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AE413 FINAL REPORT: THE GLIDER PROJECT Date of Submission: May 1, 2006 by _______________________________________ Harsh Menon [email protected] _______________________________________ Brian Pollock [email protected] Submitted to: Dr. Jeff Ashworth Aerospace Engineering In Partial Fulfillment Of the Requirements Of AE 413

Stability of Balsa Wood Glider

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Page 1: Stability of Balsa Wood Glider

AE413 FINAL REPORT: THE GLIDER PROJECT

Date of Submission:May 1, 2006

by

_______________________________________Harsh Menon

[email protected]

_______________________________________Brian Pollock

[email protected]

Submitted to:Dr. Jeff Ashworth

Aerospace Engineering

In Partial FulfillmentOf the Requirements

OfAE 413

Aircraft Stability and ControlSpring 2006

Embry-Riddle Aeronautical UniversityPrescott, Arizona

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ABSTRACT

The glider configuration chosen for this project was a conventional high-wing, T-tail configuration. This configuration was based on the configuration of common sailplanes. The design was created using several assumptions to provide a reference base if the design and configuration were to be altered. An initial model was constructed and substantial flight testing was performed to determine the most efficient configuration for the glider regarding wing location, incidence angles, and added weight. Once a configuration was chosen, a second model was constructed, exactly replicating the original model. The final model was flown a few times before distance was recorded as to prevent damage. Three flights were flown for distance, and an average distance of 111 feet was achieved.

This report details the design, construction, and flight trials for a conventional high-wing, T-tail glider. It discusses the process of why the design of the glider was chosen, along with the assumptions made initially to begin testing. An analysis on the design is presented, including calculations of the mean aerodynamic center, center of gravity, static margin, and trim velocity. Results of the final fly-off are given, including discussion on the stability of the glider during the three flights and average range achieved over three flights during the final fly-off.

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TABLE OF CONTENTS

ABSTRACT............................................................................................................ I

LIST OF TABLES................................................................................................ III

LIST OF FIGURES.............................................................................................. IV

LIST OF SYMBOLS.............................................................................................V

LIST OF EQUATIONS........................................................................................VII

1.0 INTRODUCTION.............................................................................................1

2.0 DESIGN AND TESTING.................................................................................2

3.0 ANALYSIS......................................................................................................4

CALCULATING THE STATIC MARGIN...............................................................6

CALCULATING THE TRIM SPEED.....................................................................8

4.0 CONCLUSION AND RECOMMENDATIONS...............................................14

5.0 REFERENCES..............................................................................................15

6.0 ACKNOWLEDGEMENTS.............................................................................16

7.0 APPENDIX I: MATLAB M-FILE USED FOR CALCULATIONS...................17

8.0 APPENDIX I: OUTPUTS FROM MATLAB M-FILE USED FOR CALCULATIONS.................................................................................................20

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LIST OF TABLES

Table 3.1: Final Design Parameters. ................................................................................................................. 4

Table 3.2: Assumed Parameters for Static Margin and Trim Speed. ................................................................ 5

Table 3.3: Calculating the center of gravity of the aircraft without clay. ......................................................... 7

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LIST OF FIGURES

Figure 3.1: Vertical Tail. ................................................................................................................................... 5

Figure 3.2: Horizontal Tail. .............................................................................................................................. 5

Figure 3.3: Cm vs CL curve. ............................................................................................................................... 8

Figure 3.4: Summing the moments about the c.g. with α=0, ih=0. .................................................................. 9

Figure 3.5: Summing the moments about the c.g. with α =0. ......................................................................... 11

Figure 3.6: Summing forces on the glider ...................................................................................................... 12

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LIST OF SYMBOLS

AR Aspect Ratio non-dimensional

SM Static Margin non-dimensional

S Wing Planform Area inches2

M Pitching Moment lbf-in

W Weight lbf

V Volume inches3

e Span Efficiency Factor non-dimensional

m Mass slugs

q Dynamic Pressure lbf/inches2

v Velocity ft/s

Aerodynamic Center inches

Aerodynamic Center non-dimensional

Location of Center of Gravity non-dimensional

ρ Density slugs/ft3

ηh Efficiency of the Horizontal non-dimensionalTail

dε/dα Dynamic Pressure Ratio non-dimensional

Lift-Curve Slope for an airfoil (degree)-1

Lift-Curve Slope (degree)-1

Lift-Coefficient non-dimensional

Pitching Moment Coefficient (degree)-1

Subscripts:

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H Horizontal Tail

V Vertical Tail

ih Incidence Angle on Horizontal Tail

h Horizontal Tail

wf Wing-Fuselage

0 Coefficient with all other terms 0

α Angle of Attack

aircraft Coefficient for the entire aircraft

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LIST OF EQUATIONS

Equation 3.1

Equation 3.2

Equation 3.3

Equation 3.4

Equation 3.5

Equation 3.6

Equation 3.7

SM = Equation 3.8

Equation 3.9

Equation 3.10

Equation 3.11

Equation 3.12

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Equation 3.13

Equation 3.14

Equation 3.15

Equation 3.16

Equation 3.17

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1.0 INTRODUCTION

The goal of this project was to design, build, and fly a statically stable glider constructed from balsa wood using principles of stability and control learned throughout the semester. Design constraints for the glider were defined as follows:

- maximum wing span of 18 inches- maximum chord length of 3 inches- maximum fuselage length of 18 inches- wing camber allowed- conventional, canard, or three-surface designs allowed- must utilized supplied balsa wood (wing surface: 3 x 3/32 x 36-in; fuselage: 1/2 x 3/16

x 36-in)- three competition launches allowed

Beyond those dimension constraints, overall design of the glider was left to the imagination of the student groups. After choosing a design for the glider, quantitative analysis was to be performed on the design to determine certain stability factors. The most important values to be solved for were the static margin and trim velocity of the glider. These values provided a reference of the stability of the glider and a velocity at which it should be released at for steady, level flight.

Glider designs were put to the test in a final fly-off in which each glider was flown three times. Distance was measured and an average of the three flights was recorded. The fly-off was held in the Eagle Gym with measuring tape running the length of the gym. Distance was measured from the point of release to the point at which the glider made initial contact with the floor. In the event that a glider flew longer than the distance of the gym floor, four feet of distance was added for every foot off the floor the glider made contact with the wall at.

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2.0 DESIGN AND TESTING

Design of the glider began with considerations of the wing. For simplicity, a rectangular wing with no dihedral was chosen to avoid design complications. Various dimensions were considered to find an efficient balance of wing area and aspect ratio. The full allowable wing area of 54-in2 was chosen in order to create the most lift, which provided for an aspect ratio of 6 for the wing. After finalizing dimensions of the wing, the recommendations of using and were followed. To model this glider after conventional gliders, a T-tail configuration was chosen for the arrangement of the horizontal and vertical stabilizers. Finally, the full allowable fuselage of 18-in was also used.

To begin flight testing, the vertical stabilizer was placed at the rear of the fuselage, with the horizontal stabilizer placed with no incidence angle so that the leading edges were flush. The wing was placed with no angle of attack roughly at the mid-point of the fuselage just to give a reference once changes were made based on flight performance. Since the glider had a negative static margin without any weight on the nose, a small amount of modeling clay was added.

After multiple tests of the glider with various wing positions, results showed that as the wing was moved forward on the fuselage, the glider’s trim velocity would decrease, and the gilder would pitch up considerably, climb and then pitch down and descend to the floor. Conversely, as the wing was moved aft on the fuselage, the glider’s trim velocity would increase, making it increasingly difficult to reach trim velocity; however, as the glider would not stall in flight, range was increased. Also, as more weight was added to the nose, the trim velocity would increase, keeping the glider in more steady flight. Eventually a wing position and weight was chosen so that the trim velocity was relatively high, thus keeping the glider from dramatically pitching up and carrying it acceptable distances.

As the glider was being released with an angle of attack, an incidence angle was added to the horizontal stabilizer and an angle of attack was added to the wing so that the glider could be release horizontally while still seeking a positive pitch attitude. The incidence angle in the horizontal stabilizer was created by sanding the top of the vertical stabilizer down by 1/32-in at the leading edge over a 1-in chord length, creating a slight incidence angle of -1.194 deg. The angle of attack in the wing was created by adding a simple balsa wood shim under the leading edge of the wing, giving an angle of attack of 2.566 deg.

In this configuration, the glider began consistently reaching distances of above 120-ft. As this design was simple and therefore relatively strong, it was chosen as the final design for the glider and another model was built using the same dimensions and locations for the final fly-off.

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A second model was constructed due to the substantial damage received by the first during flight testing. This model was an exact replica of the first, although a small amount of clay was required in order for the center of gravity to be at the same location. This dissimilar weight distribution between the two models was most likely caused by different densities in the balsa wood between the different pieces used.

