Design and Basic Aerodynamic Analysis of a Drone-Suspended Transport Container for Safe Biological Sample Transport

Abstract

The article addresses the issue of selecting the initial shape for a drone’s suspended transport container and its impact on the final aerodynamic properties during the flight, specifically aerodynamic drag, based on the simulated pressure differences generated by the suspended container. The motivation arose from the project ITMS2014+:313011 ATR9 titled ‘Research and Development of the Applicability of Autonomous Flying Vehicles in the Fight Against the COVID-19 Pandemic’. The project deals with the transport of biological samples from hospitals to specialized laboratories. These samples, which could be contaminated, necessitated the development of a specialized container meeting all safety criteria. Besides predefined parameters such as the maximum weight of the container, transport speed, dimensions of the internal standardized module for transporting hospital samples, and compliance with required IP (Ingress Protection) and IK (Impact Protection) standards, many other challenges related to the final design solution of the transport container had to be addressed. One such challenge was the fundamental question of what shape the transport container should have, which significantly influences the overall design and construction of the transport module. We attempted to solve this question responsibly and professionally and thoroughly substantiate our results with appropriate simulations in selected simulation software. The outcome was as expected, but it was necessary to adequately justify and support the choice of the shape of the transport container in the context of the project’s resolution. The results are universal and can be applied to other designs for shapes of transport containers in the future or by other researchers working on similar projects.

1. Introduction

The rapid expansion of aerial transportation facilitated by drones represents a transformative technological evolution. This development is driven by continuous advancements in unmanned aerial vehicles (UAVs), incorporating autonomous control systems, artificial intelligence, machine vision, high-efficiency batteries, and electric propulsion technologies, which have enabled various activities that were previously unfeasible, as indicated in [1,2,3]. Among these activities are rescue operations where drones perform targeted environmental surveys in search of lost persons or animals, as mentioned in [4,5,6,7,8,9]; data collection for obtaining mapping foundations, photographs, video recordings, or inputs for photogrammetry, as described in [10,11,12,13,14,15]; monitoring of critical technologies, including building inspections, traffic monitoring, and access control to secured areas, as noted in [16,17,18,19]; agricultural activities for data gathering about crops and their evaluation, as per [20,21,22,23,24]; delivery of goods or critical materials to locations where conventional transportation methods are inefficient for various reasons, as per [25,26,27,28,29]; and lastly, military and police applications of various kinds, as cited in [30,31,32,33].

The aerodynamics of UAVs introduce unique complexities, particularly due to the relatively small size of drones and the aerodynamic interactions between their components. These interactions have a direct impact on energy consumption, stability, and payload efficiency of drones. Computational Fluid Dynamics (CFD) simulations have emerged as a critical tool in studying and optimizing UAV aerodynamics, enabling precise modeling of airflow, pressure distribution, and drag characteristics.

For example, Cravero and Marsano (2022) [34] investigated the aerodynamic behavior of racing car wheels integrated with multi-element wings, demonstrating the intricate relationships between components and their impact on overall drag. Their findings are relevant for drone aerodynamics, where similar complex interactions arise due to the placement of payloads. Fernandez-Gamiz et al. (2018) [35] explored the modeling of Gurney flaps and microtabs using the Proper Orthogonal Decomposition (POD) method, providing insights into optimizing aerodynamic profiles under varying conditions. These studies underscore the importance of advanced numerical methods in understanding and addressing aerodynamic challenges.

In our case, following the objectives of the addressed project, we have chosen the deployment of drones for medical purposes and the transportation of biological samples. The use of drones in medicine is very specific and was largely influenced by the COVID-19 pandemic, as indicated in [36,37,38,39]. During the pandemic, there emerged a demand for the fastest possible transportation of medicines to remote or hard-to-reach areas, minimizing human contact. In the specific context of medical applications, drones have gained attention for their ability to deliver critical materials to remote areas, particularly during the COVID-19 pandemic. The pandemic highlighted the need for rapid and contactless transportation of medicines and biological samples, which are essential for timely diagnosis and treatment. Transporting sensitive biological materials, such as blood, tissues, serum, or urine, necessitates specialized containers that ensure sample integrity and comply with rigorous safety standards, including ingress protection (IP) and impact resistance (IK).

