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Design and calibration of an inexpensive digital anemometer

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S P E C I A L F E A T U R E : D I Y P H Y S I C S

www.iop.org/journals/physed

Design and calibration of aninexpensive digital anemometer

R Hernandez-Walls1, E Rojas-Mayoral2, L Baez-Castillo3 andB Rojas-Mayoral4

1 Facultad de Ciencias Marinas, UABC, Ensenada Baja California, Mexico2 Centro de Investigacion Cientıfica y Superior de Ensenada, Ensenada, Baja California,

Mexico3 Facultad de Ciencias, UABC, Ensenada, Baja California, Mexico4 Facultad de Ciencias Naturales y Exactas, Unison, Sonora, Mexico

E-mail: rwalls@uabc.mx

AbstractAn inexpensive and easily implemented device to measure wind velocity isproposed. This prototype has the advantage of being able to measure both thespeed and the direction of the wind in two dimensions. The device utilizes acomputational interface commonly referred to as a mouse. The mouseproposed for this prototype contains an optical sensor which allows it tosituate itself in space. The prototype utilizes a pendulum with an attacheddrag body. The pendulum’s drag body interacts with the fluid in motion,

causing an angle with respect to the vertical. The mouse measures thedisplacement of a sphere attached to the pendulum and calculates the angle.The resulting angle determines the relationship between the drag force andthe wind speed, thereby allowing the mouse to calculate the velocity. AMATLAB script was written to process the data received from the mouse.After calibration, the program determines the relationship between the pixelsmeasured and the pendulum’s angle, and so obtains information about thewind. This system (device and software) eliminates human error in datacollection and storage, thereby considerably reducing the time and costassociated with measuring wind velocity.

S Supplementary data are available from stacks.iop.org/physed/43/593

Introduction

One problem in meteorology is that of obtaining

reliable data in an autonomous way. In general,

meteorological instruments are expensive and

difficult to maintain. This problem can be solved

with a personal computer system. Any computer

system will contain input and output devices, such

as a mouse and a monitor. It has been shown

that a computer mouse can be used as an input

device for information [1–5]. The use of the

computer mouse as an electronic interface is analternative that avoids the design and construction

of an interface card between the computer and

a sensor [4]. In this article, a prototype of an

anemometer is proposed that utilizes an optic

sensor. Even though this prototype is similar

to a one-dimensional current meter, it has the

advantage of being able to measure the wind’sspeed as well as its direction [4].

This article is structured as follows. The

next section contains the physical preliminaries

0031-9120/08/060593+06$30.00 © 2008 IOP Publishing Ltd P H Y S I C S ED U C A T I O N 43 (6) 593

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R Hernandez-Walls et al 

for obtaining an equation used to calculate the

speed and direction of the fluid in motion with the

proposed device. The following section describesthe assembly of the anemometer, consisting of 

an optical mouse, a sphere and a pendulum.

Later, the calibration of the proposed device is

examined, followed by a description of how the

computer script captures the information. Finally,

the advantages, disadvantages and conclusions are

discussed.

Physical preliminaries

If we consider the case of a pendulum with weight

(W ), that, upon interacting with fluid in motion,

produces an angle with respect to the vertical (θ),resulting from the drag force ( F a ) that the fluid

exercises over the pendulum, then the resulting

opposing force is the tension (T ). This can be

described with a diagram of a free body, where

a balance of forces is obtained, as is shown in

figure 1. Using the trigonometric relationship

between the angles and sides of a right triangle,

the following equation is obtained:

tan θ = F a

W . (1)

Solving for the drag force in equation (1),

F a = W tan θ. (2)

The drag force of an object surrounded by

a stationary flow is defined by the following

equation [6]:

F a = 12

C d Aρv2 (3)

where C d is the drag coefficient, A is the

area of the projection of the object on a plane

perpendicular to the direction of motion, ρ is the

density of the fluid, and v is the flow speed.

Setting equations (2) and (3) equal to eachother, the following equation is obtained:

W tan θ = 12

C d Aρv2. (4)

Solving for the velocity, we find

v =

2W tan θ

C d Aρ. (5)

If we consider that the fluid and the object do

not change with time, it can be supposed that the

Figure 1. Right triangle representing the balance of forces obtained by modifying the free-body diagram.

W 

θ

T 

F a

following parameters can be considered constants,

and that they may all be included in a constant:

K ≡

2W 

C d Aρ. (6)

Then equation for the velocity is

v = K √ tan θ. (7)

If the value of the constant K is known, then

only the deviation of the angle with respect to the

vertical is necessary to obtain a measurement of 

the velocity of the flow.

