Aeromodel design a pedagogic approach.

Edgar A.Gomez1 and Oscar F. Lucero.2

Los Libertadores University,Bogota DC,Colombia

Jose D. Cardenas3

Los Libertadores University,Bogota DC,Colombia

ABSTRACT

This document aims to demonstrate the need for aerodynamic study for static and dynamic stability of an

aircraft which was started from the selection parameters of profile geometry of wing and wing

configuration and..stabilizer.

The corroboration of the data is made using a 1:2 scale model in which data were obtained under a margin of

error.

Nomenclature(Nomenclature entries should have the units identified)

Cl = airfoil lift coefficient

CL = Wing lift coeffiecient

Cd = Airfoil lift coefficient

CD = Wing drag coefficient

a = angle of attack

a0 = airfoil lift slope

a = wing lift slope

AR = aspect ratio

Sw = Wing surface

St = Horizontal stabilizer surface

Sv = Vertical stabilizer surface

i = negative incidence angle

1 Engineering student, Aeronautical engineering faculty Los Libertadores University, eagomezm@libertadores.com2 Engineering student, Aeronautical engineering faculty Los Libertadores University, oflucerof@libertadores.com3 Engineering student, Aeronautical engineering faculty Los Libertadores University, jdcardenasv@libertadores.com

CM = Pitch moment coefficient at o lift

Vh = Horizontal stabilizer tail ratio

e0 = downwash

al=0 = zero lift angle of attack

h = center of gravity in terms of chord

hac = wing aerodynamic center in terms of chord

de/da = Pitch moment coefficient slope

q = dynamic pressure

b = Spanwise

c = chord

Vl = Landing velocity

I. Introductionhe airplane aerodynamics plays an important role, in an aero model design, the effect of it, give to designer an

intuitive knowledge of how the airplane will be have, the 2D analysis for different airfoil and also the

respective correction for the 3D model.

TTo get the flight operation requirement the gross weight must to be met, and the CG location, and pitching

aerodynamic moment too; in the performance analysis the total plots and motor features are used to compute and

cheek in the airplane accomplish the flight requirements.

II. MISSION REQUIREMENTS.

The current project is a first attempt in the aircaft design, therefore and taking to account the university fatilities, we

have decided to make a aeromodel, fly indoor, that can be used in the Los Libertadores Gym football field.

The following are the requirements:

Max operative velocity can not exceed 40 m/s.

Maximum height 0.6m.

Maximum length 2.1 m.

Those first 3 requirements are putted by the wind tunnel features, as for example the maximun wind tunnel velocity,

and dimensions.

Take off distance can not exceed 5m.

It because the maximun leght of this field is about 20m.

Electrical powered by speed controller 280 motor with PBC 5.1” X 4.5” propeller.

Indoor flight.

This requirement is imposed because we already have characterized his feature, including his performance curves

for thrust, power, and motor-propeller efficiency.

High longitudinal and lateral static stability.

This requirement in due to, it will be the rated requirements for the class proffesor.

Radio controlled in circumference of 10 m of radio.

Flight range between 5 to 10 minutes.

III. BASELINE.

As a baseline will be taking different aeromodels with similar feature, but maybe the most important of them is

the Dragonfly developed by MIT students with the following characteristics:

Dragonfly

Wing span 48 in 1,2 m

Wing area 450 sq in 0,29 m^2

Weight 15 oz 0,42 Kg

Wing Loading

Chord 10 in 0,25 m

Lenght 35 in 0,889 m

Motor Grampner speed 400

Battery 8,4 V (600 mAh) 8,4 V (600 mAh)

Re 100.000 100.000

Tabla 1. Baseline airplane features.

IV. CONCEPTUAL IDEAS.

To solve the present problem different ideas were taking into account; the first one considered a hight low

aspect ratio airplane to allow us enter it in the test section without scale it, but taking into account that the

induced drag for these kind of airplanes is so large, and the thrust provided by the electric motors is not enough,

this idea was discarded, a second one was to make a biplane to allow us enter the complete airplane in the wind

tunnel test section but taking into account that we yet have the enough teorical knowledge about it, and the

interferences between the two wings are large we prefer don’t use this configuration.

