AME-441-Group-47-Proposal-Approved

PROJECT PROPOSAL
Out-of-Wind-Tunnel Dynamic Testing of Propellers
Aaron Vanlandingham, Addison Salzman, Jacob Iuele
Group 47
9/1/2016
AME 441a T/Th 9 AM

1
Introduction
The growth of the UAV industry in recent years has led to a resurgence in designing and testing
propellers at low Reynolds numbers [1]. The advent of lightweight and higher quality brushless
DC motors has made electric powered UAVs a cost-effective alternative to more expensive,
louder, and less efficient jets of comparable power output. With applications ranging from the
defense industry to commercial and recreational uses, there is an urgent need for UAV designers
to fully characterize and predict the behavior of their electric propulsion systems prior to flight.
Although static conditions can be tested simply and effectively using any number of commercially
available thrust stands, dynamic testing of propellers has historically been limited to large
companies and research institutions with access to large wind tunnels. Experimental results have
shown that a wind tunnel test section must be at least five times larger than the diameter of the
prop to avoid blockages in the experimental setup [1]. With this consideration in mind, it becomes
difficult for even the largest universities to perform dynamic testing on propellers that exceed 10
inches in diameter.
The goal of this project is to design and build a car-mounted thrust stand for dynamic testing of
propellers that can replace traditional wind tunnel testing methods. By comparing characteristic
coefficients of propellers, the aim is to quantify the consistency of data when compared with
equivalent wind tunnel configurations.
Theoretical Presentation
Within different categories of desired flight performance, the complex cross sections and twist
distributions inherent in propeller design are reduced to two variables—the diameter, tip to tip
length, and pitch, theoretical distance travelled in one revolution. For a propeller of diameter, 𝐷,
and pitch, 𝑝, the design advance ratio, 𝐽 𝐷, can be calculated according to Equation (1)
𝐽 𝐷 =
𝑝
𝐷
(1)
The design advance ratio qualitatively defines the optimal operating conditions for a propeller. As
a relationship between the rotational and free stream velocity experienced by the propeller, the
design advance ratio expresses the relative velocity at which each cross section along the propeller
has been designed to operate most efficiently [2]. The advance ratio of the propeller in dynamic
conditions can be calculated according to Equation (2) where 𝑉∞ is the free stream velocity and n
is the propeller’s rotational speed.
𝐽 =
𝑉∞
𝑛𝐷
(2)

2
In order to compare different propellers, the dynamic behavior can be non-dimensionalized to the
thrust and power coefficients shown in Equations (3) and (4), respectively.
𝐶 𝑇 =
𝑇
𝜌𝑛2 𝐷4
(3)
𝐶 𝑃 =
𝑃
𝜌𝑛3 𝐷5
(4)
For dynamic testing of propellers, the efficiency, 𝜂, of the propeller can be calculated by dividing
the output power (𝑃𝑜𝑢𝑡 = 𝑇 ∗ 𝑉∞) by the input power, 𝑃, to the motor. Simplifying in terms of the
advance ratio and non-dimensional coefficients yields Equation (5).
𝜂 =
𝐶 𝑇 𝐽
𝐶 𝑃
(5)
Experimental Setup
In order to construct an experimental setup that meets all of the design objectives and allows for
quality data to be obtained, aerodynamic and air-quality considerations, structural analysis, and
systems integration must be adequately addressed.
Aerodynamic Air-Quality Considerations
To ensure the entire propeller is immersed in the free stream, the thickness of the boundary layer
at the location of the propeller must be known. Approximating the surface of the car as a flat plate,
the Reynolds number is given by Equation (6).
𝑅𝑒 𝑥 =
𝜌𝑈∞ 𝑥
𝜈
(6)
where 𝜌 is the density of the ambient air, 𝑈∞ is the freestream velocity, 𝑥 is the location of interest
in the flow-wise direction, and 𝜈 is the kinematic viscosity of the ambient air.
Assuming the flow along the surface to be initially turbulent, the boundary layer thickness, 𝛿, is
given by Equation (7)
𝛿 =
0.385
𝑅𝑒 𝑥
0.2 𝑥 (7)

