In‐flight force estimation by flight mill calibration

The study of insect flight is important for conservation and sustainability efforts, as predicting insect dispersal can aid management programmes in tackling economic and ecological harm from, for example, invasive species. Flight mills are invaluable tools for measuring the factors of insect flight under laboratory conditions, as they lower several technical and financial barriers to conduct experiments. It is especially difficult, however, to make assumptions about the energetic cost of tethered flights conducted using different tethers, or even on different flight mills, due to the mechanical variability of the bearing friction and air resistance of the rotating assembly. This additional uncertainty necessitates a larger number of replicates for any given standard of statistical confidence. By characterising flight mill friction, this uncertainty can both be reduced in magnitude and assigned a specific, well‐defined numerical value. We present a simple methodology to characterise this friction through dynamic calibration of the flight mill, at a high statistical confidence. This study uses videography of a flight mill undergoing free velocity decay due to friction, using an in‐house developed software to extract angular velocity from video data. However, the technique is readily adaptable to other measurement techniques. Using the velocity, alongside the mass moment of inertia of the flight mill, allows us to determine the rotational friction coefficient. This friction coefficient provides precise measurements of thrust production, and therefore the energy expenditure of flight, by the tethered insect.


INTRODUCTION
The flight mill is a tool that has been used over a century to measure insect flight under lab conditions (Clements, 1955;Hocking, 1953).
Although there is variation in detailed design choices, as a general description, a flight mill is a tool that confines the flight of an insect to a circular path, by physically attaching the insect to a rigid, fixedradius rotating element.The insect may be attached to the rotating element by either a soft or a rigid tether, where soft tethers permit a small variation in position relative to the overall radius of the pivot.
The insect can then fly unlimited distances in a controlled laboratory environment, and its endurance, range and velocity can be tracked by an optical encoder (Minter et al., 2018), infrared sensor (Attisano et al., 2015) or magnetic Hall effect sensor (Evenden et al., 2014), which contribute minimally to the resistance to motion.A common feature of flight mills, though not universal, is a thin needle to support rotating element(s), thereby minimising friction.Early flight mills often used jewel bearings, where the rotating element that sits on this needle was a jewel with high mechanical hardness (typically sapphire or ruby), similar to those found in mechanical wristwatches (Rowley et al., 1968).Modern designs opt instead for polymer materials, such as PTFE (polytetrafluoroethylene, brand-name 'Teflon'), which offer similar performance at substantially reduced cost (Lago et al., 2021), or the metallic surface of a magnet used to support the weight of the assembly (Attisano et al., 2015).This latter case has occasionally been mislabelled as a magnetic bearing; however, if the rotating element is in physical contact with another surface, these are all examples of plain bearings, where relative motion is by sliding rather than rolling or by fluid gap (Juvinall & Marshek, 2019).
This background on the mechanics on the operation of flight mills is useful because the principal philosophy that motivates the use of the flight mill is that an investigator can obtain a highly controlled flight environment, at the cost of giving up a highly realistic flight environment.This high degree of control over the flight environment is achieved through a repeatable mechanical system, and therefore the characterisation of the mechanical system can provide insight into the flight environment.The rotating friction of flight mills governs the energetic cost of flight, which is invariably used as a correlator, but not an estimator, of the natural cost of flight.For example, the relative rate of insect dispersal by gender or insect mass can be determined on a flight mill in the context of disease vector movement (Kautz et al., 2016), or for conservation (Williams & Robertson, 2008).This permits systematic investigation of the myriad of factors influencing insect flight, including morphological factors such as body mass, wing size and sexual dimorphism (Evenden et al., 2014), or environmental ones such as temperature or time of day (Lago et al., 2021).In these examples, we can see that flight mill experiments can provide insights into highly specific factors affecting the dispersal process.However, a large number of replicates are required to overcome not only the variability of the insects under investigation but typically the variability between multiple individual flight mills as well.By characterising the mechanical properties of individual flight mills, the uncertainty associated with mechanical variability can be quantified, and often reduced, depending on the measured quantity.
