Acoustic Camera Mount Drag Calculations Final Lab
Report
Aquaculture Research Center
December 8, 2011
Adam Baran
Alden Blais
Elsie Mason
James Moulton
1
Table of Contents
Introduction .................................................................................................................................................. 3
Objectives ..................................................................................................................................................... 3
Theory ........................................................................................................................................................... 4
Procedure...................................................................................................................................................... 6
Apparatus, Equipment, and Instrumentation ............................................................................................... 7
Plan of Work ............................................................................................................................................... 12
Expected Results ......................................................................................................................................... 13
Uncertainty ................................................................................................................................................. 15
Results ......................................................................................................................................................... 19
2
Introduction
This report is a proposal for an experiment on finding drag forces. In the experiment, an acoustic
camera with a pan and tilt will be guided through a tow tank filled with water. The purpose of
this experiment is to determine the drag forces on the combined camera and pan/tilt system
shown in figure 1 while being guided through the tow tank at various speeds. This data will be
compared to our predicted values which were used to design the initial camera platform. We also
wish to determine the drag on our camera platform so that we can later predict the forces on it in
different flow situations in a damn spillway. These forces will allow us to know whether or not
the camera platform will tip over in various water current speeds.
Figure 1. Camera and pan/tilt system
Objectives
The experiment seeks the following information about the camera and pan/tilt system:
1. Determine the combined drag force on the camera and pan/tilt in water currents between
0 and 5 knots.
2. Determine the fastest water current speed that will allow the camera platform to remain
upright.
3
Theory
When an object is subjected to a moving fluid, a drag force is created. This drag force depends
upon the object’s drag coefficient, the velocity between the object and the fluid, density of the
fluid and the area as seen by the stream. This relationship can be seen in Eq. 1.
1
2
Fdrag  Cd    v  A 
2


