design of the 1903 wright flyer replica madras institue of technology chennai - 44

DESIGN OF THE 1903 WRIGHT FLYER

REPLICA

MADRAS INSTITUE OF TECHNOLOGYCHENNAI - 44

WEIGHT ESTIMATION

Elements Quantity Weight (N) Structure 7.3 Engine 1 5 Propeller 2 1 Landing gear 3 2.25 Servo motors 3 0.58 Radio Controls All 0.212 Fuel 0.3 litres 2.36 Mounting + belt 3 Fuel tank 2 0.6 Misc. 2.5

TOTAL WEIGHT 24.802 N

AERODYNAMIC DESIGN

Lift Calculation

As the t/c ratio of the airfoil is less than 0.05 the classical theory of thin airfoils can be employed, by using this theory all the parameters other than drag is forecasted .

CL Vs Alpha curve for inviscid flow

-1.5

-1

-0.5

0

0.5

1

1.5

2

2.5

3

-15 -10 -5 0 5 10 15 20 25

Alpha

CL

Drag Polar

Induced Drag EstimationAR for a biplane = 4 b/cSpan = 5 feetChord length = 12 inchesAR = 20Gap = 9 inches

CDi = 1/(AR)*(1+)CL2

CDi = 0.11136 CL 2

profile

Profile Drag Calculation CD wet /Cf = 1+ 1.5 (t/c)3/2 +7 (t/c)3

CDp/Cf = 60 (t/c CL/5)4

The drag polar of our model isCD = 0.1303 + 0.1277CL

2

Wing warp

Rolling moment for Both wings = 0.56 (k/c) sin (l+ k cos )2

Where c is the chord of the wing is the angle of warp from the undisturbed

configuration k is the length of wing warp

POWER PLANT SELECTION

Power available

0

10

20

30

40

50

60

70

80

90

100

1 2 3 4 5 6 7 8 9

velocity

po

we

r

1500

2500

3000

3500

4000

4500

5000

1000

5500

6000

specifications

From drag calculations the power required 0.25 bHp

Diameter of the propeller ( 2-blade propeller)10 inches

The diameter is determined from the thrust to be produced.

The ground clearance was also taken into account while determining the diameter of the propeller.

STRUCTURAL DESIGN

WING FRONT SPAR

The bending moment about X axis (Mx) = 14.96 Nm

The formula used, Mxc =(Mx-(My*Ixy/Iyy)) /( 1-Ixy²/ (Ixx*Iyy)) =36.65 Nm

Myc =(My-(Mx*Ixy/Ixx)) / (1-Ixy²/ (Ixx*Iyy)) = -108.04

Nm

The maximum stress on the front spar σz = 32 MPa

The maximum allowable bending stress for spruce wood = 41 MPa

WING REAR SPAR

The maximum stress on the rear spar σz = 40 MPa The maximum allowable bending stress for spruce wood = 41 MPa

ELEVATOR AND RUDDER SPARS

ELEVATOR FRONT SPAR REAR SPAR

RUDDER SPAR

Design of truss members

Though the diameter of the truss members are different, for fabrication simplicity all the members are designed with diameter 5 mm.

PROPELLER SHAFT DESIGN

The formula used to calculate the diameter of the shaft

Me = (M +√(M²+T²)) / 2 = 0.15306 Nm

Te = √(M²+T²) = 0.7938 Nm

Maximum bending strength of the balsa wood σb = 1.18934*10^7 N/m

τ = 2482113 N/m²

Dmoment =7.15 mm

Dtorque =7.95 mm

Therefore the required diameter for the propeller shafts = 8 mm

MATERIALS TO BE USED

S.NO COMPONENT MATERIAL

1 WING SPARS SPRUCE

2 OTHER STRUCTURAL COMPONENTS

BALSA

3 SKIN REYNOLDS PLASTIC

4 FUEL TANK PLASTIC

PERFORMANCE CALCULATION

INTRODUCTION

The performance design covers the five major calculations which are listed below

Steady level flight performance

Climb performance

Range & Endurance

Take – Off & Landing

Turn Performance

LEVEL FLIGHT PERFORMANCE

Cruising Velocity = 4.7 m/sStalling Velocity = 2.35 m/s (CLmax = 2.04)VminD = 2.64 m/sDmin = 2.423 m/sPmin = 6.09 WVminP = 2.06 m/s

