Five-Hole Thermal Velocity Probes Used for Attitude Control of Aircrafts

Tu Xiang Zheng

The ability to measure, stabilize, and control attitude is critical for any aircraft that is required to fly autonomously. Traditionally, attitude stabilization is achieved using rate gyros to sense and correct unwanted rotations in yaw, pitch, and roll. While this method is a standard feature of many autopilot systems, it is susceptible to drift during long duration flights. The reason is that rate gyros only sense angular velocities and not angular position itself. Therefore, they do not provide an absolute orientation reference. Instead, the yaw, pitch, and roll of the aircraft must be obtained by integrating the rate signals, which can lead to substantial noise induced drift. Another approach is to use the direction of gravity, as sensed by accelerometers, to estimate and stabilize attitude. But this approach can be invalid when an aircraft makes turns, which generate centripetal forces.

The use of the multi-hole pressure probes has become common to determine total and static pressures, flow velocity, and flow directions in three-dimensional flow fields with suitable calibrations. This approach is based on Bernoulli’s equation, which states that the pressure drop across the constriction is proportional to the square of the flow rate. Using this relationship, 10 percent of full scale flow produces only 1 percent of the full scale differential pressure. At 10 percent of full scale flow, the differential pressure flow meter accuracy is dependent upon the transmitter being accurate over a 100:1 range of differential pressure. Differential pressure transmitter accuracy is typically degraded at low differential pressures in its range, so flow meter accuracy can be similarly degraded. Therefore, this non-linear relationship can have a detrimental effect on the accuracy and turndown of differential pressure flow meters.

The above shortcomings can be overcome by using five-hole thermal velocity probes that provide direct information on the air stream velocity and direction that are experienced by an aircraft. Five-hole thermal velocity probes have some advantages over other methods as their maintenance, relatively low cost, and simplicity in operation. In principle, any aerodynamic body such as cylinder, sphere, wedge, or prism, with a number of holes can be used to measure three-dimensional flows. A minimum of five holes on an aerodynamic body is required to measure the four unknowns, namely, three velocity components and two angles in mutually perpendicular planes, in three-dimensional flows. However for the sake of symmetry and extended range of measurement capability, seven-hole or more probes are preferred.

The five-hole thermal velocity probes comprise not only five air flow tubes and but also five thermal velocity sensors, each of which is installed in an air flow tube. The center tube is arranged along the longitudinal direction of an aircraft to be attached and surrounded by the other four tubes in the shape of a cross. The leading edge of the four outside tubes is cut at a 45 degree angle to the center tube. Unlike multi-hole pitot pressure probes, the front end hole is communicated with the rear end hole instead of the both end holes keeping separated by the membrane of a pressure sensor. So when a flow of air stream past the tubes the sensors installed in the tubes measure the velocity or velocity components instead of the pressure difference of the flow.

Airspeed u_air, angle-of-attack (α), and sideslip angle (β) are known as the air data quantities, which are traditionally measured using pitot pressure tubs. Now these quantities can be measured using the five-hole thermal velocity probes. Assuming: a flow of air stream blows to the flying aircraft with a velocity W_air, the individual sensors of the five-hole velocity probes will measure individual signal representing individual velocity components that can be expressed as:

V_pitch1-2 =k (2)^1/2 W_air cos (α) cos (β),                                     (1)

V_yaw1-2 = k (2)^1/2 W_air  sin (α),                                                 (2)

V_center = k  W_air  cos (α) sin (β).                                               (3)

Where V_pitch1-2 is the output of the sensor in the pitch tube 1 or 2, V_yaw1-2 is the output of the sensor in the yaw tube 1 or 2, and V_center is the output of the sensor in the center tube, and k is the sensor circuit amplification factor. The airspeed u_air, angle-of-attack (α), and sideslip angle (β) can be calculated by solving the equations (1), (2) and (3).

The thermal velocity sensors used for the five-hole velocity pitot probes are produced by POSIFA Microsystems. Unlike traditional motion sensors, these new motion sensors do not rely on optical, microwave, or acoustic sound. They only rely on heat forced convection transfer. The sensor comprises a resistive heater and two thermopiles, which are integrated in a silicon substrate and supported by a thermal insulating base recessed into the silicon substrate. Since heat forced convection transfer the air flowing past the resistor will have a cooling effect on the heated resistor. By relating the temperature difference of the thermopiles, the speed air stream can be measured. They have fast response, low power consumption and compact structure. More particularly, it is easy to figurate an electronic sensor circuit that has zero offset, free temperature drift and very low noise.