Finally we decided to make the aeromodel with a common aspect ratio for them, and scale this model to make

the stability probes in the wind tunnel.

V. WEIGHT ESTIMATION

To make a conceptual weight estimation we find the weight of the most common devices in this kind of airplanes

under the fly requirements, the following were the choosen devices to operate our aeromodel:

SPEED 280 MOTOR.

Diameter 24 mm

Height 31.7 mm

Weight 42.5 g

Designed for 7.2-9.6 V operation.

Prop shaft diameter 2 mm.

ELECTRIC FLY HIGH FRECUENCY

ELECTRONICS SPEED CONTROLLER

Width 21 mm

Height 11.5 mm

Length 7 mm

Weight 8 g

3 KHz switching

APC 5.1 x 4.5 PROPELLER

Battery elctric fly 7.4V 1800mAh 25C

Voltage 7.4 V

Energy stored 1800 mAh

Dimensions 102 x 35 x 14

Weight 102 g

Futaba R2004GF 4-Channel

2.4GHz FHSS Receiver

Size: 1.54 x 1.02 x 0.39" (39 x 26 x 10mm)

Weight: 0.49oz (14g)

3 servo motor each one for one flight control.

Structural weight estimation

The structural weight estimation was made drawing a CAD model in the Solidworks software, for a common

aeromodel with similar characteristics than the MIT dragonfly, under the experience of aeromodelism course

proffesor and other experienced person in uav design.

The wing structure weight was aproximately 62 gr (0.062 Kg), doing an interpolation the horizontal and vertical

estabilizer as more or less a weight of 40 gr (0.042 Kg).

The total preliminary gross weight was more or less 300 gr (0.3 Kg).

VI. WING AIRFOIL SELECTION.

The airfoil selection was made under different criterias, the first one was the high static stability that our airplane

must have, therefore a low curvature airfoil is needed, the second one is that taking into account that those kind of

aeromodel fly at low reynolds numbers the pressure drag or shape drag is dominand rather than friction drag,

therefore a thin airfoil also is needed, and finally we need a cruise lift coeeficient similar than the dragon fly, more

or less 0.6.

For these reasons a NACA 2410 airfoil was choosen,( this is the same airfoil for the Cessna skyhwak C-172 who

flies in Re between 800000 and 1000000).

The normal polar graphs were made in the XFLR5 for Re of 50000-100000-150000-200000-3000000 and gave us

the following results; the Re 3000000 was made to compare the results with the results of NACA in their book

“Theory of wing sections”.

The plots for Re 3000000 were compared with the data written in “theory of wing sections” for Cl, Cd, and Cm the

results are in order with a maximun error percentage of 7%, it means that the data computed by XFLR5 is right.

Different aspects to talk about there are for these plots, the first one is that the stall angle is at more or less 11

degrees, the second one is that at Re of 50000 the plots varies strongly than the other plots altought ist a important

change.

Maybe the most important feature for these plots is that te pitch moment coefficient with respect to Aerodynamic

center isnt constant for low reynold numbers, and in fact there are a large negative slope for angles of attack lower

than 5 degrees and positive for angles greather than 5, this is remarkable because in stability analysis thse slope play

an important role.

Maybe the most important feature for these plots is that te pitch moment coefficient with respect to Aerodynamic

center isnt constant for low reynold numbers, and in fact there are a large negative slope for angles of attack lower

than 5 degrees and positive for angles greather than 5, this is remarkable because in stability analysis thse slope play

an important role.

VII. WING CHARACTERIZATION.

The wing sizing was made using the baseline Dragonfly, specifically in spanwise, chord, and aspect ratio; the aspect

ratio choosen was 5.5 a good aspect ratio for a trainer airplane according to Raymer[ ], also this aspect ratio was

choosen to minimize the induced drag due it is inversaly related, a straight wing was made due to it is the most easy

configuration, and was the most explained in class room.