3
For the worst-case boundary layer thickness, conditions are assumed to be at sea level using the
International Standard Atmosphere.
𝑇 15°C
𝜌 1.225 kg/m3
𝑈∞ 22.4 m/s
𝜈 1.81 ∙ 10−5
m2
/s
𝑥 2.79 m
Table 1. Assumed worst-case atmospheric test conditions.
Using the values from Table 1 in conjunction with Equations (6) and (7), the expected boundary
layer thickness is 5.07 cm.
In their book Low-Speed Wind Tunnel Testing, Pope and Harper suggest that the ratio of propeller
disk area to wind tunnel test section area, 𝐴 𝑝𝑟𝑜𝑝/𝐴 𝑊𝑇, be no greater than 0.15 in order to obtain
data of acceptable quality [3]. This rule has been stated in more recent testing such that the width
of the test section must be at least five times the propeller diameter, 𝐷 𝑝𝑟𝑜𝑝, in order to avoid
blockage effects [1]. The proposed car-mounted testbed is only constrained on one side (in contrast
to the four walls of a traditional wind tunnel). Based on symmetry, the propeller’s radius, 𝑟𝑝𝑟𝑜𝑝,
will be used in calculations in order to match the testbed’s boundary conditions. Therefore, the
minimum distance required between the center of the propeller hub and the roof of the car is
𝐻 = 5 ∗ 𝑟𝑝 𝑟𝑜𝑝 + 𝛿 (8)
The largest propeller to be tested has a 25.4 cm (10 in) diameter, which gives 𝐻 = 68.57 cm (27.0
in). In order to reduce complexity and minimize manufacturing lead times, the decision was made
to use prefabricated 36 inch rails for the vertical supports, exceeding the minimum required height
and allowing for greater adaptability. Additionally, 𝐿, the distance between the front and rear
supports of the dynamic test stand, was chosen to utilize the entire useable space on the roof rails
in order to maximize the stability of the test stand. This is shown in Figure 1.
For more detailed models and drawings, see Appendix B.

4
Figure 1. Dimensioned experimental setup where H is the distance from the roof of the vehicle to the
propeller hub and L is the distance between the front and rear roof rail clamps of the dynamic test stand.
Structural Analysis
The dynamic test stand was designed to be a highly re-usable structure that maintains its rigidity
and form through many cycles of assembly/use and disassembly. Worst-case structural analysis
was performed in order to prove that the system would remain safely attached to the car while in
use, even in the case of the failure of multiple members, as shown in Figure 2.
Figure 2. The test stand can be simplified to a pair of 2D massless vertical rods with one fixed supports,
which ignores the rear supports and represents the most extreme loading case.
𝐻
𝐿

5
There are two primary loads exerted on the test stand: the weight of the measurement equipment
on the top horizontal beam and the drag force on the front profile of the test stand. The magnitude
of the drag force was derived assuming vertical flat-plate-like components to simplify the
calculation, rather than the perforated 90 degree-angled frame legs that were actually employed.
Additionally, for simplicity and as an illustration of safety, the entire drag force is assumed to be
carried by the bolts connecting the side frame legs to the front bolts. Equipment weight was
estimated and also assumed to be carried solely by the front bolts.
Figure 3. The single fixed vertical beam model was used to determine the loads sustained by the front
clamps and ultimately the two (2) front bolts that hold the dynamic test stand to the roof rack clamps.
Using well-established mechanics equations [4], the maximum shear and normal stress
experienced by each bolt was calculated. The factor of safety (FoS) was calculated using standard
strength specifications associated with the SAE Grade 5 ¼” bolts to be used. For detailed
derivations and calculations, see Appendix D.
Calculated
Shear Stress
(MPA)
Calculated
Normal Stress
(MPA)
Maximum
Shear Stress
(MPA)
Maximum
Normal Stress
(MPA)
Shear FoS (-)
Normal FoS
(-)
0.41 517.51 496.42 827.37 1210 1.6
Table 2. Demonstration of dynamic test stand safety in worst-case conditions.
Fx
Fy
M
Fdrag = 64.6 N
Fequipment = 20 N
0.412 m
0.914 m 𝑥 = 4.
𝑥 𝑜 𝑡 = 32.3
= 20
𝑜 𝑡 = 10
𝑜 = 2 .
𝑜 𝑡 = 13.3
𝑥
o

