Abstract

Solar-powered unmanned aerial vehicles (UAVs) carry no fuel, meaning their endurance is governed by a balancing act crafted between the energy harvested from sunlight and the energy consumed throughout flight, rather than conventional fuel capacity constraints. Over multi-day missions, this balance becomes hard to predict, as solar harvesting depends on the Sun’s position relative to the UAV whilst energy consumption depends on the aerodynamic forces required to sustain flight. Both of these are also affected by flight conditions and cruise altitudes, meaning a complex optimisation problem emerges. Many simplified models treat the Sun as stationary, an assumption only valid for short missions over small timeframes and distances. In this paper, solar harvesting will be modelled through a fixed panel and gimballed panel approach, where a gimballed panel traces the Sun’s position relative to the UAV and points the panel at the optimal orientation for maximum irradiance.

Overall, this paper develops a model that investigates the energy balance aforementioned, using the example of a transatlantic crossing from London to New York. There are three overarching MATLAB models that are integrated into this energy balance: great-circle navigation, aerodynamic power consumption, and solar energy harvesting. The flight parameters have been derived from steady-level flight mechanics, standardised NACA tables, photovoltaic conversion data and solar geometry. 

Having completed the simulations, it can be seen that an idealised gimballed solar panel increases total harvested energy substantially, by 62%, but much of the additional energy that it harvests cannot be stored, since the battery charge is already full during daylight hours, where there is peak harvesting. This is shown as the minimum state-of-charge only increases by 5% for a gimballed panel, starkly lower than the 62% rise in energy harvesting aforementioned. As a result, it can be said that endurance in this context cannot be governed solely by aerodynamic efficiency or solar collection gains, but by the capacity of the battery to carry energy across extended periods of insufficient insolation.

Future work on this issue should therefore treat battery capacity as a design variable to be considered alongside altitude and cruise conditions, whilst also relaxing assumptions discussed throughout. This concept has potential real-world applications in wildfire monitoring, surveillance/law enforcement, shipping, and ocean monitoring.

1. Introduction

1.1 Motivation

Solar-powered unmanned aerial vehicles (UAVs) offer the ability of extremely long endurance without the constraints provided by conventional fuel. Their endurance is governed simply by the balance and optimisation between the electrical energy harvested by the sun, and the energy consumption by the UAV in flight. As a result, solar flight is attractive for a multitude of applications that require persistent operation, over large and remote areas. Such examples include maritime search and rescue, wildfire detection and atmospheric surveying in remote areas. This concept has been demonstrated experimentally before, with AtlantikSolar achieving an 81-hour continuous flight.(Oettershagen, et al., A solar-powered hand-launchable UAV for low-altitude multi-day continuous flight, 2015)(Oettershagen, et al., Design of small hand-launched solar-powered UAVs: From concept study to a multi-day world endurance record flight, 2017) The concept explored in this paper also explores the idea of a moveable (on the pitch and roll axis) solar panel on the UAV, allowing it to maximise the electrical energy it harvests from the sun, a concept yet to be quantified by existing studies. The primary reason this has not been integrated into mainstream UAV technology is due to the aerodynamic and mass penalties of such a gimbal system, which are noted as limitations throughout.

In general, the primary difficulty with a solar-powered UAV tends to be that the energy balance of the UAV is directly proportional to the aircraft’s flight conditions and environmental. Solar collection also depends on the position of the sun relative to the aircraft (with a non-gimballed system), which varies with latitude, time of day, and season. Furthermore, aircraft energy consumption varies on the aerodynamic forces required to maintain steady-level flight in a cruise state. These forces vary significantly with changes in airspeed, air density, and lift coefficient, with air density itself varying with altitude. Consequently, due to the balancing act of these two factors, one cannot simply consider aerodynamic or solar conditions alone, creating a complex problem.

Multiple attempts have been made to simplify or solve this problem, with some choosing to limit mission distance and time as being short relative to the sun’s position, allowing it to be treated as stationary. (Klesh & Kabamba, 2009)Others provide validated airframes and power-collection models but lack investigation into cruise-altitude or even route optimisation for a multi-day mission. (Oettershagen, et al., A solar-powered hand-launchable UAV for low-altitude multi-day continuous flight, 2015)The trade-off between altitude, flight conditions, and battery margin over a multi-day mission therefore remains unestablished, and this paper attempts to address this gap.

2. Preliminaries

2.1 Steady Level Flight

The aircraft is modelled in steady, level cruise. This is primarily due to time constraints and aerodynamical complexities involved in take-off, climb, descent and landing phases, which could further complicate the solar harvesting model mentioned later on. The diagram below contains four forces acting in the aircraft’s x-z plane: lift perpendicular to the flight path, drag opposing the direction of motion, thrust along the flight path, and weight acting vertically downwards.

