Expressive, Scalable, Mid-air Haptics with Synthetic Jets

Non-contact, mid-air haptic devices have been utilized for a wide variety of experiences, including those in extended reality, public displays, medical, and automotive domains. In this work, we explore the use of synthetic jets as a promising and under-explored mid-air haptic feedback method. We show how synthetic jets can scale from compact, low-powered devices, all the way to large, long-range, and steerable devices (Figure 1). We built seven functional prototypes targeting different application domains to illustrate the broad applicability of our approach. These example devices are capable of rendering complex haptic effects, varying in both time and space. We quantify the physical performance of our designs using spatial pressure and wind flow measurements and validate their compelling effect on users with stimuli recognition and qualitative studies.


INTRODUCTION
Most haptic technologies require direct contact with a user's body, such that an actuator can deliver energy to the skin (e.g., vibration from a motor, heat from a Peltier junction).The most successful commercial uses of haptics have been when actuators can be integrated into commonplace devices, such as smartwatches, phones, and gaming controllers.When special-purpose haptic devices are required to instrument the user, there are often aesthetic, social, setup time, and ergonomic costs.For this reason, haptic gloves, exoskeletons, vests, and similar worn accessories have seen comparatively little consumer uptake.
"Mid-air" haptic technologies aim to lessen this burden by avoiding user instrumentation.Instead, haptic effects are rendered onto a user's body in a non-contact manner, most often using air as the energy-transmitting medium.All electronics and actuators are instead built into a host appliance, such as a public kiosk, automobile, or medical device [ 46 ].Mid-air haptic approaches are also particularly valuable in cases where the hands are dirty (e.g., cooking) or where germ transmission is especially problematic (e.g., surgery).For these reasons, mid-air haptics is an active area of research in human-computer interaction.However, at present, there are only a handful of mid-air actuation approaches in the literature, with varying strengths and weaknesses.Thus, 14:2 V. Shen et al. it is desirable to continue to expand the set of technologies and approaches to better explore and unlock the potential of mid-air haptics.
In this vein, we explore an emerging haptic approach built around synthetic jets (or "synjets")simple devices capable of generating a zero-net-mass-flux jet of air.These types of jets were recently proposed and initially characterized for haptic feedback applications by Shultz and Harrison [ 60 ].We expand on this prior work by demonstrating new device functionality, providing three new quantitative and qualitative evaluations, and showcasing how synthetic jet-based devices can create expressive haptic computing interfaces.
We have found that haptic synjets have numerous attractive properties.First, their output is highly controllable, allowing for rich haptic expressivity.Not only can we modify basic parameters such as windspeed, peak pressure, and jet diameter, but the air flows can also be dynamically modulated and steered to create temporal and spatial effects.Second, range and impact forces of synjets can be large, offering more salient haptics when compared to similar techniques.Third, synjets are highly scalable, from centimeter-scale to meter-scale devices; to demonstrate, we created a series of example devices across this size spectrum, with jet diameters ranging from 1.5 mm to 125 mm.In the case of our smallest synjets, power consumption is similarly diminutive (172 mW), opening the door for inclusion in battery-powered devices such as VR headsets.And finally, synjets are relatively inexpensive-the actuators used in our demo devices range in cost between $2 and $89 USD and would cost much less with economies of scale.

RELATED WORK
We review three key bodies of research: non-air-based non-contact haptics, air-based haptics (both ungrounded contact and non-contact methods), and the scientific research and application of synthetic jets.

Non-air-based Non-contact Haptics
Examples of non-contact haptics that do not use air as a coupling mechanism are exceedingly rare.Lee et al. [ 34 ] and Jun et al. [ 27 ] were able to induce a tactile vibration on the skin through the use of a pulsed laser and colored sticker, which experienced thermoelastic deformation as a result of local heating.In a similar vein, it has been shown that laser-induced plasma near the skin can induce haptic sensations [ 29 ].HeatHapt proposed a thermal radiation type display, which selectively heated portions of the skin via an incandescent lamp and mirror [ 51 ].Even short-range electric arcs have been investigated as a means to produce hover feedback [ 63 ].At present, all of the above methods are fairly experimental with significant infrastructure and safety requirements.
Expressive, Scalable, Mid-air Haptics with Synthetic Jets 14:3 Fig. 2. High-level comparison, using exemplary systems, of the five main categories of non-contact, air-based haptic methods.Note that some values had to be estimated when not explicitly provided.Cost and power are approximate totals for the entire system.
proposed as a way to project smells for an olfactory display [ 75 ].AIREAL used five speakers and a flexible nozzle controlled by two servo motors to direct air vortex rings toward a user.AirWave [ 11 ] similarly used speakers to generate vortex rings but was only equipped with a fixed port.Shtarbanov and Bova used multiple air vortex generators and Sonovortex mixed vortices and ultrasound for 3D displays [ 15 , 58 , 59 ], while Sato et al. [ 55 ] and Takeda et al. [ 65 ] investigated using air vortex technology to generate wind sensations on a user's cheek.
Vortex-based devices have a relatively low barrier to entry.However, due to the fact that it takes a very specific volume of air to create a stable vortex at a given size, these devices offer relatively low expressivity.Once a device is created, it is often difficult to change temporal or spatial aspects of the vortex, except for its general location and coarse repetition rate.Any change in amplitude or flow characteristics disrupts the vortex and leads to improperly formed emissions.
Finally, conventional jets use continuous airflow to produce a steady or slowly pulsed force on the user, similar to synthetic jets.A large drawback of conventional jets, however, is the large amount of infrastructure required, usually including compressors, tanks, tubing, and control mechanisms such as solenoids or valves.For example, Gwilliam et al. [ 14 ] used pressurized air from a tank and a pneumatic regulator for a tiny jet that created a lump sensation on a user's finger.VaIR [ 49 ] integrated pneumatic nozzles and tubes into a head-worn device for simulating airflow in virtual reality.Suzuki et al. [ 64 ] utilized an array of air jets for an early virtual reality display, Tseng et al. [ 69 ] employed small rotating air jets around the eyes for skin-stroke effects, and Tsalamlal et al. [ 68 ] attached a nozzle to a robot as an end effector for thrust sensations.All of these air jets had to be connected to an outside container of pressurized air, creating issues in portability, wearability, mobility, safety, and long-term use.

Synthetic Jets
Synthetic jets, or acoustic streaming, as it was first called, was discovered and published by researchers Ingård and Labate in 1950 [ 21 ].It was also shown that loudspeakers, still under considerable development at the time, could be utilized to create acoustic pumps [ 6 ].Significant work on the theory behind synthetic jets, however, did not take place until the 1990s.Research by James et al. [ 24 ] and Smith and Glezer [ 61 ] put forward the "air slug" model that is still used to this day.More recently, synthetic jets have seen applications from cooling [ 41 ] and propulsion [ 66 ], to mixing fluids [ 1 ] and reducing drag [ 2 ].
A recent conference work, LRAir, was the first to propose synthetic jets as a method for producing non-contact haptic feedback [ 60 ].The authors presented a model of operation paired with initial psychophysical results.They included one actuator design, operated continuously at a 25 mm range to a single location on the hand.Building on the ideas in LRAir, this work significantly broadens the range of possible haptic effects to include time-varying effects, such as modulating jets, as well as space-varying effects through port arrays, flow focus, and vectoring.We also show how synjet devices can scale in size and number, providing examples of how they can be physically integrated into different end-user devices such as AR glasses and smart speakers, along with demo applications.Our performance evaluation augments LRAir's perception study with quantitative experiments and visualizations, and our two user studies offer new insights into the qualitative experience and discernability of synjet stimuli.

