2. Coal direct from the Black Gold mine arrives at the load out bin
via a feed conveyor and is transferred to the
lift conveyor and carried to the top of the circular load out bin.
A short chute (1 metre in height) and gate at
the base of the load out bin controls the flow of coal into each
train wagon. The load out bin is comprised of
a conical section A, a cylindrical section B and a truncated
conical section C.
Several design requirements will be specified by Black Gold Pty
Ltd for the total storage volume of the load
out bin, a range of mass flow rates at which the train wagons
can be loaded and the types of equipment that
can be selected for the design.
Students please note –
read the IMPORTANT NOTES on the last page of this document
and
the comments regarding the completion of individual
assignments in italics
Plan View
Side View
Elevation
Coal flow
3. Load out bin
supported in
square frame
of steel
road
Feed conveyor
6m
H
D = 5m
minimum
Load-
out bin
rail line
8m
Minimum
clearance 6m
Drawing not to scale
4. chute diameter d
1m high
h2
h
1
h
3
5m
Steel support
3m
Lift conveyor
length L
A
B
C
x = 3m
minimum
x D
5. Lift conveyor
variable
length X
conveyor
angle
theta 1 θ
1
h
C
the density of coal is 810 kg/m
3
cone angle theta 1 θ1
10 to 30 degrees
theta 2 = 45 degrees
2 ENG1002 – Introduction to Engineering and Spatial Science
Applications
6. 2. Design Sections
The project has been divided into three design sections, plus a
costing, to ensure that the requirements of the
project are clear. Each section of the design is to be defined by
the set of design parameters, listed in bold.
Any company submitting a design proposal must use these
variables names to identify the parameters.
Each design section requires a technical analysis which must be
summarised in the design proposal.
The Design Sections are:
1. The dimensions of the load out bin and other equipment
- the diameter of the load out bin (in m)
- the total height of the load out bin and frame (in m)
- the heights of each section of the load out bin (in
m)
) - cone and conveyor angle (in degrees)
- the volume of the load out bin (in m
3
)
– the distance from the load out bin to the road (in m) (X
and L now listed in section 2)
- the clearance over the road (in m)
7. - the maximum mass of coal in the load out bin (in tonnes)
2. The dimensions of the conveyor and related parameters
(this section may be used for the Presentation assessment)
(the width of the conveyor belt is not variable – see table 2)
– the lengths which define the conveyor (in m) (now
to be stated here)
– the maximum speed of the conveyor (in m/s)
- the maximum Mass Flow rate of the Conveyor (in kg/s)
– the power output required of the conveyor motor (in W)
-n - the Motor size selected to drive the conveyor
3. The gate and loading control and related parameters
(this section may be used for the Presentation assessment)
- the diameter of the chute (in m)
- the cross-sectional area of the chute (in m
2
)
- the Mass Flow rate into the Wagons (in kg/s)
– the time required to fill each wagon (in seconds)
– the time interval between each wagon (in
seconds)
8. – the required speed of the train (in kph)
4. The budget and costs of the components of the system
including the steel frame and support
(students are now to ignore the requirements of the steel frame)
- the surface area of the load out bin (in m
2
)
– the cost of the load out bin (to the nearest $)
– the cost of the conveyor excluding motor (to the nearest
$)
– the cost of the conveyor motor (to the nearest $)
– the total cost of the conveyor (to the nearest $)
2.1 Design Goals
The design goals for the project are to:
G1. maximise the storage volume of the load out bin
G2. maximise the rate at which coal can be loaded into the train
wagons
G3. stay within the allocated budget
ENG1002 Design project - Client Brief Version 2.0 3
10. outside the scope of the design include:
or materials not specified in versions of this
brief
3.3 Constraints (constraints have been numbered)
The following constraints apply:
C1. A maximum budget of $82,500
C2. The maximum height (H) for the design is not to exceed
18m.
C3. The load-out bin must be cylindrical in shape, with conical
ends.
C4. The minimum height for the cylindrical section of the load
out bin is to be 1m.
C5. The minimum diameter of the load-out bin is to be 5m.
C6. The angle (theta 1) of the conveyor must be between 10 and
30 degrees
C7. The train wagons hold a maximum of 100 tonne each
3.4 Assumptions
The following simplifying assumptions have been made:
-out bin is
usable, but not the chute.
of the walls of the silos and load-out bin can be
ignored in volume calculations.
how this is achieved is beyond the
11. scope of this design.
variations in
moisture content is to be ignored.
considered.
ignored
4 ENG1002 – Introduction to Engineering and Spatial Science
Applications
4.0 Technical Information (students - all this information is
new, except rho)
4.1 Load Out Bin, chute and gate control
Table 1: Technical Information relevant to the load out bin
Quantity variable value unit
Density of coal (same as in V1.1) ρ (rho) 810 kg/m
3
Cost of load-out bin (per m
2
of surface area) cB 100 $/m
12. 2
Length of wagon (wagon to wagon) Lw 12 m
Useful length of opening on the wagon Lo 9 m
Width of opening on the wagon w 1.5 m
Coal is loaded into the train wagons as the train moves
continually at a constant speed S (in kph) beneath the
chute. The gate on the chute is to be opened while the opening
in the wagon is under the centre of the chute.