It is true that the device structure of the thermal motion sensor is similar to the thermal flow sensor that we described before. But they are different in relative motion. Relative Motion is the laws of physics which apply when air is at rest on the earth also apply when air is in any reference frame which is moving at a constant velocity with respect to the earth.

Reference frame is too important in physics. We do all calculations according to the reference frames. For instance, we are on the aircraft flying in the air, the velocity of that plane with respect to the air can be measured using the thermal motion sensor. If we are on the ground the velocity of that aircraft is the sum of the velocities of plane and the wind. The velocity of the wind can be measured using the thermal flow sensor. To sum up the velocities of the aircraft and the wind, we can determine the directions and quantities of velocity of the aircraft with respect to the ground. 

Tracking Hummingbirds Using Thermal Moving Velocity Sensor

Tu Xiang Zheng

 

For many years the only way to track wildlife was to simply follow and observe the movement and habits of an animal or to capture an animal and put a tag on it and hope that at sometime in the future that same animal would be recaptured. Today, scientists have new tools to help them to track a wide variety of animals, from butterflies to great white sharks, in order to study how they use their environment, which foods are important and to gain insights into behavior and condition of the creatures as well as to identify key breeding areas that may need protection. 

There are three types of radio tracking systems available today: VHF Radio Tracking, Satellite Tracking and Global Positioning System (GPS) Tracking. But for tracking small animals these technologies are helpless because the transmitters used are so large and heavy. Today, scientists are working on ways to make the tracking devices smaller. Among them are MEMS wireless sensing systems. MEMS technology is enabling the development of inexpensive, autonomous wireless sensors with volumes ranging down to cubic mm.  Combination with miniaturized battery technology is making it possible to check even the smallest birds and insects.

In this paper we describe tracking hummingbird using a thermal moving velocity sensor and a thermal wind sensor. As shown in Fig.1, a Bluetooth thermal moving velocity sensor tag is attached to a hummingbird and a smart phone with a thermal wind sensor is hold by an observer. When the hummingbird is flying in the space the plane projection of the hummingbird flying path will display on the screen of the smart phone. The tracking range can reach 100 meters using class 1 smart phone. Technically it's possible to boost the Bluetooth range over 1000 meters, as some vendors suggest.

A thermal moving velocity sensor includes 12 sensing units each consisting of a heater and a thermopile, which are centro-symmetrically arranged on a silicon substrate. Two opposite units are configured as a pair for measuring a moving velocity component in this direction. So the whole sensor can measure 6 different directional velocity components and each two measured adjacent velocity components are 45 degree in angel. The structure of the thermal wind sensor is similar to the thermal moving velocity sensor. An only difference is that the sensing unit number of the thermal wind sensor is 4 instead of 6. The thermal wind sensor can measure 4 different wind components respectively in x and y directions. The measured data by the thermal moving velocity sensor and thermal wind sensor are collected and processed by the smart phone.

 

Reference to Fig. 2, it is more detail to explain the working principle of tracking hummingbird using the thermal moving velocity sensor and thermal wind sensor. As can be seen, a moving plane coordinate system is set on the hummingbird with a thermal moving velocity sensor and a reference plane coordinate system is set on the ground with a thermal wind sensor and a smart phone.

For the thermal moving velocity sensor the following equations can be formed according to basic trigonometric formulas:

V_yh = u + ν cos α,                                            (1)

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

V _xh  = ν sin α                                                  (3)

 α = arcsin (V_xh /υ)                                           (4)

where u is the velocity of the hummingbird, v is the velocity of the natural wind and α is the incident wind angle, which are relative to the moving plane coordinate system. This is a system of ternary linear equations. The values of the three variables u, v and α can be obtained by substituting the measured values of V_yh, V_45degree  and V_xh and cos 45⁰ = 0.525 into the system, and solving the system.

For the thermal wind sensor, the following equations can be formed according to basic trigonometric formulas:

V_yw = ν cos θ                                                   (5)

V_xw  = ν sin θ                                                  (6)

θ = arctan (V_yw/V_xw)                                       (7)

where v is the velocity of the natural wind and θ is the incident wind angle, which are relative to the ground plane coordinate system.

It should be understood that the measured value of the natural wind velocity in the ground plane coordinate system is the same as the measured value in the moving plane coordinate system. But the wind incident angle is different in the two plane coordinates. This means that the incident angle α in the moving plane coordinate system is replaced by the incident angle θ in the ground plane coordinate system.