Where: Cd: drag coefficient
ρ: density of fluid
Eq. 1
A: area of object seen by fluid’s current
v: velocity of fluid current
The drag coefficient, Cd, is a dimensionless quantity that is used to quantify the drag of an object
in a fluid. The drag coefficient is always associated with a particular surface area.
The drag force on the object at the end of the beam causes a deflection. If this deflection is too
large the test rig can fail or the data can be compromised, therefore the beam must be chosen to
keep the deflection to a reasonable limit. As seen in Figure 2, the maximum drag force will be
focused at the free end of the test rig. This beam is considered a simply supported beam which
overhangs its supports with a concentrated load acting at the end.
Figure 2. Beam deflection pattern
4
The deflection can be calculated at any location along the beam but the maximum deflection will
occur at the free end where the drag force is applied. Using basic strengths of materials theory
for a general simply supported beam which overhangs it's supports with a concentrated load
acting at the end the max deflection can be calculated by the following equation.
δmax=
𝐹𝑑 𝑎2
3𝐸𝐼
(𝐿 + 𝑎)
Eq. 2
Figure 3. Simply supported beam which overhangs supports
δmax is the deflection at the location of Fd
R1 support reaction from pinned connection
R2 support reaction from load cell
Fd is the drag force applied to the end
L, a, x and x1 are lengths measured from their respective locations
A simpler illustration of this can be seen in Figure 4, showing the forces acting on the beam.
When a moment balance is taken about the point A, at the top of the beam hinged to the test rig
extension the forces can be solved for with the known dimensions.
5
Figure 4. Forces acting on beam
F1 
l2  l1
l1
 FD
Eq. 3
where: F1 and FD are forces
l1 and l2 are lengths as shown
Equation 3 can be used to solve for the load at the location of the load cell, F1. Using predicted
values of Fd the force on the load cell can be predicted which will allow for the proper sizing of
the load cell. Equation 3 can also be solved for Fd to relate the load cell reading to the drag force
using equation 4 below.
Eq. 4
Procedure
The first step will be calibrating the load cell to obtain an equation relating the output to the drag
applied force. This will be accomplished by applying known weights to the load cell and
recording the output.
Once the load cell is calibrated testing can begin. It is desired to know if the effect of the portion
of the submerged test structure has a noticeable drag force. In order to determine this, a few runs
will be performed by towing only the apparatus through the water.
Testing of the camera and pan/tilt system will be conducted at various speeds ranging from a
desired 1 to 5 knots depending on the camera at different orientations. The orientation with the
largest and smallest surface areas will be tested.
6
Apparatus, Equipment, and Instrumentation
The test apparatus involves a vertical beam extended down from the carriage of the tow tank.
This beam will be hinged to an extension that hangs out over the edge of the carriage. A load
cell will be placed in between the beam and carriage with threaded rods to measure the force
produced by the drag of the camera. A sketch has been included in Figure 5 below.
Figure 5. Test Rig Apparatus
The beam hung from the extension will have a platform connected on the base to allow the
desired object to be attached for testing.
The testing apparatus will include a vertical beam, which will extend out from the carriage of the
tow tank. At the end of this beam, a hinge will attach and another beam will hang down into the
tank. This beam will be fashioned with a platform on the end that will be submerged in to the
water, and will attach to the object to be tested. To measure the drag force, which is our main
objective, a load cell will be placed between the carriage and hanging beam. This will allow the
beam to exert a force onto the load cell, which can then later be analyzed to find the desired
value of drag force. A sketch has been included in Figure 5 below.
The required materials for this apparatus will need to be strong enough to withstand the forces
that will be applied by the drag on the water while it is pulled through the tank. As the carriage
7
moves along, the force of the drag will cause stress/strain in the beams. To ensure that the
apparatus can withstand these stresses/strains, the material much be chosen such that there is no
question whether the materials will perform as required.
We will begin by looking at the prediction values of the drag force in order to do an analysis
which will aid in determining the force the load cell will experience. From this calculation, the
appropriate load cell may be chosen, with the best parameters to meet our needs. Using the free
body diagram seen below in Fig. 5, this force F1 can be found.
F1 
l2  l1
l1
 FD
Eq. 5
Where:
F1 = the reaction force experienced at the load cell
F2 = the reaction force experienced at the pin joint
FD = the force exerted by the drag of the water
l1 = the distance from the reaction force at the pin joint to the reaction
force at the load cell
l2 = the length from the reaction force at the load cell to the location of
the drag force
Figure 4. Forces acting on beam
Equation 5 can be used to solve for the load at the location of the load cell. To do this, the length
of the beam must be determined. The dimensions of the tow tank with the test apparatus design
can be seen in Fig. 6. Using predicted values of FD, and the lengths found, the force on the load
cell can be predicted which will allow for the proper sizing of the load cell.
8
Figure 6- Tow tank with test apparatus dimensions
The calculations to determine the maximum force applied at the load cell can be seen below.
l1  15 in
l2  42.28 in
F1 


FDmax l2  l1
l1
 190.933
lb
FDmax  50 lb
From these calculations, it can be concluded that a load cell must be
chosen to best fit the range. As the maximum load came so close to
the upper limit of the 25-200 lb load cell, it may be a better choice to select the cell that is best
for 250 lbs.
The next material that must be analyzed is the hanging beam. Figure 7 below shows the
deflection pattern of the beam. The deflection can be calculated at any location along the beam
but the maximum deflection will occur at the free end where the drag force is applied. Using
basic strengths of materials theory for a general simply supported beam which overhangs its
supports with a concentrated load acting at the end, the max deflection can be calculated by the
following equation.
δmax=
𝐹𝑑 𝑙1 2
3𝐸𝐼
(𝑙1 + 𝑙2 )
Eq. 6
9
Where:
δmax max deflection
Fd is the drag force
l1 is the distance between the mounting beam to the location of the load cell
l2 is the distance between the load cell and the location of the max drag force which is at
the center of mass of the tested object
Figure 7. Beam deflection pattern
With the values found for the length of the beam and the location of the load cell, a beam can be
chosen. Using a 2.5”x2.5” low carbon steel tube, with a thickness of 1/8th”, the deflection is
found. These calculations can be seen on the following page and show that the maximum
deflection is found to be .00126 in.
10
6
7
E  29 10  2.9  10
a  2.5
Modulus of Elasticity for Steel
in
Tube Beam Dimensions
b  2.5 in
1
t 
8 in
l1  15 in
l2  42.55 in
l1  l2  57.55
in
Total length
2
A  ( a b)  ( b  t)  0.609
4
I 
a  ( b  t)
4
 5.907
12
2
max 
in
FDmax l1
3 E I

