Mini Wind Tunnel Group S · 2018. 1. 13. · Lab Report Mini Wind Tunnel Performance 11.11.2016 . 2...

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submitted: 24.11.2016

Supervisor: Angelica Lam

Group: Dipta Majumder Ahmed Altaif

Interview

Introduction

Theory

Setup

Experimental & Evaluation Procedure

Presentation & Description of Results

Presentation & Description of Evaluation

Comparison with Expectation

Discussion of result significance

Conclusion

Reference section

Bonus points

Result: Date: Sig.:

Lab Report

Mini Wind Tunnel Performance

11.11.2016

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Table of Contents

1. Introduction .......................................................................................................................................... 3

2. Theoretical background ......................................................................................................................... 3

2.1 Characteristics of a wind profile ........................................................................................................... 3

2.2 Optimal operating point of a wind turbine: .......................................................................................... 4

3. Methodology ......................................................................................................................................... 5

3.1 Equipment used: .................................................................................................................................. 5

3.2 Experiment procedure: ........................................................................................................................ 6

3.2.1 Calibration of the system .............................................................................................................. 6

3.2.2Optimal operating point of a wind turbine ..................................................................................... 7

4. Results ................................................................................................................................................... 9

4.1 Characteristics of a wind profile ........................................................................................................... 9

4.2 Optimal operating point of a wind turbine ......................................................................................... 11

5. Discussion ............................................................................................................................................ 14

5.1 Wind profile experiment .................................................................................................................... 14

5.2 Wind turbine experiment: .................................................................................................................. 16

5.2.1 Cp vs Tip speed ratio curves: ....................................................................................................... 16

5.2.2 Power curves: ............................................................................................................................. 17

5.2.3 Difficulties in measurement: ....................................................................................................... 18

5.2.4 Stabilization of data:................................................................................................................... 19

5.2.5 Origin of errors: ........................................................................................................................... 19

5.2.6 Speed limiting of a wind tunnel: .................................................................................................. 20

6. Conclusion ........................................................................................................................................... 20

References .................................................................................................................................................. 21

Appendix A .................................................................................................................................................. 22

Appendix B .................................................................................................................................................. 29

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1. Introduction

With a view to provide electricity through clean energy technologies, many counties are exploring

different renewable energy sources. From sailing into the sea, wind has been used to pump waters and

for graining. In fact, wind energy was used to produce electricity in the late nineteenth century [1]. As

time passed by, human beings have developed modern technologies to make the best use of the wind

energy. Most importantly, harvesting as much energy as possible through interaction with wind has

been the area of interest for innovation and innovation.

Using the kinetic energy from the flowing wind, we need deep understanding of the forces exerted on

anything that comes in its way. Fundamentally, we want to use this kinetic energy into some form of

mechanical energy through a rotating body. Exerted force components i.e. drag force and lift force are

essentially used for this. Investigation on the effect of these forces in order to extract power can be

simulated by a wind tunnel. A profile can be placed in a wind tunnel to simply understand the effects.

Wind energy converters (WEC) or wind turbines are used now-a-days to generate electricity from wind

energy. However, performance of wind turbines depend on many aspects e.g. angle of attack of wind on

the rotating blades, shape of the blades etc. To investigate the theories and practical difficulties in

harvesting wind energy, a laboratory experiment was conducted as part of the course requirement of

Postgraduate Programme Renewable Energy (PPRE), University of Oldenburg.

2. Theoretical background

2.1 Characteristics of a wind profile

In order to understand how wind behaves with anything on its way or how it rotates the blades of a

wind turbine, interaction of wind with an airfoil is a good point to start with. Force exerted on an airfoil

can be split into two components i.e. drag force (FD) which works on the direction of the wind and lift

force (FL) which works perpendicular to the direction of the wind. Force components (see figure 1) are

proportional to the wind speed (u), density (ρ) and area of the airfoil (A) that’s interacting with the air.

Drag and lift forces can be calculated by using the following equations [2]:

FL =

ρ.A.CL.u

2, where CL is the lift coefficient (1)

And FD =

ρ.A.Cd.u

2, where Cd is the drag coefficient (2)

Lift and drag coefficient mainly depends on shape of airfoil, angle of attack on the airfoil, state of flow

(laminar or turbulent) and Reynold’s number1.

1 Reynold’s number is an dimensionless quantity to understand the state of flow i.e. laminar or turbulent.

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Figure 1: Drag (FD) and lift (FL) forces on an airfoil at an angle of attack α. (Ref:[3])

From Equation (1) and (2), lift and drag coefficients are dimensionless parameters which are important to

understand the interaction between airfoil and wind. Lift and drag coefficients vary quite differently for

different angle of attacks. Variation of CL and Cd with angle of attack is shown in Figure 2. In case of small

angles of attack, drag force is small. On the other hand, lift force is proportional to the angle of attack. This is

true until a certain angle of attack, with very high attack angles CL starts to decrease. This decrease in lift is

called ‘Stall’. At high angles of attack the air isn’t interacting that much with the top of the foil, rather getting

detached from it. This detachment causes the lift force to drop. Gliding angle (ε), ratio between lift and drag

coefficient is another qualitative parameter.

Figure 2:Lift and drag coefficient versus angle of attack (α) (Ref:[3])

Gliding angle can be defined as the following equation:

ε =

C

C

(3)

Higher gliding angle would mean that the lift force is higher compared to the drag force. Hence, higher

gliding angle would indicate a good profile. Good profiles have gliding angle between 50 to 70 [2].

2.2 Optimal operating point of a wind turbine:

Extractable power from the wind comes from the kinetic energy of the wind. Since, power is time

derivative of energy, wind power depends on mass flow (m’) and u2. If we know the air density (ρ), speed of

wind (u) and area covered by the turbine or swept area (A), we can calculate the mass flow. Mass flow (m’)

can be described as, m’=ρ.A.u with no time component.

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We can find the power available in wind from the following equation,

Pwind=

ρ.A.u3 (6)

Wind power can be converted to usable energy by wind energy converters (WEC) or wind turbines.

