Generation of Directional Wind by Colliding Airflows

Koichi Hirota*1

Graduate School of Frontier Sciences, University of

Tokyo

Yoko Ito

Graduate School of Frontier Sciences, University of

Tokyo

Tomohiro Amemiya*2

NTT Communication Science Laboratories, NTT Corporation

Yasushi Ikei*3

Faculty of System Design, Tokyo Metropolitan

University

ABSTRACT This paper describes an approach to interpolate the wind direction and velocity using two fans. Firstly, maps of the angle and velocity of the wind in relation to the speeds of the two fans are created. It was found that changes in the speeds of the two fans in the interpolation were not necessarily linear to the directional angles from the fans. Next, in the generation of wind, the speeds of the fans are inversely referenced from the maps using the target direction and velocity. An experiment confirmed that wind can be generated from an intermediate direction between the two fans. Through an evaluation using subjects, it was proven that a change in the direction of the wind could be recognized to some extent, although great differences in accuracy were observed among individuals. KEYWORDS: Sensation of Wind, Wind Direction, Multisensory Theater INDEX TERMS: H.5.1 [Information Interfaces And Presentation]: Multimedia Information Systems–Artificial, augmented, and virtual realities

1 INTRODUCTION Increasing the reality of a virtual environment by introducing

various sensations in addition to visual and auditory sensations has been one of the major topics of research in virtual reality. The authors have also been working on the implementation and application of a multisensory theater where sensors and displays of various sensations are integrated [1]. The generation of wind in a virtual environment is one of the topics of the study. Although the sensation of wind can be decomposed into tactile components, thermal components, etc, we usually feel it as a comprehensive sensation.

One of the typical properties perceived from wind is its direction. In the multisensory theater mentioned above, the direction of wind is also an important component of the generation of wind, and it is necessary to generate wind that will not contradict the visual presentation. In addition, the design of the wind display for a theater system imposes the restriction that the wind generation equipment, usually electric fans, must be arranged so as to not occlude the visual presentation. In addition, the number of fans should be determined considering the practical utility and cost.

Based on this background, our research investigated the interpolation of the wind direction by controlling the output of fans generating air movement from different directions. If such an interpolation is possible, wind from an arbitrary direction could be generated using a smaller number of fans. Although many studies

have dealt with the generation of wind direction using multiple fans, most of them introduced an empirical interpolation algorithm without examining the actual wind flow generated by the algorithm.

This paper reports an investigation using two fans. The airflows generated by these two fans were “mixed” at a point, and the flow that resulted from this mixture was measured to obtain the fundamental velocity and direction characteristics.

2 RELATED STUDIES The generation of wind for the purpose of increasing the reality

of a visual-audio system, or small theater, has been investigated since as early as the 1960s [2]. Recently, many researchers have investigated integrating a wind sensation into a virtual environment.

A relatively early study was carried out by Ogi et al. They developed a handheld wind display device that had six fans and could generate wind from various directions toward the user’s hand [3]. They also proposed a “data sensualization” system, wherein a 3D vector field was interactively generated through visual, auditory, and wind sensations. Regarding the wind sensation, the vector value at the hand was directly mapped to the wind vector. Although the advantage of this sensualization system was proven, no details of the algorithm for controlling the wind were discussed.

Moon et al. developed a wind device called WindCube [4]. This device composed of numerous fans arranged on a frame around the user, and wind from an arbitrary direction was generated by controlling the rotation speed of the fans by interpolating their directions. They employed an empirical algorithm for this interpolation. However, the physical validity of this algorithm was not clarified. The research also reported that the sensation of wind caused a significant improvement in the reality of an experience.

Kosaka et al. proposed and implemented a wind recording and reproduction system [5]. A measurement device called a WindCamera used an array of anemometers on a spherical surface, and a display device called a WindDisplay used fans arranged in a topology similar to the measurement device. They also evaluated the wind perception characteristics using the display device [6]. It is interesting that the provability of the wind interpolation was not mentioned because the device had a sufficient number of fans, which made the interpolation a less significant topic.

