Generalizing minimum safe operating altitudes for fixed‐wing UAVs in real‐time

This paper discusses a method of determining the minimum safe altitude of an uncrewed aerial vehicle (UAV) at any point within a designated airspace by conducting a glide reachability analysis. Recently, fixed‐wing UAVs are more regularly deployed near population centers and in extreme environments, requiring increasingly robust emergency systems and planning. The long‐ranges and adverse terrain associated with monitoring the Volcán de Fuego in Guatemala by a team from the University of Bristol (UoB) increases the likelihood that motor failure would result in the aircraft being unable to Return To Home (RTH) and impossible to retrieve. A method for delineating a boundary representing the minimum safe altitude required for the aircraft to safely glide to the airfield in the event of a motor failure was developed within MATLAB, defined by the UAV's minimum glide angle in wind. This model was subsequently compared with flight data from UoB missions around Fuego to better improve its accuracy and analyze the limitations of the missions.


| INTRODUCTION
The ever-decreasing size and the price of uncrewed aerial vehicles (UAVs) have seen an increase in versatility and deployment in nonmilitary roles (Merkert & Bushell, 2020).One such role revolutionized by the use of UAVs is field research, which often requires aircraft capable of Beyond Visual Line of Sight (BVLOS) missions.One particular area of field research already utilizing both fixed-wing and multirotor UAVs is environmental chemical sensing (Burgués & Marco, 2020).The University of Bristol (UoB) Flight Lab has been conducting long-range, high-altitude, fixed-wing UAV missions through volcanic plumes from Volcán de Fuego in Guatemala since 2017 (Schellenberg et al., 2019(Schellenberg et al., , 2020;;Wood et al., 2018).The UAV is used to collect volcanic plume samples and atmospheric measurements to help increase our understanding of volcanic ash dispersion with the ultimate aim to develop and integrate an autonomous UAV-based component into current volcano monitoring systems (U.S.G.S., n.d).UAVs provide an inexpensive and versatile chemical sensing platform capable of increasing volcano accessibility and sampling frequency to refine volcanic early warning systems to help prevent humanitarian disasters, such as the 2018 eruption which resulted in the deaths of over 60 people (Naismith et al., 2019;Pardini et al., 2019) (Figure 1).
In addition to chemical sensing, the Flight Lab has used UAVs to map the barrancas (a Spanish American word for a deep gully or canyon with steep sides; Merriam-Webster, 2022) surrounding Fuego.Understanding the path of hazardous flows, such as lava flows, lahars (an Indonesian word for volcanic mudslide), and pyroclastic flows (highly fatal avalanches of hot ash and gas) requires knowledge of the volcanic terrain.Computer modeling simulations of hazardous flows require a digital elevation model, which can be effectively derived from UAVs using structure from motion (Ireland et al., Under Review).Contrary to volcanic plume monitoring, mapping volcanic terrain requires prescribed paths at much lower altitudes, complicating optimized path planning when accounting for forced landing situations.
A forced landing is defined as any landing which was necessitated by factors beyond the aircraft's control; with the primary cause of UAV forced landings being engine failure resulting in a loss of thrust (Schneider Jr., 2004).For a UAV operating in the proximity of the Volcán de Fuego, a forced landing could result in the total loss of the aircraft.Moreover, the volcanic monitoring missions compound the likelihood of motor failure due to routinely flying through volcanic ash (F.E.M. A., 1984).Therefore it is vital to mitigate the effect of a motor failure on the safe recovery of the UAV both during preflight and real-time planning.
A method of quickly determining the minimum required altitude for a UAV gliding from any location to an airfield has been developed.The Minimum Safe Operating Altitude Model (MSOAM) defines a minimum safe altitude boundary using simplified flight paths originating from the airfield, effectively working backward to find the minimum altitude necessary for any start position.Contrary to alternative contemporary solutions for emergency path planning, the MSOAM is a general solution for an airfield as opposed to a UAV's current location.It is therefore better suited for risk reduction during mission planning and preparedness while monitoring dynamic situations with extreme wind conditions or without predetermined flight paths; notably volcanic plume interception during UoB Volcán de Fuego atmospheric research missions.The MSOAM was then compared to flight data (flight path and associated wind conditions) recorded during past UoB Volcán de Fuego missions.The work within this paper will be presented representing the UoB Ground Control Station (GCS) airfield in Guatemala, however, the MSOAM could be tailored to other scenarios and locations.

| Bristol volcanic and atmospheric research
The Volcán de Fuego is located in the south of Guatemala, with over a million inhabitants within 30 km (Venzke, 2024).Fuego is an active volcano experiencing small eruptions up to four times an hour, slightly larger eruptions every 1-2 months (Naismith et al., 2019), and occasional eruptions large enough to threaten the surrounding villages and interrupt air traffic from Guatemala's international airport located less than 50 km away.The Guatemalan Institute of Seismology, Volcanology, Meteorology, and Hydrology is monitoring Fuego to better understand its underlying activity with the ultimate aim of predicting eruptions and recommending evacuations when necessary.Remote measurements are already made using seismometers, cameras, spectrometers, and satellites; however, close-range behavior including the topography of the summit and makeup of the volcanic emissions cannot be easily measured.Fuego's crater is relatively inaccessible and while ground-based collection of ash has been undertaken (Liu et al., 2020), it is challenging to delimit particle size distributions due to the poor preservation of fine ash, meaning UAV monitoring is highly advantageous.