However, all of the wind power cannot be extracted. This is constrained by Betz limit. This concept was

developed by German Physicist Albert Betz in 1919 [4]. If all of the wind power is extracted, there will be no

incoming flow of air towards the wind turbine. Betz described that the maximum power is reached when the

wind speed behind the rotor is reduced to one third of the initial value in the front side. Ratio of extractable

mechanical power to the wind power is called Power Coefficient (CP). Betz limit results CP=16/27, which

indicates that only 59% power from the wind can be extracted. In real cases, CP obtained will be lower than

Betz Limit.

With understanding of Betz limit, we can calculate power of WEC (Pturbine) by the following:

Pmechanical=

ρ.A.Cp.u

3, where Cp ≤ 0.59 (7)

A wind turbine consists of a tower, rotor and rotor blades, generator, gearbox, nacelle, brake system and

other components. For the sake of simplification, we have considered a small DC generator. Rotor

characteristics depend largely on ‘Tip speed ratio (λ)’ which is the ratio between speed of rotor tip and wind

speed. Rotor tip speed can be calculated by multiplying angular velocity of rotor (ω) in radian/sec with the

radius of the rotor (R). Notably, pitch angle refers to the tuning of angle of attack of blades to control speed

and hence power generated. For a given pitch angle, CP(λ) characteristics of a turbine can be obtained (see

Figure 3), which will reveal that at an optimal tip speed ratio, CP will be optimum. Optimum CP implies that at

this operating point maximum power is delivered by the wind turbine.

Figure 3: Representative CP- λ curve (Ref: [5])

3. Methodology

3.1 Equipment used:

Conducted experiment can be divided in to two parts i.e. i) Characteristics of a wing profile and ii) optimal

operating point of a wind turbine. Equipment used in the experiment and the relevant information are

provided in Table 1 and 2 for two parts of the experiment.

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Table 1: Equipment used for characterization of an airfoil

Equipment Manufacturer Type or S/N Specification

Wind Tunnel ELV UNIWIND 506866 0 – 8 m/s

Airfoil - - 10 x 8 cm

Forcemeters PHYWE Windkanal 0 – 1.2 N

0 – 1.2 mN

Hoisting Drums - - -

Deflection Pulleys - - -

Counter Weights - - Wheel like

Balance Suspensions - - Spring like

Table 2: Equipment used for operation of a wind turbine

Equipment Model Brand

Mini wind turbine - -

Digital multimeter (2) M-4650B Voltkraft

Wind tunnel 506866 ELV UNIWIND

Shunt resistor (36.21Ω) - -

Real ohmic load box Mini Ω Dekade 1-1000 NBN Elektronik

Cables - -

3.2 Experiment procedure:

3.2.1 Calibration of the system

Calibration is very important in order to ensure the accuracy of the measured data. Calibration was done in

the beginning of the experiment. Airfoil under the test was placed at approximately 25 cm away from the

wind tunnel opening. The angle of attack was set to the minimum. Pointer was adjusted to the center with

use of two forcemeters with counter weights and springs on the back. Values of two forcemeters (ΔF1 and

ΔF2) were noted to find the offset values. Figure 5 and 6 shows the experimental set up of the force

measurement and wind tunnel respectively.

After performing the calibration, angle of attack -5 and 5 m/s wind speed were considered to begin with.

Due to the force exerted by the flowing wind, the profile is deflected from its original position. The profile is

brought back to its original position using the hoisting drums.

The forces F1 and F2 were measured from the newtonmeters adjusting the offset values. However,

measured forces acted at the end of the liver arm while the lift and drag forces acted on the profile. Level

arm correction was incorporated to scale the forces to FL and Fd.

This procedure was repeated for 6, 7 and 8 ms-1

wind speeds, keeping the angle of attack same. Later, angle

of attack was changed from -50 to 30

0 at 5

0 steps and the whole procedure was done for different angle of

attack with varying wind speed.

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Figure 4: Experimental setup of drag and lift force measurement with lift/drag balance with mounted

profile (1), the newtonmeters (2) and (3), two hoisting drums (5), deflection pulleys (4), the counter

weights(6) and the balance suspension(7) with setup mounting (8). [Source: Authors]

Figure 5: Wind tunnel setup with (1) wind tunnel outlet, (2) display board and (3) wind speed controller

(Source: Authors)

3.2.2 Optimal operating point of a wind turbine

In order to investigate the properties of a wind energy converter (WEC), a small miniature wind turbine was

exposed to a wind tunnel with a constant speed. Pitch angle and number of blades both could be adjusted

for the miniature wind turbine. During the experiment, a pitch angle of 200 and three flat plate blades

were used.

In order to find out the power delivered by the wind turbine, we connected a real ohmic load box to the

output of the WEC. A shunt resistor of value 36.21 ohm was connected to find out the current in the circuit.

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Two multimeters were used across the shunt resistor and WEC to calculate the voltages respectively. An

automatic multimeter with 12V DC adapter was connected to find the rotational frequency. Connection

diagram is given in Figure 6.

Figure 6: Circuit diagram of the experiment conducted (Source: Authors)

Load resistance was varied from 50-1000 ohms and corresponding delivered power was measured.

Maximum power could only be obtained at the optimum Cp and optimum tip speed ratio (λ). Power

coefficient Cp and tip speed ratio was calculated and plotted. Optimum value of Cp and Tip speed ratio was

noted down. Set up of this experiment is shown Figure 7.

This procedure was repeated for three different wind speeds i.e. 5 ms-1

, 7 ms-1

and 7.8 ms-1

(see section

5.2.6 to understand why 8ms-1

could not be achieved) . Notably, the used wind tunnel is only capable to

provide maximum 8 ms-1

of wind speed. In each of the cases, delivered maximum, optimum Cp and

optimum tip speed ratio were measured. These values were later analyzed to find out if obtained data

matches with the expected power characteristics of a small wind turbine.

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Figure 7: Connection set up during the WEC experiment where (1) outlet of wind tunnel (2) wind turbine

(3)wind speed control (4) wind speed display (5) shunt resistor (6) real ohmic load (7) automatic

multimeter to measure frequency (8) multimeter to measure voltage across shunt resistor and (9)

multimeter to measure voltage generated by the wind turbine. (Source: Authors)

4. Results

4.1 Characteristics of a wind profile

The lift and drag forces (FL and FD) were calculated from the measured values of F 1 and F2 by using the

level arm correction factor

as the following:

F =F. (

), where, F = Themeasuredvalue − ΔF (8)

And F = F. (

), where, F = Themeasuredvalue − ΔF (9)

X1 and X2 are the distances from the end of the lever arm to the profile’s center and the arm lever’s

pivot point respectively.