Principles of Operation
Synjets operate on the principles of local air pressurization, flow separation, and momentum rectification.The most common model for operation is the ejected slug model [ 61 ], which assumes  that a finite volume of air (a "slug") is exhausted from the synjet port once per oscillation.An equal amount of air is also taken into the port prior to this.This ensures that the synjet is zero-net-massflux, i.e., it does not require an external pressure source, but rather it intakes and pressurizes the "slug" of air from the environment.This process is where the technique gets its name, as a jet is "synthesized" from its surroundings.
Local air pressurization alone, however, will not create a synjet, such as in the case of a home subwoofer.Synjets additionally require high port air velocities, on the order of 10 m/s.This is sometimes quantified by saying they require high Reynolds numbers ( > 1,000) [ 41 , 72 ].This high air velocity causes the forward momentum of the ejected air to dominate the flow characteristics and leads to non-linear flow separation occurring along the sides of the jet where high-velocity air slides past low-velocity air.This separation is critical, as it ensures that the majority of the air ejected from the port remains spatially concentrated and travels in a single direction.The flow separation primarily occurs on the exhaust stroke of the synjet.During the intake stroke, air flows in from all possible directions, which causes momentum cancellation to occur in the radial direction (illustrated in the Supplementary Video).The result is a net gain in momentum between the intake and exhaust strokes, with positive momentum occurring along the axial axis of the jet that imparts energy to the user.
Rectified momentum flows can technically be formed from a single oscillation, but this is rarely how synjets are used.In this mode of operation, stable vortices can be formed that can travel further distances but are typically limited in volume and power capability (see previous work on haptic vortices for more information on this topic [ 12 , 62 ]).Instead, we focused almost entirely on cyclically driven devices, as this mode of operation allows for a steady jet of air to be formed, creating more powerful output.

Synjet Actuator Construction
Synjets actuators are very simple in construction: They require an output port, an interior chamber, and a way to pressurize air inside the chamber.An exemplary synjet actuator can be seen in Figure 3 .An actuating diaphragm (in this case, a speaker) is used to drive the interior chamber, which is made up of a spacer and top plate.A simple hole in the top plate creates an output port.
In Section 4 , we discuss design parameters at length, and in Section 5 , we list specific components we used in the creation of seven example synjet devices.

Anatomy of a Synjet
Figure 4 offers an illustration of the formation of a typical synjet over three successive cycles.Differential pressure from ambient atmosphere was recorded using a reference microphone and CNC setup (described later in Section 7 ).This actuator was driven at 45 Hz, resulting in a total period of 22 ms.The exhaust phase of each cycle is shown in the left panels, while the intake phase is shown in the right panels.The initial pressure wave emission, labeled A, looks initially similar to a vortex, and a trailing low-pressure region follows the high-pressure wavefront.The second wavefront B is then exhausted into the wake of the first.Emission B travels faster than A and is able to catch up to and collide with A in the third cycle.At t = 44 ms, it can be seen that these individual emissions are starting to build on one another, forming a continuous elevated pressure region.Emission C is able to travel into the wake of both A and B, and a steady stream of air begins to form.This process repeats over and over, as more emissions keep the high-pressure zone wake active, continuously synthesizing air jets.

General Haptic Sensation
We now briefly describe our experience with synjet haptic sensations to orient the reader and give context to this work.The haptic sensation of a synjet depends on how far the user is from the port orifice.In general, near the port ( < 6 D, D = nozzle diameter), synjets convey a sensation similar to that of a conventional jet.The cyclical nature of synjets, however, produces a vibration-like effect on the skin that co-exists with the steady force of the jet.Modulating the voltage amplitude causes modulation in the jet thrust and vibration amplitude, directly creating a parallel modulated feeling.Very rapid impulses in this near region feel like powerful vortex emissions.Farther from the port ( > 6 D and < 12 D), synjets feel more like a fan blowing; the flow is much more diffuse and turbulent, and the feeling of vibration is lost, so instead the perception is that of a cool wind or breeze.Only when synjets are very small (D < 5mm) does the effect feel similar to ultrasonic arrays, e.g., a small buzzing or pressure on a single small point.However, at this small scale, synjets only can be felt a few cm away from the port.In all cases, the sensations are easily and readily felt by the user.

IMPLEMENTATION
We now describe how synjet actuators are constructed and driven.We then explain how to achieve different flow modalities, how to adjust flow properties, and how arrays of synjets can be utilized.

Actuator Design
All the synjet actuators described in this work were built using audio speakers as the core driving mechanism.This is convenient, as speakers come in an incredible range of sizes and power ratings and are cost-optimized, high-performance devices.Simple custom enclosures were then designed around these speakers.In almost all cases, we used stacked, laser-cut acrylic pieces held together with bolts, screws, and/or acrylic weld.To facilitate replication, we have made all of our design files available online; please see Section 6 .

Port Diameter, Range
, and Speaker Size.The port diameter, labeled D in Figure 3 is the main parameter setting the range and spatial characteristics of a synjet actuator.As explained in Section 7 , the effective range is approximately 4-8 × D, and the flow focus, or spatial spread, of the jet is approximately equal to 1-2 × D. Once D is set, an appropriately sized speaker can be selected to drive the port.The speaker must be able to displace a high enough volume of air every half cycle so a synjet will form.The parameters governing this are the speaker's max excursion displacement, x max , as well as its effective cone surface area, S d .These parameters can sometimes be pulled from a speaker datasheet, or they can be roughly approximated from the speaker's basic geometry.These parameters are multiplied together to get an estimate of speaker volume displacement capability, V sluд = S d * x max .This volume can then be used to calculate the stroke ratio, SR = 4 V sluд /πD 3 .Stroke ratios over 8 are required for synjet formation [ 60 ], and we optimized for stroke ratios in the range of 12 to 20 in all of our devices.For comparison, most haptic vortex devices utilize stroke ratios between 4-5, meaning they move, on average, 4 × less volume of air per cycle.
We prototyped synjet actuators as small as 15 × 11 × 4 mm and as large as 550 × 430 × 400 mm in volume, generally tailoring speaker size to scale with port diameter, D. If a single speaker was unable to produce the required volume displacement for a given port diameter, then we either increased the size of the speaker or used additional speakers in acoustic parallel (i.e., doubling or quadrupling S d ).In this way, speaker size and quantity are intimately linked to port diameter and range.

Nozzle and Cavity
Geometry.We briefly investigated synjet port nozzle shape, as related work [ 31 ] found that nozzle geometry alone can lead to increased flow velocity.In general, we found that short ports and ports with a slight chamfer on the inside edge had less dissipation and thus more efficient flows.More work is needed in this area to quantify efficiency gains.The interior cavity volume and the length and size of the port also affect synjet system dynamics.As discussed in LRAir [ 60 ], two resonances can occur in this frequency range: a resonance of the speaker cone and its suspension and a Helmholtz resonance between the enclosed cavity air compliance and the port air mass.We avoided the Helmholtz resonance in this work, a core difference from LRAir, opting for small cavities and short port lengths, both of which increase the Helmholtz resonance frequency beyond our range of actuation.By loosening these geometric constraints, we were able to make more compact devices (at the cost of some efficiency), as well as dynamically alter port geometry for flow vectoring and focusing.We drove all of our actuators at or below their natural speaker cone and suspension resonance.In this regime, typical electromagnetic speakers are able to achieve their full rated maximum displacement, x max , with minimal dynamic loading effects.

