conceptual design of a light sport aircraft

DUSTAN GREGORY APRIL 10, 2016

Conceptual DesignLight Sport Aircraft

Table of ContentsI. Problem Definition......................................................................................................

II. Light Sport Aircraft Summary..................................................................................

III. Given Parameters and Design Mission.....................................................................

IV. Design Process.............................................................................................................

V. Design Overview..........................................................................................................

VI. Conclusion...................................................................................................................

VII. Appendix......................................................................................................................

I. Problem DefinitionCreate a conceptual design of a light sport aircraft using given design parameters, along

with a conceptual design summary, in order to complete a given design mission.

II. Light Sport Aircraft SummaryLight sport aircrafts have specific parameter values that they must be within in order to be classified as a light sport. These parameter limits are given in the following figures.

Figure 1 Vans RV-12 light sport aircraft.

Figure 2 Vans RV-12 light sport aircraft design summary.

DUSTAN GREGORY CONCEPTUAL DESIGN LSA 2

Figure 3 Glasair Merlin light sport aircraft.

Figure 4 Glasair Merlin light sport aircraft design summary.


Figure 5 Pipistrehl Virus SW light sport aircraft.

Figure 6 Pipistrehl Virus SW light sport aircraft design summary.


Figure 7 Cessna 162 light sport aircraft.

Figure 8 Cessna 162 light sport aircraft design summary.


Figure 9 Skycraft sd1 minisport light sport aircraft.

Figure 10 Skycraft sd1 minisport light sport aircraft design summary.


Figure 11 Tecnam Astore light sport aircraft.

Figure 12 Tecnam Astore light sport aircraft design summary.


In order to get a good sense about reasonable design parameters for light sport aircrafts, a summary of six light sport aircrafts is conducted. This summary includes taking given aircraft parameters such as weight, wing span, engine brake horsepower, cruise speed,…etc, and performing design performance calculations. These values are then tabularized and compared against one another in order to get a ball park interval for design parameters. The CD0 S value’s are calculated using the performance method described below.

During level flight at cruise lift is equated to weight and thrust is equated to drag due to the force balance occurring in order to have the zero acceleration condition of the aircraft. This logic along with the force balance yields the following equations.

L=W=C lq∞S

T=D=Cdq∞S

Where,

q∞=12ρU∞

2

The final equation needed in order to find the CD0 S is the equation derived for the coefficient of drag. Since the derivation is outside of the scope of this report, the result is shown below as,

Cd0=C l

2

πeAR−Cd

Where the first term is due to parasitic drag and the second term is the component attributed to the drag due to lift. Where the term πeAR is a constant related to the aircraft geometry. The design summary for light sport aircraft can be found below in table 1.

Table 1. Design Summary Results

Parameter Minimum Value Maximum Value

Empty Weight (lbs) 285 830

Power Available (BHP) 50 100

Length (ft) 14.27 23

Height (ft) 5 8.67

Wing Span (ft) 19.62 35.13

Wing Area (ft2) 65.66 132

Aspect Ratio 5.63 12.77

CD0 S (ft2) 2.66 6.81

III. Given Parameters and Design MissionCertain parameters are given in this design in order to properly set up the problem. These parameters are engine brake horsepower, propeller and efficiency, empty and gross weights, rate of climb, cruise speed, stall speed, take-off roll, landing distance, and service ceiling. There are a couple of other parameters, which will be mentioned later, that also need to be initialized in order


to get a start on the design. The following table gives the given parameters which must be met in order to call the design a success.

Table 2. Given Design Parameters

Parameter Value

Propeller Efficiency 0.79

Empty Weight >750lbs

Gross Weight ≤1320lbs

Range >400nm

Rate of Climb >500 (ft/min) @ sea level

Cruise Speed (6,000 ft) >100 knots

Stall Speed (clean configuration) <50 knots

Take-Off Roll <500 ft

Distance to Clear 50 ft object <1,500 ft

Landing Distance with Roll <500 ft

Landing Distance over a 50 ft object <1,200 ft

Service Ceiling ≥16,000 ft

The mission that is to be completed by the light sport aircraft is as follows; take off from sea level and climb until an altitude of 6,000 ft. The aircraft is to then cruise at 75% power for the full extent of its range. Once this distance is met the aircraft must make approach maneuvers at 55% power for ten minutes and ground operations for twenty minutes at 35% power. The aircraft is then to land with its cruise speed reserve of fuel.

IV. Design ProcessFor the first iteration of the design a CD0 S is chosen from the interval of CD0 S given in the light sport airplane summary in table #. The first CD0 S chosen is 4.12. From that an S and b are also chosen from the table. The next thing to take into consideration is the shape of the wing section. Choosing an airfoil will provide the needed C lmax, α stall, and α 0 l. This will allow the generation of most of the performance specifications needed to analyze if the system will complete its mission or not.

Once these parameters are set, the general dimensions are set for the aircraft height, length, and wing type. These dimensions will come into play later when corrections are made for aircraft in flight effects.

The drag due to the airfoil section is then calculated by,

Cd=Cd 0+C l

2

πeAR

where, C l, can be calculated using the equation,

L=W=C lq∞S


The stall speed in the “clean” configuration can be found using this same equation but evaluated at C lmax. Where,

q∞=12ρU∞

2

and

U stall=√ W12ρSClmax

Drag on the airfoil can finally be calculated from a similar formulaD=Cdq∞S

It is worth noting that these equations are only valid for level un-accelerated flight. These, and the following, calculations are to be done for cruise speeds between zero and one hundred and forty knots. This is done to generate the essential design curves needed for the design analysis. Conceptually, the thrust required to fly at any cruise speed is equal and opposite to the drag on the airframe at that cruise speed. This is found from the force balance used to find the equations above. This thrust required is useful for the power required calculation. The equation for power required is,

PR=DU∞

This power required can then be compared against the power available to the airframe from the engine. The power available to the airframe is dependent on the flight elevation, due to the density variations, and the efficiency of the propeller attached to the engine. The given efficiency of the propeller for this light sport aircraft is ηp=0.79. Therefore the power available to the airframe at sea level is,

PA=bhp∗ηp

By taking a look at the ratio between the power required and the power available it is then ease to know whether or not certain cruise speeds can be attained. Therefore, the following ratio is a crucial performance parameter to consider when designing an aircraft at the conceptual level

PR

P A

The maximum speed at which an aircraft can fly is when PR=PA. Altitude corrections can be made to this power available by using the following equation

PA , altitude

P A , sea level=[1.132( ρaltitude

ρsea level )n

+0.132]where n=1 in most cases. These power available corrections will be made in two thousand foot increments up to twenty-thousand feet. This will give the needed information to find the rest of the parameters needed for the design.