in

2
Area of the beam
Moment of inertial
4
3
 l1  l2  1.26  10
in
Maximum deflection
The remainder of the materials needed to design the test apparatus have less of an effect on the
outcome of the drag force data.
11
Plan of Work
Our team’s plan of work, which includes assignments with due dates, is listed below.
Plan of Work For Spring Semester
Underwater Accoustic Camera Mount
Dates
Items to be completed
Mon
1/9/2012 1/16/2012 1/23/12 1/1/12 2/6/12 2/13/12 2/20/12 2/27/12 3/5/12 3/12/12 3/19/12
Thur 1/12/2012 1/19/2012 1/26/12 2/2/12 2/9/12 2/16/12 2/23/12
Test apparatus Materials purchased
3/1/12 3/8/12 3/15/22 3/22/12
Spring Break
Fabrication of test apparatus
Set up and testing of data
acquisition
Written Progress Report of Project
Physical test done in tow tank-Final
test data taken
Results Section written
Final Project Report
12
Expected Results
The expected results for this experiment are shown in the chart below. It is expected that the largest drag force will be 119.4 lbs. This largest
force is expected to occur with a current speed of 5 knots, and when the side profile of the camera is positioned into the current. Figure 9 shows a
graphical relationship between current speeds and drag forces.
Drag Force Predictions
Kinematic
Viscosity
ν=
0.000011
Density
ρ=
1.99
Drag Coef
Camera
CD=
1.07
Drag Coef
Mount
CD=
0.761
Length
L=
0.561666667
Drag Coef
Camera Front
CD=
0.85
Camera
Pan & Tilt
Camera
Pan & Tilt
F=CD(1/2AρV^2)
Re=VL/υ
Front
Knots
0
Velocityft/sec
0
Reynolds
Number
0
Drag Force-lbf
0
0.25
0.4219525
21545.15038
0.5
0.843905
0.75
Side
Drag Forcelbf
0
Net Front
0
Drag Forcelbf
0
Net Side
0
0.057166434
0.062607603
0.119774037
0.130659883
0.042129363
0.172789246
43090.30076
0.228665735
0.250430412
0.479096147
0.522639533
0.16851745
0.691156983
1.2658575
64635.45114
0.514497903
0.563468428
1.077966331
1.175938949
0.379164263
1.555103212
1
1.68781
86180.60152
0.914662939
1.001721649
1.916384589
2.090558131
0.674069801
2.764627932
1.25
2.1097625
107725.7519
1.429160843
1.565190077
2.99435092
3.26649708
1.053234064
4.319731144
1.5
2.531715
129270.9023
2.057991614
2.253873711
4.311865325
4.703755795
1.516657052
6.220412847
1.75
2.9536675
150816.0527
2.801155252
3.067772551
5.868927803
6.402334277
2.064338765
8.466673041
2
3.37562
172361.203
3.658651757
4.006886598
7.665538355
8.362232525
2.696279203
11.05851173
2.25
3.7975725
193906.3534
4.630481131
5.07121585
9.701696981
10.58345054
3.412478366
13.99592891
Drag Force-lbf
0
13
2.5
4.219525
215451.5038
5.716643371
6.260760309
11.97740368
13.06598832
4.212936254
17.27892457
2.75
4.6414775
236996.6542
6.917138479
7.575519974
14.49265845
15.80984587
5.097652868
20.90749874
3
5.06343
258541.8045
8.231966454
9.015494845
17.2474613
18.81502318
6.066628206
24.88165139
3.25
5.4853825
280086.9549
9.661127297
10.58068492
20.24181222
22.08152026
7.11986227
29.20138253
3.5
5.907335
301632.1053
11.20462101
12.27109021
23.47571121
25.60933711
8.257355059
33.86669217
3.75
6.3292875
323177.2557
12.86244758
14.0867107
26.94915828
29.39847372
9.479106572
38.87758029
4
6.75124
344722.4061
14.63460703
16.02754639
30.66215342
33.4489301
10.78511681
44.23404691
4.25
7.1731925
366267.5564
16.52109934
18.09359729
34.61469664
37.76070625
12.17538578
49.93609202
4.5
7.595145
387812.7068
18.52192452
20.2848634
38.80678792
42.33380216
13.64991346
55.98371562
4.75
8.0170975
409357.8572
20.63708257
22.60134472
43.23842728
47.16821784
15.20869988
62.37691771
5
8.43905
430903.0076
22.86657348
25.04304124
47.90961472
52.26395328
16.85174502
69.1156983
Current Speed vs. Drag Force
Force lbf
80
70
60
50
40
30
20
10
0
Front View
Side View
0
2
4
6
Speed Knots
Figure 9 – Current Speed vs. Drag Force for Camera Mount
14
Uncertainty
This section shows the uncertainties for the predicted values of drag force on the camera and
pan/ tilt system. The drag force uncertainties will be calculated for both a side, and front view
of the camera and pan/ tilt system. This uncertainty analysis uses the Kline and McClintock
method and the below calculations were made in a Mathcad sheet.
Solution Strategy
A method for how to calculate the drag force uncertainties is shown below. Sample calculations for
uncertainties of drag forces are shown below for one case for both a side and front view of the camera
and pan/ tilt system. Along with uncertainty calculations, a list of variables with uncertainty estimates
is given below.
Drag force uncertainties for more cases are listed in the results section of this report.
List of Variables Used
Variables
Uncertainty Estimates
Side pofile Drag Force:
Fd1
wFd1
Front Profile Drag Force:
Fd2
wFd2
Side profile drag coefficient:
Cd1  1.07
wCd1  0.05
Front profile drag coefficient:
Cd2  0.761
wCd2  0.05
Density of tow tank water:
  1.94
slug
ft
Velocity of carriage/ current:
w  0.001
3
v  5.06343
slug
ft
ft
wv  0.001
s
3
ft
s
Side profile area of entire system:
A1  1.1537 ft
2
wA1  0.01ft
2
Front profile area of entire system:
A2  0.6921 ft
2
wA2  0.01ft
2
15
In order to calculate the uncertainties for drag force, an equation for drag force must be known. The drag
force on a body immersed in a fluid is:
1
2
Fd  Cd   v  A
2
Use the Kline and McClintock method for calculating uncertainty:
2
2
2
2