Drive Electronics and Signals
The drive electronics and signal pipeline for our haptic synjets is straightforward.In the vast majority of cases, we simply utilized techniques and standards already used in audio devices.Audio power amplifiers already exist, which we match to audio speakers to maximize applied power with minimal loss.We use class D audio amplifiers, which are highly efficient and capable of running from a single voltage supply.For low-powered devices ( < 40 W), we used an amplifier based on the TPA3116D2, while for high-powered devices ( > 40 W) we used an amplifier based on the TPA3255.Amplifier boards were purchased online.For the prototypes we built, we used power supplies between 5 V and 48 V, as dictated by the power requirements of the speaker and amplifier.
We used digital audio generation tools such as Audacity and PyAudio to create stimuli waveforms.For multichannel audio, we used Adobe Audition.Our software outputs audio waveforms to either a standard PC stereo headphone jack output or, in the case of multichannel audio, a multichannel USB audio interface (Behringer UMC1820).We used one audio output and one amplifier channel per actuator.One potential limitation of this audio pipeline is in generating precise lowfrequency waveforms, as many audio signal pipelines only support down to 20 Hz output.This means that low frequencies are attenuated ( −3 dB or more) for frequencies 20 Hz and below.Where low frequencies were required for prototype testing (e.g., Figure 14 ), we used a low-frequencycapable digital-to-analog converter (DAC) and increased values of the DC blocking capacitors on the power amplifier front end to ensure our desired frequency came through the amplifier unattenuated.We did not operate at these low frequencies in practice, but wished to include this detail for any future researchers wishing to operate in the very low-frequency regime.

Flow Modes
Our flow mode vocabulary consists of four main categories.Two high-energy modes-continuous and modulated-maintain a strong signal over time, while two low-energy modes-impulse and single emission-are only active for a brief period.All modes have a haptic carrier frequency, which is the frequency at which the actuators are driven, and the frequency at which they produce underlying pressure jets (Figure 4 ).These flow modes are controlled only by adjusting the voltage characteristics applied to the synjet actuator.Although we define these flow modes separately, in practice, we commonly combine them together to create high-level stimuli.

Continuous
Jet. Continuous mode jets are the strongest.They produce a steady perception of thrust as the jets readily couple to the body and produce skin indentation.In this range, an underlying vibration due to the impulsive pressure waves can also be felt, as long as it is in the frequency ranges of fast adapting afferents .Even as distance increases, overall windspeed is still significant, and thermal receptors in the skin (especially the face and hands), as well as receptors at the base of hair follicles, can sense this ambient wind.

Modulated
Jet.The modulation of continuous jets allows for changing many of the precepts from the continuous mode case and feels more like an undulating perception of thrust.Slowly adapting afferents are sensitive up to approximately 5 Hz, which allows varying forces to be felt, and jets can also be modulated at higher frequencies (10-50 Hz) to allow for rich stimulation of flutter afferents (Meissner corpuscles).It is difficult to modulate at higher frequencies, as the carrier frequency would become too high.

Impulse Jet.
Short burst stimuli can also be created by using a modulated jet with a short duration.The total stimulus lasts only a small fraction of a second, and thus there is not enough time for the windspeed to truly build.This mode of stimuli is effective for click and notificationtype feedback, and the length or number of underlying jets can be adjusted to change overall amplitude.Impulses are mostly felt via fast-adapting vibration afferents at close range and via thermal and hair-follicle afferents at long range.

Single Pulse Jets.
Extremely short duration stimuli can be created using jets consisting of a single oscillation of the speaker.Because of this short duration, they are also the least-powerful haptic mode.They can be felt by fast-adapting afferents near the port opening and thermal or hair-follicle afferents at long range.It should be noted that single oscillations can be used to create stable vortex stimuli under the right conditions [ 11 , 62 ], though that is not the focus of this work.Stable vortices can travel farther than synthetic jets without losing much energy, but they typically contain much less energy to begin with, as they cannot build up airflow in the same way that synthetic jets can.The difference between a vortex and a single jet is that the volume of air in a jet is much greater, and thus a stable vortex is unable to properly form.Nonetheless, all synthetic jet actuators can be used as vortex emitters by finely adjusting their voltage and waveform.

Flow Control
In the previous section, we described how to control synjet output using only the applied voltage to the actuator.There are, however, other ways in which we can alter the flow of a synjet by introducing additional mechanisms.

Flow Focus.
The volume flow rate of a synjet can be adjusted directly by varying the port diameter size.As a prototype implementation, we used a mechanical iris controlled by a servo motor and Arduino (Figure 10 ).By tightening the iris and thereby decreasing the port diameter, we achieve a more narrow air stream and higher air speed, while expanding the iris creates a wider and more diffuse effect.

Flow
Vectoring.The direction of the synjet can be adjusted in a number of ways.We found that simply rotating the angle of the entire synjet actuator was effective for steering; however, it is difficult to build custom gimbals for every synjet size.We also considered a nozzle that turns, similar to Reference [ 62 ], but this, too, added additional complexity and size.Instead, we discovered a simple and compact method of vectoring by controlling the relative orientation of two stacked apertures.One is a smaller outer aperture with port diameter D, while the other is a larger inner aperture (example construction in Figure 11 ).When the apertures are totally aligned, the synjet emits directly ahead as normal.However, if we offset the outer, smaller aperture to one side, then the synjet deflects in the direction of the offset.Although this makes the output port smaller, the size of the outer aperture is large enough so the offset port still creates a jet with an appropriate stroke ratio.To our knowledge, this method of steering has not been discussed in the synthetic jet literature and could be a novel method of vectoring.We achieve this vectoring in both axes by using two orthogonal push/pull mechanisms, allowing continuous angled vectoring in a compact and space-efficient form.Note that the net thrust force on the steering plate is zero, as intake and exhaust forces are inherently balanced, so the steering mechanism needs minimal mechanical constraints.

Port Arrays
Another straightforward way to increase spatial expressivity is with arrays of synjets operating together.Because synjet actuators are entirely self contained and low cost, many can be arrayed together.We showcase this approach in our VR headset and desktop computing examples (Figures 6  and 9 , respectively).Additionally, we found that it is possible to produce two synjets out of a single speaker by enclosing both the front and back half of the speaker in different cavities, each with its own port.This produces two synjets, 180 • out of phase, using a single actuator.It is even possible to selectively fire synjets from the front or back port by introducing an asymmetry in the voltage waveform (e.g., sawtooth).We used this two-ported, single-actuator concept in our AR headset example device (Figure 7 ).

EXAMPLE DEVICES & APPLICATION DOMAINS
To illustrate the broad utility, feasibility, and scalability of haptic synjets, we combined our various flow modes, flow control parameters, and array capabilities to create seven demo devices, from small to large scale.Figure 5 provides an overview of each device and the method demonstrated.Note that these example applications are not meant to be novel, but instead show how we can Fig. 6.We augmented a VR headset with six small haptic synjets (A).Effects include a large impulse firing from all synjets (user hitting a wall, B), random pulses on half of the face (user splashing a puddle, C), and sequential firing of the array for a swiping effect (car driving past the user, D).Red indicates synjet haptic output, while blue arrows denote a spatially animated effect using synjets.Fig. 7.We instrumented an AR headset with a pair of haptic synjets (A), which enables notifications (B) and animated effects for wayfinding (C & D).Red indicates synjet haptic output, while blue arrows denote a spatially animated effect using synjets.
implement familiar mid-air haptic experiences using synjets, with the accompanying benefits.We have open-sourced all design files to facilitate replication; links in Section 6 .

Virtual Reality
Starting small, we put an array of six 15.0 × 11.0 × 4.0 mm haptic synjets into a virtual reality headset (Figure 6 (A)), which work together to render haptic animations onto the sensitive skin of the face.The synjet actuators can be placed anywhere within the face cup and still be felt, due to the skin's proximity; we chose an even distribution.A multi-channel signal is generated in software and conveyed to three separate stereo audio amplifiers via a six-channel USB audio interface.We created a basic driving game as an example app.If a user crashes into an object, then a face-wide impulse is triggered (Figure 6 (B)), with all six synjets firing an impulse jet synchronously.If the user drives through a spray of water, then synjet impulses are emitted with random phases and amplitudes from the appropriate direction (Figure 6 (C)).We render a continuous wind-like effect that varies in force proportional to in-game user velocity by emitting a continuous stream from all the synjets, varying in amplitude.We can also render the wind of a car racing past the user (Figure 6 (D)) using a time-sequential swipe across the face, activating columns of synjet actuators one after the other.