Other studies have integrated a wind device into a head-mounted display. Cardin et al. implemented and evaluated a device of this type. The device had eight fans at regular intervals around the user’s head and generated wind on the head [7]. They proposed an algorithm that determined the output to the fans based on the dot products of the wind direction and fan axes. This algorithm was considered to make sense if each fan was assumed to generate a local dynamic pressure caused by the wind around the fan. Hence, this approach is possible only when the fans are placed close to a user’s skin, and is not applicable for our purpose.

Kulkarni et al. implemented a CAVE-like system integrated with a type of wind tunnel, and proposed a method to control the wind flow at the location of the user [8]. It comprised a regulator

*1 5-1-5 Kashiwanoha, Kashiwa, Chiba 277-8563 k-hirota@k.u-tokyo.ac.jp

*2 amemiya.tomohiro@lab.ntt.co.jp *3 ikei@computer.org

509

IEEE World Haptics Conference 201314-18 April, Daejeon, Korea978-1-4799-0088-6/13/$31.00 ©2013 IEEE

system that input the velocity and direction of the wind from sensors and output signals to two throttle valves. Although this approach is thought to provide an excellent environment for wind control, it would be fairly difficult to apply to a normal virtual reality system. Matsukura et al. proposed another approach to generating wind flow field [9]. Their approach uses two fans placed facing each other on an axis, and, by colliding the axial airflow from the fans, generates radial airflow; the location of the collision can be changed depending on the air speeds from the fans. This approach is interesting as a method of localizing the wind source without obstructing the user's vision.

Some studies have focused on the application of wind. Minakuchi and Kobayashi proposed an application of the sensation of wind for presenting ambient information [10]. The spatiality of the wind and compatibility with other displays were suitable in this application. Sawada et al. proposed a system that allowed a user to interact with a virtual or remote environment through a blowing action and the sensation of wind [11]. Deligiannidis and Jacob proposed the idea of increasing the sensation of locomotion by generating wind [12]. A scooter-like interface with a wind sensation was implemented and evaluated. It was proven that the sensation of wind affected not only the perception of reality but also the performance of the locomotion. These studies presented various aspects of the utility of wind.

In spite of the progress in wind devices mentioned above, there has been little investigation on wind perception characteristics. Nakano et al. carried out a pioneering research on this topic and revealed a discrimination threshold for the wind direction under the condition of the head being fixed [13]. This research provides knowledge that is quite useful in designing wind display systems. In the case of a theater environment, however, it is more practical to assume that a user can move his/her head freely.

3 APPROACH As a first step of our investigation, our research focuses on the

interpolation of the wind between two fans. Two fans are arranged at a 60° angle around an origin point (see Figure 1), where a user’s face is positioned to feel the wind, and the rotation speeds of fans A and B are controlled independently. If only one of the fans is operated, then a wind is generated from the direction of the operating fan, and the user will feel the wind from that fan. Our assumption is that, by appropriately controlling the fans, it will be possible to generate wind from any given direction between the directions of the two fans, at a velocity within the power limitations of the fans.

First, the angle and velocity of the wind at the location of the user are measured under various combinations of rotation speeds. Using these measurements, maps are obtained for the angles and velocities in the two-dimensional space of the fan speeds. Next, inversely to the measurement process, the fan speed values are referenced from the target values of the angle and velocity of the wind.

4 MAP GENERATION In this study, the angle between the axes of the two fans and the

distance from these fans to the user were determined to be 60° and 1500 mm, respectively, as shown in Figure 1. The rotation speeds of the fans were independently changed from 0 to 2000 rpm in 200-rpm steps, and the direction and velocity of the wind around the origin, or location of the user, were measured for each combination. The wind vectors were measured on the z = 0 plane in the range of ±100 mm for x and y at intervals of 50 mm (i.e., 25 points) and averaged. This measurement range was determined by assuming that wind was blown to the user’s face. For sensing stability, the sensor values at each point were sampled for 10 s at 100 Hz and averaged. The velocity was computed as the length of the vector, while the angle was obtained by projecting the vector onto the x-z plane and computing its horizontal angle.