The dimensions are as follows

Wing

Sw 0,22 m2

Spanwise 1,1 m

Chord 0,2 m

AR 5,5

The coefficients were adjusted for a finite wing due to the wing tip vortex influence with the following equations,

that was used in a MATLAB code to compute the coefficients from the airfoil data for the finite wing in each point.

The resultan plot are the following for the infinity wing with a oswald efficiency factor of 0.75 (common value for

straight wings according to raymer).

The relevan data is provided in the next table

NACA 2410

a0 α l=0 a

Re0,05 0,093 -0,5 0,0659

Re0,1 0,1 -1,25 0,0693

Re0,15 0,102 -1,5 0,072

Re0,2 0,104 -1,75 0,0712

Average 0,100 -1,25 0,070

VIII. STABILITY ANALYSIS, HORIZONTAL AND VERTICAL STABILIZER CHOOSE.

Due to one of the most important features tahat would be rated is the static stability, is needed to build a

configuration that is strongly stable, that is to say that the safety margin SM is greater than 0.4.

First of all the center of gravity must to be located because the longitudinal static stability depends in mayorie of this

point; the different devices as motor, betteries and so on are located in a tipical way from the leading edge as follows

The final C.G (center of gravity loction also depends of the tail location, therefore an iterative process was made to

put it and reach the needed contitions for the following equations alos for this process a MATLAB code was

developed to avoid had calculations.

To select the airfoil for the horizontal stabilizer a lift slope and the curvature was the dominand fact, the airfoil

NACA 0012 was selected due to of the serie NACA it was the airfoil with greatest slope; a non curvature airfoil was

selected because it doesnt produce pitching moment coefficient to the total airplane, helping with it the facilitie to

the total longitudinal stability.

The same procedure made with the wing airfoil was made to the stabilizer airfoil, and the results for the XFLR5

airfoil were:

For the finite surface the result for Re 100000 were:

The stabilizer dimensional would be like this:

Horizontal Stabilizer

St 0,033 m

Spanwise 0,3 m2

Chord 0,11 m

AR 2,7

And relevant information for the longitudinal static stability.

NACA 0012

a0 α l=0 a

Re0,05 0

Re0,1 0,11 0 0,015

Re0,15 0,11 0 0,015

Re0,2 0,11 0 0,015

Average 0,11 0 0,055

The information about downwash stream influence was extracted from XFR5 in his wing and plane design window,

the data showed below was computed for the finte wing.

Downwash angle (Re 125000)

angle ε slope

2 -1,505 -0,37

1,5 -1,32 -0,39

1 -1,125 -0,4

0,5 -0,925 -0,386

0 -0,732 -0,384

-0,5 -0,54 -0,396

-1 -0,342 -0,394

-1,5 -0,145 -0,39

-2 0,05 -0,394

-2,5 0,247 -0,396

-3 0,445

Average slope -0,39

Downwash angle at L=0 -0,242

Later than compute the iterative process in MATLAB with a lt (distance between C.G and tail A.C ) of 0.68 m the

pitch moment when CL=0, Volumne tail ratio and CM slope were:

CMcg-l=0 0,0104

dCM/dα -0,0337

Vh 0,5

It show us that the airplane is stable because the first term is positive and the second one is negative, also the

volumen tail ratio is in good margin because according to MIT criteria [] it must to be between 0.3 to 0.6 to be well

designed; now is necessary to compute the neutral point and later the static margin, those paramiters are calculated

as follows:

Replacing in them and solving for hn and S.M it gave us:

hn 0,80 m

SM 0,47

That means it is strongly stable due to 0.47 is greater than 0.4.

The absolute angle of stabilization is found with the following equation

and finally as our o lift angle is -1.25 degress the geometric estabilization angle of attack yields -0.5 degrees.

