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AAE 451
Team 1
Mike Abram
Chip Challis
Nicholas Correll
Jeremy Feldstein
Joshua Lee
Hong Liu
Leo Moroz
Jorge Perdigao
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Executive Summary The purpose of this project is to design, build, and test a remotely piloted aircraft (RPA) that provides a safety
service to the public or private sectors. There are numerous possible avenues where such a vehicle would prove to be
useful, such as search and rescue, surveying, aide delivery, and many more. While there are many ways to accomplish
these missions, the overall goal is to complete them safely without imposing any additional safety hazards onto the general
public. This means the aircraft must be very stable and easy to operate while meeting all of the performance requirements
dictated by the specific mission it will perform.
Many of the constraints and limitations outlined in the request for proposal (RFP) are derived from the public
safety concerns and the performance requirements of public safety missions. In order to ensure that the plane is simple to
operate and reliable, it must be able to be constructed in the field within 10 minutes. In order to accomplish this, it must
be modular and fit into a relatively small container for transport. In order to keep the public safe, the design and/or
operation of the aircraft must mitigate safety hazards such as signal loss, power loss, collisions, hazardous materials, and
unshielded propeller blades. In order to perform adequately in the air, it must meet various performance constraints such
as a stall velocity of less than 25 ft/s, a climb angle of more than 25 degrees, and a takeoff roll and landing roll of less than
80 ft. It must be able to achieve these requirements for at least 8 minutes and complete the mission at a maximum altitude
of 375 ft. to comply with FAA regulations.
The focus of this design was to make the aircraft as safe and easy to operate as possible. A propulsion system was
chosen to easily meet all performance requirements set forth in the RFP. The avionics built into the aircraft have features
that mitigate safety hazards such as signal loss and power loss. The nose is made from soft foam to reduce impact and the
propeller is set to a pusher configuration to prevent propeller strike. Dynamics and controls were made so the aircraft is
inherently stable and easy to fly. All of these features were put into a modular form to ensure that the aircraft can be
transported anywhere and assembled within 10 minutes.
If the aircraft can meet all of the performance requirements of the mission while mitigating potential safety
hazards, it can be considered a success. The remainder of this report will explain the process of design and analysis of
each discipline within the team. It will highlight the performance of the aircraft as well as the safety features specific to
the mission. The result is a purpose built RPA that will serve the public or private sectors in many different scenarios.
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Table of Contents
1. Mission Requirements:
a. Designed Public Safety Mission
b. Hazard analysis and prevention
c. Performance Requirements 2.
Preliminary Design:
a. Concept Generation 3.
Flight Plan:
a. Mission Profile
b. Assembly Plan
4. Aerodynamics
5. Structures
6. Propulsion
7. Dynamics & Controls
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1. Mission Requirements Mission
The public safety mission our RPA will perform is providing surveillance in the case of a missing person. The intended
user would be a public safety official attempting a search and rescue mission. The objective of the mission is to provide
visual surveillance using search patterns a saved video, and GPS locations. The GPS locations will then be mapped
alongside the images and a user could know where the image was captured. The aircraft will scanning a wide area during a
slow loiter and attempt to locate a missing person. The aircraft also must be able to fit in the specified container shown
later.
Hazards
There are many potential hazards when it comes to remotely piloted aircraft. One of the most dangerous prospects is in air
collisions. RPA have potential to damage both themselves as well as what they hit. If the other system is a manned system
it could also cause serious injuries or even fatalities. Another possibility for hazards is that to personal property. If the
RPA crashed and the batteries shorted, it could end up causing a fire. This would lead to significant property damage
which could also refer to things that the aircraft were to crash into. In addition, the aerial system could produce shrapnel
from either the propeller or another impacted component. If the propeller were to fail, it could be very dangerous. If
another component failed the failure may result in aircraft section becoming dislodged and the RPA falling to the ground
in pieces. Radio communication could also be a hazard. This could be interference on an emergency channel or with other
systems in the vicinity. In a city, the radio signals might interfere or be interfered with by local radio and TV stations. In
rural situations, it might interfere with remotely operated farming equipment working on neighboring signals.
Method of Avoiding Hazard
Hazards Operation (flight) Design Manufacturing Avoided
1 Ground Collision Use Steerable Landing Gear Steerable Landing Gear Yes
2 In air Collision Don't fly near obstacles Aircraft is maneuverable Yes
3 Battery Fire Controller cuts power if battery low Yes
4 Hazardous Fumes From Battery
Understand the potential hazard and avoid fumes Yes
5 Propeller Strike Avoid touching the moving propeller Rear Mounted Propeller Yes
6 Burn From Touching Motor Avoid touching motor when in operation or hot Yes
7 Shrapnel or Debris Be attentive during flight Yes
8 Battery Shock Know how batteries work and how to avoid shock Yes
9 Cut from damaged Composite Avoid touching sharp composites Avoid touching sharp composites Yes
10 Resin is hazardous Hazardous Materials Yes
11 Injury from using tools Understand how to safley use tools
Yes
12 Cut by Knife Be Careful Where you are cutting Yes
13 Inhalation of composite dust Wear a mask and a tyvec suit Yes
14 Burn from hot wire cutting Use the hot wire safley Yes
Avoids Hazard Hazard Not effected
Figure 1.1
Performance Requirements – The RFP provides two sets of requirements for the RPA, design requirements and safety
requirements. The design requirements of the RPA include a minimum climb angle of 25 degrees, and a stall velocity less
than 25 feet per second during level flight. The RPA must also be able to take off and land with less than 80 feet of
ground roll and must carry a 2 pound payload for at minimum, 8 minutes. Safety requirements include flight ability as
well as onsite assembly taking no longer than 10 minutes. The RPA must have the capability to communicate health,
telemetry, and payload data to a ground station at numerous points during flight.
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2. Preliminary Design The preliminary design produced contained a lifting body which would provide additional lift. The twin boom
configuration is intended to prevent people from accidentally contacting the propeller. The rear mounted propeller also
serves to prevent frontal propeller strike being the first point of contact with an object. With the rear mounted propeller the
nose will be the first point of contact instead of a more dangerous rotating propeller and motor. Two booms have been
used as opposed to one to prevent severe tail deflection.
Figure - 2.1
The preliminary design was altered; the lifting body was changed to a fuselage due to stability considerations.
A constraint diagram has been provided in figure 2.2 below.
Figure 2.2: Constraint Diagram for design space
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3. Flight Plan The flight will begin with takeoff, then climb, a sprint, and decent. The imaging mission will then run and the search and
rescue mission will be simulated. Then the aircraft will land.
Figure 3.1 – Flight Profile Figure
3.2 shows the camera will have a clear view of the ground.
Figure 3.2 – Camera Visibility Figure
3.3 shows that the aircraft can be assembled in less than ten minutes.
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Figure 3.3 – Assembly Gant Chart Figures
3.4 and 3.5 show the aircraft can fit inside the container.
Figure 3.4 and 3.5 – Aircraft disassembled in box
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4. Aerodynamics Introduction
This section of the report will cover the aerodynamic performance and design of the aircraft. The aerodynamic analysis
was conducted on a remote control aircraft with the intended purpose of completing a public safety mission. For each
portion of the aircraft, design considerations will be listed, followed by a design procedure. Then the value we have
selected for that portion of the design will be presented. Discussion of each value will follow the selection. This will be
completed for each of the aircrafts aerodynamic characteristics and constants. Mission worthiness will then be evaluated
for the aircraft which will conclude the report.
Airfoil Selection
Design Considerations – Based upon the mission of the aircraft, desirable characteristics for our airfoil are that it has a
high maximum lift coefficient which will enable low speed takeoff and stall, as well as a high lift to drag ratio to allow the
aircraft to cruise efficiently. The Reynolds number of the airfoil will be low compared to typical passenger aircraft.
Equation 1 was used for calculating the Reynolds number of the airfoil.
Equation 4.1
The aircraft will be flying at slow speeds and therefore a low Reynolds number. The airfoil will have to perform well
between Reynolds numbers of 100,000 and 250,000. The exact Reynolds numbers for our airfoil are 164790 for takeoff
and 246600 based upon a chord length of 12 inches, and flight velocities of 24.3ft/s for takeoff and 40ft/s for cruise. The
maximum altitude of the aircraft is 400 feet, but the aircraft will likely fly lower than this for a large portion of the flight
due to its mission.