Range = 1.616 km (for cruise condition)

Endurance = 5 minutes 54 seconds

CLIMB PERFORMANCE

R/C = Excess Power / WeightExcess Power = Power Available – Power RequiredMaximum rate of climb occurs at 6 m/s

VelocityPower

AvailablePower

RequiredExcess Power

R/C maxAngle of Climb

m/s W W W m/s degree

2 8 6.108897 1.891103 0.075644 2.167557

3 12 7.83886 4.16114 0.166446 3.180502

4 30 13.4841 16.5159 0.660636 9.50645

5 60 22.52976 37.47024 1.49881 17.44327

6 90 36.55183 53.44817 2.137927 20.87438

7 90 60.97091 29.02909 1.161164 9.548366

8 91 90.17925 0.820751 0.03283 0.235128

EXCESS POWER

0

10

20

30

40

50

60

70

80

90

100

2 4 6 8

VELOCITY m/s

PO

WE

R W

POWERAVAILABLE

POWERREQUIRED

Take – Off

The take-off is curved up into 3 phasesThey are ground run, transition and initial climb upto 2 m and the same is repeated for landingGround run

Vavg = 0.7 VLO (lift off velocity)

= 0.84 Vstall

r = 0.1 for grass landVLO = 2.82 m/sCLLO= 0.8 CLmax

Ground Run = 6.3 mGround Run in transition = 2.1 mGround Run in climb = 4.48 mTotal take off distance = 12.88 m

GroundRun

Transition Climb

Landing & Turning performance

Landing distance total = 17.11 mMinimum turn radius = 0.4 m Corresponding time taken = 1.15 secondsV-n diagram is a plot between the velocity and load factor ( n = L/W)It gives the structural limit (max) of the aircraft and the highest and lowest possible velocity that can be reached by the aircraftThe maximum load factor = 275/25 = 11

V-n DIAGRAM

From the v-n diagram it is clear that n is maximum for the velocity of 8 m/s and the maximum velocity can be 35.75 m/s for the n value less than 11

0

1

2

3

4

5

6

7

8

9

10

11

12

0 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35

Velocity

n

stall limit

Structural limit

Max velocity

STABILITY ANALYSIS

LONGITUDINAL STATIC STABILITY

DIRECTIONAL STATIC STABILITY

CROSS COUPLING EFFECT

Increment in Rolling moment due to pitch rate(constant for different pitch rates)

0

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0 1 2 3 4 5 6 7 8 9 10

(deg)

Incr

emen

tal R

olli

ng

mo

men

t co

-eff

icie

nt

CR

Change in yaw co-efficient for different pitch rates (in rad/s)At cruising velocity of 4 m/s

0

0.0005

0.001

0.0015

0.002

0.0025

0.003

0 10 20 30 40 50 60 70 80 90 100

Wing warp deflection angle (deg)

In

cre

men

tal

Ya

w c

o-e

ffic

ien

t C

N

0.1

0.2

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

1.1

1.2

1.3

1.4

1.5

1.5708

COST ESTIMATION

Item Cost 4 channel radio control (with transmitter, receiver, 4- servos, Connectors etc.) 15000 Engine (0.25 bhp) 4000 Balsa Wood 2500 propellers 700 Fabrication cost 1000 Skin, belt, pulley, wires, LG etc. 1500 Total 24 700

RADIO CONTROL COMPONENTS

Engine throttle is controlled by servo motor.Four channel receiver set with 4 servo motors and connectors are used.The R/C unit weighs about 0.75 N.The R/C unit is placed just below the wing so that it reduces the bending moment caused by the lift.

POSITION OF SERVOS

POSITION OF RECEIVER

PROBLEMS

We are amateur designersBut we are confident that we can overcome this problem after taking part in this workshopSince the stability of the aircraft is at a high risk we feel that flying the aircraft safely would require a lot of training