Augmented Reality
As another small-scale application, we created AR glasses with two double-ported haptic synjet actuators on the temples (see Section 4.5 for how we are able to achieve two ports with one speaker).Each synjet consists of a single 38.6 × 11.6 × 4.0 mm miniature speaker (Figure 7 (A)).The two actuators are driven by a stereo class D amplifier with a left/right stereo signal.A variety of stimuli are possible, including sharp pulses firing rapidly back and forth on both sides that could alert the user to a notification (Figure 7 (B)).Animated left and right swipes (using sequential firing of the two ports on both sides) could be used in a wayfinding application (Figures 7 (C) & (D)).These synjets operate close to, but do not touch the user's skin/hair; the 3 mm port allows for good Fig. 8.We added a time-of-flight range sensor and haptic synjet to a smart speaker.By tracking the hand's height, we can simulate a button "click" (B) as well as "detents" when manipulating a continuous value (C).Fig. 9.We integrated a 2 × 4 array of synjets into this keyboard (A).A variety of haptic effects are possible, including vibratory alerts (B), sequential firing to create swipe-like effects when, e.g., sending an email (C), or a single synjet emitting a localized stream to draw a user's attention to a specific area of the keyboard (D).Red illustrates synjet haptic output, while blue arrows denote a spatially animated effect using synjets.
coupling to the temples, so these sharp pulses and fluttering vibrations are salient.The jets cannot be felt if the ports are pressed to the skin, so the placement of the synjets on the glasses arms is an important design choice, making it difficult to make this a "one-size-fits-all" form factor.

Smart Speaker
Haptic synjets can also be incorporated into screen-less devices, such as a smart speaker (Figure 8 (A)).In this demo, we used a speaker measuring 65.0 mm in diameter with a height of 29.7 mm.We used the enclosure of a smart speaker itself as the cavity, and we drilled an 8 mm hole in the top face of the enclosure as the port.We used a VL6180 time-of-flight rangefinder to track hand height and trigger haptic effects.In addition to a "button" that can be "clicked" (Figure 8 (B)), which could provide haptic feedback for, e.g., play/pause music, we also implemented in-air detents that trigger for every 20 mm of z-height travel.The latter could offer haptic feedback when setting a continuous value, such as speaker volume (Figure 8 (C)), similar to turning a knob with detents.Using the range sensor, we also adjust the haptic stimuli strength to account for the distance of the user's hand.

Desktop Computing
For a desktop computing setup (Figure 9 (A)), we augmented a keyboard with a 2 × 4 array of haptic synjets (same speaker size as our smart speaker demo).The synjet ports were discreetly located between keyboard keys to provide above-keyboard haptics (four ports were evenly spaced between the number row and upper row of letter keys, and four ports were between the bottom and middle letter rows).The eight actuators are driven by a multichannel signal played through a USB audio interface.We created haptic applications that could alert users to various notifications or complement on-screen interactions.For example, by playing a simultaneous modulated low frequency through all eight synjets, we created a rumbling vibration to notify users when they commit an error (Figure 9 (B)).With sequential firing, we rendered left, right, up, and down swipes, creating spatial "swoosh-like" effects across the keyboard, which can be used, e.g., when sending an email (Figure 9 (C)).We can also fire a single synjet at a time, creating a localized haptic effect to draw the user's attention to a particular area of the keyboard, perhaps as part of a help feature (Figure 9 (D)).If the keyboard is positioned below a touchscreen monitor, then our augmented keyboard can complement on-screen interactions.For example, we used our setup to provide "click" feedback in the form of a single pulse jet emitting from all eight actuators.When dragging an on-screen icon, a continuous wind-like effect can be rendered, and once an applicable drop target is found, a vibratory effect can be emitted using a modulated jet.

Free-space Manipulation
Mid-air haptics are often coupled with applications employing free-space hand input (e.g., Ultraleap [ 70 ]).As a demo (Figure 10 ), we built a geospatial exploration app that uses a Leap Motion controller affixed to a haptic synjet with a computer-controlled iris (using an SG90 servo controlled by an Arduino Nano).For this demo device, we used a medium-sized speaker measuring 155.8 mm in diameter and 93.2 mm in height (note that this is the same speaker we use for our later quantitative and qualitative evaluations and is also the middle-sized device in Figure 1 ).Users can zoom in and out of the map by varying hand height, which is supported with coordinated haptics in the form of jet stream width (Figures 10 (C) & (D)).Zooming into the map, the user feels a more localized and narrow jet stream on the palm of their hand.Conversely, the stream widens and becomes more dispersed as they draw their hand farther away, zooming out.Note that even the most localized stream is still not as localized as ultrasonic haptics, and the most dispersed stream is not as wide as a fan, but by opening and closing the iris, we achieve a range of air stream widths in between.

Automotive Situational Awareness
Moving to a larger speaker size (the largest actuator seen in Figure 1 ) afforded us both greater range and haptic salience.As an example use domain, we selected driving a car-a canonical highcognitive-load task that could benefit from spatial alerts delivered by a steerable haptic synjet (Figure 11 ) integrated into a vehicle dashboard.For this demo, we used a large, powerful 12" diameter subwoofer driver paired with an efficient, mono-driven class D amplifier.We implemented a planar steering method by programmatically adjusting the offset between a larger inner aperture and a smaller outer aperture on top of an outer plate, with diameters of 75 mm and 50 mm,  respectively.The outer port plate is driven by two MG996R servo motors with rack-and-pinion gears, controlled by an Arduino Nano (Figure 11 (A)).Specifically, one rack contacts the pinion of a servo located on the y-axis and pulls the plate up or down, while the other lies on the x-axis and pulls the plate back-and-forth.This enables us to move and position the outer port with any offset over the inner, larger port.Please refer back to Flow Control (Section 4.4 ) for more details; step-bystep instructions for this assembly can be found online (see Section 6 ).This example haptic synjet could be used for blindspot awareness, creating spatially appropriate taps by emitting impulse jets onto the driver's body (Figures 11 (B) & (C)).When a pedestrian walks in front of the car, a swiping effect can be made by linearly steering a continuous jet to spatially represent the passerby (Figures 11 (D) & (E)).An intermittent modulated jet (simulating a phone ringing) could alert the user to an incoming call.Finally, a strong vibratory jet to the face could be used for drowsiness prevention (Figures 11 (F) & (G)).

Television & Console Gaming
Finally, we created our largest demo by combining multiple large speakers into a single enclosure, making it capable of emitting powerful haptic effects at long ranges.This demo was made by mounting four of the same 12" subwoofers used in the vehicle dashboard demo into a 550 × 430 × 400 mm enclosure (Figure 12 (A)).These speakers are positioned on opposite sides of one another (left and right, top and bottom) and counter-fire to minimize enclosure vibration, canceling their instantaneous momentum.We reverse-mounted the speakers, with their coils located inside the enclosure, for compactness.Since the forward and backward excursion of the cone displaces the same volume of air in either direction, this does not significantly affect the synthetic jet's physical performance.We envision such a device being placed beneath a TV, perhaps doubling as a subwoofer, to augment the native TV audio.A single signal is fed through two stereo amplifiers connected to four channels of high-power amplification.We envision this class of haptic synjet being used to enhance television or console games with wind, projectile hits, explosions, and other atmospheric effects (Figures 12 (B)-(D)).These effects are created with continuous, modulated, and impulse jets, respectively, and so much energy is output that users can still feel substantial wind flows a meter or more away.