Once the second model was completed, a few test flights were conducted to prove that its flight characteristics were equal to that of the first glider. After showing that its flight characteristics were indeed equal, the decision was made to record distances.

Upon release during the first flight, the glider began a slow left bank almost immediately. This was most likely caused by releasing the glider in a banked condition. This turn continued through the whole flight, and the glider made contact with the side wall, about seven feet above the ground. However, since the glider did not make first contact with the back wall, only the distance along the floor from release to contact was measured, and the flight distance was given as 89 feet.

The second and third flights were more successful than the first, with the glider flying in steady, level flight. In both flights, the glider flew more than the distance of the gym and made contact with the wall eight feet above the floor, resulting in flight distances of 122 feet.

Based on the distances achieved by the glider over the three flights, the average distance the glider flew was calculated as 111 feet.

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3.0 ANALYSIS

The first step of the analysis process was making certain assumptions. All the distances were measured from the nose of the glider. Our glider design parameters are listed in the table below:

Parameter Assumed ValueB (Wing Span) 18 inches

c (Chord Length) 3 inchesλ (Taper Ratio) 1

Length of Fuselage 18 inchesLocation of Leading Edge of Wing 5.5 inches

Location of Leading Edge of Vertical Tail 16 inchesIncidence Angle on Wing 2.566 degrees

Incidence Angle on Horizontal Tail -1.194 degrees

Table 3.1: Final Design Parameters.

These quantities enabled us to perform calculations to obtain the static margin and solve for the trim speed.

The wing planform area (S) was calculated using the wing span and chord and the planform area for the horizontal and vertical tails were calculated using the following relations:

Equation 3.1

Equation 3.2

The planform area of the wing was evaluated to be 54 in2. The planform area of the horizontal tail was found to be 10.8 in2 and the planform area of the vertical tail was determined to be 5.3 in2. The next step was determining the aspect ratios of the empennage lifting surfaces. Further assumptions were made, considering other aircraft as well as the need for simplicity.

The dimensions of the vertical tail can be seen below.

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Figure 3.1: Vertical Tail.

From the above figure, using a span of 3.53 in. and a planform area of 5.4 in2 we obtained an aspect ratio for the vertical tail of 2.35. For the horizontal tail, we used the following dimensions

Figure 3.2: Horizontal Tail.

These dimensions were used to calculate the aspect ratio of the horizontal tail which was determined to be 4.8. With these basic numbers, we made a few more assumptions necessary to calculate the aerodynamic center which are listed below:

Parameter Assumed Valuedε/dα 0.1ηh (Dynamic Pressure Ratio) 0.9

(Lift Curve Slope for a Flat Plate) 0.11/deg

Table 3.2: Assumed Parameters for Static Margin and Trim Speed.

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Calculating the static margin

We then calculated the lift coefficient for the wing fuselage using the following relation:

Equation 3.3

This lift coefficient was determined to be 0.0802/deg.The lift coefficient for the horizontal tail was then calculated using the following equation:

Equation 3.4

The above term was determined to be 0.0751/deg.The next two quantities to be determined were the location of the aerodynamic center of the wing-fuselage and the aerodynamic center of the horizontal tail. Since we used a rectangular wing, the location of the aerodynamic center was just the quarter chord location. Therefore, the location of the aerodynamic center was

To calculate, , we just divide by the mean chord length of the wing (which is the same as the chord length for a rectangular wing)

For the horizontal tail, the aerodynamic center was also located at the quarter chord location since it was a rectangular lifting surface too. To find , we add the distance from the nose to the vertical tail, the distance from the leading edge of the vertical tail to the leading edge of the horizontal tail and the distance from the leading edge of the horizontal tail to the quarter chord location. This results in

We then calculate by dividing the above result by the wing chord length to obtain

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These two quantities were then used in the equation below to obtain the location of the aerodynamic center of the glider.

Equation 3.5

The above equation gave us a value of 2.5719 as the location of the aerodynamic center.

We then proceeded to determine the location of the center of gravity of the glider in order to determine the static margin. The center of gravity of the airplane was determined using the following equation (assuming density ρ to be a constant)

Equation 3.6

Part Centroid ( i) Volume (Vi) i Vi

Fuselage (18/2)/3 = 3 1/2in x 3/16in x 18in = 1.6875 in3

5.06 in3

Wing (5.5+(3/2))/3 = 2.33 3in x 18in x 3/32in = 5.0625 in3

11.81 in3

Horizontal Tail (16+.5+(1.5/2))/3 = 5.75

1.5in x 7.2in x 3/32in = 1.0125 in3

5.82 in3

Vertical Tail (16+0.88)/3=5.6270 5.4in x 3/32in = 0.50625 in3

2.85 in3

TOTAL 8.26875 in3 25.5 in3

Table 3.3: Calculating the center of gravity of the aircraft without clay.

