Wind Tunnel Mk2

The wind tunnel produces time-series data from a dynamical system.

The tunnel consists of two controllable fans that push air through it, and a variety of sensors to measure variables such as fan speed, power, and air pressure at different locations. A hatch regulates an additional opening to the outside, creating an additional flow of air.

The chamber produces time-series data from up to 41 variables, including sensor measurements, control inputs, and sensor parameters. See the variables table for a description of each variable, and the map of effects between them.

Chamber diagram

See the variables table for a description of all variables.

Hardware configurations

Like all chambers, the wind tunnel can automatically load different hardware configurations, exposing different variables and behaviors of the underlying physical system. For each configuration, see the corresponding PDF for a chamber diagram, a complete description of all variables, and the causal ground-truth graph between them.

Map of effects

Here you can find a detailed description of all effects between chamber variables, together with additional experiments and figures. Throughout, we use an edge A $\longrightarrow$ B to denote that a variable A has an effect on variable B.

Short-hand notation

• A1/2 $\longrightarrow$ B, C is equivalent to the edges A1 $\longrightarrow$ B, A1 $\longrightarrow$ C, A2 $\longrightarrow$ B and A2 $\longrightarrow$ C

• We can also express this as A* $\longrightarrow$ B,C

Some text and figures in this section are adapted from the original paper (Gamella et al. 2025, Appendix III).

Graph

In what follows, we provide a detailed description and visualization of each edge (physical effect) in the above graph.

load_in/out $\longrightarrow$ rpm_in/out, current_in/out, current_in/out_raw

The fan loads (load_in, load_out) define the duty cycle of the control signal sent to the fans, affecting their speed (measured by rpm_in/out) and the calibrated (current_in/out) and uncalibrated (current_in/out) measurements of the drawn electrical current. The fans operate in an open-loop configuration. In steady-state—and keeping all other variables constant—the load has a quasi-linear effect on the load and a cubic effect on the current (Figure 1, left/center). A justification from first principles is provided in Gamella et al. (2025, Appendix IV.1.1). The effect of the fan load on its speed and current is not instantaneous, as the fan requires time to accelerate (Figure 1, right).

Figure 1

Experiment

To recreate the data for the left and center panels (steady state) using the Remote Lab:

For the right panel (impulse):

When the fan load is set to zero, the fan is completely powered off and no longer produces a tachometer signal; the resulting speed measurement (rpm_in/out) corresponds to the last measured speed (Figure 2).

Figure 2

Experiment

To replicate the experiment with the Remote Lab:

Because both fans are connected to the same power supply, the load of one fan affects the current drawn by the other, specially when both are running at high loags (Figure 3).

Figure 3

Experiment

To replicate the experiment with the Remote Lab:

res_rpm_in/out $\longrightarrow$ rpm_in/out

Changing the resolution (res_rpm_in, res_rpm_out) of the timers used in the fan tachometers also changes the resolution of the resulting speed measurement (rpm_in, rpm_out). Using a resolution of microseconds (e.g. res_rpm_in = 1) allows measuring smaller changes in the fan speed (Figure 4).

Figure 4

Experiment

To replicate the experiment with the Remote Lab:

hatch $\longrightarrow$ rpm_in/out

The two fans in the chamber operate in tandem to drive air through the tunnel (see diagram). Thus, their speeds are coupled, i.e., if one fan accelerates, the other will as well, even if no additional power is applied to it. The strength of this coupling is modulated by the hatch position, which controls a third path for air to flow into or out of the chamber; larger openings result in a weaker coupling (Figure 5).

Figure 5

Experiment

To replicate the experiment for the left panel using the Remote Lab:

For the right panel:

hatch $\longrightarrow$ hatch_angle

A magnetic encoder measures the actual position of the hatch, producing the measurement hatch_angle (in degrees). Under normal operating conditions (default values of mot_enabled/steps/max), the position of the hatch (as measured by hatch_angle) closely follows the position set by hatch (Figure 6, top left).

Lowering the resolution of the motor (mot_steps) results in a coarser hatch placement. If we lower the current delivered to the motor (mot_max) or power it off completely (mot_enabled = 0), the motor will cease to function properly, creating a mismatch between hatch and the actual hatch position measured by hatch_angle.

Figure 6

Experiment

To replicate the experiments for the plot using the Remote Lab:

load_in/out, hatch $\longrightarrow$ pressure_upwind/downwind/intake

The fan loads (load_in, load_out) and the hatch position (hatch) affect the air pressure measured by the barometers inside the wind tunnel (pressure_upwind, pressure_downwind) and at its intake (pressure_intake). See the chamber diagram for the location of these barometers.

An increase in the load of the intake fan (load_in) results in more air being pumped into the tunnel, increasing pressure_downwind and pressure_upwind; increasing the load of the exhaust fan (load_out) has the opposite effect (Figure 7, left & center). Opening the hatch creates an additional flow of air into or out of the chamber, also affecting the inner pressure measurements. While all three variables affect pressure_intake, the effect is very weak for load_out and hatch (Figure 6).

Figure 7

Experiment

To replicate the experiment with the Remote Lab:

osr_* $\longrightarrow$ pressure_*

The oversampling rate of the barometers (osr_pressure_upwind/downwind/intake/ambient) determines how many readings are averaged to produce a single measurement of the air pressure. Thus, a higher oversampling rate increases the precision of these sensors, increasing the signal-to-noise ratio of the resulting measurements (Figure 8).