According to Cartesian coordinate system conversion, the following equations are available.

y_g = x_h  sin (θ - α) + y_h  cos (θ - α)                  (8)

x_g = x_h  cos (θ - α) + y_h  sin (θ - α)                  (9)

Actually, the moving plane coordinate system can be translated to the ground coordinate system by clockwise rotation of (θ - α) degrees. After translation the data collected by the thermal moving velocity sensor can be used to calculate the velocity, flying path and moving range of the hummingbird, which are relative to the ground plane coordinate system.

This tracking technology can help determine exactly where a hummingbird is at any moment in time and often what that animal is doing. Using the data collected from a thermal moving velocity sensor, scientists can determine the day-to-day movements of a hummingbird, the size of a hummingbird's home range, what other animals share an animal's range and the types of habitats a hummingbird uses. By analyzing all this data, scientists can learn new ways to help control hummingbird populations, determine what impact development might have on a hummingbird population, and determine if there are enough individuals of a particular species in an area to allow for reproduction. 

Miniaturized Thermal Wind Sensors

Tu Xiang Zheng

A miniaturized thermal wind sensor produced by POSIFA Microsystems is shown in the above figure. The sensor is fabricated in a silicon substrate using popular CMOS and proprietary MEMS technologies. As shown in the figure, on the upper face of the silicon substrate there are four thermopiles and heaters indicated respectively by thermopile (W), thermopile (E), thermopile (N) and thermopile (S) and heater (W), heater (E), heater (N) and heater (S). They are arranged in symmetrical positions with the central point of the upper face of the silicon substrate. It should be noted that the hot junctions of the thermopiles and the heaters are disposed on a thermal insulating base that recessed into the silicon substrate. The heat generated by the heater is almost restricted in the top layer of the base because the conductive heat transfer is minimized. It is easy to understand that when wind flows over the sensor the temperature of the top layer will be reduced significantly by convective heat transfer. Since the cold junctions of the thermopiles are positioned in the outside of the base the temperature change will be detected by the thermopiles which represent the velocity of the wind.    

As can be seen, the thermal wind sensors operate by heat transfer from the heater to the flowing fluid. The term thermal implies the use of the resistive heaters within the fluid flow and the thermopiles measuring the temperature difference between the heaters and the fluid flow. As the fluid flow past the heaters increases, convective heat loss increases from the heaters. The relationship between increasing fluid flow and forced convective cooling of the heaters can be determined and used as a baseline calibration for sensing wind applications. Appropriately the heat transfer can be expressed by King’s Law that describes heat transfer from a cylinder of infinite length in terms of the resulting voltage difference and is useful for hot-wire anemometry characterization.

V = a + b * ν ^0.5                                 (1)

where: V = flow induced voltage difference; υ= wind velocity; a,b = constants.

The constants are a complex combination of fluid thermal conductivity properties and flow geometry and should be found empirically.

Combination of King’s law and Kinematics knowledge the following equations can be obtained for solving the direction and magnitude of the wind shown in the above figure.

υ_x = υ * sin(θ)                                   (2)

υ_y = υ * cos(θ)                                   (3)

V_x = a_x + b_x * υ_x^0.5                            (4)

V_y = a_y + b_y * υ_y^0.5                            (5)

 υ = (υ_x² + υ_y² )^0.5                              (6)

θ = tan​⁻¹​​(​υ_{x /} υ_y ​​​​)                              (7) 

where : υ – wind velocity, υ_x – horizontal component of wind velocity, υ_y – vertical component of wind velocity,  θ - incident airflow angle,  V_x – amplified differential signal of thermopiles responding to υ_x, V_y – ampilified differential signal of thermopiles responding to υ_y, a_x, a_y, b_x and b_y – constants of fluid thermal conductivity properties and flow geometry properties.

In the equation (2) to (7) υ and θ are variables, V_x and V_y are measured values of thermal flow sensor, and the others are constants. After getting the values of the by test and calculation the variables υ and θ can be found by solving the equations (2) to (7).

It has been subjected that the interface electronics of the thermal flow sensor operates in an offset free mode. This means that when there is no fluid flow the static (no flow) two signals of the thermopile (W)-thermopile (E) pair and the thermopile (N)-thermopile (S) pair are compensated each other and the static differential signal becomes offset free. This can be done in this way: the two heaters of a thermopile pair are derived with a fixed voltage and then the lower static output of the thermopile is compensated by a DAC modulated higher static output of the thermopile. As a result, the static differential signal of a thermopile pair is maintained constantly zero. 