Design Procedure – Airfoils were sorted by maximum lift to drag ratio at a Reynolds number of 100,000 for gathering
airfoil data. The top 100 airfoil maximum lift to drag ratio and maximum lift coefficient were evaluated in the preliminary
analysis. Airfoils with low maximum lift coefficients were omitted because of our need for a high maximum lift
coefficient. A table of high lift to drag ratio and high maximum lift coefficient values was then created while using Re of
100,000. The highest lift coefficient airfoil we could find was also included in table 1A in the appendix. Data points from
table 1A were placed in a scatterplot. The previously mentioned scatterplot of can be found below (figure 4.1).
Figure 4.1 – scatterplot of airfoil data
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60
62
64
66
68
70
1.2 1.4 1.6 1.8 2 2.2 c l max approximate
Evaluated Airfoils
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Airfoil that met the necessary criterion of being high lift and high lift to drag ratio were then run in XFLR in a 2d analysis.
Figures 4.2 and 4.3 show the maximum lift coefficient vs. angle of attack, and maximum lift to drag ratio vs. angle of
attack. The XFLR analysis was run from -5 to 15 degrees. The airfoil stall below 15 degrees for the analyzed airfoil.
Reynolds numbers of 150000 and 250000 used in the airfoil analysis were close to the values for our takeoff and cruise
velocities specified before.
Figure 4.2 - cl vs
Figure 4.3 - cl/cd vs
Value for airfoil – The s1210 airfoil was chosen based upon its high lift to drag ratio as well as its high maximum lift
coefficient. It produces a maximum 2d lift coefficient of 1.96 which is much higher than other airfoil at this Reynolds
number (excluding the s1223). We have chosen the s1210 over the s1223 because of the increased cruise efficiency.
Validation – Wind tunnel data for a tested section of the s1210 has been taken from an online source which can be found
in the appendix (Source 1). Figure 4.4 shows the test data for the s1210 at a Reynolds number of 150,000
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Figure 4.4 - wind tunnel test data
When comparing the XFLR 2d analysis to the wind tunnel section, the test data is significantly lower. The value for the
lift coefficient of the airfoil is 1.96 at a Reynolds number of 150,000 where the value for the s1210 test section is closer to
1.76. The value is similar which is expected for the difference between an airfoil when compared to a wing.
Discussion – One concern with using the s1210 is the difficulty of manufacturing. The thin trailing edge presents
manufacturing difficulties as well as structural issues. The data for lift coefficient from XFLR is higher than the tested
section from the wind tunnel but has been accounted for in later calculations by avoiding usage of the maximum 2d lift
coefficient provided by the XFLR analysis, and calculating based upon a smaller value. The highest value from the wind
tunnel that has been tested is 1.76 at a Reynolds number of 150,000. At a Reynolds number of 200,000 the lift coefficient
reached a maximum of 1.8. This shows that our chosen value for maximum lift coefficient can reach a maximum of 1.8.
The aircraft reaches its stall speed while flying with a lift coefficient of 1.77 at a speed of 24.3ft/s and an angle of attack of
13.5 degrees. The aircraft cruises with a lift coefficient of .655 and an angle of attack of -1 degrees. These lift coefficients
provide steady level flight.
Wing design
Design considerations – The wing is designed to provide sufficient lift at a stall speed 25 feet per second, as specified in
the Mission Specification document. The aircraft must also cruise efficiently. It must also be manufactureable using
available materials and manufacturing processes that can be completed quickly but efficiently.
Design Procedure – Preliminary design of the wing was first conducted. Eliminating wing configurations that are not
easily manufactureable let us with a rectangular planform. Wings with taper, sweep, twist, and dihedral were eliminated
because of manufacturing difficulties. Initial analysis was conducted on wings with 12 inch chord and 10 inch chord. The
12 inch chord wing was eliminated at first due to its excessively low aspect ratio, which could results in high induced
drag. The analysis of the 10 inch chord wing indicated insufficient lift and was then replaced with an 11in chord one. With
larger chord, the S1210 airfoil operates at higher Reynolds number with a fixed speed and therefore has higher lift
coefficient. The increased chord length also resulted in larger wing area, which also contributed to lift. After wing
geometry was selected, wing analysis began. Hand calculations of lift eventually led to programming of a MATLAB code
(which will be discussed in a following section). Through iteration using XFLR5 (fixed-lift analysis) angle of attack at
stall and cruise phases were obtained.
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The wing geometry was determined thorough an iterative process in which fixed lift analysis was performed first for each
new geometry to ensure its could generate 6.5lb lift at a speed less or equal to 25 ft/sec as specified in the RFP and angle
of attack was checked to ensure it was lower than 15 degree, which was the stall angle of attack of the airfoil.
Values for design parameters - The wing geometry is shown below.
Table 4.1 - Wing geometry
Airfoil Planform Chord [in] Span [in] Aspect Ratio
S1210 Rectangular 11 68 6.182
Discussion - Results from XFLR5 showed that the wing could generate 6.5 lb lift at 13.5 degree at 24.3 ft/sec. Lift curve
of the main wing calculated using Lifting Line Theory is shown in Figure 4.5. By combining the main wing and the tails,
which will be discussed in the following sections, the entire aerodynamic configuration was modeled in XFLR. Using
Vortex Lattice Method, the L/D plot of the entire aircraft was obtained. (Figure 4.6)
The lift to drag ratio versus angle of attack plot shows that the angle of attack corresponding to the maximum value for lift
to drag ratio was approximately -1 degree, which was the same as the cruise angle of attack of the aircraft. Thus, the wing
design was deemed to be efficient at cruise. Besides the results from XLFR5, a more accurate calculation of the L/D was
performed by the MATLAB code written by the aerodynamics group which took the fuselage drag into account. The L/D
of the aircraft at cruise was determined to be 13.06.
Because the design needed to be simple required airfoil characteristics have been achieved without the use of taper,
dihedral, sweep and twist and that analysis done on the benefits provided by wing taper and sweep indicated that the
benefits did not outweigh the difficulty of manufacturing when our timetable for completing the build phase was taken
into account, we left these geometry choices out of our design.
Figure 4.5 - Main wing lift curve
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Figure 4. vs. 𝛼
Tail Airfoil Selection
The horizontal tail needs to provide both upward and downward aerodynamic forces. Symmetrical airfoils were therefore
preferred since no consideration was needed to take the difference in aerodynamic force at different deflection angle into
account.
Other factors that influenced the tail airfoil selection were stall angle of attack and thickness. The horizontal tail should
not stall before the main wing. The thickness of the airfoil also needed to be enough to accommodate the tail booms.
Design Procedure – Choose a symmetric airfoil that has enough thickness and reasonable stall characteristics.
Discussion – NACA 0012 airfoil was chosen because it met the needed performance characteristics of the tail and could
be manufactured easily.
Tail Design
Design Considerations – The tail was designed to meet the requirements of having a stable, trimable, and controllable
aircraft. The longitudinal stability of the aircraft was majorly determined by the horizontal tail. The vertical tails of the
aircraft provide yaw stability. The elevator provides trimmability and pitching control. The rudder steers the aircraft about
its vertical axis.
The horizontal tail was designed to achieve a moment coefficient curve with a negative slope and achieve a large enough
static margin to ensure longitudinal stability. For the aircraft to be longitudinally statically stable, must be less than
zero. This means that when the aircraft is disturbed and pitches in one direction, it must have the tendency to change its
attitude in the opposite direction. In order for the derivative of the moment coefficient with respect to angle of attack to be
negative, the aerodynamic center of the entire aircraft or the neutral point must be positioned behind the center of gravity
when measured from the nose.
Another measurement of static stability is static margin (S.M), which is defined as the difference between the location of
center of gravity and neutral point in fraction of chord length. Higher static margins leads to more stable aircraft. The
static margin recommended by the textbook and internet resources is between 5%-15%.