The technologies mentioned in the paper, such as AI and computer vision, were integral to various aspects of the broader project titled ITMS2014+:313011 ATR9, Research and Development of the Applicability of Autonomous Flying Vehicles in the Fight Against the COVID-19 Pandemic. This project was extensive and involved multiple teams addressing different aspects of drone deployment and operation. Specifically, AI and computer vision were utilized in the autonomous flight systems, enabling precise navigation, obstacle avoidance, and the control of take-off and landing. Swarm control and navigation, as a concept, were explored as part of this project by another group, reflecting its potential as an exciting and developing area. However, in the current operational setup, only the flight of a single drone is considered, as it fully suffices for the rapid transport of critical samples from hospitals to specialized laboratories. This approach ensures efficient, reliable delivery without the need for the complexity of swarm management.

In this manuscript, however, we focus solely on the selection of the shape of the transport container and its influence on flight characteristics. Our primary objective was to determine how different container shapes, such as rectangular prisms, spheres, rounded cylinders, and NACA airfoil profiles, impact aerodynamic drag and flight efficiency at low speeds, aligning with the operational constraints of the drone system. Detailed evaluations of automated sample handling and structural testing of the container were not included here, as they are part of ongoing research to be presented in a forthcoming article.

We ensured that the aerodynamic analysis remained aligned with the broader project objectives while maintaining a focused scope on container design. This approach underscores the collaborative nature of the project while delineating the specific contributions of this study.

The novelty of this study lies in its focus on the influence of suspended container shape on the flight characteristics of drones. We investigated the effects of selecting basic geometric shapes commonly used for transport containers, such as rectangular prisms, spheres, rounded cylinders, and NACA airfoil profiles, and demonstrated their impact on aerodynamic performance. A key finding is that at low speeds, the specific shape of the container is not a critical factor in flight characteristics. This insight shifts the design focus towards fulfilling operational requirements of the container, such as compliance with safety standards, durability, and economic and structural considerations derived from project objectives.

Several works have explored the use of drones for medical deliveries. Du et al. (2022) developed an optimization model for drone-based medical material delivery during emergencies, focusing on routing efficiency [40]. Scott (2017) reviewed healthcare drone delivery models, emphasizing time efficiency using multimodal transportation [41]. Oxtoby (2024) analyzed case studies from the UK and Netherlands, highlighting drone transportation challenges in healthcare [42].

However, these studies lack a focus on the aerodynamic optimization of transport containers specifically designed for medical purposes, addressing safety standards and operational constraints. Our research bridges this gap by integrating advanced aerodynamic analysis with compliance with medical transport requirements, offering a novel design approach for drone-based medical logistics. This study provides a comprehensive approach to container design that prioritizes practical and operational goals while aligning with the broader context of existing research and addressing an underserved area in drone applications for medical logistics.

The methodology incorporates a comparative analysis of various container shapes, including rectangular prisms, spheres, rounded cylinders, and NACA airfoil profiles, inspired by aerodynamic principles. These designs were selected for their practicality and aerodynamic efficiency, aligning with findings from established studies, such as Liuliu et al. (2018) [43], who compared turbulence models for vortex shedding phenomena, and Cravero et al. (2021) [44], who analyzed recirculation lengths and shedding frequencies in vortex-induced flows. By building on these foundational studies, our work bridges the gap between aerodynamic optimization and practical design considerations for drone payloads.

2. Materials and Methods

In this chapter, we will describe in detail all the assumptions and premises used for our own design of the transport container in line with project ITMS2014+:313011 ATR9 titled “Research and Development of the Applicability of Autonomous Flying Vehicles in Fight Against the COVID-19 Pandemic”, as described in [45]. This includes the methodologies and procedures for the selection and testing of various shapes considered for the container. Additionally, we will describe the process of our own simulation testing, the setting up of experiments, and the methodology for their evaluation.