Figure 1 – Forces Acting on Aircraft in Steady-Level Flight

Steady level flight involves no acceleration, so these forces balance in pairs:

Together, these two conditions establish the relationship between airspeed, lift coefficient and altitude: once aircraft parameters are established, the air density at a given altitude details the airspeed required at a chosen lift coefficient. (Fidowski, Atkins, & Powell, 2019)(Anderson, 1999)

The equations for lift and drag forces are given by Equation [2] below:

Here,  V is true airspeed, ρ air density,  S is the wing reference area over which airflow occurs, and C_D   and C_L  are drag and lift coefficients. The quantity 1/2 ρV²  therefore describes the dynamic pressure. (Fidowski, Atkins, & Powell, 2019)

If we combine Equation [2] with the lift-weight balance condition in Equation [1], we get the following, Equation [3], the airspeed required to sustain a specified lift coefficient at a particular altitude:

The aerodynamic coefficients are derived from two-dimensional NACA 4415 section data. (Abbott & von Doenhoff, 1959)(Airfoil Tools, n.d.) NACA 4415 was selected due to its combination of lift-to-drag performance and sufficient thickness to accommodate both solar-cell installation and endurance structural requirements. We can calculate the Reynold’s Number of the aerofoil using Equation [4] below:

At this Reynolds number the section lift curve is markedly non-linear: the local slope falls from approximately 0.21 per degree near zero incidence to 0.06 per degree at eight degrees, a consequence of a laminar separation bubble whose extent varies with incidence. A single linear fit is therefore not representative, and the tabulated section data are used directly rather than through a lift-curve slope approximation. The drag polar is obtained by fitting the drag coefficient against the square of the lift coefficient over the same data, which does not require the lift curve to be linear. (Airfoil Tools, n.d.)(Drela, 1989)                                     

The two-dimensional data are then corrected for a finite wing. A real wing sheds tip vortices, which induce a downwash and generate induced drag proportional to the square of the lift coefficient. The downwash also reduces the effective angle of attack seen by the section, so the geometric angle of attack required to achieve a given lift coefficient exceeds the two-dimensional value by the induced angle. (Anderson, 1999)

InFor this model, there are two relevant aerodynamic operating points. The first is maximum lift-to-drag ratio, which can be calculated by differentiating   with respect to   and setting the derivative equal to zero. (Fidowski, Atkins, & Powell, 2019) This can be seen below in Eq. [7]. 

This condition occurs when parasitic drag and induced drag are equal. This is at  C_L = 0.593,  kC²_L = 0.00861, matching C_D0  exactly. The condition also occurs at minimum power, given by Eq. [8]:

Here, at the minimum power condition we can see that induced drag is three times the parasitic drag. This is because power is the product of the drag and airspeed, so the additional velocity dependence causes the optimum condition to be shifted to a higher lift coefficient.

The difference between these operating conditions matters for a long-duration solar flight, as maximum L/D ratio would minimise drag and therefore the energy required over a fixed distance. Since that energy is the product of the drag and the distance flown, it corresponds to a maximum range condition. On the other hand, minimum power minimises the electrical demand at each instant and therefore corresponds to a maximum endurance condition. 

 Figure 2 demonstrates the comparison between maximum L/D ratio and minimum power utilising the flight parameters of our aircraft that can be found in the Appendix.

2.2 Standard Atmospheric Conditions

Air density will vary significantly across the altitude range considered. A function of air density as altitude varies can be obtained, combining the hydrostatic relationships and ideal gas laws with a linear temperature profile in the troposphere. This is given in Eq. [9] and [10] below:

The constants in the equations above are:

(International Organization for Standardization, 1975)

This model is valid up to 11km altitude. This function is utilised to calculate the airspeed required to generate lift at different altitudes, as when density falls, the aircraft must fly faster to generate the same lift at a given lift coefficient, changing the power required.

2.3 Propulsion

For a propellor-driven aircraft, electrical power is the most useful measure to determine energy consumption. This is because the battery energy balance depends on the electrical consumption of the propulsion system. Eq. [11] gives the propulsion model, combining aerodynamic power requirements with the propulsion efficiency n_prop  and the constant avionics load P_av . (Fidowski, Atkins, & Powell, 2019)

2.4 Solar Position

The solar power available to harvest by the aircraft is set by the irradiance incidence on the illuminated panel area, and the conversion efficiency of the photovoltaic system. Irradiance will vary continuously with geographic position, time of day, season, and altitude, so solar harvesting must be evaluated along the trajectory of its transatlantic route, rather than being treated as a constant power source.

The Sun’s position relative to the aircraft follows from the solar declination angle, the aircraft latitude, and the solar hour angle. (Duffie & Beckman, 2013)(Cooper, 1969) For a day of year  , the declination can be approximated through the following equation:

The hour angle follows from local solar time, with H = 0  at solar noon:

The solar elevation above the local horizontal can therefore be given through the spherical law of cosines, applied to the triangle formed by the pole, aircraft zenith, and the Sun:

Here,   is the aircraft latitude. Eq. [14] is the same as computing the great-circle central angle between the aircraft and the subsolar point, since the hour angle is the longitude difference between them.

2.5 Atmospheric Attenuation

The irradiance reaching the aircraft is also reduced by absorption and scattering across the atmospheric path, and as the Sun sits lower throughout the day, the longer that atmospheric path becomes. The relative optical air mass can be approximated using the Kasten-Young formulation, which accounts for atmospheric curvature, and remains finite at the horizon. (Kasten & Young, 1989)

Flying at altitude also reduces the mass of atmosphere above the aircraft, which can be accounted for by scaling the air mass by the local pressure ratio from the standard atmosphere model described in Section 2.2. The direct normal irradiance then can be placed in an empirical clear-sky attenuation model:

Here, I₀ = 1361 Wm^-2  is the solar constant, and the coefficient 0.7 corresponds to the fraction transmitted at unit air mass. (Meinel & Meinel, 1976) The exponent 0.678 is an empirical fit accounting for non-uniformity in the distinct atmospheric layers. This model captures both the reduction in available energy as the Sun approaches the horizon and the increase in irradiance at higher cruise altitudes. Diffused and ground-reflected components of irradiance have been assumed to be negligible as part of this investigation.

