Metrics, Signal Creation and Measurement

💺💺 "First you have to create the signal, and then you have to measure it." 🛫🛫

Early in my engineering career, I worked at a test stand and RD&E facility design firm. A client, nicknamed Acme, had a design project for a replacement wind tunnel to test heat exchangers. These heat exchangers used the internal working fluid, at one temperature, exchanging heat with another fluid, usually air, at another temperature as the fluid flowed over the exterior. Heat may transfer in either direction as out or into the working fluid in the exchanger. This application removed heat.

The client provided optimistic design specifications that included excessive operational ranges for airflow and internal working fluid flow as well as thermal cycling and cycle time. The spec was coupled to excessive temperature and pressure ranges for the internal working fluid and the tunnel airflow. High relative humidity from the outside air also affected the tunnel's ability to control the windspeed and measure accurately.

The flow range spec was adversely affected by the flow "turndown ratio", the working fluid temperature range and the tunnel airflow range. The working fluid was subject to "thermal inertia" from the fluid itself. Heat transfer depends on thermodynamic properties of fluid mass, density, pressure, and time.

Figure 1: Indirect Cooling illustration from e-paper "Efficiency Technologies NFZ_EN.pdf"

The client pushed the new design to simulate a wide range of wind tunnel and test unit conditions. This range resulted from an equally wide range of heavy commercial vehicle applications and components. Their existing wind tunnel facility was located adjacent to their equipment teardown and overhaul work areas. The spec created the challenging combination of RD&E specs with a teardown overhaul test specification on a single wind tunnel.

We did not win this wind tunnel construction contract. The design and equipment selection sacrificed some of the range in the name of accuracy and the implementation hinged on cycle time. Years later, I discovered the client had implemented their own wind tunnel that was scrapped. Their wind tunnel continued to suffer from unrealistic thermal cycle times despite design advice. We learned valuable engineering lessons about spec design and measurement accuracy. We would like to share some of them with you now.

Measurements and Metrics

We can calculate the flow turndown ratio as the high flow at full scale divided by the low flow at the minimum range. The flow turndown ratio affects flow measurement accuracy due to the signal-to-noise ratio across the flow range. It's a critical design factor because sensors have interrelated sensitivity to statistical accuracy and repeatability. Accuracy at the high range comes at the cost of low range sensitivity where it suffers from a degraded signal-to-noise ratio sacrificed for the high range accuracy.

The wind tunnel spec had other design factors. The turndown ratio was over 80:1 but specified accuracy neglected this. A single flow meter would fail to simultaneously meet both sensitivity and accuracy specs across the entire range. Wind tunnel designs might overcome opposing constraints of turndown ratio versus measurement accuracy with multiple flow meters over a segmented range. This results in undesired test interruption.

The spec had neglected measurement accuracy affected by noise across the flow range. Reference supersonic orifice plates, constructed in a set of multiple flow restriction plates precision-calibrated at supersonic speeds, limit the flow turndown ratio of each plate to 3:1. Why is that? (Hint: amplified noise affects signal-to-noise dB ratio at both low and high readings). Various flow meter manufacturers claimed upwards of a 10:1 flow turndown. As a young grasshopper, my mentors cautioned me to be skeptical of claims of simultaneous accuracy and sensitivity with high ratios.

Bernoulli's Equation

This project was an opportunity to apply Bernoulli's brilliant equation, shown in Equation 1, to a real world problem. That equation relates the input fluid velocity pressure, the difference of stagnation pressure, p_t, and static pressure, p_s, of an incompressible fluid of density ⍴ to computed output flow velocity, v, passing a point at the instant of measurement. 

Equation 1 and 2: Forms of Bernoulli's Equation for incompressible fluid flow velocity.

The system also needed a manometer, similar to Figure 2, that measured ambient pressure as a reference to the atmospheric component of static pressure.

Figure 2: Manometer for Atmospheric Ambient Pressure from Wikimedia.org.

Another incredible device called a Pitot-static tube produced the differential pressure signal. These ingenious designs directly produced a differential pressure for Bernoulli's equation numerator. Two tubes of the Pitot-static measure instantaneous differential fluid pressure, similar to the ones recessed (and sometimes heated) on aircraft fuselage, for each reading.