| The Skywalker X8 UAV
The University of Bristol Flight Lab uses the Skywalker X8 fixed-wing UAV, shown in Figure 2, as the platform for the long-range, highaltitude, BVLOS missions necessary to take the ash samples and atmospheric measurements from around Volcán de Fuego.
The X8 airframe was selected as it offers a large internal payload capacity and its high cruise speed was desirable for the proposed F I G U R E 1 Image of Volcán de Fuego from the University of Bristol Ground Control Station (Schellenberg et al., 2019).
F I G U R E 2 Image of one of the University of Bristol's Skywalker X8 uncrewed aerial vehicles used to monitor the Volcán de Fuego during the January 2022 campaign.mission ranges.Unless stated otherwise, all performance analyses throughout this paper will use the aerodynamic properties calculated by Gryte (2020) shown in Table 1.The UAVs are fitted with an autopilot system running ArduPlane version 3.7.1 (Riseborough & ArduPilot Dev Team, 2016) and a First Person View camera for manual control during takeoff, landing, and ash plume interception.
Volcanic and atmospheric instruments were added to fulfill the requirements of the mission along with a thin iron-on coating to smooth aerodynamic surfaces (Wood et al., 2018) meaning an exact zero-lift drag coefficient is unknown; the implications of which are discussed in Section 4.2.

| RELATED WORK: UAV EMERGENCY PLANNING
Over the last decade, path planning for aircraft during a loss of thrust situation (Eng, 2011), and the optimization of energy-efficient maneuvers during glide (Adler et al., 2012) have been explored.
Further works have looked at the process of predetermining contingency landing paths for a UAV optimized for predicted wind conditions (Ayhan et al., 2018;Váňa et al., 2020) as well as reachability analysis of different landing options given current flight conditions (Coombes et al., 2013).Although these methods provide solutions capable of connecting the aircraft with the airfield in an emergency, they are not optimized for field-research mission planning and monitoring in real-time.
Eng (2011) describes potential emergency path planning solutions for a light fixed-wing aircraft during an engine failure.Eng developed a system with two main algorithms: one, which uses predetermined routes that connect the aircraft to the ground, and a second which adjusts the selected route to accommodate for changing wind conditions.The system was created as a demonstration platform from which automated emergency landing procedures can be tested and developed.Eng et al. (2010) implement path planning solutions to multiple airfields and subsequently investigate and compare multiple decision-making techniques designed to determine the optimum landing location.Adler et al. (2012) effectively combine these works during their investigation into the application of using uniquely generated Dubins curves (Dubins, 1957) to create optimal path planning solutions in the event of an engine failure from the onset.The main focus of Adler's work is an on-board system capable of creating energy-efficient paths while avoiding terrain; however, landing site selection and final landing approach are not discussed.The system uses a Dijkstra algorithm to determine the most efficient string of nodes from an index of predetermined maneuvers.Given a multitude of predetermined landing sites, the UAV must be able to automatically determine the preferable path with respect to the UAV's location, heading, glide performance, and current wind conditions.Ayhan et al. (2019) use forecasted weather conditions to create "contingency paths" throughout a predetermined route.Developed for long-range, high-altitude missions, the method calculates contingency landing procedures for any point along the route in the case of an engine out, forced landing situation.Ayhan's research introduces multiple airfields and no-fly zones, which the drone must avoid while accounting for the final approach to a specified airfield.This method and approach are, in essence, a combination and continuation of Eng et al. (2010), Eng (2011), andAdler et al. (2012).The contingency paths approach is calculated before launch and therefore reliant on a predetermined flight plan and the accuracy of predicted wind conditions (Ayhan & Kwan, 2019) resulting in limited flexibility.
Similar to Ayhan's preflight contingency planning, Váňa et al.
(2020) developed a method of determining the minimum required altitude, at all specified target locations, while "guaranteeing" a fixedwing UAV is capable of returning to an airfield even in a loss of thrust scenario.The method outlined creates accurate and efficient contingency emergency flight paths optimized for minimizing the necessary altitude over terrain for surveillance missions.Additionally, it is also capable of determining a precise minimum safe altitude boundary anywhere within a few km from the airfield, including obstacle/no-fly zone avoidance, using a "roadmap" of possible trajectories.However, developed for preflight path planning of autonomous UAVs, it is suboptimal for the real-time, long-range path planning required for the Fuego missions discussed in this paper, and it is unclear whether the model is capable of accounting for wind conditions.Research deployed UAVs often require purposely flexible flight plans, meaning real-time emergency planning and risk mitigation are highly advantageous.Coombes et al. (2013) analyze the maximum possible range of an aircraft experiencing a loss of thrust, with respect to its current location and applicable atmospheric conditions to determine suitable landing locations in real-time.The maximum reach of an aircraft could be used to determine whether, and more importantly, what changes in wind conditions would jeopardize the recovery of the aircraft at its current location.This approach however does not clearly illustrate the limits of a UAV mission in relation to a GCS or airfield.The use of a reachability analysis of a gilding UAV originating from the perspective of the GCS by contrast would open the possibility of determining the UAV's minimum safe operating altitudes in relation to the GCS during all stages of a mission.
Differing from the contemporary solutions outlined above, the MSOAM is not intended for exact point-to-point path planning from the perspective of the UAV, rather it was designed to minimize risk in dynamic situations where extreme weather conditions or alternate T A B L E 1 Skywalker X8 specification of aerodynamic properties.

