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.