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The static margin is expressed by the following equation:
Static Margin = (𝑋̅̅̅ 𝑛𝑝 − 𝑋̅̅̅ 𝑐𝑔 ) Equation 4.2
Tail volume is also an important parameter that influences both stability and controllability of the aircraft. The horizontal
tail volume is expressed by:
Equation 4.3
The vertical tail volume is expressed by:
Equation 4.4
The design of vertical tail focused on achieving a reasonable vertical tail volume, instead of the trimmability requirement
since there was no need to trim the aircraft around its vertical axis. The small moment generated by the rotating propeller
is neglected in this design because it acts close to the axis of rotation. The level of directional stability was determined
from the vertical tail volume.
Design Procedure - Initial tail geometry was chosen. The wing and tail combination was assembled and run in an XFLR 5
VLM1 (horse-shoe vortex method) evaluation. Analysis in XFLR5 produced equations for the lift curve, drag curve, and
moment coefficient curve of our aircrafts wing and tail. The values for the wing and tail were inserted into the MATLAB
code and the location of the neutral point and static margin were determined. The static margin was then analyzed based
upon recommended values. If the static margin failed to meet the requirements, changes were made to the tail geometry
increase the static margin. The horizontal and vertical tail volumes were calculated once the criterion for static margin was
met. The value for tail volume was then compared with the value stated in the course text. Value for design parameter -
The finalized horizontal and vertical tail geometry are listed below.
Table 4.2 - Tail geometry
Horizontal Tail
Planform Chord [in] Length [in]
Rectangular 8 18
Vertical Tail (double)
Planform Root Chord [in] Tip Chord [in] Height [in]
Tapered 8 6 7
Stability parameters calculated by the MATLAB program are listed below.
Table 4.3 - Stability parameters
Static Margin
18.2%
The static margin of 18.2% exceeded the upper boundary 15% of the recommended range by 3.2%. However, it was
considered that the small amount of additional static margin could provide additional longitudinal static stability and
prevent the aircraft from becoming unstable due to unexpected center of gravity change during manufacture.
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Figure 4.7 Wing and Tail geometry
Drag Calculation
Total parasite drag of the aircraft was calculated by adding the parasite drag from XFLR wing and tail analysis to the
fuselage drag calculated by the MATLAB program written by the aerodynamics group. The total parasite drag was
calculated to be 0.0686. The equations implemented in the fuselage drag calculation are listed in the appendix.
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5. Structures Overview
This purpose for this section is to identify and explain the process that was taken in designing the structures for our
aircraft. The decisions for material selection and structural layout of the various components are explained through our
structural analysis.
The main goal of the structural design of our aircraft was to minimize the weight as much as possible while maintaining
the aircraft’s structural integrity. The design was primarily driven by maximum load cases, which is further explained in
the design process.
With the mission highlighting public safety as a large role, many of the design were made to ensure that safety is the top
priority, such as foam exterior and rear mounted propeller. These choices were designed to reduce any impact forces and
damage to the aircraft and an object in the event of a collision.
Load path
To understand the structural integrity of our aircraft, a load path diagram was required for the first step of our analysis.
The load path provides a visual assistance in determining and understanding how all the major forces will be distributed
throughout the aircraft. By drawing the load path, we were able to comprehend how all the major forces will affect the
aircraft. In our RFP, there are four different types of major forces affecting the aircraft’s structure. The load path diagram
is shown in the figure below, where the path of each major force is highlighted.
Figure 5.1: Load Path Diagram
The first major force is the bending force that will cause bending moment stress to the wings and the tail. Since the
direction of the wing bending and the tail bending moments are different, the analysis has to be separated into two
different parts but combined at the boom holder. All the bending moment will be concentrated on the boom holder, and
transfer to the fuselage.
The second major force is the torsion force that is applied to the wing because of the air flow around the airfoil. The
torsion force is relatively low compare to the bending load, and the following calculation shows that just the fiberglass
skin wing is strong enough to neglect the torsion force of the wing.
Orange – Torsion force Green – Bending force
Blue – Propeller wash force
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The third major force is the propeller wash force which is the wind force that is pushed from the propeller. This force will
only cause minor vibrations to the tail.
Load factor
To calculate what will be the maximum load cases, we have to figure out when the aircraft will experience the most g
force. The max lift will experience when the aircraft is at max bank angle which will be 71.84 degrees using the following
equation.
Equation 5.1
When V = 70 𝑓𝑡⁄𝑠 , 𝑟 = 50𝑓𝑡 , 𝑔 = 31.17𝑓𝑡⁄𝑠2
The load factor is calculated with 150% safety factor. A safety factor of 1.5 is the typical value used, which provides a
safety net for any margin of error in analysis and unaccounted for loads.
Equation 5.2
Applying the safety factor calculated above, the maximum lift force becomes 32.5lbf for entire span of the wing.
Historical data shows that for small aerobatic aircraft, the typical load factor ranges from [-2, 5]. Using the load factor
discussed above, a V-n diagram was produced in order to display the limiting loads that our aircraft can withstand during
various speeds during flight.
Figure 5.2: V-n Diagram Landing Gear
In designing the landing gear, we had to be aware of how the load will transfer through the nose and the main landing
gears to the fuselage. Several different types of landing gears were considered, such as tricycle, tail dragger, and skid.
Ultimately, we chose the tricycle gear to reduce as much weight as possible, while still being safe enough to withstand any
hard landing forces. For the tricycle configuration, the following initial requirements were set to determine the distance
from the center of gravity to main landing gear can be calculated, as well as the distance to the nose landing gear.
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Landing Gear Requirements
Percent of Weight Carried By Nose Gear 15%
Percent of Weight Carried By Main Gear 85%
Overturn Angle >25ᵒ
Table 5.1: Landing Gear Requirements
Once these distances have been determined and verified that the correct amount of weight is carried, and the track length
has been determined from the constraint of the overturn angle, the configuration must be validated. Once the location of
each landing gear has been calculated, it is necessary to check that the tail will have enough clearance during takeoff so
that it will not strike the ground. By finding the angle between the main landing gear and the end of the aircraft, it can be
compared to our takeoff angle. As long as the takeoff angle is smaller, then there is enough clearance to confirm that the
landing gear is properly configured. To determine the results of the landing gear for our aircraft, a range of overturn
angles were used to find the optimal distances for each gear that will fit our design.
Reviewing the results from our design, it was determined that the following values are acceptable ranges in selecting a
landing gear.
Landing Gear Configuration
Height to Fuselage 6 – 7 inches
Wheelbase 12 – 16 inches
Track Length 16 – 21 inches
Table 5.2: Usable Landing Gear Configurations
Once the layout of the landing gear was calculated, the static loads were determined to verify the correct gear locations
and determine the strut loads and wheel design. These values along with the dynamic breaking load are displayed in the
appendix.
The main landing gear that has been selected is 101 gram carbon fiber landing gear. The mounting holes are not predrilled
which will allow us to choose the location where the screws will connect the gear to the fuselage.
The nose gear that we have selected is a steel steerable straight nose gear. Fitted with nylon nose gear blocks, and a
steering arm, this gear will allow the aircraft to be steerable during taxi and will also be strong enough to withstand any
loads the aircraft will experience. They will be mounted to the fuselage by screwing the landing gear to a connecting plate
that will be bonded to the fuselage. With these selections, we then had to investigate how our structures will hold up
throughout the mission.
With the landing gear selected, an analysis was required to determine that the forces from a hard landing will not cause the
landing gear or fuselage to break. In order to examine these impact loads and their effects on the aircraft, these few
assumptions were made:
• Abrupt three point landing
• Main landing gear experiences the greatest force
• Landing Gear and mounting plate were modeled as connected cantilever beams.
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The reaction forces on the nose and main gear were calculated. These forces were then decomposed into a perpendicular
force and a radial force that are along the relative axis of the landing gear. A visual representation of this model is shown
in Appendix B.5.
Using the perpendicular force to the landing gear, the bending moment was found at the corners of the landing gear. It was
assumed that these corners on the landing gear would experience the highest amount of stress, and comparing the carbon
fiber landing gear properties to the stress calculated from the bending moment, it was proved that the landing gear itself
would not break.
After determining that the carbon fiber gear will not break, the plate to attach the landing gear to the fuselage was
examined. The same value of the bending moment from the landing gear plate was assumed to be applied to the ends of
the connecting plate. Next, the bending stress was calculated at the center of the connecting plate and compared the yield
stress of the selected materials. Finally, a distributed load was calculated to find the force that is applied to the plate from
the landing gear, and its maximum deflection was determined.
