On Drag Coefficients
of Tractor Trailer Trucks
Kevin Ihlein
Kurt Toro
Ryan B. White
May 2, 2007
ME 241
Professor Roger Gans
Abstract:
The objective of this project was to reduce the drag force
exerted on tractor trailers by modifying the rear of the carrier trailer.
Three different design modifications were tested in order to observe
and calculate the total drag force reduction. We concluded that scaled
model testing can be inaccurate if Reynolds and Mach numbers are not
adequate. Although this may be true, testing showed that a
trapezoidal fin design on a blunt body model proved to reduce the drag
coefficient by 0.168 %. The calculated drag coefficient was comparable
to that of a real life model with Reynolds number similarities.
1
Introduction:
A typical semi-truck driving on the highway will expend about
65% of its total energy trying to overcome the drag forces that oppose
the truck’s motion1. The goal of this project was to modify the trailer
of existing semi-trucks in order to refine truck aerodynamics and
reduce the drag forces exerted on the trucks. Drag force, due to the
combined effects of wall shear stress and pressure forces, is defined
by:
Fd = Cd
1
ρV2A
2
(1)
Here, Cd is the drag coefficient, ρ is the density of air, V is the velocity,
and A is the cross-sectional area2. One source says that for every 2%
reduction in drag, one can expect a 1% reduction in fuel
consumption3. A reduction in drag results in an increase in fuel
economy, which would both save money and conserve natural
resources.
Figure 1 shows several key target areas on a semi-truck that
contribute to the overall drag force, but we focused mainly on the rear
of the trailer. Approximately 20-25% of the drag force on a semitruck comes from the turbulent air flows from the rear of the box
trailer3. Reducing the wake caused by the turbulent air flow at the
rear of the trailer will help reduce the overall drag force on the truck.
Figure 1 shows the target areas of the aerodynamic pressure drag.
Area of interest
Figure 1: Target Areas of Aerodynamic Drag4
We simulated trailer drag forces by experimentally testing a 1:43
scale model truck inside a wind tunnel at the University of Rochester
wind tunnel facility in Gavett Hall. The predicted drag force for our
model represented as a blunt body at a wind speed of 24.6 m/s (55
mph) was 2.02 N. The idea behind the experiment was to try to
2
reduce the contributed drag from the trailer by attaching three
different trailer design modifications to the rear, and evaluating the
drag effects. Our hypothesis was that by adding an attachment to the
trailer, the overall drag force felt by the truck would be reduced. The
three attachments that we tested were a bubble shape, a trapezoidal
fin shape, and a triangular delta shape. We also decided to test the
drag effects from the gap between the tractor and trailer. Each
attachment to the rear was tested with and without the gap closed off.
Also, a blunt body model was tested with each of the designs and used
for comparison.
Nomenclature:
A
Cd
Fd
h
Re
V
w
ν
ρ
wf
=
=
=
=
=
=
=
=
=
=
Tractor Trailer Frontal Area = w*h (m2)
Drag Coefficient = Fd / (½ ρAV2)
Drag (N)
Trailer height = 0.0889 m (3.5 in)
Reynolds Number = V*w/ν
Air Velocity (m/s)
Trailer width = .0635 m (2.5 in)
Kinematic viscosity = 1.526*10-5 m2/s
Air density = 1.184 kg/m3
Width of Full Scale Trailer = 2.44 m (8ft)
Experimental Set Up & Procedure:
We began the experiment by purchasing two 1:43 scale model
Semi-trucks from online toy store5; one was a carrier box truck and
the other was a fuel tanker truck. They came as a pair, but we only
needed the box trailer to perform our proposed project. After we
received the trucks in the mail, we were able to begin construction on
the platform that would go in the wind tunnel. Next, we constructed
the raised platform that would position the model in the center of the
air stream as opposed to on the floor where the boundary layer effects
would influence the air flow and the resulting drag forces.
The platform was built from ½ x 6 inch pine lumber that we cut
to the desired length. The boards that held the platform up were 0.14
m (5.5 in) tall and 0.14 m (5.5 in) wide. The board on which we
placed the truck was 0.51 m (20 in) long; just 0.05 m (2inches)
shorter than the wind tunnel floorboard (in the direction of airflow). A
0.038 m (1.5 in) hole was cut at a distance of 0.305 m (12 in) from
the rear edge of the board so the pole connecting the model to the
load cell could be attached. This same size hole was also cut in the
3
floorboard to allow passage of the rod. Then we sealed the open sides
of the platform with 0.9525 cm (.375 in) plexi-glass to prevent any
turbulent wind effects on the transducer rod. We inserted five screws,
two on the sides and one on the top, of the plexi-glass so that it would
tightly seal the area underneath the platform.