2.1. Operational and Technological Constraints for the Design and Construction of the Transport Container

A fundamental assumption for the design and construction of the transport container involves operational and technological constraints, which ensure the safe and efficient transport of the chosen material—in this case, hospital biological material. In our case, these constraints primarily included the following limitations derived from the project requirements:

• Weight and dimensions: The suspended transport container must have the lowest possible weight to minimize the energy requirements for transportation. Compact dimensions are necessary to facilitate transportation to various locations and future automation of loading and unloading the contents. In our case, the maximum weight of the container is considered along with the loaded sample transport module, as shown in Figure 1, with dimensions (height × width × depth) of 44 mm × 110 mm × 210 mm and a weight of 935 g. The dimensions of the suspended transport container depend on the drone used, but the maximum dimensions are (height x width x depth) 220 mm × 220 mm × 400 mm. The maximum weight of the suspended transport container, along with the fully loaded sample transport module, is set at a maximum of 3000 g.
• Damage protection: The suspended transport container must be sufficiently sturdy and durable, at a minimum complying with IP66 and IK10 standards, to protect the biological material from damage and contamination during transport. The IP66 standard, defined by the IEC 60529/EN 60529 norm, specifies that the container must be completely dust-tight (IP6X) and protected against powerful water jets from any direction (IPX6). This ensures that the container can withstand challenging environmental conditions, such as exposure to dust, rain, or cleaning processes using high-pressure water. The IK10 standard, specified in IEC 62262/EN 62262, ensures resistance to mechanical impacts of up to 20 joules, equivalent to the impact of a 5 kg object falling from a height of 40 cm. This level of protection guarantees the structural integrity of the container, safeguarding it from accidental drops, collisions, or other mechanical stresses. Additionally, the container should offer adequate protection against vibrations to prevent the devaluation of the transported biological samples by impacts and other forms of damage. In line with project ITMS2014+:313011 ATR9 objectives, impact tests were conducted by another group of researchers in collaboration with authorized certification authorities of the Slovak Republic, and the prototype designed and realized by our team successfully passed all required evaluations. The container should be equipped with an external mechanical lock controlled remotely, allowing it to be opened only from a central control point.
• Accessibility and manipulability: The container should be designed to easily accommodate and facilitate the removal of standard hospital modules with hospital samples, as illustrated in Figure 1. Additionally, the design should enable future possibility of manipulation using automated handling equipment.
• Factors influencing the flight characteristics of drones with a suspended transport container: These can be divided into several categories, such as aerodynamic, me-chemical, electronic, and environmental. Based on these categories, the selection of the simulated factor and its justification will be carried out.
• Selection of a suitable transport drone for the shipping container, in terms of standards and requirements: Standard sizes of drones vary depending on their use and type, but generally, they are usually categorized into several basic groups based on their weight and wingspan or dimensions. Each of these categories has specific rules and regulations depending on the country where the drones are used. Within these categories, further subdivisions based on wingspan, dimensions, or performance can be encountered. Manufacturers and drone designers often provide specifications that allow for comparison of different models within these categories.
• Safety and legal regulation: In the design and construction of the suspended transport container for drones, it is necessary to comply with safety standards and regulations applicable to their operation within the European Union and the bordering states of the Slovak Republic, as mentioned in references [46,47,48,49,50,51,52,53]. Considering the specification of EU project ITMS2014+:313011 ATR9, the operation is planned primarily in EU countries, especially in the Central European region, with a focus on the transportation of samples within urban areas from hospitals to laboratories.
• External climatic conditions: The container should be designed to provide sufficient protection for the samples against adverse climatic conditions, such as extreme temperatures, humidity, wind, snow, etc. An automatic thermoregulation system is preliminarily addressed as well, should the transported biological samples require it following the execution of real-world experiments.

2.2. Methodology for the Selection of the Shape of the Transport Container

The shape of the transport container is a fundamental starting point from the perspective of its design and later operational deployment. In line with the project’s objectives, we needed professional validation of our choice. A mere simple rationale for the shape selection was not sufficient. Since we could not find publications specifically addressing this issue for drones in the professional literature, we had to carry out the professional justification through simulation ourselves. Initially, we had to select basic shapes for the suspended container, which would be attached underneath the drone without cowling. The drone is structurally designed as a classic quadcopter with a cross frame, as per [54]. The container’s attachment at the bottom is due to its traditional construction and for the purpose of planned future automated manipulation of the container.