6
Systems Integration
As the testbed requires the use of several distinct systems, special attention has been devoted to
planning and testing in preparation for combining these systems into a single, integrated data
collection apparatus, as depicted in Figure 4. The test stand as previously described will interface
with the roof rails via custom clamps, as shown in Appendix C.
Data will be gathered primarily through the use of RC Benchmark’s S1580 dynamometer, to which
the motor and propeller are directly mounted. The dynamometer contains an onboard data
acquisition card that provides performance data (thrust, torque, RPM, current, voltage) in real time
to a laptop-based user interface via a USB connection. All data can be logged and exported as a
.csv file for further analysis. The team has been in contact with and has received a sponsorship
agreement from RC Benchmark to acquire a yet-to-be-released airspeed sensor that can be
integrated directly with the dynamometer’s data system Appendix G.
A wind vane (integrated with a rotary position sensor) and a pitot-static tube (connected to a
differential pressure sensor) will be used to monitor air quality, speed, and direction independently
of the primary data system in order to provide data quality assurance. The wind vane was chosen
due to its low cost and acceptable error (5%), as it will serve as a validation that the free stream is
primarily traveling normal to the front of the dynamic test stand during measurements. The pitot-
static tube, besides meeting testing requirements for sensing normal-direction flow speed, was
chosen in an effort to use the tools that are available and popular among hobbyists. The sensors
will be connected to a National Instruments data acquisition system and LabVIEW will be used to
process and view the data in real-time. Both systems are set up to record the computer time and
the instant they begin recording so that any time offset induced may be removed from the data in
post-processing.
For details on safety precautions related to this project, see Appendix A.

7
Figure 4. Layout and functional schematic of the experimental setup.
Test Procedure
The RC Benchmark dynamometer will provide the required throttle setting to hold the propeller
rotational velocity constant. The speed of the car will be increased in 3 MPH (1.34 m/s) increments
at fixed intervals until the measured thrust from the propeller is zero. This condition is known as
the windmill-condition, where the propeller does no work on the air and is instead being driven by
the air flow [1].
Measured Quantities
Throughout the test the experimental setup will record the thrust, 𝑇, rotational speed, 𝑛, and free-
stream velocity, 𝑉∞. The wind vane will be used to detect adverse crosswinds and allow for subtle
course corrections by the driver to ensure that the incoming velocity is parallel to the axial
translation of the test rig. Any adverse wind component would not provide an effective comparison
to wind tunnel tests or numerical simulations.
Inside Car
(Accessed through sunroof or window)
Outside Car
(Bird’s eye view perpendicular to roof)
Roof Rail
Pitot Static Tube
(integrated)
Wind Vane
(Rotary Position Sensor)
Dynamic
Test
Stand
Dynamometer
(RC Benchmark 1580)
Computer
Power Supply
(High Amperage)
National
Instruments
DAQ
Propeller
& Motor
Power Supply
(5 V)
Speed
Controller
𝑈∞
Pitot Static Tube
(secondary)

8
Calculated Quantities
For a propeller of a given diameter, 𝐷, there are four main metrics that characterize its
performance. Namely, there is the advance ratio, 𝐽, the coefficient of thrust, 𝐶 𝑇, the coefficient of
power, 𝐶 𝑝, and the overall efficiency, 𝜂, which are each calculated using Equations (2), (3), (4),
and (5) respectively. 𝐶 𝑇, 𝐶 𝑝, and 𝜂 will be plotted with respect to 𝐽. It is expected that the
experimental data will demonstrate similar trends to those shown in Figure 5.
Analysis
The quality of experimental data from the dynamic test rig can be compared to literature data in
wind tunnels and numerical simulations. Advanced Precision Composites (APC) is one of the
most widespread manufacturers of composite propellers for recreational applications in the United
States [5]. APC uses the NASA Transonic Airfoil Analysis Computer Program (NAIR) to calculate
lift and drag coefficients at radial stations along the propeller [5]. By integrating these sectioned
characteristics along the length of the propeller blade, Blade Element Theory can be used to predict
the overall behavior of a propeller at operating conditions [6]. There are limitations, however, in
the application of this analysis.
Figure 5. Experimental Data collected from Selig et. al. demonstrates the trends in 𝐶 𝑇, 𝐶 𝑝 and 𝜂 as prop RPM
is increased.