When operated in this mode, the offset of the thermopiles is no longer problem. Operation in this should lead to canceling all common mode noise of the thermopiles.

A further advantage of operation in this mode is that, since the thermopiles have a same temperature coefficient, the temperature drift of the output signal of the thermopiles is also automatically compensated for. 

MEMS Thermal Effect Sensors

Xiang Zheng Tu

Several MEMS thermal effect sensors have been developed by our company (POSIFA Microsystems). Among them are thermal flow sensors, thermal conductivity sensors, thermal vacuum sensors, thermal motion sensors and thermal humidity/carbon dioxide sensors. These sensors are given a first name as “thermal”, because their behaviors are related to thermal effects. Thermal effects mean the physical or chemical quantities measured by the sensors are caused by heat transfer processes.

All gases conduct heat to differing degrees, and the amount of heat transferred by a gas is determined by its 'Thermal Conductivity' (TC). The thermal conductivity sensor uses this property to accurately measure one of the two gases present in a sample of a binary or pseudo-binary mixture. In order to do so a micro-heater is created in a silicon wafer by MEMS technologies. The micro-heater is suspended over a cavity that is recessed in the silicon wafer. There is a temperature gradient between the micro-heater and the bottom of the cavity, which drives the heat energy generated by applying electrical power to the micro-heater transferring across the cavity by conduction. This results the change in the temperature of the micro-heater, which expresses a certain composition of the binary mixture in the cavity.

On the other hand, the thermal flow sensors operate based on a different type of heat transfer: convective heat transfer. More exactly the thermal flow sensors take advantages of laminar flow. This is why the thermal flow sensor is normally installed on the wall of a tube. When a fluid is forced to flow through the tube laminar flow will occur. The fluid tends to flow parallel in layers without lateral mixing, and adjacent layers slide past one another like playing cards. There are no cross-currents perpendicular to the direction _of flow, nor eddies or swirls of fluids.

Recall that a thermal flow sensor comprises a silicon chip, a resistive heater, one or two thermopiles, and a thermal insulating base. The heater and the hot junctions of the thermopiles are disposed on the surface layer of the base that is burred in the silicon chip and the cold junctions of the thermopiles are disposed outside of the base area. When a fixed electrical power is provided to the heater a temperature difference will be built up between the surface layer of the base and the outside area of the silicon chip. The thermopiles measure the temperature difference and output a voltage signal correspondingly. The temperature difference will be reduced by the forced laminar flow because convective heat transfer will take place.

This is a case of constant heat rate per unit surface area for steady, laminar, fully developed flow. The heat transfer from the surface layer of the thermal flow sensor through convection was first described by Newton and the relation is known as the Newton's Law of Cooling. The equation for convection can be expressed as:

q = h_c A dT,                                     (1)

where q = heat transferred per unit time, A = heat transfer area of the heated surface layer, h_c= convective heat transfer coefficient, and dT = temperature difference between the surface layer and the bulk fluid.

The convection heat transfer coefficient h_c for the surface layer is related to the heated surface layer Nusselt Number Nu_L by,

h_c = ( k/L) Nu_L                                        (2)

In this equation, k is the fluid's thermal conductivity, and L is the length of the heated surface layer.

The Nussult Number for this problem is given by,

Nu_L = 0.664 (Pr)1/3 (Re_L)1/2          (3)

where Pr is the fluid Prandtl Number, and Re_L is the fluid/heated surface layer Reynolds Number.

The Prandtl Number is given by,

Pr = c_p μ/k,                                         (4)

where c_p is the fluid’s thermal capacity and μ is the fluid’s viscosity.

The Reynolds Number is given by,

Re_l = ρu_fL/k,                                        (5)

where ρ is the fluid’s density and u_f  is the fluid’s velocity.

It can be seen that each fluid’s velocity corresponds a certain a certain heat transferred from the heated surface layer of the thermal flow sensor or a fixed input electrical power, because in the above equations only the fluid’s velocity is variable and the others are physical parameters of the fluid or geometrical parameters of the heated surface layer of thermal flow sensor.   

As well known all objects with a temperature above absolute zero emit heat energy in the form of radiation. Usually this radiation isn't visible to the human eye because it radiates at infrared wavelengths, but it can be detected by electronic devices such as MEMS infrared sensors. The MEMS infrared sensors measure temperature by converting infrared energy radiated from target objects into heat with MEMS thermopiles and then measuring the thermo-electromotive force resulting from temperature differences that occur across the contact points of two different types of metal.