The next parameter of interest is the rate of climb of the aircraft at a given elevation. This parameter is the speed at which the aircraft can get from one elevation to the next elevation of interest. This parameter is found by


RC=Excess PowerW

=(P A−PR )

W

and the angle of climb that corresponds to this rate of climb is

θ=tan−1( RCU ∞ )As these calculations are developed for each altitude the absolute and service ceilings for the aircraft can be found. The service ceiling is defined as the point where the aircraft can no longer climb an RC of one hundred feet per minute. The absolute ceiling is the altitude where the aircraft can still maintain flight without stalling, but can no longer climb. These parameters give a pilot and a designer an idea of how the aircraft will perform at altitude. However, another important parameter to design for is the best angle of climb. This parameter differs from the angle given above in that the angle shown in equation # is the angle that corresponds to the best rate of climb. The best angle of climb corresponds to a different speed entirely and maximizes elevation while minimizing x-distance traveled. This best angle of climb is given by,

θbest angle=sin−1 (RC )

U∞

The time that it takes to climb to a certain elevation is pertinent to a designer when it comes to predicting endurance and range performance calculations. This time can be found using the following equation,

t=∫z1

z2 dzRC

where dz indicates the change in altitude for the aircraft. Endurance and range can then be found using the following,

E=∫W 1

W 2 dWc PR

and

R=EU ∞=∫W 1

W 2 U ∞dWc PR

respectively. Where specific fuel consumption, c, is a constant value based off of the engine at a given percentage throttle.

In the conceptual design phase, safety is also a big concern behind aircraft design. Many things go into deeming a design “safe”. One of these is how far, or long, an aircraft can glide without an engine to propel it. The parameters of glide are the glide angle and the glide ratio. The glide ratio is the ratio between horizontal distance traveled per altitude lost. These governing equations are given by,

θ= 1

( LD )max

and


Glide Ratio=cot (θ)

Part of selling aircrafts is marketing its performing features. Take-off and landing distances are very important due to the limitations that can be put on where an aircraft will be stored and how far of an airstrip is needed for take-off and landing. A rough schematic of the interpretation of take-off and landing components is shown below in figure 13.

Figure 13 Figure of take-off (orange) and landing (blue) distance definitions.

The equations needed in order to find these distances are evaluated at the take-off speed. This speed is conventionally,

UT /O=1.2U stall

Ground roll approximation is given by,

xg=1.44(WS )

gρClmax(T avr

W )and

T avr=ηpPA

0.7UT /O

The distance traveled during aircraft rotation during take-off is,xr=1.2 t rU stall

Where t r is the time it takes for the rotation to occur, which is typically one second for light sport aircraft. The total take-off distance is then given by,

xT /O=xg+xr

The next take-off parameter that is a standard given for a design to present is the distance that it takes for an aircraft to clear a fifty foot tall object. This distance is calculated first and foremost by finding the radius of curvature that the aircraft will be following. This value is calculated using,

R=6.96U stall

2

g


The angle between the tip of the object being cleared and the ground is given as,

θh=cos−1(1− hR )

In order to find the horizontal distance from the take-off point to the fifty foot object simple geometric relations govern as,

xc=Rsin (θh)Which will give the distance to clear the fifty foot object for take-off as,

x50=xg+xr+xc

This process for landing is similar but very different. It begins by finding some initial geometric parameters such as the approach angle. This is given as,

θa=sin−1( 1LD

− TW )

but a good approximation for θa is around 3° for most aircraft. The flare height is the height at which the pilot initiates the “pull up” of the aircraft in order to initiate the landing. The flare height is governed by the following equation.

h f=R (1−cos (θa ) )Which gives the the distance from a fifty foot object to the flare point as,

xa=(50−hf )tan (θa )

And the distance covered throughout the flare’s execution is given as,

x f=Rsin (θa )The roll just before landing also takes some distance that needs to be accounted for, this distance is,

x fr=1.1 t rU stall

Where t r again is around one second for light sport aircraft. The final stopping roll just before landing is,

xsr=WU td

2

2g ( D+μ (W−L ) )0.7U td

The touch down speed, U td, is equivalent to 1.1U stall ,when t r is equal to one. The drag and lift should be evaluated at 0.7U td and it is worth noting that no reverse thrusters are considered during this conceptual design. The total ground roll and landing over a fifty foot object are given as,

xL=x fr+xsr

andxL 50=xL+x f+xa


respectively. The final calculations to be made for the conceptual design are the addition of flaps to the wing, which introduce a “dirty” configuration, and corrections to the calculations based on finite wing effects using lifting line theory. In order to introduce flaps, thin airfoil theory will be used as an analysis tool under all of its assumptions.

By introducing flaps to the back of the wing the effective lift coefficient can be increased, while, consequently the angle of attack at zero lift will also change. Using thin airfoil theory, along with geometry, this new lift coefficient can be found once some initial parameters are assigned. These values are the length of the cord of the airfoil as well as a target flap angle. The length of the cord is to be split proportionally into a wing section and a flap section. This cord length is also to be parameterized so that the change in lift coefficient can be true for any length cord inputted into the system. From that the following schematic, see figure 14, can be generated.

Figure 14 Schematic of Thin Airfoil Theory, in dirty configuration, with geometric parameters labeled.

The equations used in order to find the change in C lmax and α 0 l are,

ΔC l=[ 2 (π−θh )+2 sin (θh ) ] δ f

and

Δ α0 l=−[ (π−θh )+2sin (θh ) ] δf

π

Where the geometric parameters lh and l are somewhat tedious to calculate, their results are used and presented as,

θh=cos−1(1−2lhl )

It is worth noting that angles used in these equations should be in the units of radians. This will prevent many frustrations throughout calculations.