9
Blade element theory fails to consider losses associated with flow expansion behind the propeller
disk, aerodynamic losses at the blade tips, and losses associated with disturbed and turbulent flow
[6] [7]. A comparison with wind-tunnel tests conducted at the University of Illinois Urbana-
Champaign characterizes these limitations. As shown in Figure 6 the numerical simulations show
good agreement at low advance ratios but over predict performance above the design advance ratio
of 0.5.
It is expected that the experimental data collected from the dynamic test rig will resemble the
experimental data collected at UIUC in their own wind tunnels. Using uncertainty calculations, the
extent to which the dynamic test data agrees/disagrees with the experimental wind tunnel data can
be quantified.
Figure 6. Numerical analysis using Blade Element Theory shows agreement for lower advance ratios
when compared to wind tunnel testing. of the same propeller.

10
References
[1] A. J. Brezina and S. K. Thomas, "Measurement of Static and Dynamic Performance
Characteristics of Electric Propulsion Systems," in 51st AIAA Aerospace Sciences Meeting
including the New Horizons Forum and Aerospace Exposition, Grapevine, 2013.
[2] M. A. Page, Propeller Aerodynamics, USC, 2002.
[3] A. Pope and J. Harper, Low-Speed Wind Tunnel Testing, New York: Wiley & Sons, 1966.
[4] F. P. Beer and R. E. Johnston, Mechanics of Materials, New York: McGraw-Hill Inc., 2014.
[5] Advanced Precision Composites, "APC Corporate Website," Landing Products Inc., 2016.
[Online]. Available: http://www.apcprop.com/. [Accessed 1 September 2016].
[6] C. N. Adkins, "Design of Optimum Propellers," Journal of Propulsion and Power, vol. 10,
no. 5, 1994.
[7] C. F. Dougherty, T. L. Holst, K. L. Gundy and S. D. Thomas, TAIR - a
TransonicAirfoilAnalysis, Hampton: NASA Langley Research Center, 1981.
[8] R. W. Deters, G. K. Ananda and M. S. Selig, "Reynolds Number Effects on the Performance
of," in 32nd AIAA Applied Aerodynamics Conference, Atlanta, 2014.
[9] A. J. D, Introduction to Flight, McGraw Gill, 2012.

11
Appendix A - Risk Assessment & Alleviations
Test Location
El Mirage Dry Lake Off-Highway Vehicle Recreation Area, San Bernardino County
Managed by the Bureau of Land Management (BLM)
General Site Rules
 There is no speed limit on the open lakebed
o The speed limit is 15 mph within 50 feet of campsites and staging areas
o Camping is restricted to within 100 feet of the edge of the lakebed
 The dry lakebed is closed when wet or muddy
 Headlights and taillights are required when driving between one-half hour after sunset to
one-half hour before sunrise
 Motorized vehicles must yield to non-motorized vehicles
Risks
 Encountering other vehicles
 Test stand detachment from vehicle or propeller detachment from test stand
Risk Alleviations
 Testing will be conducted during off-peak times (early weekday mornings 6am to 11 am)
in order to minimize the likelihood of encountering other vehicles.
 One member of the test crew will be solely focused on monitoring the vehicle’s
surroundings
 Any member of the test crew will have full authority to halt testing at any time should
they deem any portion of the test conditions or environment unsafe.
 Each bolt on the test stand will be tightened before starting each phase of testing. Motor
and propeller mounts will be checked each time they are changed.
Test Procedure
1. Prior to each test condition, tighten each bolt on the test stand. Shake the stand at several
points to ensure no component is loose.
2. Check that all cables are properly secured.
3. Tighten bolts on motor mount and propeller
4. Brief condition to be tested, making note of and verifying:
a. Motor Type
b. Propeller Size
c. Desired RPM
d. Starting Velocity
e. Velocity Increase Step Size
f. Expected Maximum Velocity
5. Load data acquisition software and tare sensors
6. Record initial wind data prior to start of test condition
7. Conduct test condition as briefed
8. Decelerate to a full stop and place the car in park
9. Record final wind data after completion of test condition