The heat received by the thermopiles is very little and easy to dissipate by conduction. To solve this problem a micro-plate has been used to support the hot junction of the thermopiles, which is built over a cavity using low thermal conductivity materials such as a silicon-nitride, silicon dioxide or multilayered combination of these materials. 

Design of Thermal Flow Sensor Circuit

Being Offset Free, Temperature Drift Free, Noise Free and Interchangeable

Xiang Zheng Tu

1.    Schematic diagram of POSIFA thermal flow sensor

Reference to figure 1, a thermal flow sensor compromises a heater and two thermopiles 1 and 2. Suppose there is no fluid flow passing over the sensor.  The heater is heated by a filtered PWM output converted voltage generated by a microcontroller such as a PIC16 (L) F1704/8. The thermopiles will produce static outputsV_T1 and V_T2, respectively. If the filtered PWM converted voltage is set at 3V, the value of the static outputs is ranging from 30mv to 50mv and the V_T2 is always higher than V_T2 about 1.5mv. It should be noted that the filtered PWM output converted voltage contains a noise signal that is in the form of ringing with a periodic repetition. Since this noise signal is common mode to both the thermopiles, they can be canceled each other by sending to a differential amplifier for signal processing.

 

   

2.  Selecting a PWM output converted voltage for fixing the output V_T2 of the thermopile 2 at 30mv

Reference to figure 2, a comparator of the microcontroller is used to compare the output V_T2 of the thermopile 2 with a 30mv reference voltage V_Ref  provided by the microcontroller for sending out a digital output signal for adjusting PWM output converted voltage. When the thermopile 2 produces the output V_T2 equal to the reference voltage V_Ref, the PWM output converted voltage is fixed and the selection is finished.

According to our experience the thermal flow sensors with same static output have a similar sensitivity. They can be interchangeable for most of applications. 

  

3.    Creating a DAC output replacing the output of thermopile 2

Reference to figure 3, there is still no fluid flow passing over the sensor. A digital-to-analog converter (DAC) of the microcontroller is used to convert the output V_T2 of the thermopile 2 into a variable voltage V_DAC. The variable voltage V_DAC is derived by a resistor ladder and can be ratiometric with the input source. Moreover its all electrical properties maintain the same as the input source, which include the environment temperature influence and electromagnetic interference. As shown in the figure 3, the output V_T2 of the thermopile 2 is send to the DAC through an amplifier TP5552. TP5552 is used as a buffer for impedance transformation, because the recommended maximum source impedance of the input source is limited to be 10kΩ for the microcontroller, which is much lower than the impedance of the thermopiles.

4.    Adjusting the output V_DACT2 of a DAC for best match to the output V_T1 of the thermopile 1.

Reference to figure 4, the output V_DAC of the DAC is sent to the positive input of another comparator of the microcontroller and compares with the output V_T1 of the thermopile 1. The digital output of the comparator is used to change the output V_DAC of the DAC and eventually become V_DACT2 that is equal to the output V_T1 of the thermopile 1. Since them the output V_T2 is replaced by the output V_DACT2.

It should be understand that all these steps are performed without fluid flow passing over the sensor and can be done in the calibration process of the sensor and in the initiate stage of each sensor operation. 

After finishing these steps the output V_T2 of the thermopile 2 is replaced by the new reference voltage V_DACT1. The outputs of the differential output of the two thermopiles can be zero. This means the offset, temperature drift and noise of the two thermopiles can be canceled each other so that the sensor becomes the offset, temperature drift and noise free.

5.    Offset free, temperature drift free and noise free thermal flow sensor is realized by a differential amplifier

Reference to the figure 5, when a fluid flow passes over the sensor the thermopiles 1 and 2 will produce voltages -ΔV_T1 and -ΔV_T2 superimposed to the original output V_T2 and V_T1. Please note that -ΔV_T2 will be ratiomatric as V_T2 does and superimposed to the output V_DACT2, which is expressed as ΔV_DACT2. When a differential amplifier is used to multiply the difference between V_T1 - ΔV_T1 and V_T2 - ΔV_T2DAC, the common mode signals will be rejected. These common mode signals include temperature drift and electromagnetic noise. This means the thermal flow sensor becomes offset free, temperature drift free and noise free.

It can be seen in the figure that the used differential amplifier is another TP5554.  It was tolled that TP5552 is a dual chopper stabilized zero-drift operational amplifier, which features very low input offset voltage and low noise and may be operated with a relative high gain. 

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.