OPEN SOURCE HARDWARE & GETTING STARTED
We have open-sourced all our design files at https://w w w.github.com/FIGLAB/synjets .The repository also has a step-by-step guide for building a basic synthetic jet actuator, along with links to purchase parts.We also detail our iris and 2D steering demos, the most mechanically complex examples.Last, we provide all of our stimuli WAV files (listed in Figure 19 ).

STUDY 1: PERFORMANCE EVALUATION
In the first of three studies, we sought to measure and quantify the various performance parameters of our synthetic jets.This required building a custom measurement apparatus, which enabled detailed data collection for the visualization of our flow regimes.

Apparatus
We built a custom CNC platform with an operational volume of approximately 600 × 500 × 500 mm.It is controlled via an ATMega 328 microcontroller running the open-source GRBL embedded gcode parser.Movement commands were generated in Python and sent to the firmware via a USB serial interface.Data collection was also centralized in Python using a National Instruments USB DAQ (USB-6003), and the PyDAQMx interface 1 Air pressure readings were taken from an omnidirectional electret condenser microphone (Apex220) placed transversely in the jet stream.Phantom power was applied and the microphone signal was differentially conveyed to the DAQ.Windspeed data was taken using a hot wire anemometer (Modern Devices, Wind Sensor Rev. P6).This device incorporates a hot wire sensor and temperature sensor for calibration purposes.Note that the sensor is not able to capture instantaneous wind velocity due to the thermal time constant of the hot wire probe, but it can effectively capture 0-67 m/s averaged wind velocities.Voltage output signals were generated by the DAQ and amplified using various class D audio amplifiers.Applied voltage to the speaker was also monitored using a differential probe.A picture of our CNC apparatus and a closeup of the sensing head can be seen in Figure 13 .

Procedure and Calibration
At the beginning of each session, the sensor head was moved so the wind sensor and microphone were directly aligned with the port opening.Data was then collected by jogging the CNC probe head to each x and y location of a 2D cross-sectional plot and taking a time-synchronized, 4,800 Hz recording of applied voltage, pressure, temperature, and windspeed.Step size was altered between plots for appropriate resolution.For example, a 2D plot of 31 × 60 one-second recordings equates to 31 × 60 × 4,800 Hz × 1 sec = 8,928,000 points each for applied voltage, temperature, windspeed, and pressure.Instantaneous pressure for Figure 4 was calculated by dividing the recorded voltage by the sensitivity of the microphone (7.52 mV/Pa).Peak pressure was calculated by taking the max 14:15 Fig. 13.We built a CNC platform with a hot wire anemometer and reference microphone to capture detailed measurements and 2D visualizations of windspeed and air pressure (seen in Figures 1 , 4   pressure value per location over 100 ms (four complete cycles).The applied voltage was simply the recorded voltage.For Figures 16 and 17 , windspeed data was allowed to reach a steady state by applying each stimulus for four seconds.A time-averaged recording at the end of the four seconds was used.Windspeed data was calibrated using a regression from the hot wire anemometer manufacturer, which takes temperature into account.

Geometry
To inspect and describe synjet spatial properties, we chose to look at a single synjet in detail (the middle size in Figure 1 , the same one used in the Free-space Manipulation demo).The speaker itself was 155.8 mm in diameter and 93.2 mm in height.However, we describe its dimensions in terms of the port diameter D, as this parameter dominates the jet range and dispersion characteristics.We performed a series of experiments varying the applied voltage and driving frequency of a synthetic jet with a 25 mm port diameter (D = 25 mm).The natural resonance of the speaker was 45 Hz, and we applied the maximum voltage to the speaker that was still within the power rating ( ≈40 W).These parameters are used for all the experiments in this section.
We recorded peak pressure and report the results in Figure 14 .Peak pressure plots have their amplitude normalized to the 45 Hz, 1.0 case.We can see that, for a given speaker and port diameter, peak pressure output scales with applied drive amplitude.We also see that the actuator achieves maximum pressure at resonance, versus above (90 Hz) or below (22 Hz).There also appears to be a change from a more vortex-like behavior at low amplitudes to a purely jet behavior at high amplitudes.This would align with the air-slug model [ 61 ], which predicts that emissions transition from single vortices at low stroke ratio to pure jets at high stroke ratio.
On the right of Figure 14 , we took the highest amplitude case and sliced the visualization along the axial and transverse axes to show the general dimensions of the jet.The jet maintains approximately the same peak pressure to roughly 6 D (150 mm) away from the port opening.In this range, the jet also maintains a core diameter of approximately 2 D. At a range of 12 D (300 mm), the jet has lost the majority of its peak pressure, and the diameter has widened significantly.This demonstrates that there are two relevant ranges for synjets.Between 0-6 D the impulsive pressure wavefronts (also seen in Figure 4 ) maintain their shape and focus.Beyond 6 D, the jets enter a turbulent region, where the wavefront disperses and becomes much more random.

Scaling
We also wanted to validate that synjet geometry scales and remains the same general shape for various-sized port diameters.For this experiment, we took peak pressure plots as in the previous subsection, but now for the three different speaker sizes depicted in Figure 1 .We compared a small 6.5 cm diameter speaker (used in the Figure 8 prototype), the medium speaker that the rest of these experiments used (and used in the Figure 10 prototype), and a large 30.5 cm diameter speaker (used in the prototypes seen in Figures 11 and 12 ).The peak pressure plots can be seen in Figure 1 , visualized at scale.All of these speakers were actuated at their natural resonances (100, 45, and 41 Hz, respectively) at the max voltage within their power rating.As can be seen from the peak pressure plots, the general shape of the synjet does hold across different-sized actuators.This implies that we can generalize the findings from Figure 14 to both larger and smaller port diameters.

Flow Modes
To measure how jets are perceived by users, we chose a different metric-instead of peak pressure, we decided to measure average windspeed, as depicted in Figure 15 .This is because our windspeed sensor best captures how these pressure waves build on one another.Therefore, we thought it was a more useful proxy for demonstrating a synjet's influence on the human body (i.e., skin deformation).Using this sensor, we took readings at different distances from the port opening as we applied different flow modes of haptic stimuli.

Continuous Jet.
Experimental results are plotted in Figure 15 , Continuous Jet.Continuous-mode jets achieve the highest power and windspeeds, reaching 15 m/s close to the port opening ( < 4 D).As the distance increases to 8 D and beyond, windspeeds drop to about 10 m/s, which is still significant and easily perceived.

Modulated Jet.
Experimental results are plotted in Figure 15 , Modulated Jet.Close to the port ( < 4 D), these windspeeds modulate between 6 and 10 m/s.The varying windspeeds produced by the undulating wind can be differentiated by the frequency of modulation, which would change the highest and lowest windspeeds achieved.This jet modulation can also be felt in the long range ( > 8 D), oscillating between 2 and 4 m/s at the 12 D (300 mm) range.

Impulse Jet.
Experimental results are plotted in Figure 15 , Impulse Jet.For this flow mode, an exponentially decaying modulation was applied to an underlying carrier wave, as seen in Figure 15 , top row.In the small fraction of a second that this stimulus lasted, windspeeds only reached up to 0.78 m/s peak speed.Due to the short duration, little energy makes it past 4D away from the port opening, dropping to just 0.2 m/s at 8 D (200 mm).Additionally, we see that air movement dies down to almost zero after roughly a quarter of a second at all distances from the port.

Single Pulse Jet.
Experimental results are plotted in Figure 15 , Single Pulse Jet.As explained previously, single pulse jets are not the same as vortex emissions, because the large volume of air does not permit the formation of a stable vortex.As depicted in the graph for the single pulse jet, windspeeds peak around 0.3 m/s for a fraction of a second near the port ( < 4 D).As with impulse jets, windspeed diminishes quickly in both distance and time.