  Figure 3 demonstrates the effects of the differing insolation models.

2.6 Photovoltaic Conversion

The electrical power generated from an illuminated panel is:

Where A_PV is the photovoltaic cell area, η_PV  the module conversion efficiency,  η_PMMT the efficiency of the maximum-power-point tracking electronics, and   the angle between the solar direction and the panel normal. For the aircraft considered in this paper, A_PV = 1.7223 m² , as it has been taken as equal to the wing planform area. Furthermore, η_PV = .2 and η_PMMT = .95. The conversion process is entirely independent of flight conditions, so variation in harvested power arises entirely from solar geometry and atmospheric attenuation. (Duffie & Beckman, 2013)(Oettershagen, et al., A solar-powered hand-launchable UAV for low-altitude multi-day continuous flight, 2015)

3. Methods

The following sections detail the mathematics behind MATLAB models utilised in this study. Access to these models can be found through the GitHub repository linked here:https://github.com/rohaannarula/solar-uav-energy-model

3.1 Panel Orientation & Solar Collection

The incidence angle,  ɸ introduced in Eq. [17] follows from the relative orientation of the Sun and the solar panel. Both directions are represented as unit vectors in a local North-East-ηPV (NED) frame. (Fidowski, Atkins, & Powell, 2019) The solar direction is:

Here, a is the solar azimuth, measured clockwise from North, and θs is the solar elevation. The negative third component is due to the downwards axis being positive, so the Sun above the horizon has a negative vertical component. For a panel with roll angle ɸp and pitch angle θp , with yaw fixed at zero, the outward normal is:

Because both of these vectors have unit length, their dot product gives the cosine of the incidence angle directly. The result is fixed above zero, since a negative value implies the Sun lies behind the panel, and no energy is collected:

Two configurations will be evaluated. The first is a flat panel, representing the roughly horizontal photovoltaic surface of an aircraft in steady-level cruise. At a maximum lift-to-drag condition, the required lift coefficient of 0.593 is established using an average cruise angle of 1.11°. This is close to the horizontal, making a flat panel assumption reasonable. Setting both orientation angles to zero reduces Eq. [20] to exactly the sine of the solar elevation:

The second configuration is an idealised gimballed panel; tracing the Sun’s position. The required orientation is obtained by equating the panel normal to the solar direction, which yields three separate component equations into two unknowns. The East component contains the roll angle and yields the pitch by dividing the North component by the Down component, which eliminates the roll term.

Two angles are enough for the three equations because the solar direction is a unit vector, so only two of its components are independent of each other. The yaw angle does not appear, as rotating the panel about its own axis does not alter the theoretical solar panel surface presented to the Sun.

In both configurations, the harvesting of solar energy is reduced significantly when solar elevation is below 5º , at which point the atmospheric path length is long enough that available irradiance becomes negligible. The gimballed panel can be treated as an idealistic case, rather than a realisable configuration, due to multiple assumptions required, such as the requirement for near vertical pitch near sunrise and sunset.

3.2 Great-Circle Route

The aircraft must follow the shortest possible path between London Heathrow and John F. Kennedy International Aiport on a spherical Earth, which is a great-circle arc. For endpoint co-ordinates with longitude difference Δƛ , the central angle subtended at the Earth’s centre is as follows:

As a result, the great circle distance and initial heading can be calculated, where   is the radius of the Earth:

A four-quadrant arctan2 function can be used throughout, in place of a simple arctan one, since dividing the sine and cosine components would discard their individual signs and therefore lose the directional element of the heading.

As great-circle routes do not maintain constant heading, the aircraft heading will change continuously throughout crossing. Intermediate vectors can be generated through spherical linear interpolation, where   is the fractional distance along the route, and   and   are unit position vectors:

 The result can then be converted back into latitude and longitude for the solar and atmospheric calculations. The route is decomposed into 2000 equally spaced points and is plotted below in Figure 4.

3.3 Cruise State & Energy Balance

For each cruise altitude and flight condition, the energy balance model is calculated independently. Utilising parameters obtained from Section 2; we can calculate the required electrical power and flight time:

Where P_elec is the required electrical power for a given altitude and flight condition.

We can calculate solar power required using the trapezium rule, as solar power harvested varies with both time and position, and is continuously varying:

The battery can be represented as an energy reservoir with limited capacity, updated according to the net electrical power balance:

Where E_{B max} = 850 Wh = 3.06MJ  and the battery is initially fully charged. (Oettershagen, et al., A solar-powered hand-launchable UAV for low-altitude multi-day continuous flight, 2015) We can therefore calculate the state of charge, and the aircraft’s minimum state of charge over the flight:

The minimum state of charge is utilised as the primary measure of mission feasibility, as it is more informative than comparing net energy expenditure. This is because a positive net balance will not guarantee that sufficient energy is available throughout the flight.

The simulation of state of charge will be repeated for each altitude, with both cruise conditions and panel configurations. I will consider a minimum SOC requirement of 30% to consider feasibility, as assumptions discussed later diminish true viability of such a large margin.

4. Results

4.1 Solar Collection 

The great-circle route from London Heathrow to JFK New York spans 5540km. If the aircraft departs at 12.00 UTC on day 172 of the year, close to June solstice, the crossing at an altitude of 3000m encompasses 5 whole day-night cycles.