| UAV GLIDE CHARACTERISTICS
Motor failure on board the single-engine Skywalker X8 UAV results in a loss of thrust; therefore, the UAV will be considered a glider throughout the following analysis.The MSOAM as discussed is effectively a reachability analysis from the perspective of the airfield; contrary to the more common UAV reference frame.The product is a modified cone with the airfield at the apex, where the surface defines the minimum altitude required for the UAV to be able to glide safely back to the airfield at its optimum glide angle/speed.It will be initially calculated using the airfield's altitude, the maximum ceiling for the mission, and the determined minimum glide angle of the UAV adjusted for relative wind speeds and air density.The method described below for calculating the minimum glide angle is a modified version of the method developed by Coombes et al. (2013).

| Maximizing straight-line glide performance
The UAV's speed for minimum glide angle can be approximated using Equation (1), where K is a constant relative to the UAV's Oswald efficiency number and Aspect Ratio as outlined in Equation (2). (1) Note that the speed for minimum glide angle is a function of air density alone, assuming no change in the aircraft's weight during the mission due to the use of an electric motor.The sink rate related to the minimum glide speed can be found using Equation (3), where A and B are again functions of air density and the UAV's aerodynamic parameters.

V AV B V
A ρSC With the speed for minimum glide angle and the associated sink rate established, the minimum glide angle (γ mga ) can then be determined in Equation ( 4).The aircraft's glide ratio is subsequently calculated directly from the minimum glide angle in Equation ( 5) and acts as the gradient of the cone.
Finally a relationship between the current altitude (h) and maximum straight-line distance (d) from the airfield is established based on the lift-to-drag ratio.
With the relationship between distance from the airfield and altitude necessary to glide back established in one direction, the plot must be revolved around the airfield to create the 3D general solution within MATLAB (2022) for the maximum achievable range in every direction.Without the inclusion of wind, other atmospheric conditions, terrain, or no-fly zones at this stage, the same flight path should be plotted in every direction.
The 3D model's global coordinate system is defined with the x-axis relative to north-south, the y-axis relative to east-west, the z-axis relative to altitude, and the airfield centered at the origin.Each x/y component of the flight curve is calculated on true bearing of 0°( Due North) before being rotated around the z-axis by the UAV heading in each case using Equations ( 7) and (8) below.
The MSOAM has an altitude and UAV heading resolution of 1 m and each compass degree respectfully by default, however, increased or decreased resolutions are possible depending on the operator's requirements.Figure 3 is a basic MSOAM illustrating key elements described here: Due North relative to the airfield is denoted by the compass and the dark red glide path, with the other compass headings shown in the dark blue.The variation in color for the other bearings is for clarity only, and it will be used for all MSOAM figures.
The red points denote the boundary's border, limited by designated airspaces, maximum allowed altitude, or maximum distance from the airfield dependent on the operator's requirements.

| Glide adjusted for wind conditions
Wind significantly impacts the maximum glide slope of the X8 UAV, exacerbated by wind speeds surrounding Fuego which regularly measure in excess of the UAV's ideal speed for minimum glide angle (Schellenberg et al., 2019(Schellenberg et al., , 2020;;Wood et al., 2018).Therefore it is critical to account for wind within the MSOAM.The wind will be simplified as to only be | 1411 included as the component in the direction of the UAV, that is, it is assumed that no sideslip is present.The corrected airspeed for minimum glide angle in wind will be approximated using Coombes' implementation (Coombes et al., 2013) of the method developed by Bridges (1993).
The wind speed relative to the UAV glide heading was calculated using Equation ( 9) where the sign convention defines a tailwind as negative.
Bridges notes the solution produces an infinite series and therefore the optimum speed to fly in wind is impossible to produce analytically.However as Coombes mentions, a fourth order approximation can be used, shown in Equation ( 10).
where v ˆis a ratio of wind speed and the optimum speed for minimum glide angle as defined in Equation ( 11).Using the small-angles approximation, the resulting minimum glide angle in wind can be approximated as illustrated in Equation (12); V s in this case is related to the new speed of minimum glide angle in wind.Accurate and up-to-date wind speed and direction estimates are therefore crucial, the implications of which will be discussed further in Section 4.2.1.

