How to Measure Direction and Speed of True Wind on Moving Boat

Xiang Zheng Tu

With an anemometer, people can easily measure the direction and speed of natural wind or true wind. The true wind is the term most commonly used to describe sailing wind, without the effects of the motion of the boat. On a moving boat, the measured wind is no longer the true wind instead of apparent wind. The apparent wind is the wind experienced by an observer in motion and is the relative velocity of the wind in relation to the observer. On the moving boat the apparent wind is a product of three other winds: the true wind, tide wind, and motion wind.

Tide wind is the wind created by the motion of the water relative to the land. Motion wind is the wind created by the movement of the boat through the water. By combining these two winds we have boatspeed wind (speed through the water, not speed over ground).

It can be seen that the true wind is a derived number, not a measured number like the apparent wind. This means we cannot physically measure the true wind angle or the true wind speed on the moving boat. We need to calculate it using the apparent wind angle, apparent wind speed, and the boatspeed.

These measured numbers are put through something called “the wind triangle.” The end result is the true wind angle and the true wind speed. These calculations are much more useful to the sailor as they reference the sailing wind outside of the boat and allow them to think strategically.

Fortunately a highly integrated thermopile motion sensing unit has been developed. This unit can measure the speeds of the winds coming from three different directions as shown in the above figure. There are three winds blowing toward the moving boat. One is the boatspeed wind consisting of two components: the boat speed and the true wind component in the forward direction of the moving boat. The second one is the true wind component in the side perpendicular direction of the moving boat. The third one is a combination wind of the boatspeed wind and the true wind, which blows toward the moving boat at 45 degree angle to the forward direction. The combination wind also consists of two components. One is the boatspeed wind component in the direction at 45 degree to the forward direction. The other is the true wind component in the direction at α angle to the side perpendicular direction of the moving boat. The sensing unit contains three thermopile motion sensors that are disposed in the three wind passages, respectively. In operation of the sensing unit, the sensors measure each wind speeds and send out signals V_Forward, V_45digree, and V_Side, which represent their individual wind speeds. 

Reference the above figure, the following equations can be established based on basic trigonometric formulas:

V_Forward = u + ν cos α,                                    (1)

V_45degree = u cos 45⁰ + (v cos α) cos 45⁰,      (2)

V _Side  = ν sin α ,                                             (3)

where u is the speed of the boatspeed wind, v is the speed of the true wind. This is a system of ternary linear equations. The three variables u, v and α in the system can be found by substituting the measured values of V_Forward, V_45degree  and V_Side and cos 45⁰ = 21/2 /2 into the system, and solving the system.

The thermopile motion sensors actually are the thermal flow sensors produced by POSIFA Microsystems. A thermal flow sensor comprises a heater, two thermopiles and a thermal insulated base recessed in a silicon chip and supporting the heater and thermopiles. The sensor measures fluid mass flow rate by means of the heat convected from the heater surface to the flowing fluid. The sensor and the fluid can move in relation to each other. If the sensor is still and the fluid flows the sensor is functioned as a thermal flow sensor. If the fluid is still and the sensor moves the sensor is functioned as a thermopile motion sensor. This is based on the fact that any moving object can produce an apparent wind.

A simple example for the apparent wind is that a man is a riding bicycle on a day when there is no wind. Although the wind speed is zero, the rider will feel a breeze on the bicycle due to the bicycle is moving through the air. This is the apparent wind. On the windless day, the measured apparent wind will always be directly in front and equal in speed to the speed of the bicycle.

Another example is in sailing. The apparent wind is the actual flow of air acting upon a sail. It is the wind as it appears to the sailor on a moving vessel. It differs in speed and direction from the true wind that is experienced by a stationary observer.

In all these examples the thermal flow sensors or the thermopile motion sensors can be used to measure the speeds of the moving objects.

Temperature Detected by MEMS Thermopile Flow Sensors

Tu Xiang Zheng

A MEMS thermopile flow sensor provided by POSIFA Microsystems is composed of a membrane, a resistor, a thermopile and a silicon chip. The resistor and the hot junctions of the thermopile are disposed on the membrane that is suspending over a cavity. The cavity is recessed in a silicon chip and the bridges of the membrane is expended to and supported by the silicon chip. The legs of the thermopile pass through the bridges so that the cold junctions of the thermopile are disposed on the silicon chip.