Calculated lift and drag forces (FL and FD) were plotted against the square value of wind speed (u) for

each angle of attack (α°). Plotted results are shown in Figure 9-10. Notably, the results shown are for

angle of attack of -50 and 00. Measurements were done up to 300 and the remaining graphs are given in

Appendix A (Table A1).

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Figure 8: Lift and drag forces against the square value

Figure 9: Lift and drag forces against the square value of wind speed (u

Finally, the drag coefficient (

from force versus square of wind speed graphs. L

considering the following equation.

y = c . a. x ; where

y=Force

Then the drag coefficient (C

Equation (3). Findings are shown in Table (3)

Table 3: Lift coefficient, drag coefficient and gliding angle with change in angle of attack

Angle of Attack

-0.005

0.000

0.005

0.010

0.015

0.020

Lift

, D

rag

(N

)

0.000

0.005

0.010

0.015

0.020

Lift

, D

rag

(N

)

ift and drag forces against the square value of wind speed (u2

ift and drag forces against the square value of wind speed (u2

Finally, the drag coefficient (C) and lift coefficient (C) were calculated for each angle of attack (α°)

from force versus square of wind speed graphs. Linear fitting for the lift and drag curves

considering the following equation.

; wherex u and a

ρA$ (i symbolizes either lift or drag) and

C), lift coefficient (C) were used to calculate the gliding angle (

Equation (3). Findings are shown in Table (3)

Lift coefficient, drag coefficient and gliding angle with change in angle of attack

Angle of Attack

(α°)

CL CD ε (CL

-5 -0.39 0.57 -0.68

0 0.57 0.69 0.82

y = -0.0019x + 0.0079

y = 0.0028x + 0.0061

0.005

0.000

0.005

0.010

0.015

0.020

25 36 49 64

%^2 (m2/s2)

Angle of Attack (-5°)

Lift

Drag

Linear (Lift)

Linear (Drag)

y = 0.0028x - 0.0002

y = 0.0034x + 0.0023

25 36 49 64

%^2 (m2/s2)

Angle of Attack (0°)

Lift

Drag

Linear (Lift)

Linear (Drag)

2) at angle of attack (-5°)

2) at angle of attack (0°)

calculated for each angle of attack (α°)

inear fitting for the lift and drag curves were used

lift or drag) and (10)

) were used to calculate the gliding angle (ε) using

Lift coefficient, drag coefficient and gliding angle with change in angle of attack

L / CD)

0.68

0.82

Lift

Drag

Linear (Lift)

Linear (Drag)

Lift

Drag

Linear (Lift)

Linear (Drag)

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5 0.71 0.82 0.88

10 1.84 0.90 2.05

15 1.94 0.96 2.02

20 3.69 2.67 1.38

25 4.14 3.22 1.28

30 4.69 3.41 1.38

The lift coefficient (C), drag coefficient (C) and gliding angle (ε) were plotted which is shown in Figure

11.

Figure 10: Lift coefficient, drag coefficient and gliding angle with change in angle of attack

4.2 Optimal operating point of a wind turbine

Manual ohmic control strategy was deployed for different wind speeds to find out the power delivered

by a wind turbine. Set parameters considered for the experiment are given in Table 4.

Table 4: Set parameters before conducting the experiment

Aspect Set value

Shunt resistor 36.21 Ω

Radius of the wind turbine 8.5 cm

Swept area 0.0227 m2

Density of air 1.225 Kg/m3

Pitch angle 200

No of blades and types Three flat blades

Power was calculated using the measured voltage and current. Power vs. load and Cp vs. λ were plotted

for 5, 7 and 7.8 ms-1

. Optimum tip speed ratio and optimum Cp were obtained from the graphs. The

results are shown in Fig 11-16. Measured data are attached in Appendix B (Table B1-B3)

-5 5 15 25 35

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

-1.0

0.0

1.0

2.0

3.0

4.0

5.0

ε

CL,

CD

Angle of Attack (°)

CL, CD, ε (CL/CD) Vs. Angle of Attack (α°)

CL

Cd

ε (CL/Cd)

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(11) (12)

(13) (14)

(15) (16)

0E+00

1E-04

2E-04

3E-04

4E-04

5E-04

6E-04

7E-04

8E-04

9E-04

1E-03

50

10

0

20

0

30

0

40

0

50

0

60

0

70

0

80

0

90

0

10

00

Po

we

r (w

att

s)

Load (ohms)

Power vs Load curve for u=5 m/s

0.0E+00

1.0E-04

2.0E-04

3.0E-04

4.0E-04

5.0E-04

6.0E-04

9.0

E-0

3

7.6

E-0

3

9.9

E-0

3

1.0

E-0

2

1.1

E-0

2

1.1

E-0

2

1.2

E-0

2

1.2

E-0

2

1.2

E-0

2

1.1

E-0

2

1.2

E-0

2

Cp

Tip speed ratio (λ)

Cp vs λ for u=5 m/s

0.0E+00

1.0E-02

2.0E-02

3.0E-02

4.0E-02

5.0E-02

6.0E-02

7.0E-02

50

10

0

20

0

30

0

40

0

50

0

60

0

70

0

80

0

90

0

10

00

Po

we

r(w

att

s)

Load (ohms)

Power vs load for u=7 m/s

0.0E+00

2.0E-03

4.0E-03

6.0E-03

8.0E-03

1.0E-02

1.2E-02

1.4E-02

1.6E-02

9.0

E-0

2

1.1

E-0

1

1.4

E-0

1

1.6

E-0

1

2.1

E-0

1

3.1

E-0

1

3.4

E-0

1

3.6

E-0

1

3.7

E-0

1

3.8

E-0

1

3.8

E-0

1

Cp


Cp vs λ for u=7 m/s

0.0E+00

2.0E-02

4.0E-02

6.0E-02

8.0E-02

1.0E-01

1.2E-01

1.4E-01

50 200 400 600 800 1000

Po

we

r (w

att

s)

Load (ohms)

Power vs load for u=7.8 m/s

0.0E+002.0E-034.0E-036.0E-038.0E-031.0E-021.2E-021.4E-021.6E-021.8E-022.0E-02

9.5

E-0

2

1.3

E-0

1

1.7

E-0

1

2.6

E-0

1

3.3

E-0

1

3.6

E-0

1

3.7

E-0

1

3.8

E-0

1

3.9

E-0

1

3.9

E-0

1

4.0

E-0

1

4.2

E-0

1

Cp


Cp vs λ for u=7.8 m/s

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Optimum tip speed ratio versus the wind speeds is shown in Fig (17), maximum power vs. u3, ωopt vs. wind

speeds are shown in Fig (18) and (19) as well. Figure (20) represents the maximum power and Cp in the

graph versus the wind speed.