After these results, all that is left to do is calculate the 3D effects of a finite wing on the airfoil. This will decrease the effective C lmax , but will have no effects on α 0 l or α stall. This analysis will be conducted using lifting line theory. Lifting line theory considers the effects of the downwash velocity due to the induced drag by wing tip vortices during flight. Programs have been generated to simulate these effects, but, to be rigorous in the conceptual analysis, the hand calculations are presented.


Consider the monoplane equation,

μ (α−α 0 l ) sin (φ )=∑j=1

odd

An sin (nφ ) (μn+sin (φ ) )

This equation gives an even number of odd labeled terms. The monoplane equation is used, iteratively, for however many times needed in order to get the same number of equations as unknowns. This is done by using different angular positions on the wing. Solving for the coefficients of the monoplane equation give the unknown coefficients needed to evaluate the new slope, C lα, which is the slope of the C l vs. α plot. The governing equations are,

C l=C lα (α e−α0 l )and

α e=α−ϵ

where

ϵ=tan−1(−w y 1

U∞)

The downwash velocity, w y 1, can be found using the following equation

w y 1=−2Γ 0

4 b

where

Γ0=Lq∞

After these last calculations, the corrections of C lmax need to be applied to the previous calculations for all elevations. This will give a better approximation for actual performance parameters for the conceptual design step in the design process. Better approximations are outside of the scope of this introductory class. In order to get better approximations, some assigned parameters, such as the Oswald constant need to be calculated using more appropriate correlations instead of blindingly just assigning a value in an interval based on all aircraft values. This analysis also focuses just on the parameters of the airfoil and the wing. The entire aircraft area is not considered in this analysis. Therefore, drag and lift values will be skewed based on the entire surface area exposed to the plane and the shape of that area.

V. Design Overview

The following table gives the parameters found during the design process verification step of the project. This verification used known values given about a Cessna 182. The verification task is to use the design process, as described above, and apply it to the Cessna 182 in order to compare with given specs from Cessna or online values. This verification gives another indication of the validity of the design process.

Table 3. Cessna 182 Design Parameters

Parameter Value


Engine BHP 230Specific Fuel Consumption (lbs/hr-hp) 0.45Propeller Efficiency 0.79Empty Weight (lbs) 2800Payload (fuel and passengers/cargo) (lbs) 860Gross Weight (lbs) 3660Wing Span (ft) 36.08Wing Surface Area (ft^2) 174

From these initialized parameters given for the Cessna 182 the design process analysis is conducted and is shown in the following figure 15.

Figure 15 Table from design process analysis verification for Cessna 182.

This table gives the max cruise speed at sea level to be around 140-150 knots. Comparing this value to the specifications given for the Cessna it can be confirmed that this verification is very close to actual values and is a good approximation for a conceptual design. This conceptual design will be for “back of the napkin” type approximations, where actual values are not a huge concern. This analysis is more meant to see if the design is possible to complete the given mission. The other values of specifications, such as take-off and landing distances, are skewed due to the gross take-off weight used in the initializing process. These are shown in the following figure 16.


Figure 16 Table of calculated take-off and landing distances (including roll’s).

Since the initialized gross take-off weight is greater than that of the specified, the distances are significantly larger. If the designer wanted to decrease these distances, the designer needs to specify that the take-off weight needs to be significantly less in order to achieve a shorter take-off and landing distances. It is also worth noting that the landing distance shown in this figure does not take into account the “dirty configuration” with flaps down for the Cessna. This will decrease the landing distance since the lift and drag will be increased with flaps down. This correction is accounted for in the iterative process for the actual design for which this report analyzes. In conclusion, the verification process is a success; therefore, the design process is a good approximation for conceptual design values.

The design of a light sport aircraft takes on an iterative process using the design process describe in its respective section. In order to complete this conceptual design, parameters need to be initialized based upon the design summary conducted for light sport aircraft. These initialized parameters will then yield results and then are compared against the design mission to see if the aircraft can complete its mission and still meet all requirements set in the beginning of the report. The first iterative parameters are given as follows in table 4.

Table 4. First Iterative Design Parameters

Parameter ValueEmpty Weight (lbs) 755Gross Weight (lbs) 1320Wing Span (ft) 31Wing Area (ft^2) 110


Cd0S (ft^2) 6.81Airfoil Section NACA 2412

These results give values that meet some, but not all, of the design requirements. The requirements not met are cruise speed at sea level power available, and cruise speed at 6,000 ft. In order to satisfy these requirements, the design parameters need to be tweaked. The design parameters that were changed are wing span, wing area, and Cd0S. The new design parameters are given in table 5.

Table 5. Final Iterative Design Parameters

Parameter ValueEmpty Weight (lbs) 755Gross Weight (lbs) 1320Wing Span (ft) 35Wing Area (ft^2) 119Cd0S (ft^2) 3.6Airfoil Section NACA 2412

These results meet all of the given requirements. The results for the power available at altitude is plotted below in figure #.


0.00 50.00 100.00 150.00 200.00 250.000.00

10000.00

20000.00

30000.00

40000.00

50000.00

60000.00

70000.00

Power Curves

Sea Level2,000 ft4,000 ft6,000 ft8,000 ft10,000 ft12,000 ft14,000 ft16,000 ft18,000 ft20,000 ftPower Available (SL)

Speed (ft/s)

Pow

er R

equi

red

(ft-l

b/s)

Figure 17 Power curves at different altitudes up to 20,000 ft.

The power available line is only plotted for one altitude in order to keep the plot for being further convoluted. The intersection between the power available and power required lines give the maximum available speed that can be achieved for a given altitude (max cruise speed). The power available line will decrease as the altitude increases due to the density variations at altitude. This power decrease is governed by Mises equations for power loss due to density variations in altitude, found in Design Process section. The maximum cruise speed that can be achieved is around 200 feet per second at sea level altitude, and decreases with altitude increase.

Another important parameter to perceive is the rate of climb as altitude increases. This gives the designer indicators for how the plane will be able to perform at altitude. The rate of climb plot is shown in figure 18.