Using data from the table above and plugging it into equation xx, we get a c.g. location of 3.08. However, after experimentally measuring the location of the c.g, we determined the location to be (9.46875in/3in) = 3.156. Therefore, we will use the experimentally determined value of the c.g. for all further calculations. We can then calculate our static margin by using the following equation:

Equation 3.7

This equation yielded a result of -0.5841. We thus concluded that the glider was statically unstable and hence decided to use clay at the nose of the airplane to move the aircraft c.g. ahead of the aircraft aerodynamic center. We added up 1.2 oz. of modeling clay to the

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nose of the glider to move the c.g. forward. The addition of clay resulted in a new c.g., experimentally measured to be 4.53125 in., which when non-dimensional zed came out to be an of 1.51. The new static margin was then determined to be +1.06.

Calculating the trim speed

The next part of our analysis focused on calculating the trim speed of our aircraft. To calculate our trim speed, we started from the static margin. The static margin is related to slope of the Cm vs CL curve by the following relation:

SM = Equation 3.8

The graph of Cm vs CL has the following characteristic shape:

Figure 3.3: C m vs CL curve.

The point in the above graph where Cm=0 corresponds to the trim condition. The trim conditions can be obtained using two methods:

1. Using the equation shown below which describes the pitching moment coefficient in terms of the other stability derivatives,

Equation 3.9

where α is the angle of attack, ih is the incidence angle of the horizontal tail and the Cms are the pitching moment coefficients corresponding to angle of attack, incidence angle of horizontal tail etc.

2. Summing the moments on the aircraft and determining the quantity (Cm0 + ).

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Method I

Calculating

We used the lift coefficient of the wing-fuselage determined earlier (0.0802/deg) to obtain the lift coefficient at the wing incidence angle of 2.566 deg. This evaluates to

Thus the lift generated when the wing is at 2.566 deg angle of incidence is determined by using the following equation. The next step is calculating the and we do so by summing moments about the center of gravity in the figure below:

Figure 3.4: Summing the moments about the c.g. with α=0, ih=0.

Summing the moments, we get the following:

Equation 3.10

Therefore, we can calculate by multiplying 0.2058 and (2.0833 - 1.51) to give a value of 0.118.

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Calculating

We calculated the value of using the following equation

Equation 3.11

Calculating

The total is calculated by using the following equations:

Equation 3.12

= (0.0802/deg) + (0.0751/deg * 0.9 * (10.8 in2/54 in2) * (0.9) = 0.0924/deg

We know that

Equation 3.13

From this we can calculate for the aircraft, by multiplying 0.0924/deg and -1.06 to give -0.0981/deg.

We can now calculate the trim angle of attack by using Equation 9:

and setting Cm to 0. This yields the following equation:

0 = (0.118) + (-0.0981/deg)(α) + (-0.0579/deg)*(-1.194deg)

This yielded a trim angle of attack of 1.91 deg.

Method II

If we were to include the incidence angle of the horizontal tail, we would get an additional moment from the lift generated at the horizontal tail. This would result in the figure shown on the next page.

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Determining the contributions due to and horizontal tail

Figure 3.5: Summing the moments about the c.g. with α =0.

Equation 3.14

= (0.118 - (0.0751/deg * -1.194 deg*0.9*(10.8 in2/54 in2)*(5.7917-1.51)) = 0.1871.

This term represents the contribution due to as well as the incidence angle on the horizontal tail.

Generating the Lift-Curve for the Aircraft

The total of the aircraft can be found at α=0, by using the lift curve slopes of the wing-fuselage and horizontal tail determined earlier.

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Figure 3.6: Summing forces on the glider.

Equation 3.15

=(0.0802/deg*2.566deg)-(0.0751/deg*-1.994 deg)*(10.8 in2/54 in2)

= 0.2237

Therefore, the total is calculated by using the Equation 3.12:

= (0.0802/deg) + (0.0751/deg * 0.9 * (10.8 in2/54 in2) * (0.9) = 0.0924/deg

This translates to a lift curve with a slope of 0.0924/deg and a y-intercept of 0.2237.