Insects are supported by the tether in flight mill assays and do not expend energy for self-support during flight, and as a result, flight endurance might be overestimated (Minter et al., 2018;Williams & Robertson, 2008).In addition, frictional forces caused during tethered flight compared with free flight may result in an underestimation of endurance (Jactel & Gaillard, 1992;Naranjo, 2019;Ribak et al., 2017).
To address and disambiguate these contrasting concerns, it may be beneficial to analyse tethered flight in terms of energy cost, which would normalise differences in friction between individual devices, but would also require a measurement of the force produced by the insect in flight.Previous analyses of the force production of insects on flight mills have used angled rotational axes to infer force production against gravity (Ribak et al., 2017), or the mean rate at which velocity decays on the flight mill as a proxy for friction (Riley et al., 1997).In this study, we present a simple means to estimate the physical coefficients of friction of a flight mill, so that instantaneous thrust production can be determined from the velocity of the flight mill alone, which may be used to estimate aerodynamic force coefficients, energy expenditure, to normalise a set of flight mills, or to characterise the variance among a set of flight mills.Moreover, if this model for the friction of a flight mill is coupled with a model for the aerodynamic drag of the insect body itself (see, e.g., Hajati et al., 2023), it may be possible to quantify the relative magnitude of each component of thrust and drag, and thus quantify the 'underestimate' of flight performance seen in flight mills.This exploits the design and construction of the flight mill, by utilising the bearing elements as a force sensor unto themselves.This is enabled by the fact that they are composed of standard engineering components with well-understood frictional behaviour (Juvinall & Marshek, 2019).The methodology presented below will utilise overhead video to measure flight mill position, but is adaptable to many other measurement techniques for capturing the position of the mill arm over time, especially those with high spatial or temporal resolution such as optical encoders.

MATERIALS AND METHODS
The flight mill used in this study consists of two sub-assemblies (Figure 1).The bottom sub-assembly consists of the base of the mill that provides physical support, while the rotating upper sub-assembly restricts insect motion.No insect was present for this study, as the insect thrust or drag can only be determined later by comparison with the machine friction in isolation.The bottom sub-assembly consists of a rigid platform, made of acrylic in our specific example, onto which a POM (polyoxymethylene, brand-name 'Delrin') column is fitted.
A magnet is placed on the top of the column, which supports the weight of the rotating upper sub-assembly by a matching magnet on the rotating component.A guide pin made from stainless steel tubing is embedded into the POM column to restrict the motion of the upper sub-assembly, acting as the inner element of a simple plain bearing.
Dimensions for these components are listed in Table 1.The upper assembly consists of the rotational elements.A PTFE cylinder with a small hole along its axis sits around the guide pin, forming the outer bearing element, while the matching magnet fixed to the PTFE cylinder mentioned above is fixed by glue.The bearing does not rest on the guide pin, but is supported by the opposing magnets.The guide pin penetrates the PTFE cylinder to a depth of approximately 1 cm.
The variability in the tolerance between the small hole in the PTFE cylinder and the guide pin that it mates to may be a significant source of variance in the friction experienced across a set of flight mills, especially if produced by common twist drill bits.For instance, the hole in our PTFE cylinder was made with a no.70 drill bit, nominally 0.71 mm, but fit the 0.91-mm guide pin.The additional hole size is due to the fact that a drill bit cannot be fixed perfectly in the centre of the drill chuck, perfectly parallel with the drill axis or from the bit itself being bent or worn, all of which are inevitable to some degree.