Flow Focus
In this experiment, we captured data for port sizes of 15 mm and 35 mm, using the same applied voltage.Windspeed plots can be seen in Figure 16 .As depicted, the 15 mm port achieves a higher windspeed and narrower air stream, peaking at 14.1 m/s with a main flow width of about 20 mm.Conversely, the 35 mm port creates a main flow roughly twice as wide, but with a reduced max windspeed of 10.6 m/s.We note that in our free-space manipulation demo apparatus (Figure 10 ), we can dynamically alter the port diameter using a mechanical iris.

Flow Vectoring
To test the efficacy of our flow vectoring implementation, we used a 25 mm ported plate placed over a 45 mm ported plate.As a flow vectoring test, the 25 mm port was offset by 20 mm, roughly halving the size of the aperture.As can be seen in Figure 17 , this causes the flow to vector approximately 15 • .Of note, there is minimal loss in windspeed when angled, despite the smaller effective port size.In the straight emission direction, the stream reaches maximum windspeeds of 12.0 m/s, whereas the angled stream achieves 11.5 m/s.The dissipation of both streams over distance is roughly equivalent.

STUDY 2: THINK-ALOUD STUDY
While Study 1 documented and validated the performance characteristics of our synjets and their various modes of operation, we also wished to better understand the perceptual nature of their non-contact, mid-air haptic effects.For this, we ran a think-aloud study to collect qualitative feedback across different synjet sizes and flow modes, as well as flow focus and vectoring functionality.These descriptions enable retroactive comparison with existing methods while also helping to qualify our fundamental haptic parameters.

Procedure
We recruited eight participants (mean age 25.1) for a think-aloud-style study lasting roughly 30 minutes.We used the same set of outputs as used in Study 1, with both medium-and large-sized synjet devices.Figure 18 details the stimuli parameters.These were presented in order and were initially played twice to participants, after which participants could request replays as many times as they desired while thinking aloud.For the medium-sized synjet device, participants propped their arms on a rest next to the speaker, with their hand held about 15 cm above the speaker, such that the jets hit around the center of the palm.The large synjet device was placed on a table and tilted upwards at 45 degrees.Participants were allowed to either sit in a high chair or stand, such that the jets were aimed at their chests about 30 cm away.To avoid extraneous bias, participants wore over-the-ear noise-canceling headphones as well as a blindfold.After each stimulus was played, participants were prompted to describe the sensation experienced in an open-ended manner.

Flow Mode.
All participants compared the continuous jet to a wind-like sensation for both synjets.All participants also reported that they could feel an underlying frequency in the wind, with five participants describing it akin to a "vibrating" wind and two participants describing it as "high frequency."P6 compared the stimulus on the medium synjet to "sticking my hand outside the car window," and 3/8 participants described it as feeling like the "vibrations of a motor" through the air.For the large synjet device, three participants described it as a "vibrating motor," while P7 said it felt like "sticking your head out the car window."In the modulated jet regime, all participants described the feeling as more discrete than the continuous jet stimuli, with 5/8 participants describing it as a "pulsing" wind and another two describing it as "gusts" of air.For the medium synjet device, P8 felt as if someone was "shouting into my hand, with a rhythm," while P3 said the large synjet felt like "two different frequencies resonating on and in my chest."For the impulse jet, five participants accurately described it as weaker and smaller than the last two stimuli, but one participant felt that it was stronger.Three participants compared it to a "tap" sensation.On the large synjet, four participants compared the impulse jet to a brief "gust of air," with 2/8 correctly detecting that it was "trailing off."Three participants also likened the impulse jet to an "air cannon" (though this is a different flow phenomena, as noted previously in Principles of Operation).Finally, all participants described feeling the single pulse jet as very similar to the impulse jet, though 7/8 participants (correctly) described it as "weaker" and/or "smaller," with only the final participant saying it felt "stronger."Six participants described it as feeling something akin to a "soft, very light impact" (P2), "single pulse" (P1), and "puff of air" (P7 & P8).The final two participants described the sensation as also feeling like an "air cannon" (P4 & P6), but weaker than the previous impulse jet stimulus.

Flow Focus.
Every participant (P1-8) was in agreement for flow focus: The smaller aperture felt "stronger" and "more concentrated," while the larger aperture was "weaker" and "more dispersed" on both synjet sizes.P4 said that for the large synjet device, it "feels like the same fan wind was blowing, but for the [fully-open iris] I'm closer to the fan so it feels stronger and more focused, and the [narrow iris] one I'm farther from the fan so it feels weaker and more spread out ever y where."In the latter case, the participant was interpreting the change in flow shape and intensity as a change in distance, when in fact the distance was fixed (participants were blindfolded to not see this effect was being driven by a variable iris).Three participants said that for the larger aperture, they felt that they could not pinpoint the focus and that it was more like a "general sense of air" (P8).Two participants described the larger aperture as having a "smoother" flow.

Flow Vectoring.
Every participant (P1-8) was also in agreement about flow vectoring directionality, noting that the stream was, e.g., "moving from the tips of my fingers to the bottom of my palm" (P7) or "from the bottom of my chin to my stomach" (P4).Four participants described the moving jet as "going from smaller to bigger [in] area" (P8), while 3/8 participants felt the sensation stayed relatively the "same size," with one final participant feeling it was getting "more concentrated" (P1).Three participants noted that it gets "weaker as it travels" (P6), while the other five felt the force stayed the same.For the downwards continuous jet, every participant correctly detected that the air felt "localized at the base of my hand, somewhat on my wrist" (P1) or "centered on my stomach, below my sternum" (P3) (below the center of the palm/chest).Seven participants accurately described the effect as "weaker" than the standard continuous jet, with the final participant feeling that the effect had the "same strength" (P2).Four participants also felt that the area was "wider," while two thought that the area was the "same size," and the last two felt that the area was "smaller."In short, while the size of the moving haptic area varied and elicited commentary, the dominant effect that it was moving was salient.

STUDY 3: RECOGNITION STUDY
Study 1 quantified our haptic effects' physical properties.In Study 2, participants described the various haptic modes and actuation parameters, qualifying the base haptic building blocks of our synjet actuators.However, it remained unknown how distinct and discernible the stimuli created from these building blocks were from one another.Ideally, a haptic method is able to produce a rich palette of distinct haptic effects.To assess the expressivity of our synjets, we conducted a third and final study, showcasing a broad range of sizes, ranges, body locations, and spatiotemporal expressivity.For this, we ran a stimuli recognition study using the example devices from Section 5 .lists synjet device (see also Figure 5 ), flow mode, drive frequency, and user recognition accuracy.

Stimuli Set
We designed a set of stimuli that incorporated a range of methods and effects (Figure 19 ) built from our fundamental haptic parameters.These 31 stimuli are not meant to be treated as a comprehensive taxonomy, but rather as a broadly representative and illustrative set.Our goal was to create a high-level stimuli vocabulary by mixing and matching orthogonal aspects of our haptic experience.Synjet devices can achieve high expressivity not through any single mode or mechanism being incredibly expressive, but rather by combining many modes and mechanisms, triggering diverse types of tactile receptors across a range of temporal and spatial scales.