Figure 5 compares solar power generated by the flat and idealised gimballed configurations. Peak values appear similar, approximately 329W when gimballed against 291W, but the gimballed curve is broader, unlike the narrow daily peak of the flat configuration. Integrated across the crossing, at maximum L/D ratio, the two configurations collect 77.37MJ and 48.17MJ respectively, so continuous gimballed tracking yields 62% more energy harvested. The differences arise at low solar elevation, where a flat panel projects only 50% of the direct beam at 30 degrees and 17% at 10 degrees, compounding the atmospheric attenuation already present. This is represented by Figure 5.

4.2 Battery State-of-Charge

  Figure 6 below shows the battery state of charge over the same crossing. The battery reaches full capacity for several hours each day, meaning surplus energy harvested cannot be stored given current battery size constraints. Approximately 26.1 MJ is discarded across the maximum-L/D mission, exceeding the 22.02 MJ required to complete the crossing. Storage rather than collection is therefore the binding constraint, and the additional energy gathered by the gimballed panel does not translate proportionally into endurance. The minimum state of charge is a more useful measure of feasibility than net energy balance, as explained in section 3.3.

4.3 Panel Orientation 

   According to simulation, the ideal orientation requires panel roll to sweep between approximately ±60° each day and pitch to reach nearly −80° near sunrise and sunset, a range no practical mechanism could achieve, reinforcing the treatment of the gimballed case as an upper bound. The photovoltaic panel parameters can be found in the Appendix. 

4.3 Effect of Cruise Altitude and Flight Condition

Table 1 above summarises the design variables. The energy required falls only 4.3% across the entire altitude range, because drag at fixed   is independent of air density. On the other hand, battery margin falls much more sharply, from 0.437 to 0.102 under maximum L/D ratio, since greater altitudes raises power required from 43.3 to 71.4 W while night duration is unchanged. The 30% SOC requirement is only met to approximately 5 km. In terms of flight condition chosen; maximum L/D ratio consumes 15 percent less energy at every altitude, while minimum power leaves a larger reserve because it draws less overnight. This disparity grows with altitude, and at 6000m maximum L/D fails the margin requirement at 0.275 while minimum power satisfies it at 0.374. However, maximum L/D has immense benefits over minimum power in terms of practicality. The flight time of a maximum L/D condition cruise at 3000m is 39hr longer, impractical for real-world applications. Furthermore, it can be seen that a gimballed solar panel provides 62% more energy harvested at 3000m (maximum L/D), yet its minimum SOC is only 5% greater. This proves the constraint in this model is battery capacity, as most of the extra energy harvested has been discarded before it can be used, as there is simply not the storage available.

5. Assumptions & Evaluation

The performance of a multi-day crossing is governed by the interactions taking place between aerodynamics, solar geometry and finite storage rather than a specific singular parameter. The distinction between collected and usable energy is the most indicative finding. As 26.1 MJ of excess is unused against 22.02 MJ consumed, increasing collection alone offers diminishing returns unless storage is increased or surplus energy is otherwise employed. Changes in altitude selection is consequently better treated as a storage problem than an aerodynamic or harvesting one.

Several assumptions limit the quantitative accuracy of the study. The aircraft maintains steady level cruise in still air at constant mass, with launch, climb and descent neglected. The aerodynamic model uses a NACA 4415 wing polar rather than a complete aircraft polar, omitting fuselage and tail contributions; the resulting maximum L/D of 34.4 is approximately 13% more optimistic than the value inferred from published AtlantikSolar flight data. (Oettershagen, et al., A solar-powered hand-launchable UAV for low-altitude multi-day continuous flight, 2015) (Selig, Guglielmo, Broeren, & Giguere, 1995) Moreover, the solar model assumes clear-sky direct radiation, neglecting diffuse and reflected components, and neglects the equation of time (the ‘mean sun’ versus true sun position throughout elliptical orbit). Furthermore, the use of an idealised gimballed panel should be read as an upper bound, since actuator mass, angular limits and airframe shadowing are not represented.(Cooper, 1969)Finally, it is important to note that wind, cloud and other weather variations are not represented, meaning that the calculated 30% battery state-of-charge margin is likely to diminish in real-world applications.

6. Conclusion

Endurance solar flight is limited by the energy balance detailed throughout the paper, and this study’s purpose was to determine the feasibility of a such a concept of near-perpetual flight, and in what conditions it would be possible. The paper’s approach has been to utilise pre-established components where possible, in order to reduce possible error from assumptions and to provide realistic aerodynamic and photovoltaic parameters. It also means that a further exploration of this issue could lead to design models of a bespoke aircraft design, optimised for a solar UAV.

Maximum Lift/Drag ratio is the cruise condition that allows for the lowest energy requirements whilst still fulfilling the 30% SOC requirement, with 22.02 MJ over 123.4hrs at a 3000m altitude. This is measured as the optimum conditions for such a crossing. Increasing altitude reduces the flight time, and atmospheric attenuation too, yet battery margin also decreases due to an increase in power requirements.

The use of an idealised gimballed solar panel increases solar harvesting by 62%, yet most of this amount is not usable due to the battery being full at these daytime hours. We can therefore label storage capacity as a limiting constraint, yet an increase in battery capacity could come with additional complications such as mass changes etc. For applications that require persistent operation over inaccessible areas, such as maritime rescue, marine life monitoring, or wildlife monitoring, this concept could be deployed to improve real-world applications’ efficiency.

7. Bibliography

Abbott, I. H., & von Doenhoff, A. E. (1959). Theory of wing sections: Including a summary of airfoil data. Dover Publications.

Airfoil Tools. (n.d.). NACA 4415 (naca4415-il) Xfoil prediction polar at RE=200,000, Ncrit=9. Retrieved from http://airfoiltools.com/polar/details?polar=xf-naca4415-il-200000

Anderson, J. D. (1999). Aircraft performance and design. McGraw-Hill.