From the analysis explained above, it was determined that even with our maximum load factor, and a hard landing, the
landing gear will be able to withstand the loads applied. It will be strong enough to maintain its shape and keep the
fuselage and rest of the aircraft from any damage.
Structural analysis
For the structural analysis, all the analysis was conducted on the maximum load cases. The aircraft is built to withstand a 5
g load case with safety factor of 1.5. Even with the payload of 2.0 lb. this aircraft can fly up to 70 ft/s with 50 feet turning
radius. The aircraft is separated into nose, fuselage, four pieces of wing, two booms, and the tail. All the sections can be
assembled into one aircraft in 10 minutes, using various drop pins. Because our aircraft is separated into many parts, we
had to do a series of calculations on the each connection point to check rather it will hold the stress from the airplane.
Using the load path diagram discussed earlier, we have analyzed the steps for how the major loads transfer to the fuselage.
Boom, boom holder, wing, spar and the fuselage were analyzed in series of steps, and the landing gear was analyzed
separately at the end. The objective of our analysis is to insure all the connection are safe, and the boom needs to be at
least 16 inches long, and the tail deflection angle has to be less than 1.5 degrees.
Boom Analysis
For the boom analysis, first we had to figure out the optimum length for the boom. Using a hollow carbon fiber tube, the
booms dimensions are shown below in figure 3. The only force that was applied in this analysis was the point load from
the tail lift force that we received from the aerodynamics team, which was 8.2 lbf (Load factor of n=5).
Working with the D/C team, we have defined that the boom length should be greater than 16 inches and must maintain a
deflection angle less than 1.5 degrees. Using the equation for the wing tip deflection angle in Appendix B.2, it was
calculated that we will need an 18 inch boom, which would meet the requirements set for the length and deflection angle.
Since we also had to verify that the lifting force on the tail will not break the connection between boom and the boom
holder, the distance of ‘s’ was calculated using the composite beam bending equation (appendix B.3).
Figure 5.3: Boom Analysis Model
Having “s” be a distance of 2 inches, the thickness of the holder is defined so that all the connection parts can survive the
5 G load.
s
Tail lift force
Boom
T
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Wing
Unlike the boom analysis, the wing experiences the distributed force along the span. Using the max lift force we
calculated in the load factor section, the force was distributed as 0.478lbf⁄in. Using the bending stress equation listed in
Appendix B.1 we could find the bending stress on the wing and determine whether the foam core or the fiberglass skin
will fail.
Wing Component Max bending stress [psi] Yield Stress [psi]
Foam 0.63 30
Fiberglass fabric 1.24e4 6.0e4
Table 5.3: Composite Wing Stress Analysis
Also, to ensure that the tip of the wing does not twist more than 1 degree, the following equations are used to find the
minimum thickness of the fiberglass layers of the wing. The Cm value is provided by the aerodynamics team, using the
XFLR.
Figure 5.4: Equations for Skin Thickness (due to twist)
When we are using the fiber glass layer as a wing skin, the minimum thickness was 2.9e-4 inches, which is smaller than
what we had in mind for the bending analysis. With 1.2e-3 inch of fiber glass skin and solid foam body, our airplane will
not deflect more than 1° and also not break any component.
A specific aspect of our wings that raised a large amount of concern was the trailing edge. Because of the selected airfoil
and its very high camber, the trailing edge will be extremely thin. The area of concern is that with this very thing trailing
edge, it must be manufactured strong enough to not snap off at any time during flight.
The trailing edge of the wings was analyzed by modeling the entire span as a wing box around the control surface that is at
its maximum deflection (Appendix B.6). Based on the pressure distribution, the aerodynamics team was able to provide us
with the load that is experienced at the trailing edge. Taking into account our maximum load factor, the maximum
bending moment was calculated using a range of heights of the wing box which refers to the thickness of the trailing edge.
Using the same fiberglass cloth that will be used to wrap the wings, the yield stress was compared to the maximum
bending stress calculated for the various heights. Below displays the results of the limit to how thick the trailing edge must
be.
Table 5.4: Trailing Edge Thickness Results Boom Box Analysis
The boom holder analysis was somewhat the most important analysis that we did. All the tail bending moment and the
wing bending moment will concentrate into this piece. To ensure the structural integrity, only the carbon fiber square tube
J =
, S = 5.2 , C = 0.766 ft
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was sturdy enough to withstand all the forces. The following figure shows how the reaction forces will affect the boom
holder.
Figure 5.5: Boom Box Forces
Using the previously calculated reaction forces from the Boom analysis and the wing analysis, Rb1 and Rb2 are calculated
for the spars analysis.
Spars
Using the results from the previous analysis, the force on the spar was calculated. Using this reaction force that contains
all the major forces (tail bending & wing bending moment), the distance that the spar needs to be inserted into the fuselage
was calculated. Using the maximum bending moment equation, we were able to find the minimum distance for those that
will take 5 G load. The results informed us that the minimum distance the spar needs to be inserted into the fuselage is 2
inches.
Fuselage
The fuselage is made out of 6, ¼ inch birch plywood which will take all the moment forces. The fuselage analysis was
separated into two parts. Using the following figure, the A & B analysis which are side plates that holds the spars together,
and C analysis which the front and rear plate that holds the side plates.
Max bending stress [psi] Yield stress [psi]
Fuselage Plate C 7.5e3 9.0e3
Figure 5.6: Fuselage Plate Stress
The A and B analyses used the reaction forces coming from the spar and analyzes how much force it will transfers to the
front and rear plate. Using the value for those forces, the analysis of plate C was conducted to see whether the plywood
would break. Using the same bending stress equation from Appendix B.3, the maximum stress that the rear plates on the
fuselage will experience were found to be less than the yield stress of the plywood. With these results, we can confirm that
our fuselage will not fail at any instance during flight from the maximum loads.
2.2 ” 2.2 ” 4.6 ” 2 ”
Boom holder
Where boom inserted
21
Assembly of Major Aircraft Components
The RPA is split into 7 major components:
• Tail
• Two Fuselage Sections
• Four Wing Sections
These components can be seen in the figure below where the entire aircraft is assembled. The configuration of how each
main component is fixed together is discussed below, and has been simplified enough to where the assembly time
requirement of 10 minutes will be met. Each piece that can detach from the wing is assembled in the box as shown below,
which allows our aircraft for easy transport and quick assembly.
Figure 5.7: Aircraft Assembled In & Out of Box
The wings are secured to the main section of the fuselage using carbon fiber tube spars onto which the wings will slide on.
The spars are connected to the fuselage using hairpin cotter pins. The wings sections are connected to each other using flat
brackets and the inner wing is connected to the fuselage using an L bracket.
The tail is connected to mounts (boom boxes) located on the inner wings by two booms that are secured in place using a
custom made clevis-style pin. The booms are connected to the tail using the same style pins that get secured to a cap with
a pin hole onto which the boom slides, which is also glued to a tail spar. The front section of the fuselage is connected to
the main fuselage by a square boom that is pinned in place using a custom made clevis style pin.
Conclusion
Overall, each structural analysis that was discussed above proves that our aircraft will confidently be able to withstand any
load it may experience during its mission. The materials that were selected were based off of these analyses that would
meet the criteria will still minimizing the aircraft weight. The size and layout of each element of our aircraft has been
designed to meet the needs of the other discipline teams to guarantee that our RPA will complete the mission in one piece
and at an acceptable performance.
22
6. Propulsion Overview
The purpose of this section is to identify the key constraints, to list the assumptions made, and to summarize the decisions
made during the iterative design procedure. All of these items are important in understanding why each individual system
component was chosen. Once the finalized system is selected, important performance parameters will be discussed to
prove mission worthiness as outlined in the Request for Proposal (RFP).
Design Constraints & Limitations
The following constrains and limitations are required by the RFP and influence or are influenced by the propulsion system
to some degree:
Constraint Value Relates To:
Endurance 8 min Battery
Cruise Altitude 300 – 375 ft Climb Time
Takeoff Roll < 80 ft Motor/Prop
Landing Roll < 80 ft ESC
Climb Angle > 25 deg Motor/Prop
Stall Speed < 25 ft/s Thrust
Table 6.5: Constraints from RFP
As shown in Table 1 above, endurance, takeoff roll, and climb angle are very closely dependent on propulsion system
choices. An appropriate motor/propeller/battery combination must meet these constraints to satisfy the RFP requirements.