The combination of PTFE material and repelling magnets seeks to minimise rotational friction.The flight arm attached to the PTFE bearing supports the weight of the insect and defines an insect's flight path.The flight arm is made of the same stainless steel tubing as the guide pin.Rotational friction on the rotating element comes from aerodynamic drag on the rotating arm, which we would expect to be primarily viscous due to the small diameter (and thus Reynolds number) of the arm, and at the interface between the PTFE and guide pin, which is likely to exhibit viscous friction due to the small air gap present.These forces must be characterised in order to estimate the As the flight arm rotates about the central axis of the flight mill, it is possible to perform a dynamic calibration to characterise the friction affecting the flight mill, depending on the types of friction present and their relative magnitude.In a dynamic calibration, an initial rotational velocity is allowed to decay under the influence of friction alone until the flight arm comes to rest.If we assume that viscous forces dominate friction, then the physical model that describes the flight arm's rotation is as follows: where I is the total mass moment of inertia of all rotating elements, B is the coefficient of friction that we wish to determine and θ is the  (Hibbeler, 2022).Finally, the angular displacement θ is calculated from kinematic analysis of the flight arm's motion, described later in this section.The solution of Equation 1 takes the following form: where t is time, b is the rate of decay with units of t À1 and a is the magnitude of motion in radians determined by the magnitude of the impulsive starting force.Given a measurement of θ t ð Þ, the variables a and b used in Equation 2 can be determined easily by curvefitting in any standard software (the MATLAB Curve-Fitting Toolbox was used here).The quality of the regression, therefore, also provides a test of the assumption of laminar flow and, in turn, the validity of showing the components of the flight mill used in the study not drawn to scale.Individual component dimensions are shown in Table 1.The Teflon bearing rotates around the guide pin, but note that the weight of the Teflon bearing does not rest on the guide pin, but on the opposing magnets.The guide pin only ensures alignment of the bearing.
T A B L E 1 Dimensions of the rotating components of the flight mill, as well as the guide pin, as shown in Figure 1.
and therefore: Thus, the only two parameters required to find the friction coefficient B are the mass moment of inertia I and the decay coefficient b.
Determining the moment of inertia of a flight mill requires careful measurement of the geometry and mass of its rotational elements (Table 1).The rotating assembly of the flight mill is separated into where m is the mass of the component, r is the component radius tion to the moment of inertia will not be a simple sum, but the procedure for including them can be found in standard texts on classical mechanics (Hibbeler, 2022).
In order to determine the value of θ t ð Þ, flight mill kinematics were captured by overhead video of the flight mill undergoing free rotation.
The video was captured with a commercial webcam (Logitech Inc. required for the analyses.Therefore, every second video frame was discarded to reduce the number of frames that had to be processed.
Twenty-five total velocity decay profiles were collected in this way.
Due to motion blur, the flight arm often appeared stretched in a fanshaped manner.In such cases, the beginning of the fan, which represents the location of the flight arm at the start of a frame exposure, was used to determine the reference position of the arm, so that location information remained evenly spaced in time regardless of any motion blur in the images.
After reaching the end of each image sequence, the software applies Equation 2 to produce a non-linear regression model with a plot of the measured angular position along with the curve fit (Figure 4).Depending on the skill and practice of the user, the total time required to perform the above analysis on a single initiation (from capturing the video data until the coefficients a and b are determined) is approximately 15 min.
Systemic and precision uncertainties were considered for the physical measurements.The systemic uncertainties, S X , were assumed to be on the order of the resolution of the measuring tools.
Meanwhile, the precision uncertainties are calculated from t-values at a 95% confidence interval as follows (Coleman & Steele, 1999): F I G U R E 4 Velocity decay of a single rotation initiation of the flight mill arm as it slows to rest.This plot compares 187 data points with the curve fit.Secondary sources of friction become significant near rest.
where X is the measurement variable, P X is the precision uncertainty, S X is the sample standard deviation and N is the number of measurements.The total uncertainty of a measurement can be taken as follows: After obtaining the total uncertainties of each parameter, a general propagation of uncertainty formula was applied to Equations 5-7 to determine the uncertainties of the moment of inertias as follows: where r is the result as a function of j measured variables X i , U Xi values are the total measurement uncertainties and U r is the result of uncertainty.For the uncertainties of the coefficient b, only precision uncertainties were considered, as shown in Equation 8.After determining the uncertainties of I and b, the uncertainty of the friction coefficient B is simple to find in the same manner as Equation 12.