In practical tests, a variant with a pyrotechnic parachute casing and an anti-vibration mounting plate was considered, but ultimately, it was deemed unnecessary based on real world measurements performed in practice on the prototype.

The selection of container shapes was addressed pragmatically. It was conducted based on the choice of basic 3D geometric shapes that we are capable of manufacturing and that are commonly used. During the selection process, we were aware that some shapes generate significant air resistance; however, this aspect was crucial in our decision-making regarding which of these shapes to ultimately choose for our project. As variants for comparison, basic shapes such as a rectangular prism, sphere, rounded cylinder, and an airfoil shape based on the standardized NACA (National Advisory Committee for Aeronautics) 9330 profile were chosen. These shapes are basic forms commonly used for transporting goods with drones.

The study also considered additional alternative shapes that could potentially offer better performance in terms of aerodynamics, manufacturability, and compliance with the requirements for transporting biological samples. These include:

• Elliptical cylinders: These shapes could further streamline the aerodynamic profile while maintaining sufficient internal volume for sample modules. Compared to a rounded cylinder, elliptical cylinders could reduce drag more effectively, especially at higher speeds.
• Teardrop shapes: Inspired by natural aerodynamic forms, teardrop shapes might offer superior drag reduction. They are especially beneficial at speeds exceeding the operational limits of typical quadcopters, as their tapered design minimizes turbulence.
• Multi-faceted geometries: Shapes combining flat and curved surfaces, such as hexagonal cylinders with rounded ends, might balance ease of manufacturing with improved airflow management. These shapes could also provide modularity, allowing integration of additional features like thermoregulation systems.

While these alternative shapes present intriguing advantages, several factors limited their practical implementation. For example, elliptical cylinders and teardrop shapes require significantly more complex manufacturing processes, which would increase production time and costs. Multi-faceted geometries, while modular, could introduce assembly challenges and additional weight due to their structural complexity.

A common dimensional criterion was to ensure the most effective placement of a standard hospital transport module for biological samples, as shown in Figure 1. For us, the primary importance lay in the characteristics of the selected shapes, especially their aerodynamic resistance during forward movement along the x axis, as discussed in the literature [55,56,57,58,59]. A more extensive evaluation of their selection is as follows:

• The rectangular prism shown in Figure 2 represents the most basic shape a transport container can have. It is structurally simple and cheap to manufacture. It does not include unnecessary volumetric shapes that would increase the weight in the form of so-called dead weight—unused volume. From an aerial transport perspective, its frontal flat surface creates the greatest aerodynamic resistance among all the chosen shapes. It is easy to handle and suitable for automated manipulation. However, in the event of the container falling, there is a risk of rotation around its longest edge, potentially causing damage to the transported sensitive biological samples due to centrifugal rotational force. The simulation results can generally be aligned to those of a transport container in the shape of a cube, as the air pressure acting during forward flight will be approximately the same.

• Sphere shown in Figure 3: This represents another simple geometric shape for the transport container. However, its production is much more complex and complicated compared to the rectangular prism. It contains many unnecessary volumes—dead weight, which cannot be directly utilized for storing the internal hospital transport module. Hypothetically, these spaces could be used for a thermoregulation system, battery, control electronics, and mechanical locks. In terms of aerodynamic resistance, it performs significantly better than the previous rectangular prism shape. It has equal surfaces from every side. In the event of the container’s fall, with a suitably designed center of gravity, there should not be any rotation of the container and subsequent damage to the sensitive biological samples.

Figure 3. Three-dimensional model used for the basic shape—sphere.

Figure 3. Three-dimensional model used for the basic shape—sphere.

• NACA 9330 profile shown in Figure 4: This is a complex geometric shape for a transport container. Its production, however, is much more complex and complicated compared to a rectangular prism or sphere. It is a standard wing profile developed in 1933 by the National Advisory Committee for Aeronautics (NACA), the predecessor to NASA (National Aeronautics and Space Administration). Among its fundamental characteristics, it achieves good aerodynamic stability and low air resistance at flight speeds ranging from 0 to 250 km/h. It has the shape of a symmetrical bent profile with minimum thickness in the central part and maximum thickness near the wing root. In terms of the distribution of aerodynamic resistance, it performs the best among the chosen shapes for transport containers. The NACA 9330 profile is used as a reference profile in the design and testing of new wing profiles. Therefore, we have also selected it as a reference shape for the transport container in terms of its aerodynamic parameters.