These constraints are very important in that they help ensure mission safety and ease of operation in populated areas or in
untrained hands.
The following constraints and limitations are required by the propulsion team and/or other team sections in order to satisfy
non-RFP requirements. They are important in that they help ensure that the aircraft will perform appropriately during any
flight condition and install some safety factors to the design.
Constraint Value Related To:
Propeller Diameter < 13” Boom Separation
Max Motor Power > 110 Watt/lb Industry Trends
Battery Capacity 75% of Total Endurance
Loiter P/W > 45 Watt/lb Industry/Endurance
Takeoff P/W > 100 Watt/lb Industry/Endurance
Table 6.6: Non-RFP Constraints
As shown in Table 2 above, propeller diameter and motor power restrictions significantly limit propulsion component
choices. Safety precautions have to be included in the battery choice in order to account for cold weather losses and safe
operation limits. Power-to-weight ratios are another important constraint that guarantees the aircraft will perform
adequately during flight and will be discussed in more detail in Section 3.
Assumptions & Design Variables
The following figure represents the major inputs that influence the propulsion design process and the major outputs that
affect the decisions of propulsion components.
23
Figure 6.8: Major Inputs and Outputs of Propulsion Design Process
As shown in Figure 1 above, physical properties like aircraft weight, wing area, velocity, and propeller geometry have a
massive effect on the thrust and power requirements as well as system efficiencies. There are other inputs that don’t
necessarily relate directly to propulsion that are grouped under the “sub-inputs” category.
As outlined in Section 2 previously, Power-to-Weight ratios are very important constraints that help ensure flight
performance. These constraints are not set in stone; rather they come from careful assumptions that follow industry trends
and recommendations. Those assumptions are as follows:
1. Stressful maneuvers such as takeoff and climbing need a minimum 100 watts of power per 1 pound of aircraft
weight to be successful.
2. Level flight and slight turns need much less power at a minimum of 45 watts per pound.
These assumptions attempt to provide adequate endurance to meet the RFP constraints while not sacrificing performance
for stressful mission segments.
Iterative Design Procedure
The following figure highlights the general process taken to select the propulsion system.
24
Figure 6.9: Propulsion System Design Process
As shown in Figure 2 above, the first component selected was the motor. Several considerations were taken into account
including the constraints outlined in Section 1 and industry trends for appropriate power ratios highlighted in Section 1
and explained in Section 3.
Once a motor was selected, design code was used iteratively alongside manufacturer recommendations to select a
propeller that matches well with the selected motor. Too small of a propeller wouldn’t be able to absorb enough power
from the motor while too large of a propeller would take too much power to generate the thrust needed.
With the motor and propeller combination selected, more code was iterated to determine if the combination satisfied the
thrust and power output requirements while simultaneously providing enough endurance to complete the mission.
Once a combination was proven effective, the required battery capacity was used to select an appropriate battery for the
system. It had to be able to provide enough volts and amperage to satisfy the power requirements but still last long
enough for the mission. After the battery was selected, it was a simple matter of selecting a quality electric speed
controller to handle the amperage draw from the battery during extreme conditions.
The results of this design procedure are shown below in the propulsion system summary in Section 5. Other relevant
figures from the propulsion design procedure are shown in the Propulsion Appendix Sections D-F.
25
Propulsion System Summary
The following tables highlight the relevant details for each of the propulsion system components, as well as the entire
system as a whole.
Electric Speed
Controller
Turnigy Super Brain
Amp Rating 60A
Battery Type LiPo
Range 2S - 6S
Burst Current 70A
Weight 0.11 lb
Electric Motor
Great Planes RimFire
Weight 0.44 lb
Max Constant
Power
925 W
Max Burst Power 1480 W
Rated Current 50A
Burst Current 80A
kV 800
Propeller
APC Thin Electric
Diameter 12 in
Pitch 6 in
Weight 0.06 lb
Efficiency 76%
Battery
Turnigy 4S LiPo
Type LiPo
# Cells 4S
Voltage 14.8 V
Capacity 4000 mAh
Constant Discharge 30 C
Burst Discharge 40 C
Weight 0.94 lb
Table 6.7: Propulsion System Component Specifications
As shown in Table 3 above, the motor chosen is slightly overpowered to ensure it can perform in any conditions. It has
enough constant power to satisfy the power ratio constraints for maximum aircraft weight of 9 lbs. To view these power
calculations, please see the Propulsion Appendix Section B.
A 4-cell battery was chosen over a 3-cell battery due to amperage and voltage requirements. The motor would need to
draw too many amps from the 3-cell battery due to the lower voltage.
The propeller is a very common and standard APC propeller with good efficiency. The 12 inch diameter was chosen to
maximize thrust produced while still allowing clearance with the 13 inch boom constraint. A pitch of 6 inches was used to
provide acceptable top speed while not absorbing too much power.
The speed controller was chosen simply due to high quality and plenty of allowable amperage drawing. It is also
programmable which makes it possible to install safe operating limits on the propulsion system.
26
System Performance and Worthiness
This subsection will highlight system performance including thrust, endurance, and efficiencies. The following table
shows the various thrust values created by the propeller at different flight segments and velocities. The upper limit of
RPM was set at 11000 which is based on the kV (RPM/volt) value of 800 specified by the motor.
Flight Segment Flight Speed Minimum Thrust Maximum
Thrust
Max T/W
Takeoff 30 ft/s 0.8 lbs 5.4 lbs 0.77
Climb 35 ft/s 0.6 lbs 5.2 lbs 0.74
Cruise 40 ft/s 0.5 lbs 5.0 lbs 0.71
Table 6.8: Thrust Produced During Flight Segments
As shown in Table 4 above, the propulsion system is capable of producing a thrust-to-weight ratio of > 0.7 for all flight
segments which the aircraft very capable in performing stressful maneuvers according to industry trends. For a complete
graph of thrust values and calculations, please see Propulsion Appendix Section A.
Climb Angle 35.4 deg
Climb Time (to 375 ft) 18.5 sec
Table 6.9: Takeoff and Climb Performance
Table 5 above shows the calculated takeoff and climb performance of the aircraft, assuming the motor operates at 100%
throttle. The climb angle easily surpasses the constraint of 25 degrees and the time to altitude of 18.5 seconds fits well
within the estimated mission time segments detailed in the Propulsion Appendix Section B.
Overall Specifications
Weight 1.55 lb
System Efficiency 35%
Endurance 8.4 min
Cost $206.70
Table 6.6: Overall Specification and Performance of Propulsion System
Table 6 above shows the overall specifications of the propulsion system. System efficiency is adequate at 35%.
Endurance was calculated to be approximately 8.4 minutes. Even though this is close to the 8 minute constraint, many
safety factors were taken into consideration that might not be completely necessary. The cost is very high at 50% of the
entire budget. This was necessary in order to have quality, reliable parts. Details about system efficiency and endurance
can be found in Propulsion Appendix Sections A and B.
Conclusion
Overall, the propulsion team is confident that the propulsion system chosen is capable of accomplishing the mission and
meeting all constraints outlined by the RFP. All performance constraints are satisfied and the aircraft is able to meet the 8
minute endurance requirement. For any other information regarding the propulsion system that wasn’t detailed
previously, please reference the Propulsion Appendix Sections A-F at the end of the report.