You are to assume-
- that the useful length of opening Lo takes into account the
position of the wagon with respect to the chute,
such that no coal is lost over the end of the wagon.
- the gate opens and closes instantaneously and that the coal
flow into the wagon starts and stops
instantaneously (ignore any delays including the time for coal to
fall through the 1m deep chute)
- the width of the opening on the coal wagon (w) is 1.5 m
Figure 2: Proposed coal load – train loading side view
The mass flow rate into the wagon from the chute is given by:
13. √
where MFw is the mass flow rate of coal (in kg/s), a is the
cross-sectional area of the chute (in m
2
),
d is the diameter of the chute (in m) and g is gravitational
acceleration constant (in m/s
2
).
12m
LO
Load-
out bin
chute diameter d
Side View 2
Elevation
useful length of opening
Length of wagon Lw
(wagon to wagon)
15. m
2
Cost of conveyor (per linear metre) cC 700 $/m
The output power required from the motor to drive the conveyor
and raise the coal in height is given by:
( )
where P is power (in W), MFc is the mass flow rate of coal (in
kg/s), Δh is the change in height (in m),
g is gravitational acceleration constant (in m/s
2
), theta1 is the angle of the conveyor (in radians) and LF is
the Load Factor (dimensionless).
Table 3: Conveyor motor options – (costs include motor control
equipment)
Motor Size Output Power (kW) Cost ($)
M-5 50 5000
M-8 80 8000
M-10 100 10000
M-12 125 12500
16. 6 ENG1002 – Introduction to Engineering and Spatial Science
Applications
Important note to students
The sections listed above are to be used to subdivide the
analysis and design process and
identify the sections you are to use for your Technical Analysis,
Presentation and Design
Proposal assessments, as detailed in the requirements of each
assessment.
IMPORTANT: This is a closed design problem where all
information required to
complete the technical analysis, calculations and evaluation of
possible solutions will be
available in the Client Brief, your text books or other provided
assignment material. The
problem presented is a simplified version of a real design
problem, so the fine details of the
components of the proposed system are ignored.
If you find yourself seeking information beyond that provided
in the Client Brief,
17. your text books or other assignment material then you are
probably over thinking the
problem. The three assessments using this problem are able to
be completed using just the
engineering fundamentals you are studying, supported by other
course material and tools
like the spreadsheet. There is no need to research commercial
equipment.
For the Technical Analysis assessment all students must
complete a technical analysis
and prepare a short technical report on Design Section 1 (only)
of the project. Your
memorandum to a (pretend) colleague is to request a technical
analysis and short
technical report on one of either section 2 or 3.
For the Presentation assessment each student will select design
section 2 or 3 of the
project on which to complete a technical analysis and prepare a
short oral presentation.
[This can be the same as the section your request of your
colleague in your memo – that is
not important.] You are to present a summarised technical
analysis of that section of the
18. design and how it depends-on / influences any other section of
the design. The
presentation is to be prepared and delivered as if to other
colleagues in your company who
are working with you on the larger project.
For the Design Proposal assessment students are expected to
complete the technical
analysis for the whole project, model the design on a
spreadsheet, evaluate some
alternatives within the design and select a specific design
solution to recommend in their
report. The recommendation must clearly specify all of the
parameters listed in the design
sections in bold, as they define each section of the design.
Students should note there is more than one correct answer to
this problem, as several
possible solutions will meet the requirements of the design.
Furthermore - a technical analysis of a single design section
ALONE is unlikely to
identify a set of design parameters that results in the final
project design, as the
sections are somewhat dependent on each other. Hence when
you complete a technical
19. analysis on a single section of the design you are not looking
for a specific ‘answer’ to
that section.
Your analysis should show the relationships between the
parameters (eg. D, H, etc)
within a section and possibly with those in other sections of the
design. This analysis
will allow you to eliminate some of the alternative equipment
suggested (when it is evident
it cannot do the job), or you may be able to reduce the range of
values for some parameters
which offer a possible solution.
Technical Analysis Page 2
_____________________________________________________
_________________________
Technical Analysis of Proposed Coal Load Out Conveyor
System
_____________________________________________________
_________________________
Prepared by:
September, 2014.
20. Introduction
This section presents a technical report of the coal load out bin
and other equipment that are presented in figure 1. Among the
issues to be addressed in this report are the ideal dimensions of
D, H, h1-h3, θ1, V, X,L and x, hc and M. Trigonometry will be
vital in meeting this objective (Riley, Hobson, & Bence, 2006).
These dimensions are explained below.