RESULTS
The results from the kinematic video analysis show a semi-log plot of the velocity decay of all 25 initiations (Figure 5).The y-axis is the angular velocity at any moment in time relative to the initial angular velocity of that run.On such a scale, exponential decay appears as a straight line.The experimentally determined friction model is depicted here as a dashed black line.When each initiation deviates from this (or any) straight line, it ceases to be exponential at that point, presumably due to the higher order friction terms that we have neglected here.The curves collapse onto the ideal case in the region of the plot with relatively high velocities (Figure 5), and thus exhibit exponential decay in this region.Therefore, it can be con- to deviate from the linear model, these secondary sources of friction are comparable in magnitude to viscous friction at velocities on the order of _ θ ≈ 10 À1 rad=s, whereas many insects will fly in the range of 0.5-1 m/s, corresponding to _ θ ≈ 10 0 to 10 1 rad=s.Therefore, for the purposes of tethered insect flight, this is acceptable as the insects do not fly at speeds low enough for these secondary friction sources to be significant.The second type is the deviation along the x-axis, as each initiation begins to deviate from the ideal case at a different time.This deviation depends on the starting velocity of the flight arm (i.e., the value of the coefficient a).If a greater impulse is initially applied to the flight arm to start the rotation, then the rotation will last for a longer period of time.However, the velocity decay rate, which is the focus of this study, remains constant despite these caseto-case differences, as demonstrated by the equation for the ideal case, _ θ= _ θ 0 ¼ e bt , which excludes a completely.
The moment of inertia of the rotating assembly of the flight mill (Table 2) is I = 6900AE90 g Á mm 2 .With a 1.33% relative uncertainty, the process of obtaining the moment of inertia is unlikely to be a significant source of uncertainty when determining the friction coefficient.The highest contributor to the moment of inertia uncertainty is the flight arm, with an uncertainty of 1.37%.This is due to the greater Semi-log plot of all 25 induced rotations on the flight mill.The angular position starts to deviate from the fit as Coulomb friction becomes significant as the flight arm slows to rest.Each colour represents a separate rotation.The linear decay shared by all initiations early on validates the friction model for high velocities.This figure is also present in a previous manuscript (Hajati et al., 2023).
T A B L E 2 Moment of inertia, including uncertainty, for each flight mill component.The uncertainty of the flight arm dominates the total uncertainty, due to the lower resolution of measurement of its length.uncertainty in its length, as it could not be measured with callipers (0.5 mm accuracy rather than 0.01 mm).
The friction coefficient (Table 3) is determined using the following formula: B ¼ 1:03 Â 10 À6 N m s rad À1 , with a standard uncertainty of σ B ¼ 5:7 Â 10 À8 N m s rad À1 , or 5.6%.The majority of the uncertainty comes from the 5.4% relative uncertainty of the coefficient b.It is likely that increasing the number of initiations would improve this uncertainty.
As variation in flight among individual insects is significant, a relative uncertainty of around 5.6% in bearing friction is unlikely to be the uncertainty-limiting quantity for many studies, and it is likely acceptable for many applications.Therefore, this methodology of characterising and calibrating flight mills will help determine the flight characteristics of tethered insects and may provide a general-purpose tool for entomological studies.

DISCUSSION
Measuring in-flight forces of any flying animal is challenging, due to the difficulty in fixing them to a sensing device, and the small forces produced by insects in particular amplify these challenges.Direct interrogation of forces using classical force sensors can be accomplished with micro-electro-mechanical (MEMS) devices with resolutions on the order of σ F ¼ 10 À6 newtons (Takahashi, 2022).However, the physical size of such sensors can be on the order of the insect itself, on the order of 1-5 mm, and may require the use of a wind tunnel rather than a flight mill in order to eliminate the need for bridging electrical connections across a rotating joint.By comparison, if we imagine an insect flying at a forward velocity of 0.5 m/s on the flight mill used in this study, the uncertainty stated above, σ B ¼ 5:7 Â 10 À8 N m s rad À1 , corresponds to an uncertainty in force of approximately σ F ¼ 10 À6 newtons, comparable to that of more expensive and complex MEMS sensors.