   
   
   
  
 
wFd  
Fd   Cd   Fd   w  
Fd   wA   Fd   wv 
 Cd        A    v   
1
2
d
Fd      v  A
d Cd
 2
1
2
d
Fd     Cd  v
dA
 2
1
2
d
Fd     Cd  v  A
2
d
 
d
Fd  Cd   v  A
dv
0.5
Side Profile:
2
2
2
2


  
   

  
  
 
wFd1  
Fd1   wCd1   Fd1   w  
Fd1   wA1   Fd1   wv 
 Cd1 
      A1 
  v
 
0.5
2
2
2
 1
1
1
2
2
2
2
wFd1      v  A1 wCd1     Cd1 v  A1  w     Cd1  v   wA1  [ ( Cd1  v A1)  wv ] 
 2 
  2 
   2 



0.5
The drag force uncertainty for a current velocity of 5.06343 ft/s, and a side profile veiw of the camera and
pan/ tilt system is:
wFd1  1.459 lbf
16
Front Profile:
2
2
2
2


  
   

  
  
 
wFd  
Fd2   wCd2   Fd2   w  
Fd2   wA2   Fd2   wv 
 Cd2 
      A2 
  v
 
0.5
2
2
2
 1
1
1
2
2
2
2
wFd2      v  A2  wCd2     Cd2 v  A2  w     Cd2  v   wA2  [ ( Cd2  v  A2)  wv ] 
 2 