The fan device consisted of a fan blade and front grille from a circulator (KJ-D992W, Twinbird) and a motor with a speed controller (BX460A-A, Oriental Motor). The maximum rotation speed was 3000 rpm, and the wind velocity at a distance of 1500 mm was approximately 3 m/s. The wind vector was measured using a sensor that consisted of four anemometers. The details of this sensor and its calibration are given in the Appendix section.

The angle and velocity maps obtained from the measurements are shown in Figure 2. It should be noted that in the area of the map where the wind velocity is more than 2.0 m/s, it is possible that the sensor became saturated because the maximum measurable velocity of the anemometers was 2.0 m/s. The area was ignored in the fitting process stated below. The resulting map shows that the wind velocity was almost proportional to the rotation speed, although it did not necessarily have a linear relation with the speeds of the two fans. In addition, regarding the wind angle, the faster fan tended to have a dominant effect on the angle.

Because there is no model that theoretically explains these maps, the following ad hoc fittings were investigated. Regarding the velocity |𝑣|, a hyper-elliptic curve was used: |𝑣| = a (ω + ω ) / (1)where ω and ω are the rotation speeds of fans A and B, respectively. By fitting the function to the map using the least-square method, 𝑎= 1.13 10-3 and 𝑏= 3.89 were obtained. On the other hand, regarding the directional angle 𝜃, a sigmoid function was used: 𝜃 = 𝑑 1 − 𝑒1 + 𝑒 (3)

where 𝛼 is the phase angle on the map and is defined as: 𝛼 = 𝜋4 − tan ωω (2)

Similarly, using the least-square method, 𝑐= 10.1 and 𝑑= 30.0

Figure 1. Arrangement of Fans and Sensors

(a) Measured Angle [ ] (b) Measured Velocity [m/s]

Figure 2. Angle and Velocity Maps

A

BAnemometer

Fan

Fan

1000

mm

xz

y

0

200

400

600

800

1000

1200

1400

1600

1800

2000

0

200

400

600

800

1000

1200

1400

1600

1800

2000

Fan

B [r

pm]

Fan A [rpm]

30-4020-3010-200-10-10-0-20--10-30--20-40--30 0

200

400

600

800

1000

1200

1400

1600

1800

2000

0

200

400

600

800

1000

1200

1400

1600

1800

2000

Fan

B [r

pm]

Fan A [rpm]

2-2.51.5-21-1.50.5-10-0.5

510

were obtained. Reconstructed maps using these fitting functions are plotted in Figure 3. In comparison with the original maps in Figure 2, the fitting functions are thought to capture the features of the original maps. The significant difference between the maps in the area of high rotation speed is thought to be caused by the saturation of the anemometers, as stated above.

The inverse functions that give ω and ω from |𝑣| and 𝜃 are defined as follows. It is a good feature of the approach that the rotation speeds are analytically calculated rather than found by searching for a solution on the map. ωω = tan 𝜋4 + 1𝑐 log 𝑑 − 𝜃𝑑 + 𝜃 (4) ω = |𝑣|𝑎(1 + (ω /ω ) ) / (5) ω = |𝑣|𝑎(1 + (ω /ω ) ) / (6)

5 GENERATION OF WIND An experiment to generate wind using the fitting functions was

performed. The target angle of the wind was changed in a ±30° range in 10° steps. The velocity was 0.7, 1.0, or 1.3 m/s. The actual wind vector at the user’s location was measured using the sensor. The measurement procedure was the same as that used for

the map generation. However, in this experiment, the sensing area was expanded to ±500 mm in the x and y directions.