(17) (18)

(19) (20)

0.00

0.50

1.00

1.50

2.00

2.50

5 7 7.8

Op

tim

um

Tip

sp

ee

d r

ati

o (

λo

pt)

Wind speed (m/s)

Optimum tip speed ratio vs wind

speed

y = 0.0003x - 0.043

R² = 0.9908

-0.02

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0 200 400 600

Pm

ax

(w

att

s)u3 (m3s-3)

Maximum power vs U3

0

50

100

150

200

250

5 7 7.8Ro

tati

on

al

fre

qu

en

cy (

rad

/s)

Wind speed (m/s)

ωopt vs wind speed

0E+002E-034E-036E-038E-031E-021E-021E-022E-022E-022E-02

0

0.02

0.04

0.06

0.08

0.1

0.12

0.14

5 7 7.8

Cp

Pm

ax

(wa

tt)

Wind speed u (m/s)

Pmax vs Windspeed and Cp vs

Windspeed

Pmax

Cp

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5. Discussion

5.1 Wind profile experiment

It was explained earlier (see section 2.1) how after a certain angle of attack, the lift coefficient decreses. This

‘stall effect’ means that the air gets detached from the top of the airfoil. In another way, the flow is no

longer laminar. Turbulence would decrease the lift and the lift coefficient as well. Based on this argument,

Reynold’s number is an important parameter to understand the results. Since, Reynold’s number would help

us to understand the state of the flow.

Let’s have a look on the data of lift coefficient, drag coefficient and gliding angle for an airfoil of type RAF34

(ref) in Figure 21(a). If we compare this with our measured data set [see Figure 21(b)], we observed

significant difference.

Lift coefficient doesn’t show any decline within the range of angle of attack, it’s rather increasing. At low

angle of attack, drag coefficient remains fairly constant which is also observed for our measurement (up to

150). In case of -5

0, the lift coefficient is negative which is also observed for RAF34. Lift coefficient increased

fairly with a higher slope than the drag coefficient; which is aligned with the RAF34 curve. For RAF34,

maximum lift coefficient is achieved at around 140 ~15

0, above which point lift coefficient decreases.

However, this was not observed in our experiment. Notably, gliding angle value at the point of maximum lift

coefficient is around 70 for RAF34. High gliding angle indicates that the air foil RAF34 is of high quality. While

in our measurement, we reached the maximum gliding angle of 2.05 at 100

Airfoil Type RAF34 Airfoil under test

(a) Ref: [2] (b)

Figure 21: Comparison between characteristics graph of RAF34 and airfoil tested

Reynold’s number (Re) is a crucial tool to determine the behavior of the flow around the airfoil, either

laminar or turbulent flow. To do so, the air properties such as air density and viscosity as well as airfoil’s

characteristic length are required.

Re

u ∗ L

v

(11)

-20 0 20 40

-1.0

-0.5

0.0

0.5

1.0

1.5

2.0

2.5

-1.0

0.0

1.0

2.0

3.0

4.0

5.0

ε

CL,

Cd

Angle of Attack (°)

CL, Cd, ε (CL/Cd) Vs. Angle of Attack (α°)

CL

Cd

ε

(CL/Cd)

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Where, u the velocity of the flowing air, L is the characteristic length of the airfoil and v is the kinematic

viscosity of the air which is a ratio of air’s absolute (dynamic) viscosity and density.

For the considered airfoil, the characteristic length (chord length in our case) is approximately 8 cm and the

ambient temperature of the room (lab) is considered 20° C, then the kinematic viscosity is 15 x 10-6

m2/s. As

per equation (11), Reynold’s number for our considered airfoil is 42666 at 8ms-1

wind speed. Critical

Reynolds Number for airfoil type of RAF34 ranges from 50000 to 1000000 depending on the chord length

[6]. Information on type of airfoil used wasn’t available. Hence we can assume that the critical Reynold’s

number hasn’t been achieved in our case for the available maximum speed of 8 ms-1. This assumption

explains why lift coefficient was still increasing with increase in angle of attack. The flow around the airfoil is

in laminar range and yet to enter in to the turbulent region (stall point). We can conclude that the effective

lift force is still in the linear region.

The gliding angle (ε) shows a noticeable increase with the increase of α from -5° to 10°, this is due to the fact

that the lift force increases steeply, while the drag force increases slowly in this range of α. This explains the

increase of the gliding angle (ε). Afterwards, the drag force is increasing quite fast after 10° up to the

maximum angle of attack, in this case is 30°. On the other hand, the airfoil experiences a steadily increase in

the lift force, which results in the declination of gliding angle. Since, drag and lift coefficient values are in

comparable range, gliding angle values are very low.

In addition to this, we observed that even at 00 angle of attack, lift force coefficient isn’t zero. Instead it CL is

zero at an angle of attack of -2.970 (using linear interpolation). This illustrates that the airfoil was cambered

2.

Non-zero value of CL (0.57) is result of airfoil thickness and camber line geometry.

In addition to have an idea on the quality of data, we can analyze the FL and FD graphs vs. u2. According to

theory, drag and lift force are in linearly relationship with u2. By doing a linear fitting to the data we can

comment on the quality of data. See below the R-squared value3 for the measured data set in Table 5.