| Maneuvers and associated altitude loss
As the MSOAM calculates the minimum altitude required to allow the UAV to safely Return To Home (RTH), it must account for any altitude loss associated with maneuvers during the descent.Two main maneuvers are necessary, especially if motor failure in close proximity with the airfield occurs: a turn toward the runway and a runway alignment maneuver.
Within the MSOAM, a loss of thrust emergency during the outbound journey will require a 180°turn before the straight-line glide toward the airfield could be considered.The second turn for aligning the UAV with the airfield first necessitates determining the angle between the current aircraft heading and the airfield heading (delta yaw heading).Any additional altitude required to compensate The Minimum Safe Operating Altitude Model output with an exaggerated altitude axis highlighting the key features of the visualization.This simulation was run with the airfield set at sea level and a maximum allowed altitude at 1000 ft (304.8 m).
for the maneuvers will be estimated and subsequently added as a vertical offset to the MSOAM (Figure 6).The effect of the turns is typically inconsequential to the minimum safe altitude boundary over the usual 3374.2-maltitude change during the Fuego mission, especially compounded when considering nonconstant wind conditions over the duration of the 40-min mission.However, when examining the minimum safe altitude boundary in close proximity to the airfield, the maneuvers have a significant impact.
Altitude lost as a result of a turn will be calculated by determining a trade-off between sink rate and arc length, as outlined by Coombes et al. (2013) within their reachability analysis.As the bank/roll angle of an aircraft increases, so does the optimum airspeed required to minimize the sink rate (Klein et al., 2018).An approximation of the relationship between the bank angle and the banked speed for minimum glide angle can be found (Equation 13).Subsequently using the new optimum banked speed and Equation (3) for sink rate, the relationship between bank angle and associated sink rate can also be estimated through a similar method, resulting in Equation ( 14).As arc length is a function of the turn's radius (Equation 15) and the radius can be determined through the relationship outlined by Rogers (1995) and expressed by Equation ( 16); the final relationship between the turn and subsequent altitude loss can be established, Equation ( 17).

| MINIMUM SAFE OPERATING ALTITUDE MODEL
As discussed in Section 3, a method of back calculating the minimum altitude required for the UAV to glide in a straight-line back to the airfield, has been determined.This section will focus on the realworld operation of the MSOAM including restriction to designated airspaces (Section 4.1) and a sensitivity analysis to highlight the most influential aerodynamic assumptions (Section 4.2.2).For the purposes of the following analyses and unless stated otherwise, the X8 UAV will be assumed to be at maximum take-off weight (MTOW) and air density will be adjusted with altitude in accordance with the International Standard Atmosphere definition.As mentioned, a sensitivity analysis associated with the vehicle's weight, C D 0 , and wing geometry was conducted; however, the C D 0 analysis will not be discussed in detail as estimating changes to the C D 0 while in the field would be impractical.

| Designated airspace areas
The extreme ranges and maximum operating altitudes characterized by the Fuego volcanic monitoring missions require designated airspace granted by the Guatemalan General Directorate of Civil Aeronautics.A requirement for the MSOAM is therefore defining the operational areas and confining the flight paths to this designated airspace.The MSOAM is currently capable of defining up to two operational areas, each specifiable as either a cuboidal or cylindrical shape, with individual minimum and maximum permitted altitudes.Beyond the inclusion of a singular operational area, a timeefficient method of determining the transitions between boundaries is required.At the point at which the plot was limited by a boundary, an "endpoint" is recorded (indicated by red dots in Figure 8a) before an x/y position check is performed to see if it is horizontally within the secondary operational area.If the point is determined to be horizontally within the second operational area, an altitude check is performed.The endpoint's altitude is then determined to be above or below the second operational area's minimum permitted altitude; if it is determined to be above at the transition, then the exact 3D point is used as the subsequent "startpoint" for the next minimum altitude calculation.If the endpoint is found to be below the second operational area's minimum permitted altitude, the new startpoint is translated vertically to the minimum permitted altitude.Once the startpoints have been established, each is used as the origin for another minimum safe altitude analysis; initially completing a continuation of the previously calculated endpoint/heading parings (see Figure 8b).Areas of the MSOAM within no direct straight-line path to the airfield must be filled in next.The MSOAM currently uses the intercepts between operational areas as the target location for filling in the concave geometries as visible in Figure 9.The vertical offset necessary for the turn toward the GCS is also accounted for at this location; similar to the final airfield alignment maneuver discussed in Section 3.2.Although the current flight paths are not optimized for this operational area configuration due to the higher minimum permitted altitude within the second area, flying toward the intercepts closest to the airfield creates a more robust solution (shown in Figure 15).In the case of the airspace shown in Figure 7b, the most optimal route would be flying into/through Fuego as terrain is not considered, and with the UAV gliding directly to the closest boundary interception point.

| Sensitivity analysis
As atmospheric and UAV aerodynamic properties are impossible to precisely measure, especially during operation in remote locations, a sensitivity analysis will be conducted with the aim of identifying the influence of key parameters on the MSOAM.As wind has the largest atmospheric affect on the glide performance of the UAV, its effect on the optimum glide ratio will be the sole subject of Section 4.2.1.
Section 4.2.2 will cover how altering the UAV's weight and C D 0 affects its performance, as these characteristics are the most likely affected by chemical sensing equipment and field modifications.