Cooper, P. I. (1969). The absorption of radiation in solar stills. Solar Energy, 12(3), 333-346. doi:10.1016/0038-092X(69)90047-4

Drela, M. (1989). XFOIL: An analysis and design system for low Reynolds number airfoils. In T. J. Mueller (Ed.), Low Reynolds number aerodynamics (pp. 1-12). Springer. doi:10.1007/978-3-642-84010-4_1

Duffie, J. A., & Beckman, W. A. (2013). Solar engineering of thermal processes (4th ed.). John Wiley and Sons.

Fidowski, K., Atkins, E., & Powell, K. (2019). Introduction to aerospace engineering: Aero 201 course notes, Fall 2019. Ann Arbor, MI: University of Michigan.

International Organization for Standardization. (1975). Standard atmosphere (ISO 2533:1975). Geneva: ISO.

Kasten, F., & Young, A. T. (1989). Revised optical air mass tables and approximation formula. Applied Optics, 28(22), 4735-4738. doi:10.1364/AO.28.004735

Klesh, A. T., & Kabamba, P. T. (2009). Solar-powered aircraft: Energy-optimal path planning and perpetual endurance. Journal of Guidance, Control, and Dynamics, 32(4), 1320-1329. doi:10.2514/1.40139

Meinel, A. B., & Meinel, M. P. (1976). Applied solar energy: An introduction. Addison-Wesley.

Oettershagen, P., Melzer, A., Mantel, T., Rudin, K., Lotz, R., Siebenmann, D., . . . Siegwart, R. (2015). A solar-powered hand-launchable UAV for low-altitude multi-day continuous flight. 2015 IEEE International Conference on Robotics and Automation (ICRA), (pp. 3986-3993). doi:10.1109/ICRA.2015.7139756

Oettershagen, P., Melzer, A., Mantel, T., Rudin, K., Stastny, T., Wawrzacz, B., . . . Siegwart, R. (2017). Design of small hand-launched solar-powered UAVs: From concept study to a multi-day world endurance record flight. Journal of Field Robotics, 34(7), 1352-1377. doi:10.1002/rob.21717

Selig, M. S., Guglielmo, J. J., Broeren, A. P., & Giguere, P. (1995). Summary of low-speed airfoil data, Volume 1. SoarTech Publications.

8. Appendix

8.1 Model Parameters

All model parameters are sourced from the following sources:

(Airfoil Tools, n.d.)(Drela, 1989)(Fidowski, Atkins, & Powell, 2019)(Oettershagen, et al., A solar-powered hand-launchable UAV for low-altitude multi-day continuous flight, 2015)(International Organization for Standardization, 1975)(Selig, Guglielmo, Broeren, & Giguere, 1995)(Oettershagen, et al., Design of small hand-launched solar-powered UAVs: From concept study to a multi-day world endurance record flight, 2017)(Kasten & Young, 1989)

8.1.1 Airframe and Propulsion

8.1.2 Aerodynamic Coefficients, NACA 4415 at Re = 200,000

8.1.3 Solar & Electrical Power

8.1.4 Atmosphere & Mission

About the author

Rohaan Narula

Rohaan is a student at King’s College School, Wimbledon in the United Kingdom, with a strong passion for engineering, specifically its applications to environmental concerns. Interweaving aeronautical, mechanical and environmental engineering throughout his research serves as a method of balancing both ethical and efficiency concerns whilst not losing sight of the endless pursuit of optimisation in these fields. Outside of the academic world, he is a keen cricketer and guitarist.

The post Modelling Energy Balance for a Solar-Powered Transatlantic UAV Route appeared first on Exploratio Journal.

Efficient Methods for Improving Space Science Education

The space industry began in the late 1950s during the Cold War as another method of non-lethal confrontation between the US and the USSR. NASA has and continues to lead the industry in exploration and innovation, all fueled by government policy (Launius, 2000, p. 23). In the past, space exploration directly fueled US interests, which garnered public support for the industry (Launius, 2000, p. 26). However, reasonings for space exploration have changed throughout the decades, and currently space exploration has benefits that aren’t directly pushing towards US goals. Another recent development in the space industry is the growth of the private sector, with companies in the US and across the world positioning themselves to grow in the industry and make a name for themselves (Robinson & Mazzucato, 2019, p. 940). There have also been recent examples of the public and private sectors partnering for the sake of research and exploration, as seen with a recent collaboration of NASA and UC Berkeley (Rausser et al., 2023, p. 4). However, the space industry remains mostly government led in the US and is subject to the same reliance on public opinion as many other government led industries.

Literature Review

Public opinion and space policy

Since the space industry is a government led industry, it is important to recognize that it relies heavily on public opinion. The relationship between public policy and public opinion has been hard to describe in the past for social scientists, with the common phrasing being that there is a linkage between the two (Steinberg, 2011, p. 240). However, after reviewing numerous different historical public policies and the public opinions on each topic, it is shown that public opinion affects public policy a majority of the time and is dependent on many factors (Burstein, 2003, pp. 32-35). One such factor that affects public policy is issue salience, which is the relative importance an issue has to overall government procedure. The idea of issue salience as a factor in government policy relating to public opinion is more prevalent when understanding the idea of electoral accountability; the idea that elected officials won’t stray from their voters’ public opinion. Electoral accountability gauges how elected officials rely on their voters’ opinions and explains how public opinion is a driving force in government (Shapiro, 2011, pp. 984-986). In the case of space policy, an issue of low salience, public officials are elected for other more prominent issues, and as a result, space policy will take a minimal role in the driving force of electoral accountability.