Figure 3: Basic Form of Pitot Static Tube from
"Haward Technology Middle East"

Notice how Figure 2 shows one tube facing into fluid flow, looking upstream to capture stagnation pressure of the fluid brought to a standstill. Another interior tube faces away to capture the static component of pressure, which is aliased with atmospheric pressure. Computational electronics read input signals as a voltage so complete systems with Pitot-static meters include a deflection diaphragm. A wind tunnel requires additional signal conditioning and processing of the voltage output for reading the differential.

Indirect Measurement

Air is a compressible fluid. Bernoulli developed his equation for incompressible fluids. We needed other equation adjustment factors and meter calibration data for an accurate air flow measurement according to the ASHRAE Handbook on Fundamentals. Several differential air pressure measurements needed to be taken across the entire flow profile. The pressure measurements needed to be combined to capture total mass air flow through the heat exchanger volume.

Test units mounted on the bulkhead inside the tunnel needed a variety of test scenarios. We needed an accurate computation of air density as well. Density, defined as mass per unit volume, is part of Bernoulli's equation that required the manometer. We compute density indirectly by measuring temperature. The computation determined fluid pressure from the Ideal Gas Law, leading back to density. Finally, we may compute the mass air flow over the heat exchanger exterior. Except, we were still not done.

Heat exchangers use wind tunnels to measure heat exchanged with air, as well as other measurements like working fluid pressure drops across the exchanger inlet and outlet. We got a handle on mass air flow but we needed to know how much heat was removed by the air mass over the exchanger's exterior. This was affected by heat exchanged with wind tunnel component as well. So we needed to measure air temperature across at the inlet and outlet as well as the working fluid temperature differential within the heat exchanger itself.

The sensor and computational model was getting complex. We had several additional measurements, adjustments, calibrations, and so on, not to mention actual operation of the wind tunnel. Ultimately, after we computed bulk mass air flowing over the unit under test, or UUT, we still needed a picture of the differential airflow temperatures across the face of the heat exchanger. Equally critical, we measured the inlet and outlet working fluid temperatures across the face of the heat exchanger itself. The purpose of the test was to inform the operators as to the amount of heat removed, in BTU, from the engine's working thermal fluids together with a map of the heat dispersion across the entire face of the radiator or intercooler.

The amount of heat removed from a heat exchanger's working fluid was computed using indirect measurements. Also, tunnel itself had dwell times and warmup times to avoid the tunnel itself contaminating the calculations. Their engineers could also use the wind tunnel to evaluate condition and efficiency as surrogate estimates of real world performance.

Wind tunnels, and test facilities generally, use a host of indirect measurements, adjustments, approximations, models, estimations and simulations of dynamic real world conditions to predict operation across the design range.

Quantitative Metrics

By now, you might wonder how this relates to airline profit, airline metrics and reseating with the SeatBot API. Our next post talks about airline metrics and measurements to estimate flight and seat inventory performance, profitability and passenger seat satisfaction. This post described how some systems can directly measure some inputs, indirectly measure others, and use model estimations and simulations to compute a transfer function; the equation relating inputs to the outputs. We will explain our passenger preference and simulation model we used to simulate and estimate profit potential for airlines who use the SeatBot smart seating API for their passengers.

Airlines use many types of metrics. Some metrics indirectly represent seat inventory performance, price effectiveness and demand estimation. Other metrics more directly represent what they capture. The metrics discussed in this post are of the quantitative performance measures type. We will discuss leading and lagging flight performance metrics in the next post. These are related to the concept of constructing an "observer" to capture direct and indirect observations for computation. We will introduce a new metric that indirectly reflects missed revenue opportunities on every full flight as well as SeatBot API use cases of the empty seat.

Engineering Mentorship

During the aforementioned project research, several engineering mentors generously shared their insight and experience. One engineer even gave me a koan. He retired years ago but his words increased in meaning to me over the years. He left figuring out the koan as an exercise. He said, and I quote:

💺💺"First you have to create the signal, and then you have to measure it."🛫🛫

Corollary:
"You never count your money when you're sittin' at the table,
 There'll be time enough for countin', when the dealin's done."
-Kenny Rogers, The Gambler

What does that mean exactly? To be continued...