12
Crew Roles and Responsibilities
The test crew shall consist of no less than three members. All test participants will be briefed on
the testing to be conducted on the test day in question prior to the start of testing. Additionally,
all test participants will be familiar with the crew roles and responsibilities outlined in this
document.
The roles of each crew member shall be as follows:
1. Driver
The driver will be responsible for operation of the vehicle. Their sole focus will be
monitoring the environment directly ahead of the vehicle for any potential hazards.
Secondary duties will be maintaining the vehicle’s course (steering) and speed (cruise
control).
2. Safety Focal
The duty of the safety focal will be to monitor the testing environment to identify
potential safety hazards and promptly communicate relevant status updates to the driver.
The safety focal shall have full authority to halt testing at any time should they deem the
conditions unsafe.
3. Data Analyst
The data analyst will be responsible for monitoring data from both data collection
systems. Their primary focus will be on monitoring the quality of data from the
dynamometer and communicating to the driver when to proceed to the next test
condition. Their secondary focus will be on monitoring the velocity of the free stream
through the secondary data acquisition unit, ensuring the airspeed is as required per
condition and that the wind direction does not deviate more than five (5) degrees from the
vehicle’s direction of travel. This duty shall be the sole focus of the Condition Quality
Monitor if a fourth crew member is present.
4. Condition Quality Monitor (Optional)
If a fourth crew member is present, their sole focus will be on monitoring the velocity of
the free stream through the secondary data acquisition unit, ensuring the airspeed is as
required per condition and that the wind direction does not deviate more than five (5)
degrees from the vehicle’s direction of travel. The option for a fourth member is included
in order to reduce the workload of the rest of the crew.

13
Emergency Contact Information
BLM Emergency Assistance
(888) 233-6518
BLM Barstow Field Office/Field Permit Information
(760) 252-6000
El Mirage OHV Area Recorded Information
(760) 252-6011
St. Mary Regional Medical Center
18300 Highway 18, Apple Valley, CA
(760) 242-2311
Victor Valley Community Hospital
15248 11th
Street, Victorville, CA
(760) 245-8691
References
Bureau of Land Management, El Mirage Dry Lake OHV Recreation Area, Accessed September
6, 2016, [http://www.blm.gov/ca/st/en/fo/barstow/mirage.html]
Figure 7. Location of El Mirage Dry Lake OHV Recreation area with driving directions from Los Angeles.

14
Appendix B – Dynamic Test Stand Overview

15
Figure 8. Front view of the dynamic test stand model.
Figure 9. Side view of the dynamic test stand model.

16
Figure 10. Isometric view of the dynamic test stand model.
Figure 11. Close-up views of specially designed areas (from left to right: top front shoulder, bottom front
frame-leg-clamp configuration, bottom rear frame-leg-clamp configuration.)

17
Appendix C - Clamp Drawings

19
Appendix D - Structural Analysis of Dynamic Test Stand
𝐴 = 2(𝐴 𝑠𝑖𝑑𝑒) + 𝐴 𝑡𝑜𝑝 + 𝐴 𝑚𝑖𝑑
𝐴 𝑠𝑖𝑑𝑒 = (0.914 − 0.070) ∙ 0.038
= 0.032 2
𝐴 𝑡𝑜𝑝 = (1.010 − 2(0.038 )) ∙ 0.038
= 0.035 2
𝐴 𝑚𝑖𝑑 = 1.010 ∙ 0.070 = 0.071 2
𝐴 = 0.170 2
𝑥̅ = 0
̅ =
2(0.032 ∙ 0.457) + (0.035 ∙ 0.895) + (0.071 ∙ 0.133)
0.170
̅ = 0.412
Figure 12. A 2D representation of the front profile of the dynamic test stand can be used as a model to
calculate drag force and, subsequently, the loading on the bolts at the feet of the stand.
To simplify calculations and represent the worst case scenario, the frame legs of the dynamic test
stand are modeled as vertical flat plates that are perpendicular to the oncoming free stream flow
(whose direction is into the page with respect to Figure 12.)
The drag force against the front profile of the dynamic test stand was calculated using the standard
drag equation
𝑑𝑟𝑎𝑔 =
1
2
𝜌𝑢2
𝐶 𝐷 𝐴 (9)
Assuming a constant 𝜌 = 1.184
𝑘𝑔
𝑚3 free stream fluid density (correlating to 25 °C), 22.4 m/s free
stream flow speed, and a vertical 3D flat plate coefficient of drag (𝐶 𝐷 = 1.28) taken from NASA,
𝑑𝑟𝑎𝑔 =
1
2
(1.184
𝑘𝑔
3
)(22.4
𝑠
)
2
(1.28)(0.170 2) = 4. (10)
The parameters used to calculate this force are considered to represent the most extreme conditions
possible. Specifically, the maximum planned speed is 22.4
𝑚
𝑠
and the coldest conditions at El
Mirage Lake (the prospective test site) would be 25 °𝐶, which corresponds to the highest density.
0.914 m
0.070 m
0.038 m
𝑥
1.010 m
Front View of Dynamic Test Stand
0.098 m

