Test equipment (part 1)

One of the key areas for validation on the car for the next few years is the front wheel wake and front tyre squirt. If we are going to focus all of our surface design between the axles (see "Defining the scope"), it makes sense to understand and be able to accurately predict the flow features that take up about half of the available cross-sectional area in this region. Measuring surface flow vectors is relatively simple, and typically uses wool tufts or flow-vis paint, both of which are quite cheap to obtain and easy to apply. When it comes to measuring static pressures, pressure sensors add a level of complexity and cost. For measuring off-body flow, the complexity is increased significantly, as now total pressures come into play, combining local velocity vectors with static pressure, and a method of measuring both of these all somehow suspended in mid-air. The answer is an aero rake, and these are very complex to manufacture, and very expensive. So we decided they were the perfect option for a small team with a small budget. 

The first item of interest was pressure sensors, as these are applicable to many different test cases and equipment: static taps, rakes, pitot-static tubes, and yaw probes. Given the magnitude of pressure deviation from atmospheric is minimal, absolute pressure sensors were out of the question for blatantly inadequate precision, at least if we wanted them for anything less than $250 each. This left us with differential pressure sensors. The cheapest we could find were around $30 each, which still had all the technical specifications we needed so we figured we had grounds to argue a refund if they didn't work well enough. The question was then how many do we need, and how many can our budget stretch to include?

This process of procuring pressure sensors happened while the CFD environments were still being set up, so we had no results to go off in making this decision. We knew we needed one for a pitot-static tube, one or two for a yaw probe depending on what design we end up choosing, and a decent number to get sufficient rake resolution and maximise how many static pressure taps we could run at once. Assuming the wheel wake took on a vertical rectangular shape (very approximately), we decided we would probably want a reading outside and inside the wake structure on the inboard and outboard edge, giving 4 probe points laterally. Given the wheel is a little higher than it is wide, we figured having 5 probe points vertically made sense, giving 20 overall (obviously the probes may not end up being in a perfect grid). 20 sensors seemed like a good number and was just enough to push the price down to $28 each with a bulk discount, so they cost us around $560 shelf price, with a bit of sponsorship getting this down a fair bit further. This is a fair bit of money, but it's a very good deal. For even tighter budgets, there is no reason you can't run a rake with a single probe and sensor, and just move it numerous times. it's just a trade-off between available track time, and ensuring the track conditions don't change significantly over the course of the multiple test runs if the tests involve anything other than straight-line driving. It was originally our plan to get 10 sensors and shift their positions once per test, but the sponsorship allowed us to get the full 20 that we wanted.

To maximise the precision of the data, we needed sensors that were tuned to measure only the range of pressures we were expecting. We considered the maximum pressure we would ever want to measure would be for a pitot-static tube at practical Vmax (about 115 kph; theoretical Vmax with a long enough straight is about 135 kph. We kept this "spare" speed in the chosen gear ratio based on the motor efficiency dropping off at high RPM). Dynamic pressure at this speed on a day with dense air is 650 Pa. Unfortunately this was too high for a 500Pa or 2.5-inch-H2O sensor, and 1000Pa sensors seemed to be a rare breed, so we settled for 5-inch-H2O sensors, which have about twice the range we need, but this was still pretty good considering the expected error percentage of 1.5% max (+/- 18 Pa). On a wing where we might expect a peak suction of 300 Pa, this gives us a precision/error resolution of 25 points, which is plenty for validation purposes.   

Upon receiving the sensors, we handed them, our requirements, and our expected operating conditions to the low voltage team to get one of them to make us some shiny new PCBs (Figure 1) to house the sensors and spit out CAN values into the car's data acquisition CAN bus for logging. The spacious design allowed easy debugging access and easy attachment/detachment of pneumatic tubes while we were still figuring things out and calibrating resistor values. After we were happy with their performance we created a more permanent and space efficient board with all 20 sensors. 