With the help of Ken Adams, a machinist at the University of
Rochester machine shop, we designed an aluminum bracket that would
accept a threaded rod which connected it to the load cell. Figure 2
shows the schematic design drawing for the piece. This piece clamps
around the truck’s chassis, just behind the cab, securing it firmly.
After all the parts were constructed, the platform was attached by
drilling two screws into each bottom end of the platform through the
floorboard.
Machine Screws
Top Plate
Truck Chassis
Front View
Machined Aluminum
Threaded Rod
Figure 2: Machined Connector
Originally, the load cell was attached using four screws beneath
the floorboard (outside of the wind tunnel). We were encouraged by
Scott Russell to do this because the equipment is expensive and could
have been damaged inside the tunnel. A long pole connected the load
cell to the bottom of the truck, but after some testing we realized that
the pole was bent and that its threads did not secure tightly. We
needed a new method for connecting the truck to the load cell because
this way was not going to work properly.
4
After speaking with Scott Russell about what was going wrong
with the experiment, we modified the set up by placing the load cell
inside the raised platform and securely attaching it the floorboard. We
precisely cut a small hole on the bottom edge of one of the plexi-glass
walls so the load cell cord could connect back to the computer module
unharmed. After testing, it was confirmed that the shorter pole
secured the model for firmly and extracted more accurate results than
before. Figure 3 shows the entire setup.
Connector Rod
Aluminum
bracket
Load Cell
Figure 3: Experimental Setup
This photo shows the front cab of the truck with lots of masking
tape covering it. Part of it was used to close the cab-trailer gap. Tape
also covered the open windows in the doors and held them shut. We
also taped over the front wheel wells so they would not affect the drag
results.
The custom devices that were built for the rear of the trailer
consisted of paper index cards. We fitted and taped them securely, so
that the high wind speeds would not cause them to detach and be
destroyed in the wind tunnel. Using three index cards stacked on top
of each other, we constructed our specified designs to be sturdy and
withstand the high wind speeds. Three different attachments were
created; a bubble shape, a trapezoidal fin shape, and a triangular delta
shape. These were securely fastened to our model trailer using
masking tape. We chose the bubble shape and trapezoidal fin
contraption because we had seen devices like them being used on real
trailers already. We thought the triangular modification piece was
another possibility for reducing drag because it was a combination of
5
the bubble and fin shapes. Figures 4, 5, and 6 depict the actual index
card shapes that we attached to the model trailer.
Figure 4: Bubble Attachment
Figure 5: Trapezoidal Fins
Figure 6: Triangular Delta Design
The data from our tests were gathered using the computer
program LabView by National Instruments. We constructed a VI that
recorded the voltage measured by the load cell in the direction parallel
to the model. We programmed the LabView DAQ Assistant to gather
the data from Transducer Module 3 and to display the voltage in realtime on the screen and to produce a waveform graph while running
continuously. The input range was set to read from negative 5mV to
positive 5mV from channels a0 and a1. The program allowed us to
control the number of samples (100) and the rate (1000). The select
signals box converted the numerical indicator to display the parallel
axis instead of the perpendicular axis. Figure 7 shows a diagram of
the VI.
6
Select Signals
Input
Output
# Samples
Control
DAQ
Data
# Samples
Rate
Rate Control
Numeric
Indicator
Waveform Graph
Figure 7: LabView DAQ Assistant VI
Before we could test the model in the wind tunnel, we first had
to calibrate the load cell. We set the floorboard vertically on a
workbench so that the pole could be loaded in the direction that we
would be testing with the load cell. We started by hanging masses
ranging from 50 grams up to 2 kilograms at the end of the pole. Then
we recorded the measured voltages in MS Excel.
Each time we inserted the model truck and floorboard setup into
the wind tunnel, we started by recording a zero reading. We recorded
the data by reading the measured voltage off the screen and writing it
down on a notepad next to the corresponding fan speed percentage.
We felt it would be easier to insert this data into MS Excel later rather
than having LabView do it for us. After taking the initial reading, the
wind tunnel was turned on and set at a speed of 30% or 18.8 m/s.