20
Then, shifting perspective to the side profile of the dynamic test stand, simple structural analysis
can be done to calculate the approximate stresses on the bolts of the clamps that fasten the dynamic
test stand to the roof of the testing vehicle.
The side profile of the dynamic test stand is modeled as a pair of fixed, massless vertical rods to
simplify analysis and allow calculation for the largest possible loads. The drag force is assumed to
be applied at the centroid of the dynamic test stand’s front profile.
Figure 13. The dynamic test stand can be simplified to a pair of 2D massless vertical rods with one fixed
support each, which ignores the back supports and represents the most extreme loading case.
Figure 14. Using a pair of massless vertical rods with fixed supports and estimating 20 N of equipment
weight across the top structural analysis can be applied to calculate the loads on the fixed support.
Fx
Fy
M
Fdrag = 64.6 N
Fequipment = 20 N
0.412 m
0.914 m
𝑥
o

21
Using standard equations for static load analysis,
∑ 𝑥 = 0 ( 4. ) − 𝑥 = 0 (11)
∑ = 0 − (20 ) = 0 (12)
∑ 𝑜 = 0 − ( 4. )(0.412 ) = 0 (13)
which leads to
𝑥 = 4.
= 20
𝑜 = 2 .
However, these values account for the collective load of the two (2) bolts holding the frame legs
to the front clamps. Thus, assuming symmetry,
𝑥 𝑜 𝑡 =
4.
2
= 32.3
𝑜 𝑡 =
20
2
= 10
𝑜 𝑡 =
2 .
2
= 13.3
To begin analysis of the stresses that the front clamp bolts experience, perspective must be shifted
to applying the resultant forces onto the bolt.
Figure 15. The resultant loads are felt by two (2) bolts connecting the frame legs to clamps.
Fx
Fy
M
o
Fx,bolt
Fy,bolt
Mbolt
o