27
Dynamics & Controls – 7 The dynamics and controls for the RPA designed by Team 1 is designed based on the characteristics of the aerodynamics
and structures sub-teams. The control system was designed with the most input by the CAD designs. The structures and
aerodynamics teams supplied the CAD design with parameters and the controls adjusted the CAD for stability. These
values are all required by the code provided, FlatEarth. The variables, values, and sources are as follows:
variable value source
Center of gravity from nose 17.1 in Structures/CAD
Neutral point 19.135 in Aerodynamics
Aspect ratio of main wing 6.3636 Aerodynamics
Aspect ratio of horizontal tail 2.25 Aerodynamics
Propeller efficiency 0.65 propulsion
Moment of inertia (Ixx) 0.0689 slug-ft^2 Structures/CAD
Moment of inertia (Iyy) 0.2968 slug-ft^2 Structures/CAD
Moment of inertia (Izz) 0.3641 slug-ft^2 Structures/CAD
Body side area 0.7986 ft^2 Aerodynamics
Surface area of vertical tail 0.7778 ft^2 Aerodynamics
Nose to main wing LE 15.45 in Structures/CAD
Nose to horizontal tail LE 44.45 in Structures/CAD
Table 7.10: Input variables, values, and sources Sizing
The process for the design of the dynamics and controls starts with the sizing of the aft stabilizing aerodynamics. This is
done through both class 1 and class 2 sizing. The class 1 sizing is the volume method by which using historical volume
coefficients of aircrafts, the surface area of the aft stabilizers can be determined. The class 1 sizing was performed through
the following equations:
The class 1 sizing was then performed to determine validity. It was determined that the volume coefficient of 0.092903
was reasonable for the horizontal tail. In addition, the volume coefficient for the vertical tail is 0.0632257. These arbitrary
surface areas were determined through the recommendations provided by Raymer in addition to the relative size of the
overall aircraft. Raymer recommends various percentages of the aircraft surfaces be dedicated to the different control
surfaces as follows with the actual values:
Raymer Surface Chord Control Surface Chord
Aileron Chord 15%-20% 11 inch 3 inch
Elevator Chord 25%-50% 8 inch 3 inch
Rudder Chord 25%-50% 7 inch 2 inch
Surface Span Control Surface Span
Aileron Span 50%-90% 82 inch 32 inch
Elevator Span 90% 19 inch 18 inch
Rudder Span 90% 8 inch 7 inch
Table 7.11: Raymer Percentage Recommendations and actual sizing for control surfaces
With this sizing data, the dynamics and controls will be able to determine the appropriate surface area the RPA control
surfaces.
28
The next step in the determination of the controls is class 2 sizing. This process is a second, higher order method to
determine the surface area of the aerodynamic surfaces. This is done by plotting both the neutral point and the center of
gravity as a function of the surface area of the rear horizontal tail. This provides two exponential lines. The distance
between every point on the two lines is measured as a percentage difference. This percent difference is equal to the static
margin of the aircraft.
This is the difference between the neutral point of the aircraft and the center of gravity of the aircraft divided by the wing
chord. Raymer suggests a range of 10% to 20%. Our aircraft is currently at a static margin on 18.23%. This provides for
enough stability and without causing instabilities.
These two lines plotted together and displaying the static margins of 5% and 50% on the left and right respectively is:
Longitudinal X-Plot
Figure 7.10: Class 2 sizing Longitudinal X-plot to determine the horizontal tail surface area
This result is very favorable. It confirms both the class 1 and the arbitrary sizing done previously. This minimum value is
approximately 142 𝑖𝑛2. Our rear horizontal tail is currently at 144𝑖𝑛2. This is ideal because it is above the minimum value
of the static margin. The process is repeated for the rear vertical tail. It however, does not rely on the static margin, center
of gravity, or the neutral point. The vertical tail sizing is determined by the yawing moment which is experienced by the
aircraft in simulation.
This determines that the vertical tail should have a rough surface area of 369𝑖𝑛2. This compares favorably to both the class
1 sizing and the sizing done by aircraft scale for the arbitrary value was set at 338𝑖𝑛2. The output plot is as follows:
Directional X-Plot
29
Figure 7.11: Class 2 sizing Longitudinal X-plot to determine the vertical tail surface area
The Directional x-plot determines the vertical tail surface area. The goal is a directional stability of 0.001. Therefore, the
red line is plotted at that point and intersects with the 𝐶𝑛𝛽 line.
This aircraft has the ailerons as far to the outside edge of the wing as possible for controllability and to accommodate for
the split in the wing due to it being constructed in multiple sections for storage. The rudder extends the entire height of the
vertical tail and is constructed as an independent piece. The elevator is much like the rudder, being constructed as the
entire width of the horizontal tail and as an independent piece.
In addition to the aircraft being classified in multiple categories, the RPA does have some limitations. The main
limitations are the gains available to the servos for feedback and the deflection that the servos are able to provide to the
control surfaces. The gain margins can be designed to be within the limits. The deflection however, is determined both
from practical measurements and from historical data. Team 1 is expecting approximately 15 degrees of travel in either
direction for deflection of control surfaces from each servo.
Procedure:
The first thing to do after all the classifications and sizing is completed it to run the simulation for stability determined
from the root locus plot. The codes provided take the inputs through multiple steps to evaluate the inputs, compute
additional variables, and to untimely plot the transfer function. The steps of the FlatEarth program are as follows:
1. Mathematical model
a. input and validate the provided values
2. Trim
a. trim the model and develops initial conditions for simulations
3. Simulate trim
a. simulates the determined trim values
4. Simulate Perturbations
a. simulate the aircraft in all six degrees of freedom
5. Linearize and Overplot
a. Perform linear simulation
b. Overplot nonlinear results
c. Divide out the lateral and longitudinal systems
After the longitudinal and lateral systems are split, two different steps can be run to determine the transfer functions for
the roll, pitch, and yaw in the respective directions.
30
6. Longitudinal Design
a. Determines natural frequencies, plots, damping ratios
7. Lateral Design
a. Determines natural frequencies, plots, damping ratios
When the code completes the results are open loop transfer functions. The poles, damping ratios, and natural frequencies
are also determined. The steps which succeed the FlatEarth code is as follows:
1. Plot root locus
a. Plot open loop transfer functions in SISOTOOL for the best available K gain value to be determined that
will provide for stability
2. Simplify transfer functions
a. The transfer functions for each mode can be simplified into the respective flight characteristics through
partial fractions
3. Plot closed loop root locus from the partial fractions transfer functions
4. Plot step response from partial fractions transfer function
5. Plot impulse response from the original open loop transfer function
When plotting root locus, a major distinction needs to be made between the open loop and closed loop transfer functions.
The open loop transfer function is one that has no compensation or feedback characteristics and is allowed to run. The
closed loop system has a feedback controller which enables the system to correct errors that occur. Open loop systems are
therefore applicable when no significant compensation is required. In other cases, when compensation is required due to
the location of roots, a closed loop is required. The root locus is initially plotted from the open loop transfer function. The
K gain compensator used in the feedback control is initially determined from the open loop root locus as one of the real
values plotted on the break in/break away lines.
The root locus itself is determined from the poles and zeros of the transfer function which is being plotted. The real values
of the zeros are plotted on the real (x) axis and the imaginary components are plotted on the imaginary (y) axis. The shape
of the graph itself is determined through the asymptotes of the poles and the break in/break away points on the real axis.
The locations of the poles directly impact the step and impulse responses of the system. The poles determine the decay
pattern of the system. In the case of the denominator of the transfer functions, when the poles are negative the responses
will experience a decaying oscillation. The more negative the pole, the faster the decay. When the poles are on the real
axis, the system is inherently stable. However, if the poles are positive, the system will increase. If the poles are at or on
the axis, the response will oscillate but will never settle.
When the K gain compensator value increases the closed loop poles will move along the paths produced by the root locus
of the open loop transfer function. The poles move towards each other at the break in/break away point. At that point the
poles travel together towards ∞ in either the imaginary plane or the real plane depending on the transfer function.
The root locus serves a major purpose other than just providing K compensator values to compensate the open loop into a
closed loop transfer function. The root locus helps to determine the stability and handling characteristics of the RPA itself.
If the root locus has poles in the right plane, the system will be inherently unstable. This information can only be
determined from the root locus. The determined stability and handing criterion are compared to the Phugoid, Dutch roll,
and short period tables to determine validity.
31
Figure 7.12: Root Locus Example
Stability Analysis Yaw
Using SISOTOOL, the K compensator is determined to ensure a stable solution. A compensator value of -10.859 is
reasonable and within the ability of the flight gyro to be used. The simplified compensated transfer function is as follows:
Equation 7.1
Equation 7.2
This closed loop root locus has no additional static gain.
-20 -15 -10 -5 0 5
-30
-20
-10
0
10
20
30
Yaw rate feedback to the rudder: Stabilizing feedback
Real Axis (seconds -1 )
32
Figure 7.13: closed loop root locus
Figure 7.14: closed loop yaw impulse response
As the impulse response displays, the response settles at zero within 4 seconds. This means that the stabilizing feedback is
equal to the destabilizing feedback produced. The stability is confirmed through the poles and damping ratios compared to
the Dutch roll stability criterion.