When air flows over the surface of the sensor and the resistor of the sensor is heated up by a fixed input power, the output voltage of the thermopile depends on the temperature of the air.  This dependence can be seen from the input power expression:

Power = I * V = A_m * k_m * (T – T₀) / L_m + h * k_air ((T – T₀) + Am * J_r      (1)

I is the current being passed through the resistor, V is the voltage measured across the resistor, T is the temperature of the membrane and T₀ is the temperature of the air. A_m is the effective cross section area that heat is transported across the membrane, km is the thermal conductivity of the membrane, and L_m is the distance along the membrane that the temperature gradient is established, A_m is the surface area of the membrane, h_air is air natural or free convection coefficient, k_air is the thermal conductivity of air and J_r is radiation heat flux of the membrane.

The air natural convection coefficient hair can be expressed as:

h   =   C*(k_air / L) * {[ρ * g_c * β * L³ * (T – T₀)] / [μ * k_air]}n       (2)

L is the length of the membrane, ρ is the density of air, g_c is the gravitational acceleration, β is the coefficient of thermal expansion of air and μ is the dynamic viscosity. The value of constant C and exponent n are equal to 0.54 - 0.25, 1.32 – 0.25, respectively. Actually, equation (2) is an empirical formula the natural convection h of air is approximately equal to 10.45.  So it is true that the output voltage of the thermopile depends on the temperature of the air, if the membrane is kept a constant temperature above the temperature of air.

One widespread method of temperature measurement of air is thermistor-based temperature measurement, typically platinum (Pt) resistors-based. The reason is that Pt resistors are superior in terms of accurate temperature coefficient of resistivity (TCR) and, therefore, have better defined temperature dependence.

However, during the temperature measurement, one significant problem in Pt resistors based temperature measurement is that the self-heating effect causes a temperature rise in the sensor element. Self-heating effect is that when a current flows through a thermistor, it will generate heat which will raise the temperature of the thermistor above that of its environment. If the thermistor is being used to measure the temperature of the environment, this electrical heating will introduce a significant error if a correction is not made.

One of the temperature measurement methods which do not have the problem of self-heating or poorly IC-process compatible is thermopile-based temperature measurement. In additional, thermopiles is based on the self-generating Seebeck effect, this ensures that:

• the output signal generated by the thermopile which has no offset or no offset drift, because there cannot be any output signal without input power,
• the thermopile does not suffer from interference from power supplies or any physical or chemical signals except light (which can easily be shielded),because the Seebeck effect and the photoelectric effect are the only two self-generating effect in silicon,
• the thermopile does not need any biasing, and
• the read-out circuit is quite simple, only a voltmeter is required.

Moreover, the sensitivity of the thermopile is hardly influenced by variations in the electrical parameters across the wafer or by the temperature of the environment. Unlike transistors and resistors, whose sensitivity and offset depend on the position on the wafer and the temperature.

Comparison of Three MEMS Thermal Conductivity Sensors

Tu Xiang Zheng

MEMS sensors have greatly matured and proliferated in use amongst many disciplines. There has been great interest in MEMS thermal conductivity sensors due to the benefits of miniaturization: low cost, small device footprint, low power consumption, greater sensitivity, integration with on-chip circuitry, etc. which can be used to analyze a whole range of gas mixtures, provided that there are only two gases present and that the two gases have significantly different thermal conductivities. 

A single silicon wafer MEMS thermal conduction sensor has developed by the present author. The sensor consists of a heat transfer cavity with a flat bottom and an arbitrary plane shape, which is created in a silicon substrate. A heated resistor with a temperature dependence resistance is deposed on a thin film bridge, which is the top of the cavity. A heat sink is the flat bottom of the cavity and parallel to the bridge completely. The heat transfer from the heated resistor to the heat sink is modulated by the change of the thermal conductivity of the gas or gas mixture filled in the cavity. This change can be measured to determine the composition concentration of the gas mixture or the pressure of the air in a vacuum system.

In order to know the advantages of the present MEMS thermal conductivity sensors a comparison of several MEMS thermal conductivity sensors is made. The others MEMS thermal conductivity sensors were developed by Arndt et al’s and Hsiai et al’s.

 

1. Comparison and contrast between the Arndt et al.’ sensors and the present sensors are shown in Fig.1. Several significant differences between them can be found from the comparison and contrast. These significant differences include the follows:

(1) The Arndt et al.’ sensors are not single silicon wafer MEMS thermal conduction sensors. Actually it is constructed by three wafer including one base plate and two porous cover plates. In contrast, the present sensors are single wafer MEMS thermal conduction sensors that are constructed from single silicon wafers.