Table 5: Quality of data from linear regression (R2 values) for FL and FD vs u

2

Angle of Attack

(α°)

R2 value

for lift

force

R2 value

for drag

force

-5 0.72 0.87

0 0.99 0.97

5 0.90 0.93

10 0.95 0.95

15 0.96 0.99

20 0.99 0.98

25 0.82 0.98

30 0.92 0.97

2 Camber is asymmetry between the top and bottom surface of an airfoil. In cases it is done intentionally to increase

the lift coefficient [12] 3 R squared value or ‘Coefficient of Determination’ is a statistical measure to find out the accuracy of the linear fitting.

R2 value of 1 would mean a perfect linear fitting [13]

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Most of the data sets fit to the linear theoretical model. Only in three cases, R2 value is below 0.9 i.e. for lift

and drags force at -50 and lift force at 25

0. Measurement of force values need human eyes to confirm the tip

has come back to its original positive. Due to limitation of human eyes, measurement in this way will lead to

some error. Variation in the R2 value can be attributed to this error. Notably, at negative angle of attack,

linear fitting showed poor results as it’s difficult to accurately measure such small values.

It can be concluded from the discussion that the air foil is not well suited for such low Reynold’s number

which is the reason of low values of gliding angle. Maximum gliding angle of 2.05 was recorded while the

[Ref] suggested that it could only go to 4~5 if measurement were taken up to 9.5 ms-1. However,

qualitatively the measured data set is in line with the expectation from theories.

5.2 Wind turbine experiment:

5.2.1 Cp vs Tip speed ratio curves:

During the experiment, power coefficients and tip speed ratio diagram was drawn for three different wind

speeds. Pictorial comparison with the obtained figures with a usual Cp vs. λ curve is shown below:

Figure 22: Comparison with observed graphs (in red) with the representative graph of a usual Cp-λ curve

Cp vs. λ graph matches when the wind speed is high. However, at lower wind speed i.e. at 5 ms-1

, the graph

looks different. This is mainly because of less stable measured data set at lower wind speed. It is to be noted

here power coefficient along with tip speed ratio, also depends on the pitch angle. For our experiment, pitch

angle was kept constant (200). Cp usually increases with increasing tip speed ratio. At an optimum tip speed

ratio will result in an optimum Cp as well. However, if tip speed ratio is increased beyond this point, Cp will

start to decrease. The wind turbines are required to provide higher power than the maximum it can provide,

17 | P a g e

at higher tip speed ratio. Since the turbine has already reached the optimum power point, it will not be able

to provide, which will result in drop of Cp values. We observed the same trend for our measurements.

5.2.2 Power curves:

If we a look at the theoretical expected curve of the power output from a wind turbine (See Figure 23) with

respect to the wind speed, we will see that the turbine will start to produce power after a certain wind

speed (cut in speed) and power will increase with increase in speed (∝ u3). We can also observe that for our

measured data, we are within the cut-in and cut-off limit of a WEC. If we are below our cut-in limit, the rotor

will not start moving. On the other hand, usually WECs have control system to change the pitch a way that

above a certain wind speed limit (cut-off limit), WEC operate at their rated power.

Figure 23: Comparing theoretical curve with measured value of Pmax vs speed

It is evident from the graph above that Cp achieved for this experiment is very low (maximum Cp= 0.02 at

u=7.8 ms-1

), while the power in the wind is 6.6 watts at 7.8 ms-1

and our delivered maximum power is 118.48

mW, approximately 2% of the power in the wind. Notably, maximum power curve is in linear relationship

with u3 (R-squared value of 0.99) which matches the expectation with Equation (7).

Other two relevant graphs which need to be discussed are ‘Tip speed ratio vs. wind speed’ and ‘Angular

velocity vs. wind speed’. Both tip speed ratio and angular velocity is increasing with increase in wind speed.

Tip speed is inversely proportional to the wind speed, however, angular velocity at the tip also increased

with increase in wind speed. It was found that angular velocity increased by 67.54 rads-1

for increase of 1m/s

in wind speed (taking wind speed of 5 and 7 ms-1

into consideration which has been indicated in the Figure

24). We can understand that the effect of ω is much higher than the wind speed regarding the change of tip

speed ratio. Based on this, we can explain why tip speed ratio is increasing with increase in speed.

18 | P a g e

Figure 24: Analyzing λ vs wind speed and ωopt vs wind speed curves

5.2.3 Difficulties in measurement:

During voltage and current measurement for wind speed 5 ms-1

, the experiment was conducted by changing

from low resistance value to high resistance value. However, the power curve wasn’t smooth. The

measurement was then done with another approach. Measurements were done backwards from higher

value of resistance to lower. In this approach, the power curve was much smoother. Findings for both of the

approaches are shown in Figure 25. It is observed that, if we go from low to high value of resistances, the

power curve goes through unexpected ups and down. However, if go from high to low resistance, it shows a

drop of 3% to 62% in values. From the graph, it is understood that coming from high to low resistances gives

more stable results. Based on this, the other measurements were done in ‘High to low resistance’ approach.

Unstable results weren’t considered for further analysis; although they are mentioned in Appendix B (Table

B4)

Figure 25: Power vs load curve with two different measurement approaches

A possible explanation is the nature of the DC generator used, which is voltage regulation of DC generators.

A DC generator was used and from the U-I graph of the generator (see Appendix B-Figure B1), it is evident

that the used DC generator was a series wound one. Series wound DC generators have a poor voltage

regulation[7]. Due to this reason, series wound DC generators aren’t suitable for fluctuating loads. Voltage

varies a lot with increasing load current which makes measurements challenging. On the other hand, a

different approach i.e. decreasing load gradually will result in requiring less time for the measurement to be

stabilized. U-I characteristics of a series wound DC generators is shown below in Fig 15.

0E+00

5E-04

1E-03

2E-03

Po

we

r (w

att

s)

Load (ohms)

Power vs load with two approaches at

u=5ms-1

Low to High R

High to Low R

19 | P a g e

Figure 26: U-IL characteristics of a series wound DC generator (Note: Red lines indicate the change in slope of

U-I curve (Ref: [7])

5.2.4 Stabilization of data:

In case of increase in connected load to WEC, the rotor will turn faster in order to extract the necessary

power to deliver to the load. On the other hand, when the wind speed is increased, the rotor will also turn

faster to operate in the optimum tip speed ratio. This has been observed during the experiment. A time

difference of 30 seconds to 1 minute was given between subsequent data acquisition. This helped the set up

in achieving aerodynamic stabilization. Fluctuations were observed in the wind speed data (±0.1 ms-1

) shown

in the wind tunnel display. This fluctuation can also be one of the reasons why the set up needed time to

stabilize.