0.00 50.00 100.00 150.00 200.00 250.00

-2000.00

-1500.00

-1000.00

-500.00

0.00

500.00

1000.00

1500.00

2000.00Rate of Climb

Sea Level 2,000 ft 4,000 ft 6,000 ft8,000 ft 10,000 ft 12,000 ft 14,000 ft

Speed (ft/s)

Rat

e of

Clim

b (f

t/min

)

Figure 18 Plot of rate of climb as a function of speed for variation altitudes

Figure # gives a graphical means of finding the maximum rate of climb at a given altitude. This plot is also an easy way to approximate service ceilings and absolute ceilings. The service ceiling for our design is much higher than expected and cannot be seen on the plot shown. This is due to the correction of power available to the airframe at altitude. A table of these values are tabularized in table 6.

Table 6. Maximum Rate of Climb at Altitude

Parameter (Rate of Climb) Value(Max)Sea Level 1531.172,000 1455.814,000 1323.706,000 1195.638,000 1071.1210,000 949.9512,000 831.6814,000 722.1916,000 617.3118,000 514.6420,000 413.93


The best angle of climb, at sea level, is 29.59° and occurs at 20 knots and a rate of climb of 1150.13 ft/min. This value does not correspond to the best angle of climb at sea level, see table # above.

The actual power available to the airframe is less as altitude increases, which will give lower absolute and service ceilings. The actual power available to the airframe with altitude is given in the plot of brake horsepower as a function of altitude for the Rotax engine shown in figure #.

Figure 19 Rotax BHP performance at altitude.

The units used in this figure are different that the standard units used in this report analysis. The conversion can be made by knowing that 1 kW= 1.34 hp , and 1 meter = 3.28 feet. The different lines shown in this figure are the engine revolutions per minute. The maximum rpm that the engine can be run at is 5800 rpm, which yield the BHP max if 100 BHP.

For a designer, in case an engine happens to fail, glide is a concept that is considered in a conceptual design. Glide is a huge part of safety for an aircraft. Gliding can save both the passengers and the aircraft itself given the correct conditions and scenario. The glide parameters for this light sport aircraft are give below in table 7.

Table 7. Gliding Performance Parameters


Parameter Value

Glide Angle 4.47°

Glide Ratio (Horizontal Distance/Vertical Decent)

732.30

Glide Sink Rate 67.03

The values for range and endurance for the light sport aircraft are calculated using equations from the design process section. These values are calculated for maximum values of endurance

and range, which occurs at LDmax

for the range and Cl

32

Cd max

for endurance, as well as the endurance

and range calculations rated at seventy-five percent power during cruise with forty-five minutes of fuel left in reserves. The following table 8 contains the values for endurance and range evaluated at sea level.

Table 8. Endurance and Range Performance Parameters

Parameter Value

Endurance @75% (hours) 5.1

Range @75% (miles) 699.8

Endurance @Cl

32

Cd max

(hours) 24.6

Range @LDmax

(miles) 1,696.9

The last portion of the design was to run the corrections for thin airfoil theory and lifting line theory. These corrections allow for an analysis to be ran in the clean (no flaps engaged) or dirty (flaps engaged) configuration in order to better estimate aircraft performance. These corrections also allow a designer to correct for finite wing effects. It is worth noting that this analysis is done for a maximum flap deflection angle of 30°, and the lifting line analysis is performed using lift line gui and setting some initial parameters such as taper ratio, velocity, and number of wing sections. The rest of the GUI setup is based off of preset aircraft dimensions given in table 5. The C lmax –clean and α 0 l-clean are taken from given charts for the NACA 2412 airfoil. The following figures show the set up using the “lifting line GUI” (see appendix A).


Figure 20 Plot of the Drag Polar from “lifting line GUI”.

Figure 21 Plot of C l vs α from “lifting line GUI”.


Figure 22 Plot of the Lift Distribution using “lifting line GUI”.

These results are given in tables 9 and 10 respectively.

Table 9. Thin Airfoil Theory Results

Parameter ValueC lmax –clean (without flaps) 1.7C lmax –dirty (with flaps) 3.52α 0 l-clean -2°α 0 l-dirty -18.15°

Table 10. Lifting Line Theory Results

Parameter ValueC lα (slope) (1/radians) 5.02 α – geometric angle of attack 1.74

Since take-off and landing are executed in the dirty configuration, these corrections give a more accurate result for the respective distances. These results are shown in the following table 11.


Table 11. Take-Off and Landing Distance Results

Parameter ValueTake-off , xg (ft) 100Take-off, xL 50 (ft) 422Landing, xL (ft) 152Landing, xL 50 (ft) 746

The design mission is for a take-off and landing procedure in which the plane lands with forty-five minutes of fuel in its reserve. It is assumed, for this analysis, that the same amount of fuel is used during landing as in take-off. The mission that the light sport aircraft is designed to complete is analyzed and tabularized in the following table 12.

Table 12. Design Mission Results (lbs of fuel)

Parameter ValueFuel used during Take-Off @100% (lbs) 2.6Fuel used during Cruise @75% (lbs) 147.2Fuel used during Decent (lbs) 2.6Fuel used @55% for 10 min (lbs) 3.9Fuel used @35% for 20 min (lbs) 4.9

These values, combined with the given average specific fuel consumption value, give the corresponding endurance and range calculations that the light sport aircraft can accomplish. This is assuming full gross take-off with all passengers, cargo, and fuel present. The range calculations for full load are given in table 13.

Table 13. Design Mission Results (miles)

Parameter Range(miles)Take-Off 12.79Cruise 266.26Decent 12.7955% for 10min 20.8235% for 20min 34.99Total 347.67

This result does not meet the requirement for having four-hundred nautical miles of range for the light sport aircraft. Due to the nature of the type of aircraft being designed a hefty range is not expected from a light sport, therefore this range value is not an issue. If the pilot really needs to meet the distance requirement, they may consider flying without cargo, not taking the passenger, or cruising at a lower power setting.


A rough estimate of what the light sport aircraft will look like is shown below in the following figures. The figures are organized as an isometric view, top and front view, and a side view, respectively.

Figure 23 Isometric view of LSA concept.


Figure 24 Top and frontal view of the LSA concept.

Figure 25 Side view of LSA concept.

The final design summary is given below in table 14.