Calculating the Trim Angle of Attack

We know from Equation 13:

From this we can calculate for the aircraft, by multiplying 0.0924/deg and -1.06 to give -0.0981/deg.

From the Cm vs α plot, we can determine the value of α that gives a Cm=0.

Equation 3.16α = -(0.1871)/(-0.0981/deg)=1.91 deg

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This is the required trim angle of attack. We decided to use this trim angle of attack to give us a higher trim speed.

This trim angle of attack and corresponds to a CL of (0.0924/deg*1.91deg) + (0.2237) =0.3999. The trim speed is therefore calculated from the following equation:

Equation 3.17

This value for the trim velocity of the glider was verified during test flights as in level flight, the glider flew the distance of the Eagle Gym – 90-ft in roughly three seconds. By releasing the glider slightly above this trim velocity, and thus allowing it to gain altitude, the glider consistently recorded distances of above 120-ft. When recording flights for distance, due to one flight which was not straight, the glider flew an average of 111-ft.

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4.0 CONCLUSION AND RECOMMENDATIONS

The final glider fly off was the final test of whether the calculations met up with experiment. The glider average distance was calculated from an average of three throws. The first throw resulted in a total range of 89 feet. The glider yawed to the left after being released. However, the glider hit the side wall almost seven7 feet above the ground.

The next time the glider was thrown it flew straight down the gym without yawing to the right or left. The steady, level flight of the glider led it to achieve a height of eight feet above the wall. The total distance of the glider was deemed to be 90ft + (8*4) feet = 122 feet. Steady, level flight was witnessed once again in the third recorded flight of the glider. The glider hit the same spot with a total distance of 122 feet. The average of the three flights was a distance of 111feet.

Thus, the simple, conventional configuration of the glider yielded impressive results. The incidence angle of the wing combined with the T-tail of the empennage allowed the glider to accomplish a maximum distance of 122 feet. The addition of clay was essential to the success of the glider and future projects might involve reducing the dependence on clay and trying to achieve a lighter glider with a lower trim velocity.

Future analyses would also involve determining whether the glider was laterally and directionally stable as well as an analysis into the dynamic stability of the glider.

The glider is a very important educational tool and the effects of several different lifting surfaces and configurations can be studied by building different models with different wing shapes, sizes, empennages, fuselage shapes etc. Future projects would involve trying out different configurations such as V-tails, canards, etc. and documenting the effect that those lifting surfaces had on the overall performance and aerodynamics of the glider.

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5.0 REFERENCES

Yechout, T. (2003). Introduction to Aircraft Flight Mechanics. Blacksburg, Virgina: AIAA.

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6.0 ACKNOWLEDGEMENTS

Harsh Menon Design, construction, analysis, report-writing.

Brian Pollock Design, construction, flight-testing, report-writing.

Dr. Jeff Ashworth Instructor

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7.0 APPENDIX I: MATLAB M-FILE USED FOR CALCULATIONS

%Program to calculate Static Margin and Trim Speed for Glider

%Dimensions of Wing, Horizontal Tail, Vertical Tail, Fuselage.c=3; % chord length [inches]b=18; % wing span [inches]AR_wf=b/c; % Aspect Ratio of WingS=b*c; % Planform area of Wing

c_htail=1.5; %chord length of horizontal tail [inches]b_htail=7.2; %span of horizontal tail (inches)AR_h=b_htail/c_htail; % Aspect Ratio of horizontal tailS_h=b_htail*c_htail; % Planform area of Horizontal Tail

a_vt=1; % Chord length at tip of vertical tail [inches]b_vt=2; % Chord length at root of vertical tail [inches]h_vt=3.53; % Height of vertical tail [inches]S_vt=0.5*(a_vt+b_vt)*h_vt; %Planform area of Horizontal TailAR_vt=(h_vt^2)/S_vt; %Aspect Ratio of Vertical Tail

length_fuselage=18; %Length of Fuselage [inches]

%Assumptions made for Calculations

e=0.9; % span efficiency factordeda=0.1; % rate of change of downwash angle with change in angle of attacketa_h=0.9; % efficiency of the horizontal tail

%Design Parameters, Locations of a.c., c.g., etc.