Once the wind tunnel was running, we recorded each measurement
between speeds of 30% to 90%, in intervals of 10%. It turned out
that the voltage readings did not fluctuate enough to make it too
complex to read from the LabView numerical indicator on the screen.
Results:
The results presented below detail the frontal force (drag)
coefficient for the tractor-trailer combination and its components. This
drag coefficient represents the force along the axis of the vehicle in
the direction of travel. All coefficients were calculated based on the
measurements recorded by the load cell and LabView. Without wall
corrections from the wind tunnel, the computed coefficients will differ
from those of the equivalent model in free-air. However, the
differences in drag between the configurations should be
representative of the effects of the associated geometric modifications.
7
The baseline geometry for this study represents a modern
tractor trailer design with the standard aero package including a
rooftop deflector. For the first tests we left the gap between the cab
and trailer open, like on a real truck. For the second test, we closed
this gap off to see how the gap affected the drag on the model.
However, for the third test run, the truck was transformed into a blunt
body object with dimensions 0.0635 m (2.5 in) wide by 0.0889 m (3.5
in) meters tall. We did this to exclusively look at the differences
between the configurations attached to the rear of the trailer.
Calibration Results:
Table 1 displays the results of the calibration process explained
above. Here we recorded the mass that was hung from the load cell
and the voltage measured by LabView. Then we used Excel to
translate the voltages into more manageable values for analysis by
multiplying the voltage by -1000. We thought it would make the data
easier to read without the extra zeros and negative sign. If all the
voltages were transformed in this manner then there would be no
discrepancies in the results. Then we subtracted the initial value from
the subsequent values to find the scaled change in voltage called
DeltaVolts. The last column converts the mass into Newtons by
multiplying mass by the gravitational constant g=9.81 m/s. Then we
plotted Load versus DeltaVolts seen in Figure 8, and found a linear
trend line. This would later be used to translate measured voltages
from the wind tunnel tests to drag forces in Newtons.
Table 1: Calibration Data
Mass
(grams)
Raw voltage
(volts)
Raw voltage *
(-1000)
DeltaVolts
(voltage - v0)
Load
(Newtons)
0
-0.001664
1.664
0.000
0.000
20
-0.001671
1.671
0.007
0.196
50
-0.001682
1.682
0.018
0.491
100
-0.001700
1.700
0.036
0.981
200
-0.001736
1.736
0.072
1.962
400
-0.001808
1.808
0.144
3.924
500
-0.001844
1.844
0.180
4.905
1000
-0.002025
2.025
0.361
9.810
1500
-0.002206
2.206
0.542
14.715
2000
-0.002387
2.387
0.723
19.620
8
Calibration:
Load vs DeltaVolts
25.0
Load (N)
20.0
15.0
10.0
y = 27.152x
R2 = 1
5.0
0.0
0.00
0.20
0.40
0.60
0.80
DeltaVolts (-m V)
Figure 8: Calibration Plot and Trend line Equation
Using the Add Trend Line feature in MS Word, we found that the
equation relating DeltaVolts to Load is y=27.152x, where y is the load
in Newtons and x is the variable DeltaVolts in -mV. We knew that this
equation was accurate and fits the data well because the R2 value was
1. This equation was used in all of the subsequent calculations to
translate the LabView measurements into a load measurement.
Configurations:
As mentioned above, we tested each of the four trailer
configurations: baseline, bubble, fins, and delta, three times. First we
left the cab-trailer gap open, then we closed it up, and then we treated
the model as a blunt body. We recorded the measured voltages from
LabView, and then transformed the data into more manageable values
in the same manner as mentioned in the Calibration paragraph. We
used the equation y=27.152x to calculate the load, in Newtons, from
the DeltaVolts column. We also converted the percent fan speed into
airspeed by multiplying the percentage by the maximum velocity of
the wind tunnel, which was 62.6 m/s (140mph). For example, 50% of
the fan’s speed is 31.3 m/s.
9
Then, we plotted airspeed versus drag for each device attached
to the trailer. This would later allow us to find a relationship between
wind speed and drag. Figure 9 displays this plot for each of the four
devices in the open gap configuration, while Figure 10 represents the
data for the closed gap configuration, and Figure 11 for the blunt
body.