| Wind sensitivity
The MSOAM calculated optimum glide ratio for relative wind speeds was used to conduct a sensitivity analysis of wind speed on the UAV performance, resulting in Table 2.As the wind speeds surrounding Fuego have been measured at up to 20 m/s, it is important to have an understanding on how changes in the current wind conditions would likely impact the safe operation of the UAV.The sensitivity analysis was conducted by altering the wind speed present in the model as either a pure headwind or tailwind, and outputting the calculated optimum glide ratio.As the glide ratio is used to calculate the relationship between altitude above and distance from the GCS, it can be used to estimate changes in the average minimum safe altitude.
From the information displayed in Table 2, it is evident that wind speed and heading significantly impact the X8's optimum glide ratio, finding a 1-m/s change in wind speed could alter the glide ratio by 7%.Moreover, that 7% change in glide ratio could impact the UAV's glide range by 550 m when considering the distance between the GCS and Fuego (approximately 8 km), meaning it could be the difference between a safe recovery and total loss of the aircraft.
Accurate and real-time wind data are therefore necessary for flying at the minimum safe altitude.However exact wind data are practically an impossibility without the use of expensive Light Detection and Ranging systems (Bakhshi & Sandborn, 2020;Flesia & Korb, 1999).
Therefore the MSOAM should only be used as a guide.UAV-based wind measurement methods currently in service at Fuego will be discussed and assessed in Section 5.1.1;additional analysis of the wind conditions impact on the MSOAM will be conducted in Section 5.2.
F I G U R E 9 MSOAM plotted within the designated airspace, shown top-down as to complement the method outlined.The intersects between operational areas are used as the target for plots without a direct line of sight to the ground control center.MSOAM, Minimum Safe Operating Altitude Model.

| Aerodynamic property sensitivity
UAVs in environmental chemical sensing and other field research roles often require additional on-board sensors and field modifications; those coupled with the possibility of sustaining damage during operation, it is evident that an understanding of how altering key aerodynamic characteristics affect the calculated flight performance.
For this analysis, variations in the aircraft's weight and zero-lift drag coefficient (C D 0 ) will be compared with subsequent changes in the UAV's optimal glide ratio.
Table 3 displays how changes in the aircraft's weight alter the calculated optimum glide ratio within the MSOAM.All calculations were performed using a 5 m/s wind speed, represented as a pure headwind or tailwind.The presence of wind was necessary during this analysis as varying the vehicle's weight alone would not affect the optimum glide ratio when no wind was present.This is because glide ratio, also commonly referred to as lift-to-drag ratio (L/D) or glide slope ratio, is a characteristic of wing geometry and performance alone, meaning changes in the vehicle's weight only affect the optimum speed to fly; consequently when wind is present, the speed to fly must be satisfied at an alternate glide angle.
From the data presented in Changes in optimum glide ratio related to the variation of the aircraft's C D 0 value within the MSOAM were also investigated to assess its significance with respect to wind and weight.As previously mentioned, however, measuring exact changes in C D 0 while in the field is impractical and therefore the full sensitivity analysis will be considered outside the scope of this paper.In general, increases of C D 0 were moderately less impactful than a decrease of the same amount, and a 1 percent change in C D 0 results in roughly half a percent change in glide ratio.This indicates the user must be aware modifications could realistically impact the MSOAM over the operating ranges considered in this paper; given a 3% change in C D 0 due to the influence of externally mounted sensing equipment (Anderson Jr., 1991).
Overall, the aerodynamic sensitivity analysis suggests even small modifications are capable of significantly impacting the minimum safe altitude calculation, therefore suggesting accurate values should be used when possible.However, as the UAV's optimum glide ratio is far more sensitive to wind speed fluctuations (as discussed in the T A B L E 2 Aerodynamic performance data illustrating the affect of wind speed on the X8 UAV's optimum glide ratio.T A B L E 3 Aerodynamic performance data categorizing the effect of altering the UAV's weight on optimum glide ratio.

Note:
The baseline values from which all changes are compared, are displayed in bold.The optimum glide ratio was calculated with a 5 m/s wind speed as either a pure headwind or tailwind; as when operating in a zero wind environment, variation in the UAV's weight would not affect the optimum glide ratio.
MILNE ET AL.
| 1417 previous section) and variations in wind speed are more probable than the variation of either weight or C D 0 , consequently accurate wind models and estimations are far more significant.A 1 m/s difference in wind speed could result in the optimum glide ratio changing by over twice that of a 10% difference in weight or a 6% difference in C D 0 .