Procedure
We recruited 10 participants (mean age 23.6) for a study lasting 45 minutes.None of the participants were repeated from the previous study.Our example haptic synjet devices were introduced and tested in a random order.At the start of each device session, participants were played every stimulus twice and told the corresponding stimulus name.Individual paper printouts for each device session were provided, which listed all the stimuli names for easy reference.Following this brief orientation, each device's stimuli were played in a random order, repeating four times each throughout the session.This yielded a total of 1,240 recognition trials (10 participants × 31 stimuli × 4 repeats).
Participants were instructed to speak aloud the name of the stimulus they perceived.If desired, participants could request stimuli be replayed, although this was a rare occurrence (mean plays = 1.03; median plays = 1.00).To avoid confounding noise, participants wore over-the-ear noisecanceling headphones, which also played non-vocal music to further obscure any device noise.For three devices (vehicle dashboard, volumetric display, and television) where there were visible clues as to the playing stimuli (e.g., flow vectoring), participants were instructed to close their eyes for the entire device session.
We note that each device required a slightly different positioning for the user.The VR headset was worn normally with the user sitting in a chair.The AR glasses required the user to feel all four ports, which meant that it had to sit lower or higher on some participants' noses, and a short calibration period was necessary to position the device.The smart speaker prototype was interactive, so participants were signaled when they could proceed to explore the interaction space using their hands.The free-space manipulation demo device required the participant to hold their hand a short distance above the device.For the keyboard, participants were asked to position their fingers naturally on the top row of keys.For the vehicle dashboard, participants stood ~30 cm in front of the device, which was placed on a stool and angled in the direction of their chest.Finally, for the large television-oriented synjet device, participants sat on a chair 2 m away with the chair height adjusted such that the synjet was aimed at their chest.

Results
We calculated recognition accuracy by taking the number of correctly classified stimuli and dividing it by the number of times the stimulus was presented across all participants.Recognition accuracies are reported in the last column of Figure 19 , and confusion matrices can be found in Figure 20 .In summary, 19 out of 31 stimuli had 100% recognition rates, and the worst-performing stimuli had 90% recognition rates.In short, participants were able to readily perceive differences among stimuli with minimal training and exposure.This was true across all of our different flow modes, flow control, and array methods described in Section 4 .

DISCUSSION & COMPARISON TO PRIOR METHODS
We now discuss our main findings, synthesizing results across our three studies.We also compare our method to existing related methods where applicable.Comparison to specific prior work devices is also summarized in Figure 2 and Section 3.4 .We hope that by eliminating some barriers presented by other mid-air haptic methods (i.e., high cost, difficulty of building, large size) while preserving some of the more important capabilities of haptics (expressivity, saliency, integratability), synjets will be explored in more detail by the haptics and HCI communities.Although there is still room for improvement, as we detail below, the more accessible mid-air haptic methods become, the more widely they will be used.

Scale
Our haptic synjets are built from speakers, which means they can be readily built at any scale at which commercial speakers are sold.We verified that synjet characteristics such as peak pressure, actuator power, and range scale with physical size (the volume of the actuator).Likewise, the intensity of the sensations also scales relative to synjet size, as we found qualitatively through our think-aloud study.Overall, the possible range of sizes for synjets is similar to that of fans, which also come in commercial sizes from tiny to massive.Conversely, scaling is much more difficult for ultrasound arrays, where cost significantly increases with size, as well as conventional air jets, as larger compressed tanks can be very unwieldy.Vortex devices also struggle with scaling due to having more physical constraints on device properties.

Range
The reach of a synthetic jet is directly correlated with the diameter of its port, as discussed in the limitations of Reference [ 60 ], so theoretically any range of synthetic jet is achievable as long as an appropriate actuator is chosen and the correct volume flow rate is achieved.Across our example devices, the smallest synjets worked in an HMD placed 2 cm from the face, whereas our largest TV demo stimulated users 2 m away, demonstrating the potential range of actuation.This range can be similarly obtained in fans or conventional jets, as they both consist of streams that can be modulated through changing amplitude, but both vortices and ultrasound are limited in their reach due to physical limitations.

Power Consumption
Figure 5 includes power consumption numbers for all seven of our example synjet devices.These measurements represent total power draw, including the amplifier and the actuator components.As an example calculation, our smallest synjets consumed 0.17 W when active.Thus, if a haptic effect lasts, on average, two seconds, then this would consume 1 mWh of energy and is negligible when compared to, e.g., an Oculus Quest 2's 14,000 mWh battery.As synjets get larger, of course, they consume more power-up to 41.7 W measured from our largest television demo-and these larger devices will typically require wall power.We note that all of our devices are prototypes, built from off-the-shelf speakers meant for audio and not haptic purposes.Thus, we believe there is potential for optimizing power consumption.For instance, in LRAir [ 60 ], the authors were able to utilize acoustic resonances to reduce power consumption by a factor of two.Our power consumption ranges from that of fans, which are low-powered, to that of ultrasound arrays that consume a lot of power, with vortex devices falling somewhere in between.There is no easy direct comparison to conventional jets, but in general, these require energy-hungry air compressors.

Flow Mode Efficacy
We experimentally validated the rendering capability of our four flow modes-continuous, modulated, impulse, and single pulse-both quantitatively and qualitatively.We qualified the base sensations of these building blocks in our think-aloud study (Study 2) through participant responses.Each has a variety of parameters (e.g., waveform shape, modulation frequency, amplitude, duration, decay) that can be tuned to create rich and distinctive effects, and the individual drive signals can also be superimposed and concatenated to create a nearly endless set of haptic stimuli.We demonstrated a broadly representative sample of these stimuli in our recognition study (Study 3), which included a set of diverse applications with clearly recognizable effects.This expressivity and saliency is higher than that of fans and vortices, which are largely constrained to one type of wind flow each.Our flow modes can be recreated nearly equivalently on conventional jets, while ultrasound devices are extremely localized and therefore more expressive along the spatial dimension of their output.

Flow Vector Efficacy
In our flow vectoring prototype (vehicle dashboard demo, Figure 11 ), the flow could be steered in roughly a 40 °cone (i.e., ±20 °).In Study 1 (performance evaluation), we quantified the wind flow dynamics at 0 °and 15 °emission angles and found there was a minimal drop in peak wind speed (4.5%).In Study 2, every participant recognized and noted the animated movement of the flow and pinpointed accurately where it was aiming.Thus, unsurprisingly, in Study 3, all 10 participants had 100% recognition rates for up/down/left/right swipes, proving that our flow vectoring approach performed successfully as a haptic parameter to create varying stimuli.

Flow Focus Efficacy
Anecdotally, we felt that flow focus was a more subtle and less effective haptic sensation.This can be seen in Figure 16 from Study 1, where the larger aperture does have a wider stream and slower peak speed, but without too sharp of a difference.Nonetheless, it was sufficiently effective for all participants in Study 2 to describe small and large flow focus differently.Participants also achieved 100% recognition accuracy on the small and large flow focus stimuli in Study 3. Future 14:23 work using a superior mechanical iris with a broader range of aperture width could potentially yield more focal dynamic range, leading to a more expressive effect.

Spatial Dispersion
Because synthetic jet streams begin to disperse at ~4 × the port diameter, and because the synthetic jet diameter is roughly 1-2 × the port diameter, there exists a precision-to-range ratio that must be considered when designing a synjet device.Smaller ports inherently produce more spatially precise jets, but they can only be felt when the body is close to the port.Conversely, large port synjets can operate from further away, but the jet of air and actuation area are larger and more imprecise.The narrow stream on smaller synjets can reach a precision close to ultrasound in the close range, while the larger stream can feel more like the wind from a fan, which is more dispersed.

Noise
Audible noise is an inherent byproduct of most air-flow-based devices, especially those that require high-pressure waves to be transmitted through the air, which is also an issue discussed in the limitations of Reference [ 60 ].As captured in our technical evaluation, peak pressures of around 200 Pa can be achieved, but these pressures only exist for very short periods of time, and only in the direct line of the jet very near the port orifice.Away from the jet, the pressure dissipates, which can also be seen in our pressure-recording plots.To capture real-world noise data on our devices, we measured the dBA in front of the ears while using each device in its normal use case.We chose the dBA scale because it includes a perceptual model of loudness that describes our sensitivity to audible noise, and it inherently accounts for the placement of the device by being measured from the ears.We found that our devices all stayed within the range of 57.5-79.8dBA, documented in Figure 5 .The quietest of these, the AR Glasses, has the sound level of a normal conversation, while the loudest application is the television box, equivalent to city traffic while sitting inside your car, according to the CDC [ 5 ].These measurements are all within the parameters of noise safety levels.To further counter this noise limitation, we designed all of our stimuli except one (the VR stimuli) to use low-frequency carriers and modulation.However, while the noise level remains safe to use with our actuators, these transient and other artifact noises may still be distracting.We hope that, when designing synjet applications, these may be able to be covered up with synchronized sound effects.