The biggest driving factor limiting positive public opinion comes from lack of education of the general public in relation to space science and its benefits (Bensaude-Vincent, 2001, p. 107). It is a myth that US spaceflight has been constantly supported by public opinion, even throughout the 1960s at the height of the space race (Whitman Cobb, 2015, p. 13). Data shows that the general public supports spaceflight in pursuit of state goals and achievement rather than just space exploration for the sake of exploration, indicating education of the goals and possibilities for space exploration is lacking (Launius, 2003, p. 169). This lack of education relates to another aspect of public policy in economics, which is a more political concept, but is still limited by the general public’s lack of education in the field (Walstad, 1997, p. 202).

Educating America’s youth

The most effective way to reach large numbers of children and give them proper education of space science would be through the public education system. There have been many numerous expansion efforts by NASA and other government programs to push space science in k-12 schools to further this education that is sorely lacking in the US (MacLeish et al., 2012, p. 191). However, there are numerous faults in the public education system which would make pushing space science difficult for a large organization such as NASA.

The alternative to formal education through the school system would be informal education through social media. There have been numerous attention grabbing aspects of space science that garner more attention in social media (Hwong et al., 2017, p. 481). Additionally, social media has a larger outreach to education for the less fortunate, while public education is not the same everywhere in the US (Greenhow & Lewin, 2015, p. 8). Connecting this form of informal education and the public school system would be beneficial, but there are still many other methods of learning that are unaccounted for (Hofstein & Rosenfeld, 1996, p. 90).

Connecting youth education to space policy

Our learnings in the previous sections show that youth education would push for improved public policy, pushing for better government policy and therefore space policy. Space exploration is one of the few technological fields that is pioneered by government agencies, and as a result, public opinion has a major effect on space policy changes (Metzger et al., 2013, p. 27). In the US, there is a lack of education about space science and how it benefits our everyday lives. Researching this topic could show how space science knowledge could be spread to the youth of the US in the most efficient way, which could be used by government agencies trying to increase public opinion in regards to space policy. Learning which methods are best for space science education could also have implications towards efficient methods of education in other fields (Shaghaghi & Antonakopoulos, 2012, pp. 179-182).

Gap in understanding

Though research has been done in relation to influences on public opinion of space science, there is a lack of information comparing methods of education in relation to space science. There are many avenues for education towards space science, informal and formal, but finding the best avenue will allow for efficiency in space science education. This leads us to the research question: How can organizations promoting space science optimize their methods for high school space science education to spread knowledge and benefit space policy in the future?

Method

To figure out which method of education is best for educating the youth in space science, the method chosen for research was an experiment. There were also short questions administered before and after the experiment to better control extraneous variables that may affect the results, which will be discussed later.

Participant selection

I aimed to gather 18-21 participants, consisting of 6-7 students for each of the 3 different methods of education present in the experiment. All of the participants were students of a central Texas high school. I gathered participants by offering them incentives such as partial service credits for various honor societies and brownies. The ingredients list for the brownies can be found in Appendix A. All of the participants were sent consent forms and for those under the age of 18, their parents were sent a notification email as seen in Appendix B. All of the participants maintained anonymity through a lettering system. This experiment was given IRB approval.

Experimental procedure

The first step in this experiment was to sit down and ask the opening questions to the participants. Two questions were asked, “rate your current support for space policy on a scale of 1-5” and “what past experiences have you had in regards to that topic and how have they influenced your level of support”. The response to the second question was coded into various categories of influence in space science, those being: family, in-person experience, social media, school, and curiosity of space. These categories were based on a previous study which attempted to dissect the influences that can change space policy support in young adults (Kalmbach & Ralston, 2021, p. 10). After those answers were recorded, participants were randomly assigned to one of three different methods. The three different methods were a video, a podcast, or reading assessment, all about the benefits of space science. The participants then spent between 15-40 minutes engaging in their respective learning material. Once the participants completed their learning, they were then asked one question, “What were the most interesting aspects of space policy that you learned about and why”. The response to this question was recorded word for word with no audio being taken. The next step in the experiment was to set up a meeting time about a week later, which took about five minutes of the participant’s time, and was simply a meeting to ask the last question once again. The participant’s response was recorded again word for word. The complete questions and script can be found in Appendix C.

Data analysis

There is one independent variable and one dependent variable in this experiment. The independent variable is the method of education, which will be one of three tools, a video, a podcast, or a reading passage. The Youtube video was created by Mark Rober and is called “Is NASA a waste of money?”. It discusses the benefits of NASA and why the government puts money towards the organization. It is designated as the representation for social media influence due to its nature as a more interactive and relatable experience, as well as being created by a well-known “influencer”. The podcast is called TechStuff and the episode title is “Technology we can thank NASA for”. It is another piece of media that describes the technologies NASA has created, and I designated it as a representation of the curiosity factor. The reading passage was published by The Planetary Society and is titled “Why space exploration is always worthwhile”.

This passage is similar to the other two pieces of media and describes the benefits of NASA. This method of education represents the formal education method which is what is being given in science classes through public education. The dependent variable in the study is a qualitative measure on how well the student picked up information. This is based on the student’s response to the post-experiment question which was asked directly after the experiment and then again a week later. Both of the responses of question 3 were used to score each participant on their ability to learn about space science. Participants were given a point for each phrase that matched the phrases they said the first time they answered the questions, as well as a point if their second response matched the length of the first response. Thus, the score that they were given was used to compare the three learning methods in the graphs. The first graph compared the average score of participants from the three different groups. The second graph compared the average score of participants from the three different groups with the average prior support each group had, which comes from the pre-experiment questions.