· D the diameter of the load out bin (in m)
· H the total height of the load out bin and frame (in m)
· h1to h3 the heights of each section of the load out bin (in m)
· θ1 (theta 1) cone and conveyor angle (in degrees)
· V the volume of the load out bin (in m3)
· X, L and x lengths which define the conveyor (in m)
· hC the clearance over the road (in m)
· M the maximum mass of coal in the load out bin (in tonnes)
Figure 1: Proposed coal load out equipment
To begin with, D will be assumed to be at minimal value, which
has already been stated as being 8m. The selection of D as 8m is
because this falls within the allowable minimum and maximum
limits, making it acceptable in terms of size and volume that it
will carry. The selection of this dimension will affect the length
of x as presented below.
If D is 8m, this will mean that:
· The radius of section B in figure 1 will be , making it
· x =
· = 8 – 4
· = 4 m
Other dimensions for x and D, depending on the selected size of
D are presented in the table below
Table 1: Values of x and D
X
D
3.00
10
3.50
21. 9
4.00
8
4.50
7
5.00
6
5.50
5
The values above have been established from the expression
In order to obtain the value of H, trigonometric equations will
be used to relate these distances (Bolton & Bolton, 2012).
Assuming that the load out bin is perfectly vertical and the
surface on which it stands is horizontal, the intersection
between H and X will be at a right angle. Therefore, the relation
between H and X will be as follows:
Where tan 1 =
Therefore, H = X*
This is because the angle ay the top of load out bin is the same
as the angle of intersection between the lift conveyor and the
horizontal surface.
From the above, L will be expressed as
In order to determine h1-h3, it will be represented as a
difference between H and (5m + d). Where d, as mentioned in
figure 1, is the chute diameter, which is 1m. This will be
represented in equation form as:
= X*
But d + 1m
X*
The cone conveyor angle θ1 (theta 1), as has already been
mentioned earlier, will be obtained by the formula below:
Tan 1 =
Therefore, θ1 = tan-1
V, which is the volume of the load out bin, will be calculated by
22. calculating the volumes of sections A, B and C in figure 1
separately.
The volume of A, which will be conical, will be determined by
the formula () (Riley, Hobson, & Bence, 2006).
Figure 2: Volume of a conical structure
Source: Riley, Hobson and Bence (2006)
Applying the above formula, the volume of A will be (). This
can be presented as:
VA = ()
Section B is cylindrical and thus, its volume will be estimated
by the formula
Thus, VB =
Finally, the volume of section C, being conical too, will be
estimated by the formula ()
Thus, VC = ()
The total volume of the whole load out bin will therefore be VA
+ VB + VC
VA + VB + VC = () + + ()
= () + + ())
Thus, V= () + + ())
In order to establish the length of hC as presented in figure 1,
trigonometric relations will also be used.
Tanθ1=
=
But tan θ1 =
Therefore,
And hC =
Finally, M which is the maximum mass of the coal in the load
out bin will be calculated with the value of D at 10, which
results in the minimum value of x. (see table 1).
Therefore, applying the formula of V
V= () + + ())
Replacing D/2 with 5, the volume will be as follows:
V= () + + ())
V=
23. =
Mass will therefore be V*density, which is 810 kg/m3*
However, at maximum volume, θ1 is at 10◦
Therefore, tan θ1= 0.17633
But h1=
= 5*0.17633 = 0.8816 m
Then, given that θ2= 45◦, h3 = D/2 = 5m
V=
V=154 + 78.54h2
Mass = 810 (154 + 78.54 h2)
= (124740 + 63617.25 h2) kg
= (124.74 + 63.617 h2) tonnes
Conclusion
The expressions that have been presented above provide
guidance on how the dimensions of the different elements of
section 1 can be obtained. As presented in the equations above,
most of the dimensions are affected the value of others. An
estimation of the maximum mass that can be supported by the
coal bin is essential in guiding the materials that can be used in
the provision of support for the entire load.
References
Bolton, W. & Bolton, W., 2012. Mathematics for Engineering.
New Jersey: Routledge.
Riley, K.F., Hobson, M.P. & Bence, S.J., 2006. Mathematical
Methods for Physics and Engineering: A Comprehensive Guide.
Chicago: Cambridge University Press.
Requirements
Students must prepare and deliver their presentation as if to a
group of colleagues within the same company. Student are also
required to review 3 other student's presentations. Students are
24. to assume their colleagues are familiar with and are working on
other sections the same project. Students must treat the
assessment as a real engineering presentation.
Each student is required to:
1. prepare and present a short (5 to 6 minute) oral presentation
on the technical analysis for one section of the design project
and explain how it links-with/influences one other section of the
design. The section selected as the focus of the presentation
must be chosen from either the section 2 or 3 of the design
project. It may be the same as the section you requested in your
memo or not, this is not important.
The presentation must include: a title slide; a professional
format; mention of the project and the Client Brief; a diagram
clearly identifying the relevant section of the design; a brief
technical analysis of the section and any key findings; a clear
explanation of how this section links to another; a graph to
demonstrate the link between the two sections. Penalties will
apply if you exceed 7 minutes.