Figure 4 shows plots of the wind vectors on the x-y plane under all conditions. These plots suggest that the direction of the wind vector about the origin point, or about the user’s face, was changed according to the change in the target angle, and that the change in velocity was reflected by the wind intensity. On the other hand, the figure presents some issues with this approach. For example, the collision of the winds from the two fans causes a

(a) Angle [ ] (b) Velocity [m/s]

Figure 3. Fitting Functions for Maps

(a) Target Velocity 0.7 m/s

(b) Target Velocity 1.0 m/s

(c) Target Velocity 1.3 m/s

Figure 4. Plots of Wind Vectors

0

200

400

600

800

1000

1200

1400

1600

1800

2000

0

200

400

600

800

1000

1200

1400

1600

1800

2000

Fan

B [r

pm]

Fan A [rpm]

30-4020-3010-200-10-10-0-20--10-30--20-40--30 0

200

400

600

800

1000

1200

1400

1600

1800

2000

0

200

400

600

800

1000

1200

1400

1600

1800

2000

Fan

B [r

pm]

Fan A [rpm]

2-2.51.5-21-1.50.5-10-0.5

-400

-200

200

400

0

-400-200 200 4000 -400-200 200 4000 -400-200 200 4000 -400-200 200 4000 -400-200 200 4000 -400-200 200 4000 -400-200 200 4000

y[m

m]

x [mm] x [mm] x [mm] x [mm] x [mm] x [mm] x [mm]

Velocity 0 0.5 1 [m/s]

-30 -20 -10 0 10 20 30

-400

-200

200

400

0

-400-200 200 4000 -400-200 200 4000 -400-200 200 4000 -400-200 200 4000 -400-200 200 4000 -400-200 200 4000 -400-200 200 4000

y[m

m]

x [mm] x [mm] x [mm] x [mm] x [mm] x [mm] x [mm]

Velocity 0 0.5 1 [m/s]

-30 -20 -10 0 10 20 30

-400-200 200 4000

Velocity 0 0.5 1 [m/s]

x [mm]-400-200 200 4000 -400-200 200 4000 -400-200 200 4000 -400-200 200 4000 -400-200 200 4000 -400-200 200 4000

-400

-200

200

400

0

x [mm] x [mm] x [mm] x [mm] x [mm] x [mm]

y[m

m]

-30 -20 -10 0 10 20 30

511

flow with vertical components around the upper and lower parts of the fusion area. In addition, the area in which the desirable flow is generated appears to be relatively narrow.

Figure 5 shows the angle and velocity of the average vector around the area of the user’s face. The area and measurement interval were the same as those used for the map generation (25 points from ±100 mm in the x and y directions). This plot proves that the direction of the wind changed almost linearly, whereas its velocity was approximately stable independent of the direction.

6 PERCEPTION OF WIND A preliminary experiment to evaluate the perception of the

wind generated by the proposed approach was carried out. The equipment arrangement used in this experiment is shown in Figure 6. Four fans were placed at angles of ±30° and ±90° from the origin point. The sitting position and height of the chair for the subject were tuned so that their nose was approximately located at the origin point. The subject was asked to indicate the direction of the wind by turning their head so that it faced in that direction. The orientation vector of their face was measured using a magnetic sensor (FASTRAK, Polhemus), and the angle of orientation on the x-z plane was computed by projecting the

vector onto the x-z plane. The target direction of the wind was changed in the range of

±60° in 5° steps (25 directions), and wind was generated in a randomized order. Wind was generated using two fans that were close to the target direction of the wind. For example, the 50° direction was generated using fans A and B in Figure 6, whereas fans C and D were not operated.

Each subject experienced wind blown from 25 directions (10 sets). The number of subjects was seven (4 male and 3 female, ages 22-47). The subject was asked to close eyes and to wear headphones playing white noise to eliminate visual and auditory cues. The results for the individual subjects are plotted in Figure 7(a)–(g), and a summary of the results of all subjects is shown in Figure 7(h). Most subjects perceived almost continuous changes in the wind direction using the proposed interpolation method. Regarding subject 3, or Figure 7(c), there is a large step at around 10°, which means the subject could not perceive wind from the front. Moreover, the plot obtained for subject 4 has a similar step,