Experimental device

The main purpose of this project is to measure

the drag angle with an optical computer mouse.

The mouse is positioned on the upper portion

of a sphere, which has free movement, while apendulum is attached to the lower portion of the

sphere. When the pendulum interacts with fluid in

motion, it changes its alignment, thereby causing

the attached sphere to rotate. The mouse detects

the rotation of the sphere, as shown in figure 2.

It was necessary to build a device that first

allowed the free movement of the sphere when

the drag object was interacting with the fluid,

and second, allowed the mouse to detect the

movement of the sphere. The device is mounted

on a triangular frame, inside which a sphere is

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Design and calibration of an inexpensive digital anemometer

Figure 2. Effect of the drag force on the pendulum.

mouse

sphere

pendulum

drag body

flow

supported by skate bearings that allow the free

movement of the sphere without changing its

relative position with respect to the mouse. A

board with a circular hole in the centre is affixed

to the top of the frame. The mouse is attached

to the board so that it can detect the movement

of the sphere through the hole in the board.

Since the mouse detects any displacement of the

surface below it by optical means, the mouse

has to be fixed to the upper part of the structurein such a way that it stays within a small and

constant distance to the sphere without making

any contact. A pendulum is attached to the

bottom of the sphere. A vane is used as a drag

body and is attached to the opposite end of the

pendulum. When the vane interacts with the fluid,

the movement is transmitted to the sphere by the

pendulum. The mouse then detects the movement

(figure 3).

The optical mouse is capable of measuring the

pixels of the rotating surface of the sphere, but not

the angle (θ) resulting from the sphere’s rotation.

It is necessary to determine the relationship

between the measured pixels and the drag angle

of the pendulum.

Pixel–angle relation

For the rotation of the sphere, caused by an angle

(θ), there exists a specific quantity of pixels.

Therefore the angle (θ) can be defined as

θ = α · pixels. (8)

Figure 3. 3D model of the prototype.

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R Hernandez-Walls et al 

0

0

10

15

20

25speed (mph)

tan1/2 (θ)

30

35

40

45

50

55

0.5 1.0 1.5 2.0 2.5 3.0 3.5

Figure 5. Calibration of the prototype with a protractor.

Equation (8) describes a straight line with slope α.

Substituting equation (8) in (7):

v =

tan(α · pixels) · K . (9)

For the components:

vx = tan(αx · pixelsx) · K  (9.1)

vy =

tan(αy · pixelsy) · K . (9.2)

The following section contains a description of 

how the estimation of the constant K was carried

out.

Calibration

A commercial weather gauge (SELL-O-CRAFT

Sheboygan) was used for the calibration of the

Figure 6. Angles plotted against the horizontal

displacement of the cursor in pixels.

500

pixelsx

0

2

4

6

8

10

12

14

16

100 150 200 250 300 350 400

proposed device. The weather gauge measures

wind speed based on the same physical principles.

The angles with respect to the vertical (θ)

were measured and the corresponding wind speeds

obtained via the weather gauge were plotted with

velocity (miles per hour) on the vertical axis and√ tan θ on the horizontal axis (figure 4). A linear

regression with a correlation coefficient of 0.993

produced the following equation:

v = 15.179√ tan θ. (10)

The experimental device was calibrated

to measure the velocity of the air with K 

(equation (7)) equal to the slope of equation (10).

The drag body must have the same weight (W ) and

area (A) as the drag body of the weather gauge.

For obtaining the pixel–angle relationship,

a protractor was placed on the base of the

cage assembly (figure 5), and for each angle of 

inclination (θ) the movement of the surface of the

sphere was measured in pixels by the mouse in

both the x-axis and the y-axis.

The measurements of the pixels against theangles are shown in figures 6 and 7. The

equation obtained from the linear regression, with

a correlation coefficient of 0.995, for the x-axis

was

θx = 4.16× 10−2 · pixels.

For the y-axis, with a correlation coefficient of 

0.998, the equation obtained was

θy = 5.09× 10−2 · pixels.

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Design and calibration of an inexpensive digital anemometer

Figure 7. Angles plotted against the vertical

displacement of the cursor in pixels.

00

2

4

6

8

10

12

14

16

50 100 150 200 250 300

pixelsy

Therefore the value of the constant in equa-

tion (9.1) is αx = 4.16 × 10−2, while in equa-

tion (9.2), αy = 5.09× 10−2.

