All airplanes use pressure measurements in order to make real-time calculations of wind speed. In an airplane, these pressure measurements are obtained using a pitot-static tube.
A pitot-static tube has openings that measure the stagnation pressure and the static pressure. Recall that stagnation pressure is the sum total of the static pressure and the dynamic pressure, so the pitot-static tube is used to measure the dynamic pressure and therefore the flow velocity.One method to correlate wind speed to pressure using the pitot-static tube is by using a fluid manometer.
A fluid manometer is generally a U-shaped glass tube that is partially filled with liquid. One arm of the manometer is connected to the stagnation pressure port on the pitot-static tube, and the other to the static pressure port. In stagnant air, where this is no difference between the static pressure and stagnation pressure, the manometer fluid height difference is zero.
When the manometer experiences a pressure differential, it is visualized by a change in fluid height. The pressure differential, or dynamic pressure, is calculated from delta H using this equation. Here, rho L is the density of fluid in the manometer and G is gravitational acceleration. This relationship is used to calculate the wind speed by substituting it into the velocity equation. We can then solve for the free-stream velocity, V infinity, using the free-stream density, rho infinity.
However, fluid manometers are bulky, and require manual reading onboard the aircraft. Thus, a more convenient method to measure the pressure differential is to use a pressure transducer in place of the manometer. This enables us to convert the pressure differential into an electrical signal.
A capacitance pressure transducer is based on the working principle of a capacitor, which consists of two conductive plates separated by an insulator. Capacitance is measured by the following equation, where mu is the dielectric constant of the insulator material, A is the area of plates, and D is the spacing between the plates.
To make the capacitance pressure transducer, one of the conductive plates is replaced by a flexible conducting diaphragm. When pressure is applied, the diaphragm deflects causing a change in the spacing between the plates D, resulting in a change in capacitance. The electronics in the transducer are calibrated to generate specific current changes for corresponding deviations in capacitance. Thus, a current reading corresponds to a given applied pressure.
Like the manometer, the pressure transducer is connected to the pitot-tube and is calibrated in a wind tunnel with known wind speeds. This enables us to generate a mathematical relationship between current and pressure, and by extension, current and wind speed.
In this lab demonstration, we will use a pitot-static tube in a wind tunnel connected to a pressure transducer. We will then calibrate the pressure transducer at various wind speeds and determine the relationship between voltage and speed.
For this experiment, you'll need to use a wind tunnel with its own calibrated pressure transducer and ability to reach a dynamic pressure of 25 psf. You will also use a standard pitot-static tube and a differential U-tube manometer with colored water to calibrate this differential pressure transducer.
To begin, mount the pitot-static tube inside of the wind tunnel on the top of the test section using a vertical sting mount. Ensure that the probe is at the center of the test section. Align the pitot tube with the direction of flow, so that the primary port faces directly into the air flow.
Next, align the top of the manometer fluid to the double O-ring marker on the glass tube. If the reading on the main scale does not correspond to zero, align the fluid to a different reference point, and record the offset height.
Use a T-connector to split the flow from one tube to two, then connect the stagnation and static pressure outlets on the pitot-static tube, to the corresponding ports on the U-tube manometer. Mount the pressure transducer outside of the wind tunnel test section on a vertical surface. Set up a standard voltage supply to power the pressure transducer and a multimeter to read the output current. Then, connect the stagnation and static pressure outlets to the corresponding pressure ports on the transducer.
Now, secure the wind tunnel doors and switch on all of the systems. Then, take readings of the wind tunnel transducer pressure, the manometer height, and the differential pressure transducer current. Record the measurements for the no airflow condition as the base line zero reading. Now turn on the wind tunnel, and set the dynamic pressure in the test section to one psf.
Once the flow has stabilized, record the transducer pressure, the manometer height difference, and transducer current. Increase the dynamic pressure setting in the wind tunnel in steps of one psf, up to a maximum setting of 20 psf, recording the data at each step. In order to check for hysteresis, decrease the dynamic pressure in steps of one psf, back down to zero psf, again recording data at each step. When all of the measurements have been collected, shut down all systems.
Now, lets take a look at the results. First, we look at a plot of the manometer height readings with increasing and decreasing dynamic pressure. Two measurements are shown here for each trace. One is the actual manometer reading, and the other has been corrected with the offset height of 0.8 inches. We can calculate the manometer pressure from the manometer height, using the simple equation shown. Here, we use the density of the liquid in the manometer, which is in this case water, gravitational acceleration, and the manometer offset and height measurements.
Now that we have calculated the pressure from the manometer reading, we'll plot it against the pressure transducer current readings. To obtain the calibration curve for the pressure transducer, we'll fit the increasing and decreasing data separately, resulting in two linear best fit equations.
However, we see that the increasing and decreasing data line up. So we can conclude that the pressure transducer does not exhibit hysteresis. Thus, we can simplify to a single calibration equation, thereby enabling us to measure pressure using the current reading from pressure transducer, rather than the bulky fluid manometer. By connecting the pitot-static probe to the calibrated transducer, we can directly measure the dynamic pressure and therefore, wind speeds.
In summary, we learned how pressure differentials measured during flight correlate to flow velocity. We then calibrated a pressure transducer by subjecting a pitot-static tube to varying wind speeds, and determined the relationship between voltage and wind speed.