Poles Natural Frequencies Damping Ratios
-20±23.452i 3.909 0.313
-1.224±3.713i
Table 7.12: natural frequencies, damping ratios of closed loop yaw transfer function
Dutch Roll Mode
Category Class zmin
A I-IV 0.19
Level 1 B I 0.08
C I,II,IV 0.08
Table 7.13: Stability criterion for Dutch roll mode
The damping ratio of 0.313 is well above the minimum damping ratio of 0.08 for level 1, category B, class 1 flight. This
results in a stable yawing moment and a controllable flight characteristic.
Pitch
Using SISOTOOL, the K compensator is determined to ensure a stable solution. A compensator value of –15.229 is
reasonable and within the ability of the flight gyro to be used. The compensated open loop and simplified compensated
transfer function is as follows:
Equation 7.3:
Equation 7.4
This closed loop root locus has no additional static gain.
33
Figure 7.15: closed loop pitch root locus
Figure 7.16: closed loop pitch impulse response
As the impulse response displays, the response does not settle immediately. This means that the stabilizing feedback is
less than the destabilizing feedback. This decay though is due to the poles being closer to the imaginary axis. The fact
though that the oscillations have a period of 4 seconds and the maximum amplitude is 0.001 makes this a reasonable plot.
Poles Natural Frequencies Damping Ratios
-20.188±23.583i 8.844 0.807
-6.952±5.097i 30.822 0.649
Table 7.14: closed loop pitch transfer function natural frequencies and damping ratios
Phugoi d Mode
Level 1 z>0.04
Level 2 z>0
-25 -20 -15 -10 -5 0 5
-30
-20
-10
0
10
20
30
Pitch rate feedback to the elevator: Stabilizing feedback
Real Axis (seconds -1 )
34
Table 7.15: Phugoid mode stability criterion
The damping ratios of 0.807 and 0.649 are well above the minimum damping ratio of 0.04 for level 1, flight. This results
in a stable pitching moment and a controllable flight characteristic.
Roll
Using SISOTOOL, the K compensator is determined to ensure a stable solution. However, due to roll being inherently
unstable, the SISOTOOL is not able to compensate this mode. The simplified compensated transfer function for the short
period is as follows:
Equation 7.5
Equation 7.6
This closed loop root locus has no additional static gain.
Figure 7.17: closed loop roll root locus
-50 -40 -30 -20 -10 0
-30
-20
-10
0
10
20
30
40
Roll rate feedback to the aileron: Stabilizing feedback
Real Axis (seconds -1 )
35
Figure 7.18: closed loop roll impulse response
As the impulse response displays, the response does not settle immediately. This means that the stabilizing feedback is
less than the destabilizing feedback. This response though is acceptable because the roll is inherently unstable and the roll
is a short time mode. Since the roll impulse response is stable for multiple seconds at a time, the mode will remain stable
for the duration of the maneuver.
Poles Natural Frequencies Damping Ratios
-21.299±22.448i 39.67 1
-37.070
Table 7.16: closed loop roll natural frequencies and damping ratios
Short Period Mode
Category A&C Cate gory B
zmin zmax zmin Zmax
Level 1 0.35 1.30 0.30 2.00
Level 2 0.25 2.00 0.20 2.00
Level 3 0.15 -- 0.15 --
Table 7.17: short period stability criterion
The damping ratio of 1 is well above the minimum damping ratio of 0.3 and still below the maximum of 2.0 for level 1,
category B flight. This results in a stable rolling moment and a controllable flight characteristic.
Conclusion
In conclusion, using the class 1 and class 2 sizing methods in conjunction with the structures and aerodynamics teams to
determine a good static margin, the aircraft is able to produce dynamics that are reasonable and controllable according to
stability criterion for the different modes.
In the longitudinal direction, the pitch has poles that are close to the imaginary axis. This leads to a long settling time for
the decay of the response. However, since that amplitude is below the movement response of the servos being used, the
motions are reasonable and we are satisfied in the controllability of the aircraft in this direction. If modifications need to
be made to improve stability there are options to consider including elevator and flap deflection, increasing the fuselage
length, and moving the payload to provide a more favorable center of gravity.
The lateral stability of the aircraft is proven by the root loci and the stability criterion of both the Dutch roll and the short
period motions. The roll is inherently an unstable mode yet it has a small amplitude and a period of over 1 second. This
will enable the aircraft to be able to complete all maneuvers we have assigned it in the mission parameters. The yaw of the
aircraft is the most stable movement of the aircraft. This is due to the tail sizing to be within the class 2 sizing and the
fuselage wetted area. Both of the lateral motions have damping ratios above the minimum values of the stability criterion
and in the case of the short period, also below the maximum value.
36
Appendix A
Aerodynamics:
Database references:
Table A1
Wing Profiles cl/cd max cl max approximate alpha cl max (approximate)
e385-il 68.8 1.57 13.0
AH 79-100 68.8 1.66 8.0
E216 68.8 1.55 13.0
FX 63-100 67.7 1.56 11.0
FX 63-120 67.1 1.65 14.0
SG6043 66.5 1.65 14.0
fx 63-110 66.1 1.58 12.0
s1210 66.0 2.00 12.0
AH 79-100 B 65.9 1.65 8.0
OAF095 AIRFOIL 65.7 1.43 10.0
s4022 65.1 1.45 12.5
FX 63-110 65.1 1.60 12.0
MH115 64.9 1.61 12.0
e66-il 64.6 1.40 12.0
FX 63-137 64.5 1.70 15.4
GOE 195 64.4 1.53 12.0
GOE 500 64.4 1.58 12.5
PSU 94-097 64.1 1.40 12.0
E64 64 1.30 10.0
WORTMANN 63.9 1.70 15.0
NACA6409 63.7 1.50 12.5
GOE 225 63.5 1.86 12.0
GOE 63 63.3 1.70 13.0
GOE 233 63.1 1.75 10.0
GOE 431 62.8 1.70 10.0
GOE 304 62 1.62 14.0
s1223 59.2 2.10 11.0
37
Source 1 - http://airfoiltools.com/search/index - Database of airfoils sorted for max lift coefficient to drag coefficient.
Source 2 - http://m-selig.ae.illinois.edu/uiuc_lsat/Low-Speed-Airfoil-Data-V1.pdf - An article on low speed high lift
airfoil.
MATLAB codes for solving equations
Design Considerations – A MATLAB code has been written which is intended to calculate basic aerodynamic parameters
and the static margin for the aircraft. It was based upon hand calculations in the back of the textbook and the referenced
equations from the notes.
Design procedure- MATLAB Code
Basic Aerodynamic Parameters
Calculating 𝑪𝑴 derivative due to elevator deflection
Equation 1A
Where 𝜂: 𝑡𝑎𝑖𝑙 𝑒𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑐𝑦
Equation 2A
𝐿𝑖𝑓𝑡 𝑐𝑢𝑟𝑣𝑒 𝑠𝑙𝑜𝑝𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑡𝑎𝑖𝑙
Calculating 𝑪𝑳 derivative due to elevator deflection
CLde = etah*(Sh/S)*ElevEff Equation 3A
Equation 4A
Equation 5A
𝜏 𝑖𝑠 𝑑𝑒𝑡𝑒𝑟𝑚𝑖𝑛𝑒𝑑 𝑓𝑟𝑜𝑚 𝑡ℎ𝑒 𝑐𝑢𝑟𝑣𝑒 𝑏𝑒𝑙𝑜𝑤.
Figure 1A - 𝜏
Stability - MATLAB - Calculating Neutral Point
38
Equation 6A
𝑋̅̅̅ 𝑎𝑐 ℎ :𝑝𝑜𝑠𝑖𝑡𝑖𝑜𝑛 𝑜𝑓 𝑎. 𝑐 𝑜𝑓 ℎ𝑜𝑟𝑖𝑧𝑜𝑛𝑡𝑎𝑙 𝑡𝑎𝑖𝑙
Equation 7A
Equation 8A
is determined from the curve on P.618
: Fuselage maximum width
: Fuselage maximum length
Discussion – The MATLAB code produces accurate results when checked with hand calculations and is based upon a
sample calculation from the textbook. The values outputted by the MATLAB code have been trusted because of this.