  2 
   2 



0.5
The drag force uncertainty for a current velocity of 5.06343 ft/s, and a front profile veiw of the camera and pan/
tilt system is:
wFd2  0.881 lbf
Uncertainty Results
The calculated uncertainties for drag force have reasonable values. With the fastest current
used, 5 knots or 8.43905 ft/s, a drag force uncertainty of 4.241 lbs was found for the side view
of the camera system. Figure 10 displays uncertainties for drag force vs. current speed for both
a side and front view of the camera and pan/ tilt system.
It is notable to mention that the drag coefficient created the largest uncertainty. This is
because of the irregular shape of the acoustic camera and pan/ tilt. Rough approximations
were made in order to calculate the drag coefficients.
Due to the fact that the uncertainty measurements have reasonable values, all under 4.5 lbs,
the experimentally measured drag forces are expected to be accurate with our predictions.
17
Uncertainty for Drag Force vs. Current
Speed
Drag Force Uncertainty (lbs)
4.5
4
3.5
3
2.5
2
Side Profile
1.5
Front Profile
1
0.5
0
0
2
4
6
8
10
Velocity/ Current Speed (ft/s)
Figure 10 –Drag Force Uncertainty vs. Current Speed for both Side and Front Profile of System
18
Results
Testing of the drag on the camera and pan/tilt system has been completed. The set up, as well as the test
apparatus and attached camera system can be seen below in Figures 1 and 2. More detailed descriptions
and dimensions of these test pieces can be found above in the apparatus, equipment and instrumentation
section of this report.
Figure 2- Test rig mounted to carriage
Figure 1-Test apparatus assembly
All data was recorded using LabView software and processed in a MatLab program written by Colleen
Swanger. The LabView software saved data in a single column file in order to increase the write speed.
The MatLab software took this single column of data and distributed each data point into its respective
column. The final plotted results of the runs are presented as averages over the entire test run due to the
large quantity of values taken during the tests. The data was noisier than expected and every run tended
to have an oscillation about an average value. Despite these unexpected problems with the data there was
a clear average once plotted and not enough “outlier” data points to throw off that average. The cause of
the oscillation is unknown at this time however we believe it is due to slack in the cable driving the cart or
oscillations in the AC motor. Plots containing the raw data from each test run can be seen in the
appendix, these clearly show the oscillations and outliers in the test data.
19
The purpose of these tests was to determine the drag force exerted on the camera and pan/tilt system when
placed in water current. The data acquired from the load cell has been converted using the theory
presented above in the theory section. The plot below shows drag force vs. current speed for both the
front and side orientation of the camera system as well as the test apparatus by itself. Since the data
recorded includes drag from the test apparatus that force has been subtracted from the plotted values
shown below.
Drag Force vs. Current Speed
Actual
14
Drag Force (lbs)
12
10
8
Front Orientation
6
Side Orientation
4
Test Rig Only
2
0
0
0.5
1
1.5
2
2.5
3
Current Speed (ft/s)
Figure 3. Drag force vs. Current speed front and side orientation and test rig only
The plot below shows the actual and predicted values of the drag force acting on the camera and pan/tilt
system. The predicted values are all higher than the experimental values which is clearly shown in figure
4 below. Some of the predicted values are up to 30% higher than the actual values, which is much higher
than the values predicted by our uncertainty report. Since the actual values are lower than predicted this
will not affect the design of our platform. The forces exerted on the platform will be lower than expected