| MSOA model comparison against flight data
As discussed in the previous section, wind speed and direction data recorded during the Volcán de Fuego ash-sampling missions can be incorporated into the MSOAM and compared to the flight path to retroactively assess if motor failure during the mission could have resulted in the loss of the aircraft.Two missions will be studied within this section, the missions flown on January 13, 2022 and March 26, 2019 introduced in Section 5.1.The January 13, 2022 mission will be analyzed as comparable multirotor and radiosonde data were recorded.The March 26, 2019 mission was selected as wind speeds present during this mission were significantly higher than any of the January 2022 campaign; meaning the threat to the UAV failing to RTH was potentially most severe at that time.F I G U R E 13 Clearance between the MSOAM and the recorded flight path for the January 13, 2022 mission using the moving mean wind speed data generated in the method described in Section 5.1.1.GPS, Global Positioning System; MSOAM, Minimum Safe Operating Altitude Model.wind direction would not have endangered the mission at the wind speeds present.Figure 15 illustrates a hypothetical scenario using the wind speed data recorded on March 26, 2019 and an unfavorable southwest by south (SWbS) wind heading, i.e. with the wind heading reversed, results in a headwind as the UAV is gliding toward the airfield.Within Figure 15, the inefficient boundary generation method is also clearly visible (as discussed in Section 4.1) with discontinuities originating from the vertices of the cuboid airspace boundary.
In addition to analyzing past missions, the MSOAM can be used to estimate the likelihood that weather conditions would jeopardize proposed mission profiles.Figure 16 outlines another hypothetical scenario capable of endangering the mission again using the unfavorable wind heading SWbS and a linearly increasing wind speed from 10 m/s at the GCS to 25 m/s at 4000 m/s.Extreme caution would be necessary in this scenario during the manually controlled loiter phase as the UAV would be operating near or at the safe operating boundary.The situation is exacerbated when considering the ash plume target location since the plumes would drift downwind thus increasing the range to intercept far beyond the boundary.Fortunately, as previously mentioned the plume interception mission profile includes a highaltitude target location, meaning wind speeds in excess of 20 m/s at a southwestern heading would be required to endanger the UAV.However, significantly less powerful winds would be required to endanger missions with an alternate target location at a lower altitude.For example, mapping the barrancas surrounding Fuego would place an emphasis on minimum altitude flying in a multitude of directions, placing even emphasis on accurate, reliable, and current wind data.It is paramount to only use the MSOAM as a rough guide in its current configuration as terrain is currently not accounted for within the simulation.
In conjunction with the target location, the manually controlled final approach to the airfield must also be analyzed.During the March 26, 2019 mission the UAV throttle percentage log indicated a small burst of power was applied during the final approach.Figure 17 overlays the throttle percentage data and flight path recorded upon the final approach.It is evident the UAV slipped below the minimum safe altitude boundary and only reentered after the throttle was applied.The event indicates that if the UAV had experienced motor failure at some point during the descent, it would not have reached the airfield with this flight path.

| CONCLUSIONS AND FURTHER WORK
The novel Minimum Safe Operational Altitude Model developed in MATLAB outlined by this paper delineates the theoretical minimum limit from which a UAV could glide to a ground station in the event of a motor failure when considering wind conditions, simplified maneuvers required to return and align with the runway, and the aerodynamic properties of the aircraft.It was optimized for real-time mission monitoring during dynamic situations using a generalized reachability analysis from the perspective of the airfield; differing from previous UAV emergency path planning methods that focus on specific path planning related to the UAV's current position or a predetermined flight path.A sensitivity analysis was conducted to investigate the influence of key parameters on the accuracy of the model which found that wind had by far the most significant impact on the glide range of the UAV.For field research operations, it would Figures 4 and 5 illustrate the effect of linearly increasing wind speed with altitude, creating the upward curves and cresting effect.As the wind speed increases, the UAV is required to fly at larger glide angles as to compensate for the faster relative airspeed.As the relative headwind increases beyond the UAV's optimum speed to fly, the resulting glide angle necessary to maintain the specified airspeed approaches 90°, creating the breaking wave affect in Figure5.
the UAV's speed and sink rate for the duration of a turn established, the altitude loss can be calculated using a function of arc length.U R E 4 MSOAM plotted with a maximum radius of 8 km from the airfield showing the effect of a 195°or south by west wind linearly increasing from 10 m/s at the airfield to 20 m/s at 4000 m altitude.Parameters: Airfield Alt, 1137 m; Maximum Alt, 4000 m.MSOAM, Minimum Safe Operating Altitude Model.F I G U R E 5 MSOAM plotted with a maximum radius of 8 km from the airfield showing the effect of a 15°or north by east wind linearly increasing from 15 m/s at the airfield to 35 m/s at 4000 m altitude.Parameters: Airfield Alt, 1137 m; Maximum Alt, 4000 m.MSOAM, Minimum Safe Operating Altitude Model.
represents the relationship between the altitude lost over the duration of a turn for the UAV's aerodynamic properties, delta yaw heading, and specified bank angle.It was determined that the optimum bank angle for minimum altitude loss is 45°; further, this approximation should not be used at high bank angles (>80°).