Latency
The latency of haptic synjets depends on actuation distance and output windspeed.For example, our free-space manipulation demo has a continuous stream windspeed of 15 m/s, so when the user holds their hand ~20 cm away, it takes ~13.3 ms for the flow to reach their hand.This is faster than vortices, which reach peak speeds of 7-9 m/s [ 12 , 62 ] and would be about the same latency as fans or conventional jets, depending on their windspeed output as well.Ultrasound arrays work by creating a constantly present node in space, so they operate essentially instantaneously.Like most mid-air haptic methods, synjets ultimately have more latency than most traditional contact haptic devices, such as vibration motors, which propagate through solid materials at thousands of meters per second (again, essentially instantaneous) and can be coupled directly to the skin.

Cost
In the small quantities we ordered, our synjet example devices cost between $6 and $410 USD.This cost accounts for the amplifier(s) and speaker(s) for a single device, which can consist of multiple synjet actuators.For example, $410 was the cost of our television device, which had two amplifiers and four large speakers, each costing $88.95 (Figure 5 , actuator cost column).Note that the construction materials we used were sheets of acrylic bought in bulk and screws or glue, so we consider these costs negligible.Amplifiers themselves are commodity parts and cost us between $4 and $35 USD in single quantities.In commercial volumes, these prices would be considerably less.The low costs of our cheapest synjet devices (~$6) are similar to fans, with the more middle-expense devices being comparable to vortex devices.All haptic synjets are cheaper than most conventional jets and much cheaper than all ultrasound arrays.

DIY Accessibility
Haptic synjets are an accessible technology to the DIY community.There are only four components necessary to create a bare minimum haptic synjet: a DC power source (i.e., lab power supply), an amplifier, a speaker, and an airtight chamber with a port.This chamber can be made out of any number of materials; we used layered acrylic pieces sealed with either acrylic weld or nuts and bolts.As noted, speakers and amplifiers are very common and inexpensive parts, easily purchased on e-commerce websites.For more information on how to make a synjet actuator, see Section 6 .

Special-purpose Actuators
The synjets presented in this article were built using conventional speakers and subwoofers that can be bought directly from parts suppliers.As explained in Section 3 , however, the actuation comes from the displacement of the speaker cone rather than its acceleration, and audio speaker designs typically optimize for the acceleration aspect.This means that speakers are generally made to operate above resonance and reproduce sound.Haptic actuation can occur below the rated frequency range of the speakers we used, but the speakers would either be incapable or be overdriven and eventually break.When choosing speakers for our applications, we looked for models that had a more optimal surface area and cone displacement, which typically meant woofer-and subwoofer-type devices.These performed at a better frequency range for haptic actuation than full-range speakers, mid-range speakers, or tweeters, but were still sub-optimal, and we believe we could further optimize a driver if we designed our own custom-built synjet actuator in future work.Our envisioned actuators need to eliminate sound while still producing large amounts of air displacement at tactile frequencies, which is a different, but adjacent problem to current speaker design.This would require a solid membrane that could be displaced mechanically in some way to a large maximum, and it could be cut into the exact surface area needed for a particular application.

CONCLUSION
In this article, we presented a thorough investigation of an actuation method for producing midair haptic feedback using synthetic jets.We described how synthetic jets are able to launch localized high-pressure jets out in front of a device using nothing but conventional speakers encased in ported chambers.We characterized the operation of these devices using pressure and windspeed measurements and further showed how air streams can be steered and focused with simple mechanical mechanisms.We created seven example applications using a variety of synjet sizes and methods and demonstrated a broad haptic stimuli vocabulary to showcase the expressiveness of our devices.We conducted three studies, answering different fundamental research questions.Overall, due to their low cost, ease of accessibility, and scalability, we believe that haptic synjets can unlock many new and interesting uses for mid-air haptic feedback.

Fig. 1 .
Fig. 1.Left panel: Three examples of haptic synjet actuators with their respective jets visualized with peak pressure recordings (common scale).Right three panels: The same three haptic synjets (A-C) firing into a tank of milk for illustration.

Fig. 3 .
Fig. 3. Exploded diagram of an example haptic synjet actuator used in the experiments of Section 7 .Also shown is the port diameter, D, and the conceptual difference between the exhaust and intake phases.

Fig. 4 .
Fig. 4. Time evolution of a synjet over the initial three oscillations.The left column is in phase with jet exhaust, while the right column is in phase with jet intake.

Fig. 5 .
Fig. 5.We built seven example synjet devices, spanning a variety of use domains, sizes, and constructions.

Fig. 10 .
Fig. 10.In this mid-air input demo, a variable diameter synjet actuator (A & B) haptically conveys geospatial zoom level (C & D).Inset frames provide a close-up of the iris.

Fig. 11 .
Fig.11.We built a haptic synjet actuator with the ability to steer in two dimensions (A).This could be integrated into, e.g., an automotive dashboard to render spatial haptic effects.Photos B, D, and F illustrate how the black plate moves (orange arrow) to vector the air flow.This could render spatially appropriate taps for blind spot awareness (B & C) or a continuous effect to indicate a pedestrian crossing in front of a user's vehicle (D & E).Finally, a strong vibratory effect to wake the driver when drowsy (F & G) is also possible.Red illustrates synjet haptic output, while a blue arrow denotes a spatially animated effect using synjets.

Fig. 12 .
Fig. 12.We created one very large haptic synjet prototype (A), capable of strong effects at longer ranges.Here, a user is playing a console game haptically augmented with wind (B), projectile (C), and explosion effects (D).
Fig.13.We built a CNC platform with a hot wire anemometer and reference microphone to capture detailed measurements and 2D visualizations of windspeed and air pressure (seen inFigures 1 ,4 ,14 ,16 ,and 17 ).

Fig. 14 .
Fig. 14.Left: Peak pressure visualizations of synjets at different drive frequencies and amplitudes.Amplitudes are normalized to the 45 Hz, 1.0 case.Right: A more detailed examination of a single jet, with peak pressure data plotted on two axes (orange lines).D = port diameter.

Fig. 15 .
Fig. 15.Four modes of operation driven by different applied voltage waveforms.Here, we plot real-world data from a windspeed sensor at different characteristic distances; D = port size of synjet.

Fig. 16 .
Fig. 16.Results from our flow focus experiment.Top row: Left is a 2 D windspeed visualization from a 15 mm port, and right is from a 35 mm port.Bottom row: Two slices (blue and orange lines) taken at different distances from the port, charting windspeed over distance.

Fig. 17 .
Fig. 17. Results from our flow vectoring experiment.Top row: Left is a 2 D windspeed visualization from a standard port, and right is vectored flow (note inset photos).Bottom row: Three slices (blue, orange, and green lines) taken at different distances from the port, charting windspeed over distance.

Fig. 18 .
Fig. 18.Parameters of the stimuli played for participants during the think-aloud study.

Fig. 19 .
Fig.19.Overview of haptic stimuli used in our user study.Table lists synjet device (see also Figure5), flow mode, drive frequency, and user recognition accuracy.

Fig. 20 .
Fig. 20.Confusion matrices from our recognition study, one per example synjet device.Please refer to Figure 19 for stimulus details.