(2) The heat transfer cavity of the Arndt et al.’ sensors can not be arbitrary shape because it is formed by KOH etching that limits the shape of the cavity to be bounded by the (111) crystal planes of the silicon wafer. Compared with the Arndt et al.’ sensors, the heat transfer cavity of the present sensors can be arbitrary shape because it is by anodization in HF solution which is not governed by the crystal structure of the silicon wafer.

(3) The side wall of the heat transfer cavity of the Arndt et al.’ sensors can not be curved due to limitation of the crystal structure of the silicon wafer. On the contrary, the side wall of the heat transfer cavity of the present sensors can be curved due to its formation without limitation of the crystal structure of the silicon wafer.

(4) The Arndt et al.’ sensors have two heat transfer cavities with one on the top of the base plate and the other on the bottom of the base plate. Unlike the Arndt et al.’ sensors, the present sensors only have one heat transfer cavity.

(5) The two heat transfer cavities of the Arndt et al.’ sensors with each is formed by bonding a silicon base plate and a porous plate together. Contrasted with the Arndt et al.’ sensors, the heat transfer cavity of the present sensors are formed inside the silicon wafer without using an additional wafer.

(6) The Arndt et al.’ sensors have two adhesive layers that are used for bonding three different plates together. Conversely the present sensors have no adhesive layers because it is a single wafer structure without wafer bonding.

In summery, almost no similarities between the Arndt et al.’ sensors and the present sensors have been found. There is impossible for the Arndt et al.’ sensors to teach the present sensors.

2. Comparison and contrast between the Hsiai et al.’ sensors and the present sensors are shown in Fig.2. It can be found that the Hsiai et al.’ sensors and the present sensors are related to different types of sensors according to the following reasons:

The Hsiai et al.’ sensors are fluid shear stress sensors that are based on heat transfer by fluid convection. But the present sensors are gas thermal conduction sensors that are based on heat transfer by gas conduction.

The Hsiai et al.’ sensors do not need a heat transfer cavity because fluid convection occurs over the diaphragm. However the present sensors do need a heat transfer cavity because gas conduction occurs inside the cavity.

The cavity of the Hsiai et al.’ sensors have no bottom used for heat sink because they have no heat transfer function. Nevertheless the heat transfer cavities of the present sensors have a bottom so that the heat generated by the heater on the top of the cavity can be transferred to the bottom through the gas filled in the cavity.

In view above mentioned three major differences between the Hsiai et al.’ sensors and the present sensors, it should be very clear that the present thermal conduction sensors are not able to learn from the Hsiai et al.’ fluid shear stress sensors.

3. The present sensors are fabricated using porous silicon micromachining technique instead of KOH etching micromachining technique that is used by Arndt et al. and Hsiai et al.

(1) KOH etching of silicon is an anisotropic etching. The main characteristics of this micromachining technique can be listed as:

Etch rates of crystallographic planes are: (100) > (110) > (111)

(111) family of crystallographic planes are the “stop” planes

producing standard anisotropic etching structures: V-grooves and pyramidal cavities

From these characteristics it can conclude that the cavities of the Arndt et al.’ sensors and the Hsiai et al.’s sensors are pyramidal cavities with (111) sidewall planes, because they all use KOH etching to create their cavities. It also can be conclude that the heat transfer cavity with curved sidewalls provided by the present sensors can not be created using KOH etching technique.

(2) In addition to KOH micromachining technique, a porous silicon based micromachining technique is more and more widely used for MEMS devices fabrication. Porous silicon layers can be fabricated by partially electrochemical dissolution of silicon wafers with etching masks covered on the surface of the silicon wafers. Then the porous layers are etched away to form microstructures including cavities. The shape of the cavities is determined by the etching masks without limitation based on the silicon crystallographic structure. Like the present sensors the cavities of the sensors can have arbitrary shape and curved sidewalls.

4. Conclusion

Comparing and contrasting between the Arndt et al.’s sensors and the present sensors and between the Hsiai et al.’s sensors and the present sensors have been made respectively. Six significant differences between the Arndt et al.’s sensors and the present sensors have been found. It can be seen that it is impossible for the present inventor to learn from the Arndt et al.’s sensors for designing and fabricating the present sensors. Three major differences have been found between the Hsiai et al.’s sensors and the present sensors. Actually, the Hsiai et al.’s sensors and the present sensors belong to different sensor types. It is not able for the present inventor to learn how to design the present sensors from the Hsiai et al.’s sensors. Moreover the present sensors use porous silicon based micromachining technique for fabricating the present sensors, which is different from KOH micromachining technique used by the Arndt et al.’s sensors and the Hsiai et al.’s sensors. Hwy the heat transfer cavity with arbitrary shape and curved sidewalls provided by the present sensors can not been created in the Arndt et al.’s sensors and the Hsiai et al.’s sensors, because they all use KOH micromachining technique instead of porous silicon based micromachining technique.