Figure 8

Experiment

To replicate the experiment with the Remote Lab:

offset/sps/res_current_* $\longrightarrow$ current_*

The chamber produces calibrated measurements (in Amperes) of the electrical current drawn by the fans (current_in/out) and the hatch motor (current_mot). For each measurement, the chamber also returns the underlying raw, uncalibrated measurements (current_in/out_raw, current_mot_raw), which take values in the range [-2¹⁵, 2¹⁵] (the output of the sensor's ADC).

We can independently control three parameters in each sensor:

• offset_current_* : the reference voltage. Changing it creates an additive shift in the uncalibrated measurements (*_raw) but is largely compensated for in the calibrated measurements (Figure 9, right).

• sps_current_* : the oversampling rate, i.e., how many readings are averaged to produce a single measurement. Lower values correspond to higher oversampling rates, increasing the noise-to-signal ratio of the resulting measurements. Both the calibrated and uncalibrated measurements are affected (Figure 9, center).

• res_current_* : the measurement range—and thus the resolution—of the sensor. Higher values correspond to smaller measurement ranges, increasing the resolution but saturating the sensor if the actual values fall outside this range (Figure 9, right). Changes to res_* result in a shift and scaling of the uncalibrated measurements (*_raw).

Figure 9

Experiment

You can replicate the experiments for this plot with the Remote Lab. For the left panel (varying offset_current_in):

For the center panel (varying sps_current_in):

For the right panel (varying res_current_in):

offset/sps/res_mic $\longrightarrow$ mic, mic_raw

The chamber produces calibrated measurements (mic, in Volts) of the signal produced by the tunnel microphone (see diagram). It also returns the raw, uncalibrated measurements (mic_raw) produced by the underlying analog sensor, which produces values in the range [-2¹⁵, 2¹⁵] (the output of its ADC).

As for the current measurements, we can individually control three parameters of the sensor:

• offset_mic : the reference voltage. Changing it creates an additive shift in the uncalibrated measurements (mic_raw) but is compensated for—up to a small effect—in the calibrated measurements (Figure 10, right).

• sps_mic : the oversampling rate, i.e., how many readings are averaged to produce a single measurement. Lower values correspond to higher oversampling rates, increasing the noise-to-signal ratio (i.e., precision) of the resulting measurements. Both the calibrated and uncalibrated measurements are affected (Figure 10, center).

• res_mic : the measurement range—and thus the resolution—of the sensor. Higher values correspond to smaller measurement ranges, increasing the resolution but saturating the sensor if the actual value falls outside this range (Figure 10, right). Changes to res_mic result in a shift and scaling of the uncalibrated measurements (mic_raw).

Figure 10

Experiment

You can replicate the experiments for this plot with the Remote Lab. For the left panel (varying offset_mic):

For the center panel (varying sps_mic):

For the right panel (varying res_mic):

load_in/out,hatch $\longrightarrow$ mic

The speed of the fans, controlled by the loads load_in/out, affect the overall noise level and the amount of air flowing through the exhaust and over the tunnel microphone, affecting its calibrated and uncalibrated measurements mic, mic_raw (Figure 11, left). The position of the hatch also modulates the amount of air flowing over the microphone, affecting its readings (Figure 11, right).

Figure 11

Experiment

To replicate the experiment for the figure using the Remote Lab:

mot_enabled/max $\longrightarrow$ current_mot , current_mot_raw

The variable mot_max controls the amount of electrical current delivered to the hatch motor, and mot_enabled switches the motor on or off. Thus, both affect the calibrated (current_mot) and uncalibrated (current_mot_raw) measurements of the electrical current drawn by the motor. As opposed to the fan currents, the effect of mot_max/enabled on the current measurements is instantaneous, i.e., faster than the measurement rate (Figure 12, left). The relationship between mot_max and current_mot, current_mot_raw is non-linear (Figure 12, right).

Figure 12

Experiment

To replicate the experiment for the left panel (impulse) using the Remote Lab:

For the right panel:

External influences

The tunnel barometers producing the measurements pressure_upwind/downwind/intake/ambient are all affected by natural variations in local atmospheric pressure at our location in Zurich (Figure 13, left). In other words, atmospheric pressure acts as a confounding factor between these measurements.

Controlling for local atmospheric pressure & sensor drift

The measurements produced by the ambient barometer (pressure_ambient) are unaffected by the other chamber variables (excluding osr_pressure_ambient), and act as a proxy for the local atmospheric pressure. Subtracting them from the other measurements can partially remove its effect. However, since all barometers experience sensor drift (Figure 13, right), the effect cannot be completely removed by this simple approach.

The sensor drift, which over time converges to a stable point (Figure 13, right), can create an additional correlation between the barometer measurements.

Figure 13

Experiment

To replicate the experiment for the plot using the Remote Lab:

Variables table

Below is a glossary of the chamber variables discussed on this page.

Citation

If you use this documentation, our open-source datasets, or Remote Lab in your scientific work, please consider citing:

References

[PDF] Gamella, J.L., Peters, J. & Bühlmann, P. Causal chambers as a real-world physical testbed for AI methodology. Nat Mach Intell 7, 107–118 (2025).