Table 14. Final Design Results

Parameter ValueEmpty Weight (lbs) 755Gross Weight (lbs) 1320Wing Span (ft) 35Wing Area (ft^2) 119Cd0S (ft^2) 3.6Airfoil Section NACA 2412C lmax –clean (without flaps) 1.7C lmax –dirty (with flaps) 3.52α 0 l-clean -2°α 0 l-dirty -18.15°Take-off , xg (ft) 100Take-off, xL 50 (ft) 422Landing, xL (ft) 152Landing, xL 50 (ft) 746Max Cruise speed @6,000ft, U∞ max (knots) 120Stall Speed (clean) (knots) @sea level 45.66Stall Speed (dirty) (knots) @sea level 33.13Rate of Climb max@sea level (ft/min) 1531.17Service Ceiling (ft) >20,000Absolute Celing (ft) >22,000

VI. Conclusion

The design of the light sport aircraft, as given above, is designed as a fun airplane. Sort of analogous to a sports car. These types of planes are for shorter trips filled with faster cornering, fast roll rates, and minimum comfort. These types of planes are not designed to be un-comfortable, but since the trips are not as long as that of other planes, creature comforts are not as big of a design concern. This design met all of the design requirements but fell short on the range portion of the design mission. In order to meet this requirement the pilot will need to compensate with either speed of travel, or gross take-off weight in order to increase the range of travel.


VII. References

Figliola, Richard. AircraftStaticPerformanceNotesforME423/623.Clemson, SC. 2014

BRP-Powertrain GMBH&Co KG. Rotax. OperatorsManualforRotaxEngineType912Series. 2015.


VIII. Appendix

Given Matlab Code

Lifting Line GUI

IX. %Ben Grier >> Calcuatlaions Converted from Dr. Figliola's X. %Wing2.exe in FortranXI. %K Term Lifting Line TheoreyXII. %GUI Layout and Design by Ben GrierXIII. XIV. function [] = liftingline_GUI()XV. XVI. XVII. set_up=0;XVIII. XIX. %Runs only the first time through to set up figure & buttons.XX. if(set_up<1)XXI. %initialize();XXII. %normalized unitsXXIII. width=800;XXIV. height=600;XXV. left=50;XXVI. bottom=50;XXVII. XXVIII. %Creates Figure on ScreenXXIX. fig=figure('Units','pixels','pos',[left, bottom,

width, height],...XXX. 'Name','Lifting Line Theory');XXXI. XXXII. %gets figure properties in pixel unitsXXXIII. set(fig,'units','pixel');XXXIV. pos_pix=get(fig,'position');XXXV. width_pix=pos_pix(3);XXXVI. height_pix=pos_pix(4);XXXVII. set(fig,'units','normalized');XXXVIII. XXXIX. box_button_height=.08;XL. box_button_width=180/width;XLI. Left_pos=.02;XLII. XLIII. XLIV. %Defines all the buttons and space locations on

figureXLV.


XLVI. button_calc=uicontrol('units','normalized','pos',[Left_pos,1-box_button_height-.05,box_button_width/2,box_button_height],'string','Calculate',...

XLVII. 'fontsize',12,'callback',@button_calc_Callback);XLVIII. button_close=uicontrol('units','normalized','pos',

[Left_pos+box_button_width/2,1-box_button_height-.05,box_button_width/2,box_button_height],'string','Close',...

XLIX. 'fontsize',12,'callback',@button_close_Callback);

L. LI. Aspect_box=uipanel('Title','Aspect Ratio','pos',

[Left_pos,.75,box_button_width,box_button_height]);LII.

Aspect=uicontrol('Style','edit','units','normalized','pos',[.02,.02,.95,.98],'Parent',Aspect_box,'BackgroundColor','white','horizontalAlignment',...

LIII. 'left','FontSize',12,'FontWeight','light','String','7.52');

LIV. LV. Air_speed_box=uipanel('Title','Velocity (knots)','pos',

[Left_pos,.65,box_button_width,box_button_height]);LVI.

Air_speed=uicontrol('Style','edit','units','normalized','pos',[.02,.02,.95,.98],'Parent',Air_speed_box,'BackgroundColor','white','horizontalAlignment',...

LVII. 'left','FontSize',12,'FontWeight','light','String','100');

LVIII. LIX. Wing_Loading_box=uipanel('Title','Wing Loading

(PSF)','pos',[Left_pos,.55,box_button_width,box_button_height]);LX.

Wing_Loading=uicontrol('Style','edit','units','normalized','pos',[.02,.02,.95,.98],'Parent',Wing_Loading_box,'BackgroundColor','white','horizontalAlignment',...

LXI. 'left','FontSize',12,'FontWeight','light','String','12.8');

LXII. LXIII. Taper_box=uipanel('Title','Taper Ratio','pos',

[Left_pos,.45,box_button_width,box_button_height]);LXIV.

Taper=uicontrol('Style','edit','units','normalized','pos',[.02,.02,.95,.98],'Parent',Taper_box,'BackgroundColor','white','horizontalAlignment',...

LXV. 'left','FontSize',12,'FontWeight','light','String','.69');

LXVI. LXVII. Wing_Twist_box=uipanel('Title','Geometric Twist

(Degrees)','pos',[Left_pos,.35,box_button_width,box_button_height]);LXVIII.

Wing_Twist=uicontrol('Style','edit','units','normalized','pos',


[.02,.02,.95,.98],'Parent',Wing_Twist_box,'BackgroundColor','white','horizontalAlignment',...

LXIX. 'left','FontSize',12,'FontWeight','light','String','-3');

LXX. LXXI. Altitude_box=uipanel('Title','Altitude (ft)','pos',

[Left_pos,.25,box_button_width,box_button_height]);LXXII.

Altitude=uicontrol('Style','edit','units','normalized','pos',[.02,.02,.95,.98],'Parent',Altitude_box,'BackgroundColor','white','horizontalAlignment',...

LXXIII. 'left','FontSize',12,'FontWeight','light','String','9843');

LXXIV. LXXV. Zero_box=uipanel('Title','Zero Lift Angle','pos',

[Left_pos,.15,box_button_width,box_button_height]);LXXVI.