Measuring Bike and Wind Velocities Using Thermal Motion Sensors

Xiang Zheng Tu

It is widely acknowledged that cycling is one of the best ways for people to achieve good health and fitness. There are more than a billion bicycles in the world, twice as many as automobiles. In recent years bike production had climbed to over 100 million per year, which is compared to 50 million cars. Bicycles were introduced in the 19th century and since then have been and are employed for many uses: recreation, work, military, show, sport etc. In the USA, people use bikes for slimming and better feeling, but other countries people use bikes mostly for transportation needs. For these reasons in some countries bikes are especially popular.

How many calories burn when cycling?  It is best to known that the energy consumed by cycling which can be expressed as:

P = C_m * V_b* [ c_d  * A * ρ/2 * ( V_b + V_w )² + F_rg  + V_b * C_rvn ],        (1)

where P is rider's power, V_b is velocity of the bicycle, Vw is wind speed, C_m  is coefficient for power transmission losses and losses due to tire slippage, C_d  is air drag coefficient, A is  total frontal area (bicycle + rider),  ρ is air density, C_rVn is coefficient for the dynamic rolling resistance, normalized to road inclination; C_rVn = C_rV*cos(β), C_rV  is coefficient for velocity-dependent dynamic rolling resistance, β  is  inclination angle, F_rg  is rolling friction (normalized on inclined plane) plus slope pulling force on inclined plane. As seen from equation (1), the energy consumption depends on many factors including two variables: cycling velocity and wind velocity. The other factors are coefficients relating to cycling conditions.

It is worth to point out that the equation (1) is only for rough calculations, because some coefficients usually are not available. Fortunately, bicycles are used mostly in the flatlands. In this case most of the coefficients can be assumed as constant and the energy consumption of a cycling can be simply calculated using measured bicycle velocities and wind velocities.

As shown in the above figure, a thermal motion sensing system is used to measure the bicycle velocity and the wind velocity respectively when a man is riding a bicycle. The sensing system is installed in a concentric tube with an inner tube and an outer tube. Several small holes are drilled around the outside of the two ends of the outer tube and two end holes are communicated through the outer tube. A large hole is drilled through the axis of the inner tube, which is separated from the outer tube by the tube wall. The concentric tube is pointed in the direction of the bicycle traveling. According to the principle of relative motion, an air flow caused by the cycling passes through the large hole. The air flow comprises two components: a cycling flow and a wind flow. The cycling also causes another air flow which passes through the outer tube. Since the outside holes are perpendicular to the direction of the bicycle traveling any head wind or tail wind can not enter the outer tube. So this air flow only comprises the cycling flow.

Referencing to the above figure, there are two thermal motion sensors in the concentric tube. One of them is disposed on the wall of the outer tube, which is used to measure the total velocity V_t of the air flow passing through the inner tube. The other is disposed on the wall of the inner tube, which is used to measure the cyclist velocity V_c of the air flow passing through the outer tube. The total velocity V_{t  is} related to the cycling in a head wind or a tail wind and is equal to the sum of the cyclist velocity V_c and the head wind velocity V_hw  or the tail wind velocity V_tw. So the wind velocity can be calculated by

V_hw = V_t - V_{c ,}       V_tw = V_t + V_c         (2)

The thermal motion sensor is made using both microfabrication techniques and Micro-Electro-Mechanical Systems, or MEMS technologies and operated based on gas convective heat transfer. The sensor comprises of a thermal insulated base recessed into and surrounded by a silicon chip. A heating resistor and the hot junctions of a thermopile display on the surface of the base. The cold junctions of the thermopile display on the surface of the silicon chip near the base edge. The heating resistor is heated to maintain a continuous overheat between the resistor and the air flowing over the surface of the sensors. The thermopile is functioned as a temperature sensor. Both the actuations are performed by a POSIFA proprietary integrated circuitry.

The POSIFA proprietary integrated circuitry is an 8 bit MCU based microcontroller, since the thermal motion sensors applications do not involve a lot of number crunching, just waking up periodically to check for sensors input and making a decision on it. A low noise programmable operation amplifier is embedded into the microcontroller. This is done in order to match the thermal motion sensors with very low inherent noise.  The offset of the thermal motion sensors can be completely canceled by programmable hearting of the sensor resistor. This can be realized using a modulated DAC output of the microcontroller. Actually the DAC output here is used as a controllable precision voltage source. The DAC resolution provided by the microcontroller is required to be reasonable high. 