Algorithm and script

The computer program for the calibration of the

prototype was written in MATLAB, since it offers

functions to obtain information from input devices

such as the mouse. The script is shown in box 1.

In order to obtain the coordinates of the

position of the cursor, it is necessary to obtain the

dimensions of the monitor. For this the function

get is utilized, as follows:

get (0, ‘screensize’).

In order to start using the prototype it is necessary

to set the initial position of the cursor. The

following function is utilized:

set (0, ‘PointerLocation’, [x, y]).

The function that obtains the position of the cursorwhen the prototype is in operation is

get (0, ‘PointerLocation’).

Advantages and disadvantages

The materials of the proposed digital anemometer

are available at low cost. The software was

designed with elementary programming concepts,

making the reading and storage of the measured

digital data and its subsequent processing efficient.

Box 1. MATLAB script for calculating wind velocitywith a mouse. This script is also available as asupplementary data file in the online version of the

journal at stacks.iop.org/physed/43/593.

The calibration of the prototype is simple.

The high correlation coefficients obtained suggest

that the measurement of the wind velocity is

reliable.

This system can be easily adapted for other

environments, such as marine coastal zones or

fluid mechanics laboratories. It is possible to

measure the velocity in two dimensions of almost

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R Hernandez-Walls et al 

any flow by calibrating the prototype for that

specific fluid.

The main disadvantage of this prototype isthat the mouse must be kept dry.

Conclusions

The measurement range depends on the drag body

and the precision depends on the volume of the

sphere: the bigger the sphere, the greater the

precision.

It has been shown that an optical mouse can

be used as an inexpensive sensor of geophysical

variables: in this case, the velocity of the wind

(speed and direction).

Acknowledgments

The authors acknowledge Andrea Lievana-Mac

Tavish for her suggestions and comments. The

first author also acknowledges support from SNI,

UABC and from SEP-CONACYT (Mexico) under

grants UABC-325 and SEP-2004-C01-47285.

Received 14 May 2008, in final form 30 July 2008

doi:10.1088/0031-9120/43/6/005

References[1] Ochoa O R and Kolp N F 1997 The computer

mouse as a data acquisition interface:application to harmonic oscillators Am. J. Phys.

65 1115–8[2] Yang Z and Maeda R 2000 Automatic micro flow

rate measurement using a modified computermouse device 1st Annual Int. IEEE-EMBS

Special Conf. on Microtechnology in Medicine

and Biology (France) pp 288–91[3] Modesto-Ortiz M, Martınez Y and Gonzalez J I

2003 Observaciones De Nivel Del Mar Con

Instrumentos De Bajo Costo. Reuni´ on Anual De

Geofısica (Mexico: UGM) p 159[4] Hernandez-Walls R, Luna-Hernandez J R,

Rojas-Mayoral E and Navarro-Olache L F 2004Dispositivo electronico, de facil construccion,para medir la velocidad de un fluido Rev. Ing.

Hidr´ aulica M´ exico 19 121–8

[5] Ng T W 2003 The optical mouse as an inexpensivedevice SPIE Proc. ETuF4 (San Diego, CA)

(Bellingham, WA: SPIE Optical Engineering

Press) pp 1–3[6] Roberson J A 1980 Engineering Fluid Mechanics

(Boston, MA: Houghton Mifflin)

Rafael Hernandez-Walls received hisPhD in optics from CICESE, Ensenada,Mexico. He currently works as aprofessor and researcher at the School of Marine Sciences of the UniversidadAutonoma de Baja California (UABC)where he teaches physics andcomputation, focusing on thedevelopment of new technologies for usein marine sciences.

Evaristo Rojas-Mayoral is a studentcurrently working to obtain his Master’sdegree in physical oceanography fromCICESE, Ensenada, Mexico. In 2005, heearned his Bachelor’s degree inoceanography from the UniversidadAutonoma de Baja California. Since2001, he has worked on the design andimplementation of new methods andtechnologies for measuring differentproperties of geophysical fluids.

Leonardo Baez-Castillo is a studentworking to obtain his Bachelor’s degreein physics from the UniversidadAutonoma de Baja California, Ensenada,Mexico. During his academic career, hehas participated in the design andconstruction of instrumentation for bothphysics and oceanographic laboratories.He is currently in the process of completing his thesis in biophysics,carrying out his research in the laboratoryof Animal Reproduction andImmunology.

Braulio Rojas-Mayoral is a studentworking to obtain his Bachelor’s degreein physics from the Universidad deSonora, Hermosillo, Mexico. Hisprincipal interest is in numericalmodelling and the realization of appliedexperiments.

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