Up next was acquiring pitot-static tubes, Kiel probes, and yaw probes. Pitot-statics came in at around the $80 for decent quality ones which is already very expensive. Enter the Kiel probe, at a couple hundred dollars each for low order quantities, and much the same for yaw probes. At this point I figured, how hard can it be to make our own?

Pitot-static

We already had a single pitot-static tube from a few years ago when it was used simply as a more accurate measure of speed than the sub-par wheel speed sensors being used at the time (except when it was windy). We only need one of these, as its job is to measure velocity and the only velocity we are really interested in is the car's free-stream airspeed. For the Kiel probes, we ordered a couple metres of stainless steel tubing at 2mm and 4mm outer diameters (both with 0.2mm wall thickness), and 20 metres of flexible pneumatic tubing at 2mm inner diameter. We used a resin printer to make the inlet shape, which to start with we tried a typical pitot inlet shape for simplicity. We weren't hopeful about achieving yaw insensitivity but figured it was worth a test to save some difficult printing and assembling jobs. We set this test tube up as a full pitot-static out of interest to see if it would return values acceptably close to the off-the-shelf model. Both probes are shown in Figure 2, and from looking at them you'd never know that one cost $80 and one cost $9. 

We took the tubes to the wind tunnel for testing (Figure 3), mounting them as close to the middle of the cross-section as we could. We also took the sensor boards to test at the same time as we needed to make a pressure-voltage map for them, which we were really hoping would be the same for all the sensors, with different constant voltage offsets at worst. 

In tests conducted between 5 ms-1 and 20 ms-1, the custom pitot-static tube performed to the same precision and values as the OEM probe, proving resin printing and the use of silicone as a sealant were perfectly acceptable. The differential pressure sensors also demonstrated very small fluctuations around a stable value, with no hysteresis errors within the precision of the measurements taken. Voltage offsets between the sensors were significant, so we installed different resistors depending on the offset to avoid clipping at either end of the pressure range. The remaining smaller offsets can be dealt with by simply measuring and applying the offset to the recorded data, as we found these offsets remained constant throughout the voltage range. Yaw angle tests were conducted by adjusting the motorised load cell angle to which the probe was mounted, allowing precise angular measurements (Figure 4). 

As expected, the pitot-static tube design performed very poorly in yaw tests, with differential pressure readings changing by 8% with only 5 degrees of yaw in either direction. This error was reduced to 6% when considering only the total pressure by leaving the differential sensor open to atmosphere instead of connected to the pitot tube static ports, but this is still far too sensitive to be suitable for rake application. The results at a number of intermediate airspeed are shown in Figure 5, including the yaw test. We gave up after one yaw test as even if other speeds show a lower sensitivity, we need consistency throughout the airspeed range. The upper and lower bounds of measurement seen in Figure 5 were later substituted with more rigorous testing for different sources of uncertainty, discussed later in this post. 

Kiel probe

We've shown the custom pitot-static tube is perfectly adequate for its job, but we'll still use the single OEM probe for its expected increased durability. After proving our expectations that the dynamic inlet shape on the pitot tubes were highly sensitive to yaw angle, I set about designing a yaw-insensitive inlet shape that was still able to be manufactured by resin printing.

A Kiel probe works by forcing freestream flow to be redirected parallel to the dynamic port before being expelled out the sides of the probe downstream of the port. This wa smy first experience with Kiel probes, so I wasn't sure what the critical design criteria were, or how they would affect the readings it gave. Some research and comparison of different available models suggested most of the design intricacies were focussed on maximising the stability of the reading, and that just achieving the yaw insensitivity would not be too difficult. Of course, we still want both of these characteristics though. I drew up an inlet design aimed at being strong enough to be resin printed, and not break under reasonable handling and use. The size of the stainless steel tubing led to an inlet design that was larger in diameter than the 4mm tubing, meaning there would be some flow curvature over the outlet/bleed holes. This may artificially increase the flow velocity past the dynamic inlet but this doesn't matter, as long as we can still get a consistent and smooth pressure map from the probe. The custom inlet CAD model is shown in Figure 6, looking somewhat like a flamethrower.