Figure 6
Figure6is a visualization of how the necessary additional altitude to account for maneuvers calculated above is implemented into the MSOAM.As mentioned previously, exact flight paths are not computed, and as such the additional altitude is added solely as a vertical offset within the minimum safe altitude boundary.In this specific example, a 30-m radius from the airfield is examined; such close proximity means the affect of a 180°turn is significant.The makeshift airfield at the Fuego GCS used to recover the ash-sampling fixed-wing UAVs is unidirectional due to limitations imposed by terrain and surrounding vegetation.Therefore UAV's returning along a 25°heading, would require a 180°turn to align with the field.

Figure
Figure7ais the airspace requested by the UoB Flight Lab ahead of their October 2021 campaign, Figure7bis the MSOAM rendered operational areas, matching the airspace restrictions as initially requested.Although the rendered airspace does not include exclusion/no-fly zones or terrain, the MSOAM will consider all yellow boundaries inviolable.The designated airspaces are defined as follows within the MSOAM: The cuboid is aligned with the GCS and Fuego's crater, encompassing both with a 1750 m radius, from the airfield's elevation 1137 m (3730.3ft) above mean sea level (AMSL) up to 18,000 ft (5486.4m) (AMSL).The cylindrical area originates at Fuego's crater with a 5000-m radius, with a minimum permitted altitude set at 10,000 ft AMSL (3048 m) and a maximum also set to 18,000 ft AMSL (5486.4m).

F
I G U R E 6 An MSOAM within 50 m of the Fuego airfield; MSOAM cut in half highlighting how the vertical offset required to compensate for the unidirectional airfield alignment maneuver is incorporated.The airfield is orientated at an approximate heading of 25°.MSOAM, Minimum Safe Operating Altitude Model.The airspace-limited MSOAM initially calculates the minimum altitude boundary within the first operational area identically as described in Section 3.1, only limiting the plots to the horizontal geometry of the first operational area.Currently the plots are limited within cuboid geometries using the built-in MATLAB 2D convex hull function evaluating the x/y location of each point until the boundary is found.The convex hull brute force method decreases the time efficiency of the MSOAM.However, alternate methods including using the MATLAB built-in inpolygon function and computationally more efficient boundary location methods could be used to decrease computation time.Cylindrical operational areas are not evaluated using the same function however, instead comparing the cylinder's radius with the distance from the cylinder's origin to each point being evaluated; resulting in a faster evaluation.

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I G U R E 7 Comparison between the requested airspace in October 2019 and the designated airspace represented within the MSOAM.This model will be used when analyzing past mission data.(a) Airspace requested from the GDCA for the fixed-wing UAV Volcán de Fuego monitoring missions ahead of the October 2019 campaign.Note: This was not the final granted airspace geometry; a cylinder originating at Fuego's crater extending to the GCS was defined as the airspace granted to the UoB campaigns examined in this paper.(b) The airspace model used within the MSOAM, shown here in the configuration as requested by the GDCA.No-fly zones are excluded, however, the model will be limited to the inner geometry meaning the minimum permitted altitude within the cylinder operational area will be enforced.GCS, Ground Control Station; GDCA, General Directorate of Civil Aeronautics; MSOAM, Minimum Safe Operating Altitude Model; UAV, uncrewed aerial vehicle; UoB, University of Bristol.F I G U R E 8 Separation of the MSOAM airspace for visualization of key components and methods.(a) MSOAM limited to the first cuboid airspace boundary connecting the GCS to the Mouth of Fuego.(b) MSOAM completed for both designated airspaces illustrating the transition between the two zones with different minimum allowed altitudes.GCS, Ground Control Station; MSOAM, Minimum Safe Operating Altitude Model.

Flight
log data from March 2019 and multiple January 2022 UoB missions around Volcán de Fuego was analyzed to better understand the wind conditions present during the missions and validate the MSOAM.Within Section 5.1, the flight paths and mission profile will be discussed.Section 5.1.1 contains a comprehensive analysis of UAV-based wind estimation methods currently used at Fuego.Section 5.2 will combine the flight paths and estimated wind data to create an MSOAM specific to those missions.5.1 | Flight data analysisWithin this section a comprehensive analysis of a UoB X8 mission flown on March 26, 2019 in addition to a general analysis of the January 2022 UoB campaign will be conducted.Using flight paths (example shown in Figure10) and associated wind estimates, an MSOAM can be calculated and overlaid relative to the flight path thus highlighting whether the UAV was at risk of being unrecoverable due to motor failure at any point during that mission.The missions have been separated into three phases: climb, loiter, and descent.The climb phase is flown autonomously on average taking 18 min and is characterized by the switchback maneuvers used to optimally climb to the required altitude for intercepting the volcanic plumes.During the loiter phase, the UAV was manually flown to intercept the plumes, experiencing the highest variation in atmospheric conditions over the duration of the mission.Typically 8-16 min long, this phase was heavily dependent on timing Fuego's eruptions and wind conditions, both of which impacted the plume interception points.Finally the descent phase was another autonomous section taking roughly 12 min to descend from 4000 m back down to the airfield at 1137 m.The majority of the descent phase consists of a corkscrew maneuver, where the UAV circles above the GCS during the descent.An in-depth analysis of the 2019 mission will be conducted as many key elements characteristic of the fixed-wing UAV wind estimation method are accentuated.The March 2019 campaign was subject to significantly higher wind speeds than were present during the January missions, with peak wind speeds measured at 20 m/s.5.1.1 | Accurate and real-time estimated wind dataThe X8 UAV on-board Flight Control Unit runs Ardupilot EKF2 Estimation software (a 24 State Extended Kalman Filter) capable of calculating wind speed and direction using the difference between measured airspeed and North, East, Down Velocity measurements.Analysis of data from six previous missions was conducted to determine the feasibility of utilizing fixed-wing UAV-derived wind speed estimates to create a real-time safe operating model and postmission analysis utilizing averaged wind speed profiles.The analysis indicates that further refinement of the current fixed-wing wind speed estimation is required as the data exhibits significant variance and discontinuities present in the data which can be primarily attributed to the UAV maneuvering.Additionally, three other factors were identified: atmospheric changes over time, gusts, and the effect of the geographical features on the local atmospheric conditions(Corby et al., 1960), specifically the peak of Volcán de Fuego (3763 m).F I G U R E 10 Example GPS flight path recording by the X8 UAV during the March 26, 2019 mission.The phases of the flight, climb, descent, and loiter (above 3800 m) are color coded appropriately.All fixed-wing flight data assessed within this paper followed a similar flight path.GCS, Ground Control Station; GPS, Global Positioning System; UAV, uncrewed aerial vehicle.