22
To simplify analysis, the bolt was assumed to be a cylindrical beam.
Figure 16. The bolt was modeled as a circular beam with d = 0.0064 m and L = 0.0508 m.
NOTE: y originates from the neutral axis.
Then, employing standard mechanics of materials equations [4], the shear and normal stresses on
the bolt can be calculated.
The maximum normal stress experienced by the bolt occurs at y = -0.0032 m, where it experiences
tension both from the axial force Fx and from the bending moment Mbolt,
𝜎 𝑛 𝑚𝑎𝑥 =
𝑜 𝑡(𝑑 2⁄ )
𝐼𝑐𝑟𝑜𝑠𝑠
+
𝑥 𝑜 𝑡
𝐴 𝑐𝑟𝑜𝑠𝑠
=
(13.3 )(0.0032 )
(8.24 × 10−11 4)
+
(32.3 )
(3.22 × 10−5 2)
= 𝟓𝟏𝟕. 𝟓𝟏 𝑴𝑷𝒂
𝜏 𝑚𝑎𝑥 =
4 𝑜 𝑡
3𝐴 𝑐𝑟𝑜𝑠𝑠
=
4(10 )
3(3.22 × 10−5 2)
= 𝟎. 𝟒𝟏 𝑴𝑷𝒂
With these calculations and readily available standards about SAE Grade 5 ¼” bolts, a factor of
safety (FoS) analysis can be completed.
SAE Grade 5 ¼” Bolt
Strength Specifications 𝑭𝒐𝑺 =
𝑴𝒂𝒙 𝑨𝒍𝒍𝒐𝒘𝒆𝒅 𝑳𝒐𝒂𝒅
𝑴𝒂𝒙 𝑪𝒂𝒍𝒄𝒖𝒍𝒂𝒕𝒆𝒅 𝑳𝒐𝒂𝒅
𝝈 𝒏 𝒂𝒍𝒍𝒐𝒘𝒆𝒅 𝒎𝒂𝒙 (𝑴𝑷𝒂) 𝝉 𝒂𝒍𝒍𝒐𝒘𝒆𝒅 𝒎𝒂𝒙 (𝑴𝑷𝒂) 𝝈 𝒏 𝒎𝒂𝒙 𝑭𝒐𝑺 (−) 𝝉 𝒎𝒂𝒙 𝑭𝒐𝑺 (−)
827.37 496.42 1.6 1210
Table 3. Analysis shows that there is at least an FoS of 1.5 for both normal and shear stresses.
While it may seem that there should be a focus on increasing the normal stress FoS, it is important
to recall the assumptions that were made at the beginning of this analysis. It was assumed that the
entire load of drag and equipment would be on the two (2) front clamp bolts that act as a fixed
support. In reality, there is significant additional support by the presence of the angled frame legs
that connect the front profile of the dynamic test stand to rear clamps.
Fx,bolt
Fy,bolt
Mbolt
o
d = 0.0064 m
y
L = 0.0508 m
𝐼𝑐𝑟𝑜𝑠𝑠 =
1
4
𝑟4
= 8.24 × 10−11 4
𝐴 𝑐𝑟𝑜𝑠𝑠 = 𝑟2
= 3.22 × 10−5 2

23
FEA
The dynamic test stand assembly was simplified into a single, rigid frame to allow for the
performance of finite element analysis. Specifically, the maximum von Mises stress as well as
maximum resultant displacement were simulated. The material assigned for simulation was
galvanized steel, which is most similar to the real material that will be used.
Figure 17. Each “foot” of the dynamic test stand was modeled as fixed geometry (shown in green), while
a distributed force of Fdrag = 64.6 N was applied over the entire front profile of the dynamic test stand
(shown in purple.)
The final mesh size that allowed for satisfactory convergence for von Mises stress and resultant
displacement (minimum 5% relative change between iterations) was 3.81 mm.
Figure 18. A global mesh size of 3.81 mm was used to achieve satisfactory convergence for both von Mises
stress and resultant displacement.

24
Mesh Size
[mm]
Max von Mises [MPa]
Max Displacement
[mm]
Δvon Mises [%] ΔDisplacement [%]
25.4 41.0767 1.3867 - -
12.7 44.1673 1.9863 7.52 43.24
6.35 49.0115 2.0866 10.97 5.05
5.08 52.9944 2.0954 8.13 0.42
3.81 53.7831 2.1010 1.49 0.25
Table 4. After achieving satisfactory convergence (Δ ≤ 5%), the maximum von Mises stress experienced
by the test stand was found to be 53.8 MPa while the maximum resultant displacement was found to be
2.10 mm.
The corresponding plots reveal where the maximum von Mises stress and maximum displacement
occur, respectively.
Figure 19. FEA results show that the maximum von Mises stress (53.8 MPa) occurs at the corner between
the middle and side bar of the dynamic test stand (annotated by the balloon in the figure.)

25
Figure 20. FEA results show that the maximum resultant displacement (2.10 mm) occurs at the center of
the middle support bar of the dynamic test stand (annotated by the balloon in the figure.)
Since the yield strength of galvanized steel is approximately 204 MPa and the maximum von
Mises stress calculated for the dynamic test stand was 53.8 MPa, the Factor of Safety is ~3.8.
With regards to resultant displacement, 2.10 mm is negligible and none-critical to the operation
or safety of the dynamic test stand.

28
Appendix G – Tyto Robotics (RC Benchmark) Invoice

29
Appendix H - McMaster-Carr Invoice

AME-441-Group-47-Proposal-Approved

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