5.2.5 Origin of errors:

We have observed the variation of data during our analysis. However, the variation is because of

measurement errors coming from different sources. A real ohmic load (with 1% accuracy) was used for

variation of load connected to the WEC. However, ohmic values of these loads were taken from the rating

instead of measuring their real values. This might play a role during the calculations. Same brand of

mutimeter used during the experiment, has an accuracy of ±0.05% [8]and we have used two. Losses

incurred in the cables will add up to the error as well.

In addition to that, value of shunt resistance (36.21 ohm) wasn’t negligible when compared to the load

(5~6%) at which the maximum power was withdrawn. It can be stated that, the load was 36.21 ohm higher

every time we set the load to a certain value. Uncertainty in this procedure comes from the tolerance of the

used resistances (1% each for load and shunt resistances, 0.05% for each multimeter). Another possible

reason behind the error is not taking temperature coefficient of resistors (TCR) into consideration. 50 4ppm

/0C of TCR mentioned in the datasheet of similar type of decade boxes[9], this will change the resistance

value and increase the error.

It can be noted that the two voltmeters were used to find the voltage generated by the WEC. Another way

to measure is to find out the current by an oscilloscope. However, most suitable approach will depend upon

the accuracy level of the available measurement devices.

4 Ppm= parts per million

20 | P a g e

Figure 27: Current measurement through an oscilloscope. (Ref: [10])

5.2.6 Speed limiting of a wind tunnel:

During the experiment with the WEC, it was observed that the wind speed could not be increased beyond

7.8 ms-1

. We know that speed of air behind the rotor blades is less than incoming speed. Betz limit implies

that the speed can only be reduced to one third of the incoming speed. It is highly likely that the speed

limited or reduced of the wind tunnel was due to the installation of the wind turbine in the wind tunnel.

Wind speed could be adjusted to 5, 6 or 7 since at that point the tunnel was able to provide more speed.

However, it cannot reach its maximum speed under free condition (8 ms-1

) anymore if a WEC is installed. In

another way, it can be said that for a closed loop wind tunnel, a load or hindrance like the wind turbine, the

flowing speed will be less than usual. This explains why we could not go beyond 7.8 ms-1

. Turning of the

rotor pushes the air tangentially in other direction [11] which is the reason behind reduction in wind speed.

Figure 28: Diversion of air direction due to rotor rotation (Ref: [11])

6. Conclusion

To summarize the findings and learning from the experiment, we could conclude the followings:

• Airfoil used in the experiment to understand drag and lift forces was operating in the laminar flow

state. Maximum gliding angle of 2.02 was recorded at 100 angle of attack. Lift coefficient (CL)

showed increasing trend for considered angle of attacks (-50 to 30

0).

21 | P a g e

• Reynold’s number of the airfoil at the maximum available wind speed was 42666. This should be

below the critical Reynold’s number for the airfoil under consideration. Low Reynold’s number

ensured that the airfoil could not achieve the maximum lift coefficient.

• At a zero angle of attack, lift forces can be available due to the camber of airfoil.

• R squared values indicates that in low angles of attack (-50), linear fitting between force vs. square of

wind speed didn’t work out due to the difficulties in measuring small values accurately.

• Maximum power delivered by the wind turbine was 118 mW which is only 1.8% of the available

power of wind. Maximum power coefficient was 0.18 at wind speed of 7.8 ms-1

.

• DC generator was used for the experiment on wind turbine. It was found out that measuring from

higher resistance to lower resistance ended up in a smoother power curve. This interesting finding is

attributed to the type of DC generator used i.e. series wound.

• Errors coming from the measurement techniques e.g. human eye or accuracy level of data were

discussed in detail to understand the reasoning for fluctuations.

In a nutshell, this experiment confirmed the theories which are used to harvest the energy in wind to usable

electricity. However, in real situations, discrepancies were also observed during the experiment and the

reasons behind were also explored in details.

References

[1] Wind Power n.d. https://en.wikipedia.org/wiki/Wind_power (accessed November 24, 2016).

[2] PPRE stuff. Physical Principles of Renewable Energy Converters. WS 2016-17. 2016.

[3] John T, Weir T. Renewable Energy Resources. 3rd ed. 2015.

[4] Betz’s Law n.d. https://en.wikipedia.org/wiki/Betz’s_law (accessed November 24, 2016).

[5] Turbine components n.d. http://mstudioblackboard.tudelft.nl/duwind/Wind energy online

reader/Static_pages/Cp_lamda_curve.htm (accessed November 24, 2016).

[6] Airfoil Tools n.d. http://airfoiltools.com/airfoil/details?airfoil=raf34-il (accessed November 24, 2016).

[7] Series Wound DC generators n.d. http://nuclearpowertraining.tpub.com/h1011v2/css/Series-

Wound-Dc-Generators-93.htm (accessed November 24, 2016).

[8] Metex. Digital Multimeter Operating Manual M4650CR M4630CR. n.d.

[9] Prazisionsdekaden. n.d.

[10] Keithley & Tektronix. Analyzing Device Power Consumption Using a 2280S Precision Measurement

Supply. n.d.

[11] Gurit. Wind Turbine Blade Aerodynamics. WE Handbook- 2- Aerodyn. Loads, n.d., p. 7.

[12] Camber (Aerodynamics) n.d. https://en.wikipedia.org/wiki/Camber_(aerodynamics) (accessed

November 24, 2016).

[13] Coefficient of Determination n.d. https://en.wikipedia.org/wiki/Coefficient_of_determination

(accessed November 24, 2016).