lambda=1; %Taper Ratioih_wing=2.566; %Angle of incidence on the wing [degrees]ih_htail=-1.194; %Angle of incidence on horizontal tail [degrees]

loc_ledwing=5.5; %location of the leading edge of the wing [inches]loc_ledvtail=16; %location of the leading edge of the vertical tail [inches]loc_ledhtail=17; %location of the leading edge of the horizontal tail [inches]xac_wf=(loc_ledwing+(0.25*c))/c %location of the aerodynamic center of the wing fuselage [non-dimensionalized by dividing by chord length]xac_h=(loc_ledhtail+(0.25*c_htail))/c % Location of aerodynamic center of horizontal tail [non-dimensionalized by dividing by chord length]

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%CALCULATING THE STATIC MARGIN

%1. Calculating the Lift-Curve Slopes for the Wing-Fuselage and Horizontal%Tail and the Aerodynamic Center

Cla_wf=0.11/(1 + ((57.3*0.11)/(pi*e*AR_wf)))Cla_h=0.11/(1 + ((57.3*0.11)/(pi*e*AR_h)))xac=(((xac_wf)+((Cla_h/Cla_wf)*eta_h*(S_h/S)*xac_h*(1 - deda)))/(1 + ((Cla_h/Cla_wf)*eta_h*(S_h/S)*(1-deda))))

%2. Calculating the location of the C.G.

fuse_cg=(length_fuselage/2)/c; %Non-Dimensional Location of cg of Fuselage wing_cg=(loc_ledwing+(c*0.5))/c; %Non-Dimensional Location of cg of Winghor_cg=(loc_ledhtail+(0.5*c_htail))/c; %Non-Dimensional Location of cg of horizontal tailvert_cg=(loc_ledvtail+((a_vt^2) + (a_vt*b_vt) + (b_vt^2))/(3*(a_vt+b_vt)))/c; % Non-Dimensional Location of center of gravity of vertical tail

%Volumes of the different parts of the gliderfuse_vol=length_fuselage*.5*(3/16); %Fuselage Volume [inches^3]wing_vol=S*3/32; %Wing Volume [inches^3]hor_vol=S_h*3/32; %Horizontal Tail Volume [inches^3]vert_vol=S_vt*3/32; %Vertical Tail Volume [inches^3]

xcg=((wing_cg*wing_vol)+(hor_cg*hor_vol)+(fuse_cg*fuse_vol)+(vert_cg*vert_vol))/(hor_vol+wing_vol+fuse_vol+vert_vol);exp_cg=3.156;

%Static MarginSM=xac-exp_cgnewxcg=1.51; % New Aircraft CG with Clay [experimentally determined]NewSM=xac-newxcg

%CALCULATING THE TRIM SPEED

%Using Method I with Approximations for eta_hClwf=Cla_wf*ih_wing; %Lift Coefficient of Wing at Given Incidence Angle

%Summing Moments at AOA=0, ih=0Cm0=Clwf*(xac_wf-newxcg) Cmih=-Cla_h*eta_h*(S_h/S)*(xac_h-newxcg) % Cmih has error associated with assuming an efficiency for the horizontal tail

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Cla_aircraft=Cla_wf+(Cla_h*eta_h*(S_h/S)*(1-deda)) %Cla_aircraft has errors associated with assuming eta_h, dedaCma=-NewSM*Cla_aircraft Trim_AOA1=(-Cm0-(Cmih*ih_htail))/(Cma)

%Using Method II with Lesser Approximations

%Summing Moments at AOA=0Cm0bar=Cm0-(Cla_h*eta_h*ih_htail*(S_h/S)*(xac_h-newxcg))

%Summing Forces at AOA=0 in the Z-directionClaircraft_AOA_0=(Cla_wf*ih_wing)-(Cla_h*ih_htail*(S_h/S))Trim_AOA2=-Cm0bar/Cma

Cl=Claircraft_AOA_0 + (Cla_aircraft*Trim_AOA2)trim_v=sqrt((2*(0.125))/(Cl*(2.0481e-3)*(54/144)))

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8.0 APPENDIX I: OUTPUTS FROM MATLAB M-FILE USED FOR CALCULATIONS

xac_wf =

2.0833

xac_h =

5.7917

Cla_wf =

0.0802

Cla_h =

0.0751

xac =

2.5719

SM =

-0.5841

NewSM =

1.0619

Cm0 =

0.1180

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Cmih =

-0.0579

Cla_aircraft =

0.0924

Cma =

-0.0981

Trim_AOA1 =

1.9077

Cm0bar =

0.1871

Claircraft_AOA_0 =

0.2237

Trim_AOA2 =

1.9077

Cl =

0.3999

trim_v =

28.5284

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