Investigators may attempt to estimate forces by measuring the momentum surplus in the flow around the insect, or the deformation of the supporting structure for the insect, using sophisticated and often laser-based optical techniques (Dickenson & Gotz, 1996).The current method, meanwhile, can make use of already-existing equipment in a novel way to expand their measurement capabilities.While the above methodology used videography as a measurement technique, the analysis does not depend on that choice of technology.No matter how data are collected, the analysis can be replicated with either of the two the following procedures: 0. In either procedure, data are first formatted as angular position versus time, separated into individual initiations (individual examples of free-decay from an impulsive start until stationary).
The included software provides this as an output automatically for videography. (Continues) 1. Angular position is the curve fit against the function θ ¼ a 1 À e bt Þ À for each run.
1. Angular position data θ t ð Þ can be differentiated with respect to time to find _ θ.The entire time series is normalised by the initial value and converted to a log scale, log _ θ= _ θ 0 À Á .
2. The individual values found for b can be averaged to provide its estimate value, and the uncertainty of this estimated is determined using Equation 8.
2. All runs can be superimposed onto each other as if they are a single data set.
3. The parameter log _ θ= _ θ 0 À Á can be fit against a straight line, log e bt À Á ¼ bt, simultaneously against all data sets in the initial linear region.
The second procedure (fitting all data sets at once on a logarithmic scale) is likely to be more robust against individual, run-to-run noise.In this case, estimating the uncertainty of the velocity decay rate requires a different methodology from that detailed here.Procedures for determining the standard uncertainty of regression parameters can be found in many statistics textbooks (Freund et al., 2006).In either case, once data are in an appropriate format, analysis is very rapid, less than a second, in any programming environment.Although the procedure used here is time-intensive, that is an artefact of the videography approach.If flight mills are equipped with rotation sensors that output position as a function of time, the total time to calibrate a set of mills could be reduced to minutes.This would permit robust, friction-controlled comparisons between insects on different devices and eliminate (or at least quantify) uncertainty due to differences in individual device friction.
Previous authors have used flight mills as a measurement device like this before, including using the inertia of the flight mill to estimate the force of friction (Ribak et al., 2017).In that instance, the friction torque was determined as a function of velocity without a decomposition to determine the coefficient of friction.This would require computing the friction torque multiple times for different forward velocities, if, for instance, observing multiple insects flying at different speeds.Likewise, flight mill resistance has been previously characterised as a mean value over a range of velocities throughout a decay in velocity to determine flight mill inertia (Riley et al., 1997).By interrogating coefficient of friction specifically, an investigator is able to characterise force production and energy use across a wider range of time and velocity scales.If rotation is captured at sufficient temporal resolution, force generation can be measured on timescales ranging from as little as a single-digit number of wingbeats occurring in tens of milliseconds, up to thousands of rotations of the flight mill over hours or days.
Consider, for instance, a long-duration flight composed of many rotations of a flight mill.The work done by an insect against the friction of the flight mill is as follows: where dW is an element of work, F ! is the thrust produced by the insect along its flight path x ! and R is the radius of the flight arm.For a flight mill measuring distance (and thus velocity) once per rotation via, for example, a Hall effect sensor or optical gate, the integration of Equation 11 for the work done over one rotation yields the approximate solution: where W i is the work done over the ith rotation of the mill, and t i and t iÀ1 are the timestamps at which the Hall effect sensor was triggered on consecutive rotations.The total work done over the flight would then simply be as follows: Note that this is a portion of the aerodynamic work of the insect to overcome the friction of the flight mill, rather than the total work that would include the aerodynamic drag of the insect body itself.On adjacent flight mills with different coefficients of friction, this estimate of aerodynamic work may provide a means of normalising energy expenditure between apparatus, which may appear due to small manufacturing differences when making estimates of flight performance, or provide an additional metric for endurance in addition to dimensional range or endurance (i.e., in units of length or time).