The pre-experiment interviews will have one quantitative and one qualitative measure. The quantitative measure was the participant’s prior stance on space policy, and it factored into data analysis when I compared the ability to pick up information about space policy to a participant’s prior stances. The qualitative measure that was found was a participant’s past influences in space policy, and those were sorted into categories and addressed as limitations of the study. This info was also used as data to help answer the research question. There were two graphs made for this aspect of the data, the first graph being a graph of the number of times each prior influence was present from question 2, and the second graph showed the average prior support from each prior influence based on questions 1 and 2. The average prior support for each method was also used to create the second graph from the experiment portion of the data.

Limitations of the method

Parental, academic, religious, and many other prior influences could impact a person’s ability to change or positively view space science. It has been proven that these influences can affect a young adult’s stance on space policy (Kalmbach & Ralston, 2021, p. 10). Although this study was specifically targeting young adults, it can be inferred that the same influences that affect the young adult’s in this study could be present for our student participants. The pre-interview questions conducted attempted to account for these prior influences, but they will still have an impact on our participant’s ability to change their stance.

Another possible source of error in the results could be the varying academic performance levels of the participants. Everyone’s brain functions differently, and it is well known that some students are more apt at picking up information than others. During the study, participants were not subject to any questions regarding their general academic performance or any other test which may be able to account for their level of academic understanding. The code used to determine which source of information was the most successful was dependent on the amount of information remembered by each student, allowing for academic performance to not have a big influence on the study.

Findings

The purpose of this study is to identify which methods of education will best educate high school students such that that method could benefit future support of space science. My hypothesis going into this study is that social media is the most effective way to educate high schoolers in space science education. Through my research, there were two sections of data which can help us answer this question. The first section will be based on what prior influences have affected students in the past, and whether they have been successful in garnering support for space policy. The second part was experimenting with different methods of education to see which ones were successful in educating students. Both of these parts will help us come to an overall conclusion regarding how to best educate students and gain support in space science.

As seen in the graph, the curiosity factor associated with space is one that is most commonly seen in my sample of students. Following closely are the effects of schooling, in-person experiences and social media. The effect of in-person experiences could be heightened for this sample, as it is made up completely of Central Texas high school students, and driving to NASA’s Johnson Space Center is only a couple hours away. With the lowest number of answers, both family/relatives and future aspirations have 3 appearances in this sample. Therefore, it can be seen that space science may not be the most popular dinner conversation topic. It can also be seen that in my sample of 20, only 3 students had their sights set on a field relating to space science, which makes sense as many high school students can be undecided on what career they want to pursue.

Each student was allowed to have as many prior influences as they pleased, which is why the total number of each of the bars on the graph doesn’t add up to 20, the total number of participants.

This graph moves us on to the experimental portion of the experiment. Each of the 20 participants were scored for their levels of information remembered, and then their averages were taken and put on this graph. The average score among all participants was 1.55, and can be seen by the dashed line across the graph. As seen in the graph, the social media method (video) was the most effective, generating a score almost 20% higher than the average score across all participants. The curiosity factor, represented by the podcast, almost hits the 1.55 average score, with a score of 1.50. The lowest performing score was the formal schooling method, represented by the reading passage, receiving scores just over 20% below the average of 1.55. This information is important to answering the hypothesis, but consideration must be made for the prior influences on the participants.

This graph illustrates the success of the social media method compared to the other two methods. In this graph, it is more beneficial to be in the lower right corner, as that means the participants began with a lower level of support prior to the experiment, but still excelled in remembering information from the video. While it is random which participants receive which method, the lower prior support should theoretically have given the social media method a slight disadvantage compared to the other two methods. While the other two methods, curiosity factor and formal schooling, both started out at similar levels of prior support, the curiosity factor can be seen to be more successful in educating its participants. It is important to also recognize that the scale of the y-axis on this graph is greater, to provide more evidence of the disparity in prior support of the three different methods. Overall, this graph furthers the idea that social media is more effective and supports my hypothesis to the research question.

This graph brings us back to the short interview questions asked at the beginning of the experiment. As seen in the graph, future aspirations have the highest level of support per person. This makes sense, as many students who are decidedly going into a field related to space science are highly likely to support space policy. The other three highest supported influences are social media, school, and curiosity factor, with social media and school tied for .9 and curiosity factor slightly ahead with a score of .915. In-person experience is also well performing with a score of .8, but yet again that could be influenced by the participants in this study and their proximity to the Johnson Space Center in Houston. With the lowest score, family relationships have a lower level of prior support, which also coincides with it having the lowest frequency of all of the prior influences present. This data is also helpful in answering the research question, and partnered with the experimental scoring portion could give us a significant conclusion.

Analysis

Although the data taken in the experiment was helpful to answering the research question, statistical significance must be taken into account. For Figures 1 and 3, the portion of the data coming from the experimental aspect, statistical analysis was conducted using an ANOVA calculator. The results can be seen in Table 1.

This test was used to compare the scores of each group. One of the significant statistics given to us is the F statistic, which is in the 95% region of acceptance, and implies that there are no outstanding differences in means between groups compared to the means in the groups. This is good for the data, but the most important value given is the P-value. Unfortunately, the P-value is .3846, indicating that the data is not statistically significant. Expanding upon that, this P-value indicates that there is too high a chance (38.46%) of rejecting a correct hypothesis, meaning a significant conclusion can’t be made based on the data.