Zero=uicontrol('Style','edit','units','normalized','pos',[.02,.02,.95,.98],'Parent',Zero_box,'BackgroundColor','white','horizontalAlignment',...

LXXVII. 'left','FontSize',12,'FontWeight','light','String','-2.095');

LXXVIII. LXXIX. Sections_box=uipanel('Title','Number of Wing

Sections','pos',[Left_pos,.05,box_button_width,box_button_height]);LXXX.

Sections=uicontrol('Style','edit','units','normalized','pos',[.02,.02,.95,.98],'Parent',Sections_box,'BackgroundColor','white','horizontalAlignment',...

LXXXI. 'left','FontSize',12,'FontWeight','light','String','8');

LXXXII. LXXXIII. LXXXIV.

Graph_box=uibuttongroup('Title','','units','normalized','pos',[.35,.05,.6,box_button_height],'SelectionChangeFcn',@group_Callback);

LXXXV. Lift_Distr = uicontrol('Style','radiobutton','units','normalized','pos',[.02,.02,.3,.98],'Parent',Graph_box,'BackgroundColor',[.925,.914,.847],'horizontalAlignment',...

LXXXVI. 'left','FontSize',12,'FontWeight','light','String','Lift Distribution');

LXXXVII. Drag_Polar = uicontrol('Style','radiobutton','units','normalized','pos',[.4,.02,.4,.98],'Parent',Graph_box,'BackgroundColor',[.925,.914,.847],'horizontalAlignment',...

LXXXVIII. 'left','FontSize',12,'FontWeight','light','String','Drag Polar');

LXXXIX. CL_alpha = uicontrol('Style','radiobutton','units','normalized','pos',


[.75,.02,.25,.98],'Parent',Graph_box,'BackgroundColor',[.925,.914,.847],'horizontalAlignment',...

XC. 'left','FontSize',12,'FontWeight','light','String','CL vs Alpha');

XCI. XCII. graph=axes('units','normalized','pos',

[.35,.2,.6,.75]);XCIII. set(graph,'units','pixels','fontsize',14)XCIV. button_calc_Callback();XCV. endXCVI. XCVII. function button_close_Callback(hObject,eventdata)XCVIII. close all;XCIX. endC. CI. function group_Callback(hObject,eventdata)CII. if(get(Lift_Distr,'value')==1)CIII. button_calc_Callback(hObject,eventdata)CIV. endCV. if(get(Drag_Polar,'value')==1)CVI. button_calc_Callback(hObject,eventdata)CVII. endCVIII. if(get(CL_alpha,'value')==1)CIX. button_calc_Callback(hObject,eventdata)CX. endCXI. endCXII. CXIII. function button_calc_Callback(hObject,eventdata)CXIV. CXV. %Gets values from boxesCXVI. clearCXVII. AR = str2double(get(Aspect,'String'));CXVIII. VKn = str2double(get(Air_speed,'String'));CXIX. V=VKn/.5396;CXX. WLPSF = str2double(get(Wing_Loading,'String'));CXXI. WLoad = WLPSF*6895/144;CXXII. Lambda = str2double(get(Taper,'String'));CXXIII. Twist = str2double(get(Wing_Twist,'String'));CXXIV. K = str2double(get(Sections,'String'));CXXV. AltF = str2double(get(Altitude,'String'));CXXVI. Alt=AltF*.3048;CXXVII. AlZero = str2double(get(Zero,'String'));CXXVIII. CXXIX. T=288.15-.0065*Alt;CXXX. Expt = -((9.81/(-.0065)/287)+1);CXXXI. Rho = 1.225*(T/288.15)^Expt;CXXXII. CXXXIII. %Computing Theta, Y, and CCXXXIV. for(J=1:K)CXXXV. Theta(J) = pi*J/2/K;


CXXXVI. CosTh(J) = cos(Theta(J));CXXXVII. SinTh(J) = sin(Theta(J));CXXXVIII. Y(J)=CosTh(J);CXXXIX. C(J) = 1.-(1.-Lambda)*CosTh(J); %chord

transformation pg321CXL. endCXLI. CXLII. for(J=1:K)CXLIII. D1=1/C(J);CXLIV. D2=pi/(AR*(1+Lambda)*SinTh(J));CXLV. CXLVI. for(N=1:K)CXLVII. I=2*N-1;CXLVIII. D(J,N) = (D1+D2*I)*sin(I*Theta(J));CXLIX. endCL. endCLI. CLII. AL1=3;CLIII. AL2=6;CLIV. CLV. for(J=1:K)CLVI. Alabs(J) = (AL1+Twist*CosTh(J))*pi/180;CLVII. endCLVIII. CLIX. A=D\transpose(Alabs);CLX. CLW1=pi^2*A(1)/(1+Lambda);CLXI. CLXII. for(J=1:K)CLXIII. sum=0;CLXIV. for(N=1:K)CLXV. sum=sum+A(N)*sin((2*N-1)*Theta(J));CLXVI. endCLXVII. CL1(J)=2*pi/C(J)*sum;CLXVIII. endCLXIX. CLXX. %///////////////////////////CLXXI. CLXXII. for(J=1:K)CLXXIII. Alabs(J) = (AL2+Twist*CosTh(J))*pi/180;CLXXIV. endCLXXV. CLXXVI. A=D\transpose(Alabs);CLXXVII. CLW2=pi^2*A(1)/(1+Lambda);CLXXVIII. CLXXIX. for(J=1:K)CLXXX. sum=0;CLXXXI. for(N=1:K)CLXXXII. sum=sum+A(N)*sin((2*N-1)*Theta(J));CLXXXIII. endCLXXXIV. CL2(J)=2*pi/C(J)*sum;