Forces can also be reconstructed at much smaller timescales.For instance, in a similar study (Hajati et al., 2023), wing-tip positions were determined using calibrated high-speed video at a resolution of 5 Â 10 À4 s (Figure 6).
The average forward velocity of the insect can be determined from the wing-tip positions by applying a linear curve fit to the x-position of the wingtip, which, for this example flight, produces a value of U ¼ 0:90 m s , σ U ¼ 1:5%.Given the radius of the flight mill used in this study, this corresponded to a thrust production over these five wingbeats of T ¼ 4:03 Â 10 À5 N, σ T ¼ 5:1%.This precision permitted the correlation of thrust production to wing kinematics at a quality of R 2 ¼ 0:99, and distinguishing thrust production between sexes at a statistical confidence of P < 10 À3 in that study.Furthermore, it was found that insects flapped their wings at very high dimensionless amplitudes, much higher than the optimal range for cruising flight (Dabiri, 2009).Such high amplitudes correspond to higher force coefficients, which may be required to overcome the friction of the flight mill, such that the work to overcome the friction of the flight mill may be a good estimator of the total work.studies, as well as provide estimates for aerodynamic energy expenditure.The above technique, however, is currently labour-intensive and using video to measure angular position is highly inefficient.Efficiency was not our goal, as this was a proof of concept.The basic process described here can be conducted more rapidly by automating the determination of the decay rate, which would make the process viable for large-scale studies (i.e., calibrating dozens of individual flight mills).

CONFLICT OF INTEREST STATEMENT
The authors declare that there is no conflict of interest.
IN-FLIGHT FORCE ESTIMATION BY FLIGHT MILL CALIBRATIONforce coefficients generated by an attached insect.In this study, we characterise these frictional properties of the upper rotational assembly.
angular position of the flight arm.Here we use dot notation for derivatives, such that _ θ and € θ are the angular velocity and acceleration of the flight arm, respectively.This model has been previously used to determine the friction behaviour of a flight mill.In that instance, however, the friction torque B _ θ was left as a combined term without extracting the friction coefficient B (Ribak et al., 2017).This linear relationship between friction and velocity assumes a laminar flow both around the flight arm and in the gap between the guide pin and PTFE bearing, where the coefficient B is a device-specific value for the sum of both sources of friction.If the calibration procedure is applied to a multi-device study, these steps should be repeated for all individual flight mills in a given study, as the coefficient of friction B may change due to manufacturing tolerances.An estimate of the Reynolds number using standard air properties and the average initial velocity of the flight arm measured in this study gives a value of approximately Re ¼ 30, using the flight arm diameter as the reference length, well within the laminar region.Meanwhile, the mass moment of inertia I is obtained through careful measurements of the dimensions and mass of the flight mill components Equation 1 as a model.In addition, should Equation 2 provide a highquality solution to the decay rate of the flight arm velocity, it simultaneously provides a value for the overall coefficient of friction of the device, B. The coefficient a represents the overall magnitude of motion (that is, the number of times the arm will spin before slowing to a stop), and while it is a necessary output of direct curve-fitting, it ultimately does not have any impact on the estimate of the coefficient of friction B. The coefficient b, however, is of critical interest and its value determines both the magnitude of B and the uncertainty in that estimate σ B .This can be seen by substituting our solution for θ into Equation 1 and simplifying, which allows us to obtain an estimate for B: three components: the flight arm, the PTFE bearing and the magnet around the bearing.Each component can be approximated as a geometric primitive with a well-established moment of inertia.The flight arm, for instance, is approximated as a hollow cylinder, the PTFE bearing as a solid cylinder, and the magnet as a thick-walled hollow cylinder.The moments of inertia are taken about the central rotating axis as follows:

(