22 | P a g e

Appendix A Table A1: Lift and drag forces (FL and Fd), lift and drag coefficients (CL and Cd) for different wind speeds with

change in angle of attack (-50 to 30

0 at 5

0 steps)


Wind speed (U) (m/s) U2 F1 (mN) F2 (mN) FL (N) FD (N) CL Cd

5 25 11 21 0.004968 0.009484 0.040553 0.077419

6 36 10 22 0.004516 0.009935 0.025602 0.056324

7 49 9 35 0.004065 0.015806 0.016928 0.065833

8 64 -3 37 -0.00135 0.01671 -0.00432 0.053283



5 25 6 14 0.00271 0.006323 0.02212 0.051613

6 36 12 18 0.005419 0.008129 0.030722 0.046083

7 49 17 27 0.007677 0.012194 0.031976 0.050785

8 64 25 36 0.01129 0.016258 0.036002 0.051843



5 25 17 24 0.007677 0.010839 0.062673 0.088479

6 36 32 31 0.014452 0.014 0.081925 0.079365

7 49 37 36 0.01671 0.016258 0.069595 0.067714

8 64 41 52 0.018516 0.023484 0.059044 0.074885



5 25 30 19 0.013548 0.008581 0.110599 0.070046

6 36 60 25 0.027097 0.01129 0.15361 0.064004

7 49 80 33 0.036129 0.014903 0.150475 0.062071

8 64 90 49 0.040645 0.022129 0.129608 0.070565



5 25 60 23 0.027097 0.010387 0.221198 0.084793

6 36 70 32 0.031613 0.014452 0.179211 0.081925

23 | P a g e

7 49 100 43 0.045161 0.019419 0.188094 0.08088

8 64 120 57 0.054194 0.025742 0.172811 0.082085


Wind speed (U) (m/s) U2 F1 (N) F2 (N) FL (N) FD (N) CL Cd

5 25 0.04 0.01 0.018065 0.004516 0.147465 0.036866

6 36 0.07 0.04 0.031613 0.018065 0.179211 0.102407

7 49 0.11 0.06 0.049677 0.027097 0.206903 0.112856

8 64 0.16 0.1 0.072258 0.045161 0.230415 0.144009



5 25 0.04 0.04 0.018065 0.018065 0.147465 0.147465

6 36 0.14 0.06 0.063226 0.027097 0.358423 0.15361

7 49 0.17 0.11 0.076774 0.049677 0.319759 0.206903

8 64 0.18 0.14 0.08129 0.063226 0.259217 0.201613



5 25 0.1 0.06 0.045161 0.027097 0.368664 0.221198

6 36 0.11 0.08 0.049677 0.036129 0.281618 0.204813

7 49 0.2 0.12 0.090323 0.054194 0.376187 0.225712

8 64 0.24 0.17 0.108387 0.076774 0.345622 0.244816

24 | P a g e

Table A2: Lift and drag coefficients (C

attack (-50 to 30

0 at 5

0 steps)

Angle of Attack (α°)

Figure A1 (a-h): Lift and drag forces against

(α°). (Note: Linear fitting for the lift and drag

0.000

0.005

0.010

0.015

0.020

Lift

, D

rag

(N

)

ift and drag coefficients (CL and Cd) calculated from slope of F vs u2 graphs

Angle of Attack (α°) CL Cd ε (CL/Cd)

-5 -0.39 0.57 -0.68

0 0.57 0.69 0.82

5 0.71 0.82 0.88

10 1.84 0.90 2.05

15 1.94 0.96 2.02

20 3.69 2.67 1.38

25 4.14 3.22 1.28

30 4.69 3.41 1.38

: Lift and drag forces against the square value of wind speed (u2) at different angles of attack

inear fitting for the lift and drag forces are indicated by the dashed lines)

(a)

y = 0.0028x - 0.0002

y = 0.0034x + 0.0023

25 36 49 64

%2 (m2 /s2)


graphs for different in angle of

ε (CL/Cd)

0.68

) at different angles of attack

indicated by the dashed lines)

Lift

Drag

Linear (Lift)

Linear (Drag)

25 | P a g e

0.000

0.005

0.010

0.015

0.020

Lift

, D

rag

(N

)

0.000

0.005

0.010

0.015

0.020

Lift

, D

rag

(N

)

(b)

(c)

y = 0.0028x - 0.0002

y = 0.0034x + 0.0023

25 36 49 64

%2 (m2 /s2)


y = 0.0028x - 0.0002

y = 0.0034x + 0.0023

25 36 49 64

%2 (m2 /s2)


Lift

Drag

Linear (Lift)

Linear (Drag)

Lift

Drag

Linear (Lift)

Linear (Drag)

26 | P a g e

0.000

0.005

0.010

0.015

0.020

Lift

, D

rag

(N

)

0.000

0.005

0.010

0.015

0.020

Lift

, D

rag

(N

)

(d)

(e)

y = 0.0028x - 0.0002

y = 0.0034x + 0.0023

25 36 49 64

%2 (m2 /s2)


y = 0.0028x - 0.0002

y = 0.0034x + 0.0023

25 36 49 64

%2 (m2 /s2)


Lift

Drag

Linear (Lift)

Linear (Drag)

Lift

Drag

Linear (Lift)

Linear (Drag)

27 | P a g e

0.000

0.005

0.010

0.015

0.020

Lift

, D

rag

(N

)

0.000

0.005

0.010

0.015

0.020

Lift

, D

rag

(N

)

(f)

(g)

y = 0.0028x - 0.0002

y = 0.0034x + 0.0023

25 36 49 64

%2 (m2 /s2)


y = 0.0028x - 0.0002

y = 0.0034x + 0.0023

25 36 49 64

%2 (m2 /s2)


Lift

Drag

Linear (Lift)

Linear (Drag)

Lift

Drag

Linear (Lift)

Linear (Drag)

28 | P a g e

0.000

0.005

0.010

0.015

0.020

Lift

, D

rag

(N

)

(h)

y = 0.0028x - 0.0002

y = 0.0034x + 0.0023

25 36 49 64

%2 (m2 /s2)


Lift

Drag

Linear (Lift)

Linear (Drag)

29 | P a g e

Appendix B

Table B1: Measured voltage, current, power, angular velocity, tip speed ratio and power coefficient for

different loads at 5 ms-1

Load

(Ω) Voltage(V)

Voltage

shunt

(V)

Current (A) Power

(W)

Angular

velocity

(rad/s)