(a) Wind Angle

(b) Wind Velocity

Figure 5. Direction and Velocity of Generated Wind

(a) Geometry

(b) Arrangement

Figure 6. Experimental Setup

(a) Subject 1

(b) Subject 2

(c) Subject 3

(d) Subject 4

(e) Subject 5

(f) Subject 6

(g) Subject 7

(h) All Subjects

Figure 7. Characteristic of Perception

-40

-30

-20

-10

0

10

20

30

40

-40 -30 -20 -10 0 10 20 30 40

Mea

sure

d An

gle

[]

Target Angle [ ]

0.7 m/s

1.0 m/s

1.3 m/s

00.20.40.60.8

11.21.41.6

-40 -30 -20 -10 0 10 20 30 40

Mea

sure

d Ve

loci

ty [m

/s]

Target Angle [ ]

0.7 m/s

1.0 m/s

1.3 m/s

B

CNose ofSubject

Fan

A

DFan

Fan

Fan

-80

-60

-40

-20

0

20

40

60

80

-80 -60 -40 -20 0 20 40 60 80

Perc

eive

d [

]

Presented [ ]-80

-60

-40

-20

0

20

40

60

80

-80 -60 -40 -20 0 20 40 60 80

Perc

eive

d [

]

Presented [ ]

-80

-60

-40

-20

0

20

40

60

80

-80 -60 -40 -20 0 20 40 60 80

Perc

eive

d [

]

Presented [ ]-80

-60

-40

-20

0

20

40

60

80

-80 -60 -40 -20 0 20 40 60 80

Perc

eive

d [

]Presented [ ]

-80

-60

-40

-20

0

20

40

60

80

-80 -60 -40 -20 0 20 40 60 80

Perc

eive

d [

]

Presented [ ]-80

-60

-40

-20

0

20

40

60

80

-80 -60 -40 -20 0 20 40 60 80

Perc

eive

d [

]

Presented [ ]

-80

-60

-40

-20

0

20

40

60

80

-80 -60 -40 -20 0 20 40 60 80

Perc

eive

d [

]

Presented [ ] -80

-60

-40

-20

0

20

40

60

80

-80 -60 -40 -20 0 20 40 60 80

Perc

eive

d [

]

Presented [ ]

512

although it is relatively small. Subjects were asked also to answer to the questionnaire after

the experiment. The questionnaire asks about both rating and comments on the difficulty of perception, the unnaturalness of wind, and the easiness of the task. The result of the rating is shown in Figure 8.

Comments are summarized as follows (count of answers in round brackets): Regarding the difficulty of perception, the identification of direction was difficult (3), the sensation of facing toward the wind was not clear (1), and there were some cases where the wind was coming from various directions (1). Regarding the unnaturalness of the wind, the wind did not seem to be homogeneous (3), the face got cold by the wind and it made the perception more difficult (1), and sometimes wind was felt coming from more than one direction (2). Regarding the easiness of the task, the task was monotonous and drowsy. (2), the duration of the experiment was too long (1), the hairband used for mounting the sensor was uncomfortable (1).

The difficulty of perception and the unnaturalness of wind must be evaluated in comparison with the presentation using only one fan, so the rating itself does not necessarily indicates the advantage or drawback of the proposed approach, however, comments from the subjects suggest some problems specific to our approach: in some conditions or state of the subject, the flow of the wind is not felt sufficiently mixed as a single stream. One of the reasons for this problem is considered that, as stated in Section 5, the area of fusion of wind is relatively narrow. Because the head motion during the experiment is free to the subjects, it is possible for the head to get out of the area.

It should be noted that, for the target angles of ±30°, just one fan was operated. If the interpolation of wind is causing any difficulty of perception by the mixture of wind, it is expected that the variance of these specific conditions in Figure 7(h) are significantly reduced compared with others. However, there was no apparent difference in the variance of perception specific to the angles of ±30°; the variance was significantly larger at -20° and 15°, while significantly smaller at 20° and 25° (p<0.01).

7 CONCLUSION In this paper, an approach to the interpolation of wind using two

fans was proposed. Maps of the angle and velocity of the wind in relation to the speeds of the two fans were created based on measurements, and fan speeds corresponding to the target angle and velocity were computed using these maps. The feasibility of this approach was evaluated using both measurements of the generated wind and perception experiments using subjects.