Fuselage Parasite Drag Calculation
Where is length diameter ratio of fuselage
Equation 9A
Equation 10A
For Turbulent flow
Equation 11A
Where ≈ 0
Equation 12A
Assuming M≈ 0 the relationship above is reduced to
Equation 13A
Where R is the Reynolds number of the fuselage
Reynolds number we have used is that of the chord which made our calculation inaccurate
Equation 14A
39
Appendix B Structures:
i. Maximum Bending Moment
ii. Wing Tip Deflection Angle
iii. Composite Wing Bending Stress Analysis
iv. Boom support
maximum bending moment =
P = tail lift force = length of boom holder to the tail edge
E = young’s modulus I = Moment of inertia
When, M = maximum bending moment E = young’s modulus of the material I = inertia of each materia l
40
ℎ1 = 0.038” ℎ2 =
0.15 − ℎ1 = 0.112"
v. Landing Gear
41
𝑉 𝑛𝑜𝑠𝑒 = 𝑊 𝑎 + 𝑏
𝑓 ∙ 𝜇 ∙ 𝑎 ∙ ℎ 𝑐𝑔 𝑎 + 𝑏 + 𝜇 + ℎ 𝑐𝑔
𝑉 𝑚𝑎𝑖𝑛 = 𝑊 − 𝑉 𝑛𝑜𝑠𝑒
42
vi. Trailing Edge
vii. Structures Summary
L
A B
w
𝑀 𝑚𝑎𝑥 = 𝑤 𝐿
2
8
𝛿 𝑚𝑎𝑥 = 5 𝑤 𝐿
4
384 𝐸𝐼
34 ” 3 ”
h TOP VIEW Cross
Section
43
Aircraft Geometry Value Units
Wing area (ft^2) 5.2 ft^2
Main wing chord 11 inches
Main wing semi-span 34 inches
Horizontal tail full span 18 inches
Horizontal tail chord 8 inches
Vertical tail root chord 8 inches
Vertical tail tip chord 6 inches
Vertical tail height 7 inches
Structure Material
boom carbon fiber tube
wing foam with fiberglass fabric, plywood ribs
wing spar carbon fiber tube
fuselage plywood
tail foam core, plywood ribs
44
viii. Weight &Center of Gravity Summary
Weight
Center of Gravity Location
Component X Y Z
[lb] [kg] [in] [cm] [in] [cm] [in] [cm]
Front Fuselage 2.13 0.97 7.17 18.21 -0.19 -0.47 0.02 0.04
Main Fuselage 1.06 0.48 22.17 56.31 -0.57 -1.46 0.00 0.00
Right Wing 0.47 0.21 19.87 50.47 0.06 0.14 16.90 42.93
Left Wing 0.47 0.21 19.87 50.47 0.06 0.14 -16.90 -42.93
Tail 0.15 0.07 48.38 122.89 1.56 3.96 0.00 0.00
Right Boom 0.10 0.04 35.51 90.20 0.04 0.10 7.29 18.52
Left Boom 0.10 0.04 35.51 90.20 0.04 0.10 -7.29 -18.52
TOTAL 4.47 2.03 188.48 478.74 1.00 2.53 0.02 0.05
C.G. 15.97 40.56 -0.16 -0.40 0.01 0.02
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Appendix C
Dynamics & Controls:
The next step is to determine the classification of the aircraft itself to identify the design constraints and performance
comparisons. These identifications will be relevant to determine the stability of the aircraft.
Table 18: Flying quality levels to determine classification
The RPA which is being designed by Team 1 will be a Level 1 aircraft. This is because the aircraft is stable and will
manage the mission appropriatley. The aircraft will be designed to fly with ease for it is in a civilian setting.
Table 19: Class cases to determine classifications The
RPA will be in the Class 1 category for simple sizing standards.
Table 20: category cases to determine classification
The RPA will fit into the Category B section because the aircraft will not have to conduct precision maneuvers or rapid
course corrections for the mission which has been laid out.
Equation 1C
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Equation 2C
Equation 3C
Equation 4C
Equation 5C
Equation 6C
The next step is to determine the classification of the aircraft itself to identify the design constraints and
performance comparisons. These identifications will be relevant to determine the stability of the aircraft.
47
Appendix D Propulsion
A. Thrust Calculations and Data
Figure 19: Thrust vs. Velocity at Various RPM
𝑇ℎ𝑟𝑢𝑠𝑡 = 𝐶𝑇𝜌𝑛2𝐷4 Equation 1D
Figure 3 above shows the various values of thrust that are produced with varied RPM and velocity. The data points were
calculated using the equation shown directly under Figure 3.
B. Battery and Endurance Calculations
Figure 20: endurance calculations based on amp draw and flight times
𝑃𝑜𝑤𝑒𝑟 (𝑊𝑎𝑡𝑡𝑠) = 𝑉𝑜𝑙𝑡𝑎𝑔𝑒 (𝑉) ∗ 𝐶𝑢𝑟𝑟𝑒𝑛𝑡 (𝐴) Equation 2D
48
𝐸𝑓𝑓𝑖𝑐𝑖𝑒𝑛𝑐𝑦 𝐹𝑎𝑐𝑡𝑜𝑟 = 𝐶𝑜𝑙𝑑 𝑊𝑒𝑎𝑡ℎ𝑒𝑟 (0.9) ∗ 𝑆𝑎𝑓𝑒 𝐷𝑖𝑠𝑐ℎ𝑎𝑟𝑔𝑒 𝐶𝑎𝑝𝑎𝑐𝑖𝑡𝑦 (0.8) Equation 3D
Equation 4D
Equation 5D
Figure 4 above shows the calculations to determine the battery capacity needed to accomplish the mission time constraint.
All of the main equations used are shown directly below Figure 4. The efficiency factor was determined from 10% cold
weather loss and 80% safe discharge. Endurance is calculated based on flight segment percentages and the desired
amperage draw during those segments. The desired amperage draw is based on the resulting power to weight ratios and
the constraints outlined in the propulsion section.
C. System Efficiency Calculations
𝜂𝑠𝑦𝑠𝑡𝑒𝑚 = 𝜂𝑜𝑝𝑒𝑟𝑎𝑡𝑖𝑛𝑔 ∗ 𝜂𝑝𝑟𝑜𝑝 ∗ 𝜂𝑚𝑜𝑡𝑜𝑟 ∗ 𝜂𝑔𝑒𝑎𝑟𝑏𝑜𝑥 = (0.656) ∗ (0.768) ∗ (0.69) ∗ (1) = 35% Equation 6D
Operating efficiency is dependent on how closely the aircraft operates to minimum power velocity as shown below in
Figure 5 below. Propeller and Motor efficiencies are dependent on how closely the aircraft operates to their most efficient
RPM levels. The gearbox efficiency is 100% because the aircraft does not use a gearbox.
Figure 21: Minimum power required
D. Propeller Data
0 5 10 15 20 25 30 35 40 0
5
10
15
20
25
30
35
40
Velocity (ft/sec)
Aircraft Power required vs trim speed for a turn radius of 50 ft
Minimum power of 21.0203 ft-lbf/sec is achieved at a speed of 25 ft/sec.
The lift coefficient at this minimum power condition is 1.8054.
Operating power of 32.0271 ft-lbf/sec is required at an operating speed of 40 ft/sec The operating efficiency of your aircraft is 0.65633 The operating lift coefficient at this condition is 0.92717.
49
0 0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45
Advace ratio, J=V/(nD)
Figure 6: propeller geometry
Velocity (ft/sec)
Figure 7: Climb Performance E. Motor Data
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Figure 8: Motor performance at varied amperage
F. Constraint Diagram
0 20 40 60 80 100 120 0
200
400
600
800
1000 Motor Properties
Motor Properties
0 20 40 60 80 100 120 0
500
1000
1500
2000 Aircraft climbing at 35 ft/sec will consume 34.8 amps of current.
0 20 40 60 80 100 120 0
0.2
0.4
0.6
0.8
1
Current (amp)
Aircraft climbing at 35 ft/sec will consume 34.8 amps of current. Motor efficiency at climb is 0.8.
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Figure 9: Constraint Diagram for design space