Statistical analysis was also conducted based on Figures 2 and 4, regarding the pre-experiment questions and prior influences. A t-test was conducted to compare the relationship between frequency of prior influences and prior support for each prior influence. The two tailed p value was .0002. This value indicates that the data is considered extremely statistically significant, which means greater significance must be placed on this data to create a conclusion and answer the research question. The results of this aspect of the data are consistent with the results from the less significant aspect of the study, so the differing statistical significance of the two aspects won’t cause two different possible answers to the research question. However, before examining the data and crafting an answer to the research question, there are many limitations based around analysis of the data that must be discussed.

Limitations of the data

The most prevalent limitation that appeared in the study after examining the data was the prevalence of in-person experience reported. All of the participants of this study attend a Central Texas High School that is about a 3 hour drive from NASA’s Lyndon B. Johnson Space Center in Houston. Along with this, the majority of the high school’s student body is made up of the middle or upper class, making traveling to visit the Johnson Space Center a viable option for a majority of the students participating in the study, if not all. Knowing this, the prevalence of in-person experiences must be taken under consideration for feasibility in answering the research question. However, the average prior support, which was a positive .8 (as seen in Figure 4), can be taken into account but still with some caution. Although it is a mean and therefore the prevalence of the in-person experiences isn’t significant, the type of in-person experience is important. There must be caution in using the success of in-person experiences in generating prior support for the study as in-person experiences could mean anything from a mini volcano demonstration by a science teacher to seeing a rocket launch. Therefore, the prevalent in-person experience of visiting Johnson Space Center is not as feasible for other high school students in areas not close to any NASA center, especially the midwest and western states (excluding California). Overall, the prevalence and positive support generated from in-person experiences in this study shouldn’t be weighted as importantly as other influences when answering the research question due to the nature of the proximity of student participants to the Johnson Space Center.

Another major aspect of the data that must be discussed is the outstanding prior support for space policy demonstrated by those with future aspirations as a prior influence (shown in Figure 4). Although there were only 3 participants who recorded future aspirations as a prior influence (Figure 2), all of those 3 participants answered a 5 when asked to rate their support for space policy on a scale of 1 to 5. This happens because students who are set on entering a field related to space science are highly likely to support that field and therefore support space policy. In hindsight, it may have been better to clarify what inputs caused someone to go into that field or have those future aspirations, as that may have been more helpful to answering the research question, but the organization of the questions and the study didn’t account for that. Through this limitation and the limitations of the results of in-person experience as a prior influence, the other 4 influences in Figure 4 can be seen more clearly as curiosity factor, schooling, and social media tied as the most beneficial prior influence and then family/relatives being by far the least beneficial prior influence.

Answering the question

Having addressed limitations in the data, the research question can be answered and more implications of the study can be evaluated. Before conducting the study, I hypothesized that social media would be the most effective form of space science education for high school students to improve future space policy. This hypothesis has been largely supported by my data, with social media performing exceptionally well in both aspects of my study as seen in Figures 3 and 4. The data from Figure 3 is in extreme favor of social media as the most effective method of education, but it is important to remember that its data isn’t statistically significant enough to make a significant conclusion on. However, the data from Figure 4 also supports social media as one of the most effective methods. This data must be taken accounting for the limitations of the future aspirations and in-person experiences influences, as well as understanding that this data has a high level of statistical significance in accordance with its t-test. In Figures 3 and 4, curiosity factor also performs well, performing better than schooling in Figure 3 and exceeding social media ever so slightly in Figure 4. Thus, it must also be taken into account as a possible answer to the research question. Having discussed all of this, the research question can be answered by saying that social media is the most effective method of education in regards to space science for high schoolers, with other methods inducing the curiosity factor of space being similarly effective in educating high school students.

Coming full circle, this conclusion can bring us back to the lit review and main purpose of this study, which was finding ways to improve public support for space policy. As discussed before, the most important way to improve public support for space policy is to improve education in the field (MacLeish et al., 2012, p. 191). Therefore, it can be concluded that space organizations such as NASA should push for more social media presence to appeal to high schoolers, which will further their education and therefore future support for space policy. With the results of this study, social media was represented by a Youtube video, but social media could be represented by other mediums, although it is unknown based on this study how effective they would be. The other effective method discussed was implementing the curiosity aspect of space exploration. This is the aspect of human’s innate desire to explore the unknown, to be curious. Organizations such as NASA could present space and its nature as an endless undiscovered galaxy to push the curiosity aspect of space exploration, therefore furthering future support for space policy among high schoolers.

Conclusion

Overall, this study has shown that social media is one of the most effective ways to educate high school students about space science. It also presents the curiosity factor of space exploration as another way to draw attention to the field. Both of these methods can be used to improve public support for space exploration, therefore garnering support for the industry as a whole.

This study could also have implications for education as a whole outside of just space science. Other fields could see the success of education through social media, and could work to improve their presence on social media. However, the difference between social media of space science and other forms of social media education is unknown right now and could be the subject of future research. This information also is more beneficial to space organizations, which as described in the literature review, makes education of high school students more impactful.

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About the author

Rahul Gupta

Rahul just graduated from Vandegrift High School and will attend the Cockrell School of Engineering at UT Austin in Fall 2024, majoring in Aerospace Engineering. In his free time, Rahul loves playing soccer, reading, and playing chess.

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