Tip

speed

ratio

Cp

50 0.16 0.065 1.80E-03 3E-04 31.62544 0.54 1.7E-04

100 0.26 0.08 2.21E-03 6E-04 26.80832 0.46 3.3E-04

200 0.41 0.066 1.82E-03 7E-04 34.97648 0.59 4.3E-04

300 0.52 0.056 1.55E-03 8E-04 36.23312 0.62 4.6E-04

400 0.6 0.054 1.49E-03 9E-04 38.7464 0.66 5.1E-04

500 0.65 0.045 1.24E-03 8E-04 39.37472 0.67 4.6E-04

600 0.75 0.044 1.22E-03 9E-04 40.8408 0.69 5.2E-04

700 0.79 0.04 1.10E-03 9E-04 40.8408 0.69 5.0E-04

800 0.81 0.036 9.94E-04 8E-04 42.09744 0.72 4.6E-04

900 0.87 0.036 9.94E-04 9E-04 40.00304 0.68 5.0E-04

1000 0.92 0.033 9.11E-04 8E-04 41.05024 0.70 4.8E-04


different loads at 7ms-1

Load

(Ω) Voltage(V)

Voltage

shunt

(V)

Current

(A)

Power

(W)

Angular

velocity

(rad/s)

Tip

speed

ratio

Cp

50 0.8 0.36 9.94E-03 8.0E-03 46.49568 0.56 1.7E-03

100 1.3 0.32 8.84E-03 1.1E-02 54.45440 0.66 2.4E-03

200 1.8 0.27 7.46E-03 1.3E-02 70.79072 0.86 2.8E-03

300 2.5 0.27 7.46E-03 1.9E-02 80.63440 0.98 3.9E-03

400 3.4 0.31 8.56E-03 2.9E-02 108.90880 1.32 6.1E-03

500 5.7 0.394 1.09E-02 6.2E-02 162.94432 1.98 1.3E-02

600 6.3 0.37 1.02E-02 6.4E-02 175.92960 2.14 1.3E-02

700 6.7 0.34 9.39E-03 6.3E-02 183.88832 2.23 1.3E-02

800 6.8 0.318 8.78E-03 6.0E-02 188.91488 2.29 1.3E-02

900 7.12 0.26 7.18E-03 5.1E-02 196.87360 2.39 1.1E-02

1000 7.2 0.26 7.18E-03 5.2E-02 195.82640 2.38 1.1E-02

30 | P a g e


different loads at 7.8ms-1

Load

(Ω) Voltage(V)

Voltage

shunt

(V)

Current

(A)

Power

(W)

Angular

velocity

(rad/s)

Tip

speed

ratio

Cp

50 1.3 0.53 1.46E-02 1.9E-02 54.66384 0.60 2.9E-03

100 1.85 0.46 1.27E-02 2.4E-02 73.72288 0.80 3.6E-03

200 2.98 0.45 1.24E-02 3.7E-02 100.53120 1.10 5.6E-03

300 5.04 0.56 1.55E-02 7.8E-02 148.70240 1.62 1.2E-02

400 7.02 0.6 1.66E-02 1.2E-01 191.84704 2.09 1.8E-02

500 7.8 0.55 1.52E-02 1.2E-01 207.97392 2.27 1.8E-02

600 8.16 0.48 1.33E-02 1.1E-01 215.72320 2.35 1.6E-02

700 8.22 0.43 1.19E-02 9.8E-02 219.91200 2.40 1.5E-02

800 8.4 0.38 1.05E-02 8.8E-02 222.00640 2.42 1.3E-02

900 8.5 0.35 9.67E-03 8.2E-02 226.82352 2.47 1.2E-02

1000 8.6 0.32 8.84E-03 7.6E-02 229.75568 2.50 1.2E-02

2000 9.4 0.17 4.69E-03 4.4E-02 240.01824 2.62 6.7E-03

Table B4: Discarded values of measured voltage, current, power, angular velocity, tip speed ratio and power

coefficient for different loads at 5ms-1 with low resistance to high resistance approach

Load

(Ω) Voltage(V)

Voltage

shunt (V)

Current

(A)

Power

(W)

Angular

velocity

(rad/s)

Tip

speed

ratio

Cp

20 0.19 0.12 3.31E-03 6.30E-

04 29.74048

0.08 3.62E-04

30 0.27 0.11 3.04E-03 8.20E-

04 29.32160

0.08 4.72E-04

40 0.29 0.11 3.04E-03 8.81E-

04 30.99712

0.08 5.07E-04

50 0.26 0.106 2.93E-03 7.61E-

04 26.18000

0.07 4.38E-04

60 0.2 0.07 1.93E-03 3.87E-

04 31.41600

0.09 2.22E-04

100 0.36 0.08 2.21E-03 7.95E-

04 26.80832

0.07 4.58E-04

500 0.78 0.05 1.38E-03 1.08E-

03 33.71984

0.09 6.20E-04

600 0.78 0.05 1.38E-03 1.08E-

03 33.71984

0.09 6.20E-04

700 0.85 0.04 1.10E-03 9.39E-

04 50.47504

0.14 5.40E-04

900 0.9 0.036 9.94E-04 8.95E-

04 40.63136

0.11 5.15E-04

31 | P a g e

1000 1.15 0.04 1.10E-03 1.27E-

03 51.10336

0.14 7.31E-04

1100 1.05 0.035 9.67E-04 1.01E-

03 43.35408

0.12 5.84E-04

2000 1.41 0.027 7.46E-04 1.05E-

03 48.17120

0.13 6.05E-04

3000 1.61 0.019 5.25E-04 8.45E-

04 49.21840

0.13 4.86E-04

4000 1.41 0.011 3.04E-04 4.28E-

04 41.46912

0.11 2.46E-04

5000 1.523 0.01 2.76E-04 4.21E-

04 41.88800

0.11 2.42E-04

100000 1.88 0.006 1.66E-04 3.12E-

04 45.23904

0.12 1.79E-04

Figure B1: Terminal voltage of DC generator vs. load current at wind speed of 5ms-1

while the load current

was increased slowly.

00.10.20.30.40.50.60.70.80.9

1

Te

rmin

al

vo

lta

ge

(V

)

Load current (amp)

Terminal voltage vs load current

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