It is widely acknowledged that cycling is one of the best ways for people to achieve good health and fitness. There are more than a billion bicycles in the world, twice as many as automobiles. In recent years bike production had climbed to over 100 million per year, which is compared to 50 million cars. Bicycles were introduced in the 19th century and since then have been and are employed for many uses: recreation, work, military, show, sport etc. In the USA, people use bikes for slimming and better feeling, but other countries people use bikes mostly for transportation needs. For these reasons in some countries bikes are especially popular.

How many calories burn when cycling?  It is best to known that the energy consumed by cycling which can be expressed as:

P = C_m * V_b* [ c_d  * A * ρ/2 * ( V_b + V_w )² + F_rg  + V_b * C_rvn ],        (1)

where P is rider's power, V_b is velocity of the bicycle, Vw is wind speed, C_m  is coefficient for power transmission losses and losses due to tire slippage, C_d  is air drag coefficient, A is  total frontal area (bicycle + rider),  ρ is air density, C_rVn is coefficient for the dynamic rolling resistance, normalized to road inclination; C_rVn = C_rV*cos(β), C_rV  is coefficient for velocity-dependent dynamic rolling resistance, β  is  inclination angle, F_rg  is rolling friction (normalized on inclined plane) plus slope pulling force on inclined plane. As seen from equation (1), the energy consumption depends on many factors including two variables: cycling velocity and wind velocity. The other factors are coefficients relating to cycling conditions.

It is worth to point out that the equation (1) is only for rough calculations, because some coefficients usually are not available. Fortunately, bicycles are used mostly in the flatlands. In this case most of the coefficients can be assumed as constant and the energy consumption of a cycling can be simply calculated using measured bicycle velocities and wind velocities.

As shown in the above figure, a thermal motion sensing system is used to measure the bicycle velocity and the wind velocity respectively when a man is riding a bicycle. The sensing system is installed in a concentric tube with an inner tube and an outer tube. Several small holes are drilled around the outside of the two ends of the outer tube and two end holes are communicated through the outer tube. A large hole is drilled through the axis of the inner tube, which is separated from the outer tube by the tube wall. The concentric tube is pointed in the direction of the bicycle traveling. According to the principle of relative motion, an air flow caused by the cycling passes through the large hole. The air flow comprises two components: a cycling flow and a wind flow. The cycling also causes another air flow which passes through the outer tube. Since the outside holes are perpendicular to the direction of the bicycle traveling any head wind or tail wind can not enter the outer tube. So this air flow only comprises the cycling flow.

Referencing to the above figure, there are two thermal motion sensors in the concentric tube. One of them is disposed on the wall of the outer tube, which is used to measure the total velocity V_t of the air flow passing through the inner tube. The other is disposed on the wall of the inner tube, which is used to measure the cyclist velocity V_c of the air flow passing through the outer tube. The total velocity V_{t  is} related to the cycling in a head wind or a tail wind and is equal to the sum of the cyclist velocity V_c and the head wind velocity V_hw  or the tail wind velocity V_tw. So the wind velocity can be calculated by

V_hw = V_t - V_{c ,}       V_tw = V_t + V_c         (2)

The thermal motion sensor is made using both microfabrication techniques and Micro-Electro-Mechanical Systems, or MEMS technologies and operated based on gas convective heat transfer. The sensor comprises of a thermal insulated base recessed into and surrounded by a silicon chip. A heating resistor and the hot junctions of a thermopile display on the surface of the base. The cold junctions of the thermopile display on the surface of the silicon chip near the base edge. The heating resistor is heated to maintain a continuous overheat between the resistor and the air flowing over the surface of the sensors. The thermopile is functioned as a temperature sensor. Both the actuations are performed by a POSIFA proprietary integrated circuitry.

The POSIFA proprietary integrated circuitry is an 8 bit MCU based microcontroller, since the thermal motion sensors applications do not involve a lot of number crunching, just waking up periodically to check for sensors input and making a decision on it. A low noise programmable operation amplifier is embedded into the microcontroller. This is done in order to match the thermal motion sensors with very low inherent noise.  The offset of the thermal motion sensors can be completely canceled by programmable hearting of the sensor resistor. This can be realized using a modulated DAC output of the microcontroller. Actually the DAC output here is used as a controllable precision voltage source. The DAC resolution provided by the microcontroller is required to be reasonable high.