causing the platform to be stronger and more stable than originally designed for.
20
Drag Force (lbs)
Drag Force vs. Current Speed
Actual and Predicted
20
18
16
14
12
10
8
6
4
2
0
Front Orientation
Side Orientation
Test Rig Only
Front Orientation Predicted
Side Orientation Predicted
0
0.5
1
1.5
2
2.5
3
Current Speed (ft/s)
Figure 4. Drag force vs. Current speed actual and predicted for both camera orientations
The coefficient of drag for the combined camera and pan/tilt system has also been calculated to allow for
predictions at any current speed. The table below shows the drag for each test run as well as the
corresponding coefficient of drag calculated from that test run. The overall coefficient of drag is an
average of all these values and was found to be 1.52.
Table 1. Drag force and coefficient of drag calculated for each test run
Current
Speed
(ft/s)
Run
Drag Force
on Camera
(lbs)
1.5
1.5
2
2
2.5
2.5
1
1
1.5
1.5
2
2
2.5
2.5
5
7
8
9
10
11
12
13
14
15
16
17
18
19
4.007692308
4.173076923
6.565384615
6.701923077
9.257692308
9.173076923
2.682692308
2.709615385
5.340384615
5.221153846
8.746153846
8.221153846
13.18076923
12.72115385
Camera
Drag Force
w/o Test Rig
Drag
3.157692308
3.323076923
5.219230769
5.355769231
7.657692308
7.573076923
1.832692308
1.859615385
4.492307692
4.373076923
7.4
6.875
11.58076923
11.12115385
Cd
(Camera +
Pan/Tilt)
Average Cd
Front
Average Cd
Side
2.0382531
2.1450069
1.8950354
1.9446108
1.779462
1.7597994
1.1983746
1.2159793
1.3055395
1.2708891
1.2096919
1.1238692
1.2116033
1.1635174
1.92702795
1.21243304
21
Appendix
Run 5 Front Orientation 1.5 ft/s
100
90
80
Force (lbs)
70
60
50
Run 5
40
30
20
10
0
0
5000
10000
15000
Run 7 Front Orientation 1.5 ft/s
100
90
80
Force (lbs)
70
60
50
Run 7
40
30
20
10
0
0
5000
10000
15000
22
Run 8 Front Orientation 2.0 ft/s
100
90
80
Force (lbs)
70
60
50
Run 8
40
30
20
10
0
0
2000
4000
6000
8000
10000
Run 9 Front Orientation 2.0 ft/s
100
90
80
Force (lbs)
70
60
50
Run 9
40
30
20
10
0
0
2000
4000
6000
8000
10000
23
Run 10 Front Orientation 2.5 ft/s
100
90
80
Force (lbs)
70
60
50
Run 10
40
30
20
10
0
0
2000
4000
6000
8000
Run 11 Front Orientation 2.5 ft/s
100
90
80
Force (lbs)
70
60
50
Run 11
40
30
20
10
0
0
2000
4000
6000
8000
24
Run 12 Side Orientation 1.0 ft/s
100
90
80
Force (lbs)
70
60
50
Run 12
40
30
20
10
0
0
5000
10000
15000
20000
25000
Run 13 Side Orientation 1.0 ft/s
100
90
80
Force (lbs)
70
60
50
Run 13
40
30
20
10
0
0
5000
10000
15000
20000
25000
25
Run 14 Side Orientation 1.5 ft/s
100
90
80
Force (lbs)
70
60
50
Run 14
40
30
20
10
0
0
5000
10000
15000
Run 15 Side Orientation 1.5 ft/s
100
90
80
Force (lbs)
70
60
50
Run 15
40
30
20
10
0
0
5000
10000
15000
26
Run 16 Side Orientation 2.0 ft/s
100
90
80
Force (lbs)
70
60
50
Run 16
40
30
20
10
0
0
2000
4000
6000
8000
10000
Run 17 Side Orientation 2.0 ft/s
100
90
80
Force (lbs)
70
60
50
Run 17
40
30
20
10
0
0
2000
4000
6000
8000
10000
27
Run 18 Side Orientation 2.5 ft/s
100
90
80
Force (lbs)
70
60
50
Run 18
40
30
20
10
0
0
2000
4000
6000
8000
Run 19 Side Orientation 2.5 ft/s
100
90
80
Force (lbs)
70
60
50
Run 19
40
30
20
10
0
0
2000
4000
6000
8000
28
Run 20 Test Rig Only 1.0 ft/s
100
90
80
Force (lbs)
70
60
50
Run20
40
30
20
10
0
0
5000
10000
15000
20000
25000
Run 21 Test Rig Only 1.0 ft/s
100
90
80
Force (lbs)
70
60
50
Run 21
40
30
20
10
0
0
5000
10000
15000
20000
25000
29
Run 22 Test Rig Only 1.5 ft/s
100
90
80
Force (lbs)
70
60
50
Run 22
40
30
20
10
0
0
5000
10000
15000
Run 23 Test Rig Only 1.5 ft/s
100
90
80
Force (lbs)
70
60
50
Run 23
40
30
20
10
0
0
5000
10000
15000
30
Run 24 Test Rig Only 2.0 ft/s
100
90
80
Force (lbs)
70
60
50
Run 24
40
30
20
10
0
0
2000
4000
6000
8000
10000
Run 26 Test Rig Only 2.5 ft/s
100
90
80
Force (lbs)
70
60
50
Run 26
40
30
20
10
0
0
2000
4000
6000
8000
31
Run 27 Test Rig Only 2.5 ft/s
100
90
80
Force (lbs)
70
60
50
Run 27
40
30
20
10
0
0
2000
4000
6000
8000
32