where r i and r o are inner and outer radius, respectively) and h is the component length.Thirteen measurements for each dimension were repeated for this individual flight mill, spread over different dates and times of day to provide an uncertainty for the mean value subject to minor thermal expansion due to variation in room temperature.The masses were measured with a digital balance (ProScale LCS 100) with a 0.01 g resolution, while the radii were measured with a 0.01-mm resolution calliper (Mastercraft 6 00 digital calliper).As the axis of rotation passes through the centre of each component, the total moment of inertia of the rotating assembly can be found as the simple arithmetic sum of the moment of inertia of each of the components.If there are additional rotating components that are not centred on the axis of rotation, such as pickup for a Hall effect sensor, their contribu- C920) at 1920 Â 1080 px 2 resolution at 30 Hz, from approximately 30 cm above the plane of the flight arm (Figure2), providing a resolution of approximately 0.25 mm/px (for reference, a 1 px error at the end of the flight arm corresponds to an angular error of approximately 10 À3 rad).As we were only interested in flight arm angle, no camera calibration or camera model was required.For investigators attempting to replicate this methodology, video is not the ideal way to measure angular position.Video was used in this study to minimise additional sources of inertia or friction of a sensor component mounted to the flight mill, as this work is primarily intended as a proof of concept.Counting-based sensors, including magnetic Hall effect sensors or optical gates, especially those with higher resolution such as encoders, would be well-suited for this task and would be more suitable for automation of the following analysis.We manually induced the flight mill to rotate (by hand, flicking to best approximate an impulsive start), and data extraction from the overhead video began immediately after contact.This inductionF I G U R E 2The experimental set-up for collecting video data of the free-decay of rotation.The webcam is approximately 30 cm above the plane of the flight mill and is centred on the rotational axis, providing a resolution of approximately 0.25 mm/px. of flight mill rotation was desirable for the analysis because it provided variation in the movement of the arm.Some degree of randomness was beneficial as highly repeatable initial velocity could mask higher order behaviour in our governing equation.The video was first converted into an image sequence, and then analysed in MATLAB app developed in-house, available in the Supplementary Material, to extract the flight arm position over time.In the app, the user selects the appropriate image files to analyse, and the app displays images in sequence.The user then indicates the location of the axis of rotation on the image by mouse click, and the software cycles through the image sequence.At each image frame, the user clicks on the flight arm with a mouse click, and the angle made between the origin and the flight arm is stored (Figure 3, the software is available in the Supplementary Material).The 30 Hz frame rate of the video had greater temporal resolution than what was Interface of the MATLAB application for tracking the flight mill rotation.The axis scale is inconsequential as only the angle of rotation is tracked.The FPS selection box allows the use of non-standard fps recordings without impacting time.The red crosshair is aligned with the rotational axis to set the origin.
cluded that the viscous friction model is accurate to explain tethered insect flight on a flight mill, which occurs at these higher velocities.As the induced rotations of the flight mill arm start to slow, two types of deviations from the ideal case appear.The first is the deviation along the y-axis due to the viscous friction having a smaller overall share of the force as the flight mill arm slows, and other sources of friction, such as Coulomb friction, start to have a substantial effect.Based on the velocities at which friction begins Values and uncertainties of the parameters used in the calculation of the coefficient of friction.The uncertainty of the rate of decay b is the primary source of the overall uncertainty. b Studying the flight characteristics of insects provides insight into flight dispersal processes and may aid in environmental initiatives.Flight mills represent an inexpensive, simple method to determine these flight characteristics of insects.A major limitation of flight mills is the poor characterisation of the additional frictional forces caused by the tethered flight apparatus itself.In this article, we present a procedure to characterise the friction of the rotating elements in a flight mill to an uncertainty of approximately AE5%.This uncertainty can likely be improved at the expense of additional measurement time.Characterising a flight mill using this technique to this level of accuracy takes approximately 5 hours, if position is determined by videography.The obtained friction can be used to calculate aerodynamic force coefficients such as lift C L and drag C D with high accuracy in insect flight An example trace of wing-tip position from data presented inHajati et al., (2023) by high-speed video, showing approximately five wingbeats, and separated into vertical and horizontal distance.In this figure, the x-axis is aligned with the direction of flight, while the y-axis is aligned with the axis of the flight mill.