Drag vs Airspeed:
Open Gap
4.00
3.50
3.00
Drag (N)
2.50
2.00
1.50
1.00
0.50
0.00
0.0
10.0
20.0
30.0
40.0
50.0
60.0
Airspeed (m/s)
Baseline
Bubble
Fins
Delta
Figure 9: Drag vs. Airspeed: Open Gap Configuration
Drag vs Airspeed:
Closed Gap
4.00
3.50
3.00
Drag (N)
2.50
2.00
1.50
1.00
0.50
0.00
0.0
10.0
20.0
30.0
40.0
50.0
60.0
Airspeed (m/s)
Baseline
Bubble
Fins
Delta
Figure 10: Drag vs. Airspeed: Closed Gap Configuration
10
Drag vs Airspeed:
Blunt Body
10.00
9.00
8.00
Drag (N)
7.00
6.00
5.00
4.00
3.00
2.00
1.00
0.00
0.0
10.0
20.0
30.0
40.0
50.0
60.0
Airspeed (m/s)
Baseline
Bubble
Fins
Delta
Figure 11: Drag vs. Airspeed: Blunt Body Configuration
From these plots, we used the Add Trendline feature of MS Excel
to show us the equations that related airspeed in meters per second to
drag in Newtons. Table 2 shows the given trend line function and its
corresponding R2 value for the open gap configuration including all
data points. The closed gap configuration and blunt body results are
in Table 3 and Table 4 respectively. We knew that these equations
were extremely accurate because each R2 value was within .001 to 1,
which would mean that the function fits the data closely.
Table 2: Open Gap Functions
Configuration
Trend Line Function
Baseline
Y=0.0007x2 + 0.0181x
Bubble
Y=0.0011x2 - 0.0009x
Fins
Y=0.001x2 - 0.0032x
Delta
Y=0.0012x2 - 0.0057x
R2 Value
.9991
.9994
.9997
.9994
Table 3: Closed Gap Functions
Configuration
Trend Line Function
Baseline
Y=0.001x2 + 0.0011x
Bubble
Y=0.0011x2 - 0.0031x
Fins
Y=0.0011x2 - 0.0049x
Delta
Y=0.0013x2 - 0.0089x
R2 Value
.9999
.9999
.9990
.9991
Table 4: Blunt Body Functions
Configuration
Trend Line Function
Baseline
Y=0.0018x2 + 0.0084x
Bubble
Y=0.002x2 + 0.0018x
Fins
Y=0.0018x2 + 0.0054x
Delta
Y=0.0036x2 - 0.0356x
R2 Value
.9995
1.0
.9999
.9980
11
Reynolds Number Calculation:
In order for us to determine the necessary airspeed for our
model to represent a full scale truck, we first had to calculate the
Reynolds number:
Re = V*w/v
(2)
We multiplied an airspeed V of 24.6 m/s (55 mph) by the
characteristic width of a full scale trailer wf, 2.44 m (8ft), then divided
by the kinematic viscosity of air, 1.56x10-5 m2/s. The resulting
Reynolds number was 3.84x106. Using the theory of similitude from
our Fluid Dynamics course, we could calculate the necessary airspeed
for the model to actually simulate a real truck at highway speeds. The
Re was multiplied by the kinematic viscosity, and then divided by the
characteristic length of the model truck w, .0635 m (2.5 inches). The
resulting airspeed U was 944.1 m/s.
Drag at Highway Speed:
Next, we were able to calculate the drag that the model truck
would experience at the adjusted highway speed. For our model to
represent a truck at 24.6 m/s (55 mph), it would have had to be going
944.1 m/s. It would have been impossible to test the model at this
airspeed because the wind tunnel had a maximum speed of 62.6 m/s
(140 mph). That is why we found the above equations relating
airspeed to drag for the model. Table 5 lists the drag forces that the
model would have experienced at 944.1 m/s for each of the
configurations.
Table 5: Predicted Drag on Model at 944.1 m/s
Configuration
Trailer Device
Drag (N)
Open Gap
Baseline
641.0
Bubble
979.6
Fins
888.3
Delta
1064.2
Closed Gap
Baseline
892.4
Bubble
977.5
Fins
975.8
Delta
1150.3
Blunt Body
Baseline
1612.3
Bubble
1787.7
Fins
1609.5
Delta
3175.2
12
We wanted to do more statistical analysis to see if there was
another, perhaps improved, relationship between airspeed and drag on
the model. This is why we decided to see how lines would fit to the
last few points of the data, excluding the zero values and lower fan
speed readings. We did this because we noticed that the graphs
started to appear more linear than quadratic, and we could also tell by
the voltage steps leveling out. This meant that the difference between
the values of DeltaVolts of two points was the same as the difference
between the point next to it. Tables 6, 7, and 8 include the trend line
functions for only the higher speed readings and the calculated drag at
944.1 m/s.