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Figure11to best mitigate the affect of estimation errors and changes to atmospheric conditions as previously mentioned.

Figures
Figures 13 and 14 illustrate that without the consideration of terrain, the average wind conditions present at the time of the missions were not a concern regarding the safe return of the UAV in relation to ash collection.The relatively short mission range compared to the high altitude differential could still facilitate UAVs with poor optimum glide ratios to safely RTH, even in the event of motor failure during the loiter phase.During the March 26, 2019 mission the GCS was observed to be located directly downwind from the volcano meaning the high wind speeds present were not a concern to the mission as visible in Figure14.Additionally, with this favorable north east by north (NEbN) wind heading, the UAV would still be capable of gliding safely to the GCS regardless of gusts or a realistic outright increase on average wind speed.More significantly, even large changes in the

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I G U R E 14 Clearance between the MSOAM and the recorded GPS flight path data for the March 26, 2019 mission using the moving mean wind speed data shown in Figure 11a.GPS, Global Positioning System; MSOAM, Minimum Safe Operating Altitude Model.F I G U R E 15 Hypothetical scenario showing the clearance between the MSOAM and the recorded GPS flight path data for the March 26, 2019 mission using the associated moving mean wind speed data but with an unfavorable southwest by south wind heading.This figure illustrates even the relatively high wind speeds recorded during the mission would not have endangered the mission originating from any heading.GPS, Global Positioning System; MSOAM, Minimum Safe Operating Altitude Model.F I G U R E 16 Hypothetical scenario showing the clearance between the MSOAM and the recorded GPS flight path data for the March 26, 2019 mission using an unfavorable wind heading and linearly increasing wind speed with altitude from 10 m/s at the GCS to 25 m/s at 4000 m altitude.From this figure it can be concluded extreme wind speeds at an approximate southwest by south heading are required at Feugo for the ash plume sensing missions to be in jeopardy.GCS, Ground Control Station; GPS, Global Positioning System; MSOAM, Minimum Safe Operating Altitude Model.therefore be advised that either a multirotor UAV or balloonmounted radiosonde be launched ahead of the mission to estimate initial wind conditions in conjunction with fixed-wing estimated wind speed data for real-time analysis.The model's short runtime facilitates the incorporation of new data into the model as it becomes available, amalgamating new data with preflight measurements from other sources or generic/simulated data to best mitigate changing conditions.The MSOAM was compared with flight data from UoB Volcán de Fuego monitoring missions within Section 5, illustrating the model's functionality as a postmission analysis tool and outlining its operation in preflight and real-time applications.The MSOAM could also be adapted for use in other UAV-based research, including offsite analysis of proposed missions.Future work will focus on improvements to the UAV flight mechanics, including consideration of the UAV's current speed, momentum, and crosswind flight performance, in addition to the inclusion of no-fly zones and terrain within the MSAOM.

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I G U R E 17 The MSOAM boundary represents the minimum altitude necessary to reach the airfield in engine failure emergencies, and it is visible in this figure that the UAV breached this minimum safe altitude.The overlaid throttle data from the mission show the pilot applied over 40% throttle to regain sufficient altitude to reach the airfield.(a) Overview of the final approach flight path overlaid with throttle data during the March 26, 2019 mission and associated MSAOM boundary generated given the wind data available from the mission.(b) Side profile of the final approach flight path overlaid with throttle data during the March 26, 2019 mission and associated MSOAM boundary illustrating the altitude deficit of the UAV during this approach.MSOAM, Minimum Safe Operating Altitude Model; UAV, uncrewed aerial vehicle.