled cylindrical
pressure vessel with a length of 2.5 m and radius of 35 cm (Fig.
Q1), assuming a state of plane stress.
Figure Q1: Cylindrical pressure vessel
(i) The yield stress of the material is 440 MPa and the safety
factor to be used in the design is 3. Using the von Mises
criterion, calculate the maximum allowable pressure for a
wall thickness of 1.5 mm.
[10 marks]
(ii) The Young’s modulus of the material is 120 GPa and
Poisson’s ratio is 0.33. Calculate the two-dimensional strain
components and at the surface of the pressure
vessel under these conditions.
[4 marks]
FEEG1050W1
Page 4 of 10
(iii) Draw Mohr’s circle for this strain state and determine the
magnitude of the maximum shear strain in any orientation.
Clearly annotate your drawing with the values of the relevant
shear strains, position of the centre and principal strains.
[6 marks]
(iv) How would the principal strains change if the storage tank
was subject to an additional torsion load Explain your
reasoning.
[5 marks]
[Total 25 marks]
FEEG1050W1
Copyright 2022-23 v02 University of Southampton Page 5 of 10
Please answer each question in a separate document
2. The Strenuis Ardua can be configured as a heavy-lift transport
aircraft for conveying humanitarian aid. The thrust force of the
aircraft’s engines depends on the angular velocity , the inlet
diameter , and the fluid density .
(i) Derive an expression for the non-dimensional thrust.
[5 marks]
(ii) Find the thrust of a -scale model engine rotating at
500 rpm, given that the full-scale engine has an inlet
diameter of 1 m and generates 300 kN at 1000 rpm.
Take the density of air to be 1.23 kg m 3
.
[3 marks]
The Strenuis Ardua has a maximum speed of 600 km hour 1 and
a service ceiling (maximum altitude) of 8 km. The inlet to each
engine (1 m diameter) leads to an axial compressor that has an
outlet-inlet pressure ratio of 30 ∶ 1 and a temperature change of
Δ = 800 .
(iii) Given the data in Table Q2, determine the back work
required to drive the compressor at the maximum speed at
both sea level and at 8 km altitude. Take values of =
287 J kg 1 K
1 and = 1004 J kg 1 K
1
. Account for the
inlet kinetic energy but assume that the outlet kinetic energy
is negligible.
[10 marks]
Table Q2: Atmospheric properties
Altitude Pressure (Pa) Temperature (K)
Sea level 1.00 × 105 288
8 km 0.35 × 105
236
FEEG1050W1
The design team are considering the use of disposable rocket
units attached to the side of the fuselage, to facilitate shorter
take-off runs. One such rocket is shown in Fig. Q2.
Figure Q2: Rocket bottle diagram
(iv) The solid fuel is burning at the rate of 435 3

1
. If the
density of the fuel is 900 3 calculate the exit velocity
given the density of fluid at the exit is 0.2 3
.
[3 marks]
(v) Calculate the vertical component of the thrust force.
[2 marks]
(iv) Calculate the horizontal component of the thrust force.
[2 marks]
[Total 25 marks]
Page 6 of 10
FEEG1050W1
Page 7 of 10
Please answer each question in a separate document
3. The Strenuis Ardua, when configured for commercial flight, is
propelled by two engines each providing a constant thrust
= 300 kN. The mass of the aircraft body (excluding the
wheels) is = 180 × 103 kg.
Figure Q3a: The Strenuis Ardua on a runway
Model the aircraft as a rigid body with the dimensions given in
Figure Q3a. The mass centre is at point .
For questions (i)-(iii) neglect air resistance, lift, rolling resistance,
the mass of the wheels and friction between the ground and the
tyres. Consider the moment in time when the aircraft starts to
accelerate and undergoes rectilinear translation along the
runway.
(i) Draw the free-body and kinetic diagrams of the aircraft. The
vectors must be drawn at the correct points of application on
the aircraft. For this purpose, you can use the drawing
available in Figure Q3b or you can create a similar one
yourself.

= 9 m
= 6 m = 25 m
= 3 m
2
FEEG1050W1
[5 marks]
Figure Q3b: Drawing for your diagrams.
(ii) Find an algebraic expression for the (linear) acceleration of
the aircraft and calculate its value.
[2 marks]
(iii) Find an algebraic expression for the normal reaction on the
nose wheel at and calculate its value.
[10 marks]
The aircraft is fitted with eight identical wheels of mass
= 100 kg each, radius of gyration = 0.4 m and radius
= 0.6 m. At the end of the runway and just before the nose
wheel lifts off, the aircraft is travelling at = 250 km hour 1
. The
wheels are rolling without slipping.
(iv) Calculate the ratio between the kinetic energy of all the
wheels and that of the aircraft body.
[8 marks]
[Total 25 marks]
Page 8 of 10
FEEG1050W1
Page 9 of 10
Please answer each question in a separate document
4. The following problems have arisen in the design of the avionic
systems for the Strenuis Ardua.
Figure Q4a: Sensor circuit
(i) The circuit for a sensor in its neutral position can be
represented by the circuit shown in Fig. Q4a. Sketch a graph
of out versus out for the circuit.
[5 marks]
(ii) The Boolean function is written in its sum-of-products form
as:
= . . + . . + . . + . . + . .
Simply as far as possible using the Karnaugh map
method. Your answer should include the Karnaugh map.
[9 marks]
FEEG1050W1
Page 10 of 10
Figure Q4b: Circuit with variable capacitor
(iii) An inductive load of 3 Ω resistance and 20 mH inductance is
connected in parallel with a variable capacitor C, across an
AC supply ( ) = 100√2 cos(200 ) V, as shown in Fig. Q4b.
Using complex phasor analysis:
(a) Write an expression for the current supplied by the AC
supply.
[5 marks]
(b) Calculate the capacitance of the variable capacitor which
will result in the minimum current from the supply.
[2 marks]
(c) Calculate the current, and the active power provided by
the AC supply at this capacitance.
[4 marks]
[Total 25 marks]
END OF PAPER