Table 6: Open Gap Functions
Configuration
Trend Line Function
Baseline
Bubble
Fins
Delta
y
y
y
y
=
=
=
=
0.085x - 1.6291
0.0967x - 2.1586
0.102x - 2.6518
0.1076x - 2.6337
.9994
.9999
.9998
.9965
Table 7: Closed Gap Functions
Configuration
Trend Line Function
Baseline
Bubble
Fins
Delta
y
y
y
y
=
=
=
=
0.0954x
0.0954x
0.0998x
0.1193x
-
2.2536
2.1993
2.4256
3.0682
y
y
y
y
=
=
=
=
R2 Value
1
1
.9994
.9999
Table 8: Blunt Body Functions
Configuration
Trend Line Function
Baseline
Bubble
Fins
Delta
R2 Value
0.2039x - 5.186
0.2039x - 5.0412
0.3037x - 9.4851
0.308x - 7.9012
R2 Value
.9946
.9994
.9918
.9994
Calculated Drag
(N)
78.6
89.1
93.6
98.9
Calculated Drag
(N)
87.8
87.9
91.8
109.6
Calculated Drag
(N)
187.3
187.4
277.2
282.9
Drag Coefficient Calculations:
After calculating the Drag that the model would experience at
speeds representing a full scale truck at highway speeds, we then
calculated the drag coefficient using the equation:
Cd = Fd / (½ ρAV2)
(3)
Here, ρ is 1.184 kg/m3, A is 0.0057 m2, and V is 944.1 m/s, and D is
the calculated drag from above. Tables 9, 10 and 11 show the
calculated values of the drag coefficient for each attachment and
13
configuration, including both statistical methods; quadratic and linear.
The bold values came from the formulation with the highest R2 value.
Table 9: Open Gap Drag Coefficients
Configuration
Quadratic Cd
Baseline
0.2134
Bubble
0.3258
Fins
0.2954
Delta
0.3539
Linear Cd
0.0261
0.0296
0.0311
0.0329
Table 10: Closed Gap Drag Coefficients
Configuration
Quadratic Cd
Baseline
0.2968
Bubble
0.3251
Fins
0.3245
Delta
0.3825
Linear Cd
0.0292
0.0292
0.0305
0.0364
Table 11: Blunt Body Drag Coefficients
Configuration
Quadratic Cd
Baseline
0.5362
Bubble
0.5944
Fins
0.5353
Delta
1.056
Linear Cd
0.0623
0.0623
0.0922
0.0941
Percent Differences:
Here, we calculated the differences in the drag coefficients
between the baseline configuration and the respective trailer
attachments from the blunt body tests based on the recorded data and
not the calculated drag forces. We did this because the differences
between drag using the quadratic and linear functions were too
dissimilar. Also, the blunt body shape was the only one that we could
predict the drag force. Table 12 displays the measured drag from the
test model at 70% fan speed, or 44 m/s, and the coefficient of drag,
as well as changes in the coefficients. We chose the 70% fan speed
data because we thought the higher speeds were more inaccurate due
to the model vibrating in the wind tunnel. Table 13 shows the percent
difference in drag coefficients for the calculated drag for the model
simulating highway speeds at 944.1 m/s.
Table 12: Percent Change in Drag Coefficient at 44 m/s
Blunt Body
Drag @ 44 m/s
Drag Coefficient
(N)
Baseline
3.801
.5875
Bubble
3.910
.6043
Fins
3.720
.5749
Delta
5.566
.8603
14
% Change
+2.85 %
-2.14 %
+46.4 %
Table 13: Percent Change in Drag Coefficient at 944 m/s
Blunt Body
Drag Coefficient
% Change
Baseline
0.5362
Bubble
0.5944
+10.9%
Fins
0.5353
-0.168%
Delta
1.056
+96.9%
Discussion and Conclusions:
From our experimental results, we concluded that the testing of
our scaled model produced some inconclusive results that showed the
baseline model truck having the least amount of drag force. For our
first scenario with the gap open between the truck and the trailer, we
calculated a drag force of 641 N, which was what the model truck
would experience at 944.1 m/s. Therefore, the result of the drag
coefficient was 0.2134. When the bubble piece was attached to the
rear of the trailer, we observed an increase in drag force, which was
338.6 N. This opposed the results from full scale real-world trucks.
For real-world trucks, this bubble attachment generated a decrease in
drag, making the semi truck more fuel efficient. When we tested the
truck with the trapezoidal fin attachment, the drag force was 888.3 N,
increasing the drag coefficient from 0.2134 to 0.2954. This
attachment had also been tested on real-world trucks but its decrease
in drag is not as efficient as that of the bubble reference. For our
purpose, this trapezoidal attachment also created an increase in drag.
Finally, our last test for the open gap was testing the triangular
attachment. This attachment resulted in the least amount of drag
reduction, and also as a safety factor we would not recommend the
fabrication of it. The drag force created form the attachment was
1064.2 N. The increase in drag coefficient went from 0.2134 to
0.3539.
For our testing of the model truck with the gap sealed between
the trailer and the truck, we concluded that the results were again
erroneous. When the truck was tested without any modifications to
the trailer, the drag force was 892.4 N. The drag coefficient was
calculated to be 0.2968. When the bubble piece was attached at the
rear of the trailer, its drag force was 977.5 N, increasing the drag
coefficient from 0.2968 to 0.3251. The trapezoidal attachment
resulted in a drag force of 975.8 N and increasing the drag coefficient
to 0.3245. The triangular piece, as before, resulted as the most
inefficient modification to the trailer.
15
Finally, when we analyzed the blunt body performance, we found
that its baseline drag force was 1612.3 N at a scaled value of 944.1
m/s. It experienced a much higher drag force because the blunt body
was not as streamlined as the model truck. Its drag coefficient at this
speed was 0.5362. The predicted force on the blunt body was 2.02 N
at 44 m/s, and the actual drag force obtained was 3.801 N, producing
a drag coefficient of 0.5875. This is very comparable to the drag
coefficient of a full scale truck. One source stated that the drag
coefficient of a modern tractor trailer, weighing around 40 tons and
traveling at 24.6 m/s, produced a drag coefficient of approximately
0.6. When we attached the bubble piece, the drag force was increased
to 1787.7 N at 944.1 m/s, which also increased the drag coefficient to
0.5944. As for the trapezoidal piece, we concluded that the drag force
was reduced to 1609.5 N at 944.1 m/s. This decreased the drag
coefficient from 0.5362 to 0.5353, which is a 0.168% reduction. The
blunt body model is nearly the best representation of a full scale truck
that is obtained from our experiment.
After analyzing the data, we concluded that our experimental
testing of the scaled model truck provided inconclusive results. A
reason for these results being questionable is that our model truck was
too aerodynamic and streamlined for the wind tunnel testing area.
Also, the size of the model was just not big enough to give results that
can be applied to real life applications. Using a larger model would
result in a lower calculated air speed using the similitude theory. If we
had chosen a larger scaled model, then the truck would have been too
large for the testing area and the side wall effects from the wind would
have affected our results too greatly to draw any conclusive results.
As for the testing of our blunt body object, we saw a reduction in drag
of 2.14% at 44 m/s, when our trapezoidal fin modification was
attached. This result was superb because this application is being
used on some real life trucks today, and is what we expected.
Future Work:
With our experimentation complete, we concluded that not all
scaled wind tunnel testing can be applied to real life applications. One
must consider the comparison between Reynolds numbers and Mach
Numbers in order to find relevant parameters to be used for
experimentation.
For our project, we established that the testing area of the wind
tunnel is undersized for this type of simulation of a semi truck. With
other projects developing to decrease drag on semi trucks, a larger
16
testing area must be developed in order to use scaled testing. The
larger the model the more accurate and applicable this scaled testing
could be.
References:
1
http://www.llnl.gov/str/May03/McCallen.html
2
Çengel, Yunus A. 2007 Heat and Mass Transfer: A Practical Approach 3rd ed.
McGraw-Hill: New York, NY.
3
http://www.engineering.sdsu.edu/~hev/aerodyn.html. Department of Mechanical
Engineering, San Diego State University. 14 February 2007.
4
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