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.