One of our future works is expansion of our approach to two-dimensional control. It is expected that the direction of wind can be controlled also in the vertical angle using more than three fans arranged on a spherical surface. This two-dimensional control may also mitigate the problem of vertical wind flow stated in Section 5. For this purpose, maps of higher dimension must be

created. Feasibility of the approach and the perception of wind generated by the approach will be investigated.

Although, in this paper, flow of air was visualized based on measurement, use of CFD simulation in combination with the measurement will be helpful to understand the wind field. It may also be possible to create the maps based on the simulation if it has sufficient precision.

Improvement of the wind device is another topic of future study. From the experiment it became clear that the current device has rather sharp directivity. Using fan of larger size is expected to mitigate the problem, and is also good for reducing operation noise of the device. Some kind of diffusers may be useful to cause the similar effect.

ACKNOWLEDGEMENT This research was carried out as part of a project that is supported by the National Institute of Information and Communication Technology (NICT).

REFERENCES Y. Ikei, K. Abe, K. Hirota, and T. Amemiya: A Multisensory VR

System Exploring the Ultra-Reality; Proc. VSMM2012, 71-78, 2012. M. Heilig, Sensorama, U.S. Patent #3,050,870, 1962. T. Ogi, M. Hirose: Multisensory data sensualization based on human

perception; Proc. VRAIS'96, 66-70, 1996. T. Moon, G.J. Kim: Design and Evaluation of a Wind Display for

Virtual Reality; Proc. ACM Symposium on Virtual Reality Software and Technology, 122-128, 2004.

T. Kosaka, H. Miyashita, S. Hattori: Development and Evaluation of Immersive 3D Wind Display; IPSJ Symposium Series, vol. 2007(4), 105-112, 2007. (in Japanese)

T. Kosaka: WindStage (WindDisplay & WindCamera); Journal of the Society for Art and Science 8(2), 57-65, 2009. (in Japanese).

S. Cardin, F. Vexo, D. Thalmann: Head Mounted Wind; Proc. 20th Annual Conference on Computer Animation and Social Agents, 101-108, 2007.

S. Kulkarni, C. Fisher, E. Pardyjak, M. Minor, J. Hollerbach: Wind Display Device for Locomotion Interface in a Virtual Environment.; Proc. World Haptics Conference 2009, 184-189, 2009.

H. Matsukura, T. Nihei, H. Ishida: Multi-sensorial field display: Presenting spatial distribution of airflow and odor; Proc. IEEE VR 2011, 119-122, 2011.

M. Minakuchi, S. Nakamura: Collaborative ambient systems by blow displays; Proc. TEI '07 Proceedings ITE'07, 105-108, 2007.

E. Sawada et al: BYU-BYU-View: a wind communication interface; SIGGRAPH '07 ACM SIGGRAPH 2007 emerging technologies, 2007.

L. Deligiannidis, R.J.K. Jacob: The VR Scooter: Wind and Tactile Feedback Improve User Performance; Proc. 3DUI 2006, pp. 143-150, 2006.

T. Nakano, S. Saji, Y. Yanagida: Indicating Wind Direction Using a Fan-Based Wind Display; Proc. EuroHaptics2012, vol. 2, 97-102, 2012.

APPENDIX: SENSOR CONFIGURATION AND CALIBRATION The velocity of the wind was measured using anemometers

with a temperature sensitive resistor (6312/0941, Kanomax). Similar to hot-wire anemometers, these estimated the velocity by measuring the amount of heat dissipated by the thermal transfer from the airflow. In a case where this sensor is used alone, it is assumed that the wind flow is perpendicular to the axis of the resistor. Otherwise, the effect of the thermal dissipation decreases, and the velocity of the wind is underestimated. If the relationship between the angle and reduction ratio is given, it becomes

Figure 8. Subjective Rating of the Task

1 2 3 4 5

Easiness ofTask

Unnaturalnessof Wind

Difficulty ofRecognition

easy difficult

natural unnatural

tiresome easy

513

possible to estimate a three-dimensional wind flow vector by using more than three sensors with different orientations. This method of measuring the wind vector is frequently employed for hot-wire anemometers, and generally requires careful calibration. In our research, a similar method was applied using four sensors. In the rest of this section, details of the sensor configuration and calibration method are provided.