CLXXXV. endCLXXXVI. CLXXXVII. for(J=1:K)CLXXXVIII. CLA(J) = (CL2(J)-CL1(J))/(CLW2-CLW1);CLXXXIX. CLB(J) = CL1(J)-CLA(J)*CLW1;CXC. endCXCI. CXCII. clcCXCIII. fprintf('******** Nomenclature ********\n');CXCIV. fprintf('J\t\tSection Number\n');CXCV. fprintf('a(J)\t\tSlope of CL vs angle of attack at

section J\n');CXCVI. fprintf('Alpha(J)\tAbsolute angle of attack of

section J\n');CXCVII. fprintf('CDv(J)\t\tInduced drag coefficient of

section J\n');CXCVIII. fprintf('CLW\t\tLift coefficient of wing\n\n');CXCIX. CC. fprintf('Lift coefficient of this wing behaves as

follows:\n');CCI. fprintf('CLW = %.3f For root abs alpha = %.2f\

n',CLW1,AL1);CCII. fprintf('CLW = %.3f For root abs alpha = %.2f\n\

n',CLW2,AL2);CCIII. CCIV. fprintf('For the following flight conditions:\n');CCV. fprintf('V = %.0f knots, Wing Loading = %.0f,\

n',VKn,WLPSF);CCVI. fprintf('At altitude = %.0f ft, Density = %.4f

Kg/m^3,\nTemperature = %.2f\n\n',...CCVII. AltF,Rho,T);CCVIII. CCIX. CLWF = WLoad/(.5*Rho*(V*1000/3600)^2); %CLW

calculated using simple static flight characteristicsCCX. ALF = AL1+(AL2-AL1)*(CLWF-CLW1)/(CLW2-CLW1); %Simple

interpolation to find absolute angle of wing at rootCCXI. for(J=1:K)CCXII. Alabs(J) = (ALF+Twist*CosTh(J))*pi/180;CCXIII. endCCXIV. A=D\transpose(Alabs);CCXV. CCXVI. for(J=1:K)CCXVII. sum=0;CCXVIII. for(N=1:K)CCXIX. sum=sum+A(N)*sin((2*N-1)*Theta(J));CCXX. endCCXXI. CL(J)=2*pi/C(J)*sum;CCXXII. endCCXXIII. CCXXIV. for(J=1:K)CCXXV. sum=0;


CCXXVI. for(N=1:K)CCXXVII. I=2*N-1;CCXXVIII. sum=sum+I*A(N)*sin(I*Theta(J))/SinTh(J);CCXXIX. endCCXXX. ALind(J) = -pi/(AR*(1+Lambda))*sum;CCXXXI. CDind(J) = -CL(J)*ALind(J);CCXXXII. M(J) = CL(J)./Alabs(J);CCXXXIII. ALind(J)=ALind(J)*180/pi;CCXXXIV. endCCXXXV. CCXXXVI. sum=0;CCXXXVII. for(N=1:K)CCXXXVIII. sum=sum+(2*N-1)*A(N)^2;CCXXXIX. endCCXL. CCXLI. CDindw=pi^3/(AR*(1+Lambda)^2)*sum;CCXLII. sum=0;CCXLIII. KM1=K-1;CCXLIV. CCXLV. for(J=1:KM1)CCXLVI. sum=sum+(M(J)*C(J)+M(J+1)*C(J+1))*(Y(J)-Y(J+1));CCXLVII. endCCXLVIII. CCXLIX. Mbar=sum/(1+Lambda);CCL. ALabsw=CLWF/Mbar*180/pi;CCLI. Spanef = (CLWF*CLWF/(pi*AR))/CDindw;CCLII. DLTA = (1/Spanef)-1;CCLIII. Effar = AR*Spanef;CCLIV. Algeo = ALabsw+AlZero;CCLV. CCLVI. fprintf('\tSectional Properties Under Flight

Conditions\t\n');CCLVII. fprintf('J\tCl(J)\ta(J)\tAlpha(J)\tCDv(J)\n');CCLVIII. for(J=1:K)CCLIX. fprintf('%.0f\t%.3f\t%.3f\t%.3f\t\t%.5f\

n',J,CL(J),M(J),...CCLX. ALind(J),CDind(J));CCLXI. endCCLXII. CCLXIII. fprintf('\nWing Characteristics Under Flight

Conditions Specified:\n');CCLXIV. fprintf('Lift Coefficient of Wing, CLW = %.3f\

n',CLWF);CCLXV. fprintf('Induced Drag Coefficient of Wing = %.4f\

n',CDindw);CCLXVI. fprintf('Delta = %.3f\n',DLTA);CCLXVII. fprintf('Absolute Angle of Attack of Wing = %.2f\

n',ALabsw);CCLXVIII. fprintf('Absolute Angle of Attack at Root = %.2f\

n',ALF);


CCLXIX. fprintf('Average Mean Lift-Alpha Slope of Wing = %.2f\n', Mbar);

CCLXX. fprintf('Geometric Angle of Attack of Wing = %.2f\n\n',Algeo);

CCLXXI. CCLXXII. %/////////////////////////Radio button

choices////////////////////////////CCLXXIII. CCLXXIV. if(get(Lift_Distr,'value')==1)CCLXXV. J=1:K;CCLXXVI. plot(Y,CL/CLWF,'-x'); %this is bs right now.CCLXXVII. title('Lift Distribution');CCLXXVIII. ylabel('Cl/CL');CCLXXIX. xlabel('y/s');CCLXXX. grid on;CCLXXXI. set(gca,'fontsize',14);CCLXXXII. endCCLXXXIII. CCLXXXIV. if(get(Drag_Polar,'value')==1)CCLXXXV. CCLXXXVI. %Vary the velocity to get CLW vs CD curve.CCLXXXVII. dp_res=100;CCLXXXVIII. Velocity = linspace(60,500,dp_res)/.5396;CCLXXXIX. for(i=1:dp_res)CCXC. CCXCI. AL1=3;CCXCII. AL2=6;CCXCIII. CCXCIV. for(J=1:K)CCXCV. Alabs(J) = (AL1+Twist*CosTh(J))*pi/180;CCXCVI. endCCXCVII. CCXCVIII. A=D\transpose(Alabs);CCXCIX. CLW1=pi^2*A(1)/(1+Lambda);CCC. CCCI. for(J=1:K)CCCII. sum=0;CCCIII. for(N=1:K)CCCIV. sum=sum+A(N)*sin((2*N-1)*Theta(J));CCCV. endCCCVI. CL1(J)=2*pi/C(J)*sum;CCCVII. endCCCVIII. CCCIX. for(J=1:K)CCCX. Alabs(J) = (AL2+Twist*CosTh(J))*pi/180;CCCXI. endCCCXII. CCCXIII. A=D\transpose(Alabs);CCCXIV. CLW2=pi^2*A(1)/(1+Lambda);CCCXV.