The vertical tail just was sized using the Vertical volumen tail ratio criteria that for common aeromodels accordin to

MIT [] must to be 0.2 to 0.05, therefore and trying to put the vertical stabilizer aerodynamic center in the same point

that the AC of horizontal stabilizer, a tapered configuration was selected with the following dimensions:

Vertical Tail

Sv 0,019

Spanwise 0,2 m

C root 0,11 m

C tip 0,08 m

Mean Chord 0,095 m

AR 2,12

Therefore using the next equation for Vv

We get 0.053 that is in the lower limit for the MIT criteria.

IX. FLIGHT PERFORMANCE.

To get the total lift and drag polar for the performance analysis, is needed to compute the the contributions of each

one surface of the airplane, with respect to a specific surface area.

Taking into account that the total lift and drag is the sumatory of them we get:

Another MATLAB code was realesed to make point by point calculations for the 2 surfaces available polars,

obiously taking into account the tail incidence with respect to the wing geometric angle of attack.

The following to polars were obtained for Re 100000, the ost problably flight regime.

Also is important to note that the notation for the angle of attack in the plots showed above, are the same than the

wing angle of attack.

The first performance analysis that would be made is the steady flight analysis when the thrust,and power required

would be compared with the thrust, and power available for the electric motor speed 280.

For this steady flight contidition the lift must to be equal to weight, and thurst equal to airplane drag; a common

equation that relates them with the required thrust to maintain level flight at different speeds at sea level and Bogota

geometric altitude is the following:

We can see that the velocity at lower thrust required is aproximately 7.5 m/s that correspond to an angle of attack of

4.5 degrees for each graph.

It show us that for the 280 Speed Motor the trush required at thsose speeds is available in the data provided by MIT

studies for the current motor, we can see that every configuration 7 volts, 5 volts, 4 volts or 3 volts serve us to thrust

the airplane in level flight.

For these graphs the lowest power required is in a velocity aproximately 6 m/s,at this value the motor power

available at 7.4 volts is aproximately 4.2 W that is greater the 2 W required, For maximun efficiency we choose our

cruise speed in 6.75 m/s that is the half of the minimun thrust required and minimun power required.

X. WIND TUNNEL TEST MODEL

The wind tunnel test is made in Re between 100000 and 150000 keeping the dynamic scale from the real airplane,

the test model was a ½ of the real aeromodel, the center of gravity was calibrated to get the same distance from the

LE to CG in term of chord, the following is the CAD model for the current work.

XI. CONCLUSIONS

Pitch moment in airfoil for Re lower than 500000 are so unsatable, changes must to be made in the

longitudinal static equations.

The trim angle of attack is so small about -0.5 degrees, and must to be corrected to 4 degrees that is the

angle at cruise speed; due to current aeromodels that cant have trim controls, the tail design must to be

optimized.

Structural weight must to be corrected due to is was a bad estimation.

The electric motor choosen is so ussefull, thus it reaches the operation requirements.

Wind tunnel test must to be made when trim angle is corrected, because at not trimmed angle of attack the

airplane generates a small lift if not negative lift.

Vertical tail must to optimized because it isnt under lower vertical volumen ratio limit

When the scaled model is made, a dimensional reduction produces a change in the total wing are but not in

the aspect ratio, is keeps constant and provide us the same lift slope, therefore the same curves for the finite

wing made in the model can be applied in the scaled model.

XII. REFERENCES

[1] Fundamental of flight; Jhon Anderson; Mac Grawn Hill International; Fifth edition;2005.

[2] Theory of wing section; Iran H Abott, Albert Von Doefholf; Dover Books; 1940.

[3] Dynamic of flight; Bernard Etkin; Lloyd Duff; Jhon willie and song LTDA, fifth edition.

[4] Airplane aerodynamics and performance; Jan Roskam; Chan Tau, Dar corporation; 1997

[5] MIT unified engineering, design competition lectures; Aircraft design basic rules; spring 2005

[6] Aircraft design a conceptual approach; Daniel Raymer; AIAA, 1992

[7] Tutorial de XFRL5.