I designed these custom probes to have a two-part assembly for easy installation; the whole probe is held together with just the friction of the pneumatic tubing in an interference fit between the inner and outer tubes. This saves lots of time setting up at the track when there's up to 20 probes to install. Figure 7 shows the assembled probe, the two separate parts, and the pneumatic tube interface between the parts. 

Another wind tunnel test session was conducted for the new custom Kiel probes to determine their pressure map, yaw sensitivity, and sources of uncertainty. The tests we conducted are summarised below.

Sensor Linearity 

A test of all 20 sensors to ensure there were no issues with them, and to measure linearity of the voltage offset across the airspeed range of interest, against a reference sensor (chosen arbitrarily). The largest measured deviation from linearity for any sensor was 0.040 V. 

Sensor Repeatability

"Random" airspeeds were chosen to jump between to ensure the reading was the same for each airspeed and not dependent on the prior airspeed. Results showed no hysteresis error within the recorded precision. 

Kiel probe manufacture tolerance

Testing all 20 Kiel probes on a single sensor (chosen based on having the least linearity deviation in the previous tests) to ensure slight differences in manufacture tolerance such as the airtight seals, and the length of the probe or inlet, were not affecting the measurements obtained. The largest deviation for any speed between any two probes was 0.005 V, or 0.1% of the voltage range. This was considered low enough to be negligible and thus all probes were treated as equivalent.

Voltage-pressure map

Using a single sensor and probe to create a map of recorded voltage across the airspeed range of interest, converting airspeed to expected total pressure, referencing the atmospheric conditions and calibrated wind tunnel static pressure sensors (Figure 8).  

Yaw sensitivity

Using the same Kiel probe and sensor, the angle was adjusted from 0 (parallel) until a significant change in reading was observed. This was repeated in both directions with identical results, for two airspeeds. This test showed readings remained stable up to 35 degrees for both airspeeds. There was some slight fluctuation from a constant value as angle changed while still below 35 degrees, with a maximum deviation of 0.025 V (Figure 9). 

OEM sensors are typically accepted as having somewhere in the range of 40-45 degrees of yaw insensitivity, so achieving 35 degrees (which is expected to be more than sufficient for the target application) is a good result for a first custom design. 

Total uncertainty calculation

Uncertainty estimates for a measurement taken using an arbitrary sensor with an arbitrary Kiel probe were calculated based on these results using a simple sum of squares, or 2-Norm approach, with an additional 1.25 factor of safety. 

U_Total = sqrt((U_Linearity)^2+(U_Manufacture)^2+(U_Yaw)^2+(U_Noise)^2)

U_Total = sqrt((0.04)^2+(0.005)^2+(0.025)^2+(0.005)^2)

U_Total = 0.048 Volts = 14 Pascals

This was a pleasing result given the sensor datasheet estimated a rather vague "error" as being 1.5%, or around 18 Pa (for the sensor alone). 

Temperature sensitivity

The sensors were placed on a heated bed while connected to a Pitot-static tube in constant airflow. An average change of around 0.1 V was noted for every 10 degree change in temperature, between 10 and 40 degrees Celsius. This seems worrying, but is only an issue if temperature changes significantly within a test session, which is unlikely considered we expect individual track test runs to take less than 10 minutes each, with the sensors insulated from direct sunlight. Calibration of the 0-value before each run is otherwise all that is required to combat this sensitivity, which can be done automatically in code. 

Sensor hysteresis

Conducted after wind tunnel testing, this was a qualitative test based on supplying a quick (~1s) burst of air to the sensors and ensuring the live output showed acceptably low lag and accurately/smoothly sampled the "shape" of the burst from ambient to max pressure to ambient again.