CCCXVI. for(J=1:K)CCCXVII. sum=0;CCCXVIII. for(N=1:K)CCCXIX. sum=sum+A(N)*sin((2*N-1)*Theta(J));CCCXX. endCCCXXI. CL2(J)=2*pi/C(J)*sum;CCCXXII. endCCCXXIII. CCCXXIV. for(J=1:K)CCCXXV. CLA(J) = (CL2(J)-CL1(J))/(CLW2-CLW1);CCCXXVI. CLB(J) = CL1(J)-CLA(J)*CLW1;CCCXXVII. endCCCXXVIII. CCCXXIX. CLWF_dp(i) =

WLoad/(.5*Rho*(Velocity(i)*1000/3600)^2); %CLW calculated using simple static flight characteristics

CCCXXX. ALF = AL1+(AL2-AL1)*(CLWF_dp(i)-CLW1)/(CLW2-CLW1); %Simple interpolation to find absolute angle of wing at root

CCCXXXI. for(J=1:K)CCCXXXII. Alabs(J) = (ALF+Twist*CosTh(J))*pi/180;CCCXXXIII. endCCCXXXIV. A=D\transpose(Alabs);CCCXXXV. CCCXXXVI. sum=0;CCCXXXVII. for(N=1:K)CCCXXXVIII. sum=sum+(2*N-1)*A(N)^2;CCCXXXIX. endCCCXL. CDindw_dp(i)=pi^3/(AR*(1+Lambda)^2)*sum;CCCXLI. endCCCXLII. CCCXLIII. plot(CLWF_dp,CDindw_dp);CCCXLIV. ylabel('C_D');CCCXLV. xlabel('C_L');CCCXLVI. grid on;CCCXLVII. set(gca,'fontsize',14);CCCXLVIII. endCCCXLIX. CCCL. if(get(CL_alpha,'value')==1)CCCLI. CCCLII. %Vary the velocity to get CLW vs alpha curve.CCCLIII. cla_res=20;CCCLIV. Velocity = linspace(60,1000,cla_res)/.5396;CCCLV. for(j=1:cla_res)CCCLVI. CCCLVII. AL1=3;CCCLVIII. AL2=6;CCCLIX. CCCLX. for(J=1:K)CCCLXI. Alabs(J) = (AL1+Twist*CosTh(J))*pi/180;CCCLXII. end


CCCLXIII. CCCLXIV. A=D\transpose(Alabs);CCCLXV. CLW1=pi^2*A(1)/(1+Lambda);CCCLXVI. CCCLXVII. for(J=1:K)CCCLXVIII. sum=0;CCCLXIX. for(N=1:K)CCCLXX. sum=sum+A(N)*sin((2*N-1)*Theta(J));CCCLXXI. endCCCLXXII. CL1(J)=2*pi/C(J)*sum;CCCLXXIII. endCCCLXXIV. CCCLXXV. %///////////////////////////CCCLXXVI. CCCLXXVII. for(J=1:K)CCCLXXVIII. Alabs(J) =

(AL2+Twist*CosTh(J))*pi/180;CCCLXXIX. endCCCLXXX. CCCLXXXI. A=D\transpose(Alabs);CCCLXXXII. CLW2=pi^2*A(1)/(1+Lambda);CCCLXXXIII. CCCLXXXIV. for(J=1:K)CCCLXXXV. sum=0;CCCLXXXVI. for(N=1:K)CCCLXXXVII. sum=sum+A(N)*sin((2*N-

1)*Theta(J));CCCLXXXVIII. endCCCLXXXIX. CL2(J)=2*pi/C(J)*sum;CCCXC. endCCCXCI. CCCXCII. for(J=1:K)CCCXCIII. CLA(J) = (CL2(J)-CL1(J))/(CLW2-CLW1);CCCXCIV. CLB(J) = CL1(J)-CLA(J)*CLW1;CCCXCV. endCCCXCVI. CCCXCVII. CLWF_cla(j) =

WLoad/(.5*Rho*(Velocity(j)*1000/3600)^2);CCCXCVIII. ALF = AL1+(AL2-AL1)*(CLWF_cla(j)-

CLW1)/(CLW2-CLW1);CCCXCIX. for(J=1:K)CD. Alabs(J) = (ALF+Twist*CosTh(J))*pi/180;CDI. endCDII. A=D\transpose(Alabs);CDIII. CDIV. for(J=1:K)CDV. sum=0;CDVI. for(N=1:K)CDVII. sum=sum+A(N)*sin((2*N-1)*Theta(J));CDVIII. end


CDIX. CL(J)=2*pi/C(J)*sum;CDX. endCDXI. CDXII. for(J=1:K)CDXIII. M(J) = CL(J)./Alabs(J);CDXIV. endCDXV. CDXVI. sum=0;CDXVII. KM1=K-1;CDXVIII. for(J=1:KM1)CDXIX. sum=sum+(M(J)*C(J)+M(J+1)*C(J+1))*(Y(J)-

Y(J+1));CDXX. endCDXXI. CDXXII. Mbar=sum/(1+Lambda);CDXXIII. ALabsw=CLWF_cla(j)/Mbar*180/pi;CDXXIV. alpha(j) = ALabsw+AlZero;CDXXV. endCDXXVI. CDXXVII. plot(alpha,CLWF_cla);CDXXVIII. hold on;CDXXIX. fplot(@(x)2*3.14*pi/180*(x-AlZero),

[AlZero,max(alpha)],'red');CDXXX. hold off;CDXXXI. xlabel('alpha, deg');CDXXXII. ylabel('C_L');CDXXXIII. legend('Lifting Line','Thin

Airfoil','Location','NorthWest');CDXXXIV. if(Twist~=0)CDXXXV. text(.5,.05,'Warning: C_L may become

unstable at low AOA with a non-zero twist')CDXXXVI. endCDXXXVII. grid on;CDXXXVIII. set(gca,'fontsize',14);CDXXXIX. endCDXL. CDXLI. endCDXLII. CDXLIII. end

Solidworks Drawings

(see attached sheets)


conceptual design of a light sport aircraft

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