Figure 9 shows the configuration of the sensors, where the axis of the resistor of each sensor is kept at 45° relative to the x-y plane; two of them are perpendicular to the x-axis, whereas the others are perpendicular to the y-axis. The distance between the sensors was determined so that they were as close as possible while avoiding thermal interference. Using this sensor configuration, the angular range of measurement is theoretically within 45° of the z-axis. However, the actual range will be a little smaller, because when the angle between the wind vector and the axis of the resistor decreases, the measurement error increases.

Because, in our experiments, the direction of the fans was changed within a range of 30° from the front, this measurement range was considered to be sufficient.

First, the output reduction in relation to the angle of the wind was measured. The output value of a sensor was measured while rotating it around an axis that was perpendicular to the axis of the resistor. The measurement was performed under different wind velocities, which were generated using different fan rotation speeds. The results are shown in Figure 9.

Then, the following function was fitted to the measured result, y = A|𝑣| cos(𝑥) + 𝐵|𝑣| (7) where 𝑥 is the angle, 𝑣 is the velocity of the wind, and 𝑦 is the output of the sensor. By using the least-square method, 𝐴 = 0.5636 and 𝐵= 0.4364 were obtained. In Figure 10, the fitting function is overlaid (i.e., thin black lines). In addition, individual differences in the gain among the four sensors were compensated by tuning the gain of each sensor to the average value.

Next, the relationship between wind vector 𝕧 and the resulting sensor output was developed. Let us suppose that the direction of the axis of a resistor is 𝕒 , then the angle of 𝕧 relative to the perpendicular plane of the resistor, which is denoted as 𝑥 , is calculated by 𝑥 = cos 𝕒 ∙ 𝕧|𝕒 ||𝕧| − 𝜋2 (8)

and the measured value will be y = A|𝑣| cos(𝑥 ) + 𝐵|𝑣| (9) In the configuration described above, there are four sensors, and

the orientations of their resistor axes are as follows. 𝕒 = +1/√2, 0, −1/√2 𝕒 = −1/√2, 0, −1/√2 𝕒 = 0, −1/√2, −1/√2 𝕒 = 0, +1/√2, −1/√2

(10)

Hence, the estimated y (𝑖= 0–3) values are defined as functions of 𝕧 . Using these equations, the inverse problem is solved to estimate 𝕧 from the actually measured values of Y (𝑖= 0–3). In our study, the problem was solved using a search algorithm, where y ≡ (y , y , y , y ) and Y ≡ (Y , Y , Y , Y ) were considered to be four-dimensional vectors, and a 𝕧 that minimized |𝕪 − 𝕐| was sought.

Figure 11 shows the direction of the wind measured by the algorithm; the sensor unit was rotated about its y-axis while the rotation speed of the fan was changed to 900, 1100, and 1300 rpm. The results suggest considerable linearity in the wind angle independent of the velocity, along with sufficient resolution of the velocity, which was also independent of the wind angle.

(a) Configuration

(b) Implementation

Figure 9. Sensor Configuration

Figure 10. Fitting a Sinusoidal Function

(a) Wind Angle

(b) Wind Velocity

Figure 11. Evaluation of Calibrated Sensor

45

4545

45

x

y

z

Wind

Resistor

8 mm

8 m

m

0

0.5

1

1.5

2

2.5

-100 -50 0 50 100

Mea

sure

d Va

lue

[m/s

]

Angle [ ]

200 300400 500600 700800 9001000 11001200

-50

-30

-10

10

30

50M

easu

red

Angl

e [

]

Actual Angle [ ]

1300rpm1100rpm900rpm

0

0.5

1

1.5

2

2.5

Mea

sure

d Ve

loci

ty [m

/s]

Actual Angle [ ]

1300rpm1100rpm900rpm

514