Figure 4. Three-dimensional model used for the basic shape—NACA 9330 profile.

Figure 4. Three-dimensional model used for the basic shape—NACA 9330 profile.

• Rounded cylinder shown in Figure 5: This is another one of the simple geometric shapes for a transport container. Its manufacturing involves the production of the middle cylindrical part and the side hemispherical shapes. However, its production is again more complex and complicated than that of a rectangular prism or sphere, though not as complex as the NACA 9330 profile. It again contains unnecessary volumes—dead weight, which cannot be directly utilized for storing the internal hospital transport module. However, these spaces could be used for a thermoregulation system, battery, control electronics, and mechanical locks. In terms of aerodynamic resistance, it performs significantly better than the previous shape in the form of a rectangular prism. It has equal surfaces on each side. In the event of the container’s fall, with a suitably designed center of gravity, there should not be any rotation of the container and subsequent damage to the sensitive biological samples.

Figure 5. Three-dimensional model used for the basic shape—rounded cylinder.

Figure 5. Three-dimensional model used for the basic shape—rounded cylinder.

2.3. Methodology for Testing the Suitability of the Shape of the Transport Container

To evaluate the suitability of the transport container’s shape, we utilized the simulation software environment Dassault Systèmes SOLIDWORKS Premium, as described in [60]. As outlined in Section 2.2, the selection of container profiles was pragmatic, aimed at minimizing the complexity of aerodynamic analyses. Further investigations into airflow patterns around the profiles were deemed unnecessary unless initial results derived from the analysis of aerodynamic drag along the x axis proved inconclusive. The selected simulation platform provides sufficient complexity for conducting these analyses.

The parameters for the simulation were defined based on the detailed specifications outlined in Table 1. To ensure consistency and standardization, the framework utilized the SI metric system. The analysis type was set to “External”, reflecting the objective of evaluating airflow impact and aerodynamic resistance acting on the container’s surface. Air was chosen as the medium for simulation, with its thermodynamic properties configured as follows: temperature at 293.15 K (20 °C), pressure at 101.325 kPa, and a density of 1 kg/m³.

For the evaluation, the container was subjected to velocity increments starting at 5.556 m/s (20 km/h) and increasing up to 66.667 m/s (240 km/h) in steps of 5.556 m/s. Special emphasis was placed on the velocity range up to 60 km/h, corresponding to the maximum operational speed of the drone under current construction constraints. Higher velocities were examined to simulate scenarios involving VTOL (Vertical Take-Off and Landing) carriers, capable of achieving greater speeds. This analysis was aimed at identifying critical aerodynamic resistance thresholds and assessing structural demands for future VTOL applications.

Key simulation goals included the measurement of Static Pressure, Total Pressure, Dynamic Pressure, and aerodynamic forces along the x and y axes. These metrics allowed for a comprehensive understanding of airflow behavior and drag effects around the selected container shape. Geometric parameters were simplified to a uniform domain of 1 m × 1 m × 1 m to ensure medium accuracy without compromising computational efficiency.

Discretization settings were also configured, as described in Table 1. A global mesh size of “Medium” (Mesh Level 3) with an automatic minimum cell size was selected to balance computational cost and resolution. To capture near-wall flow effects accurately, the non-dimensional wall distance (y+) was maintained in the range of approximately 1–5.

Boundary conditions were applied as follows: The inlet was set to variable air velocities starting at 20 km/h and increasing incrementally; the outlet was defined with a static pressure of 0 Pa, and the walls were modeled with a no-slip condition to reflect fixed surfaces. For turbulence modeling, a k-ε two-equation model was employed, ensuring a balance between computational efficiency and solution accuracy. The numerical scheme incorporated the Finite Volume Method using a second-order upwind scheme for spatial discretization and the SIMPLE algorithm for pressure–velocity coupling.

By adhering to these parameters, the simulations provided essential insights into the aerodynamic performance of the container. This step is critical for optimizing its design for use in drone-based logistics, including potential adaptations for VTOL carriers.

Table 1. The simulation settings in simulation software environment Dassault Systèmes SOLIDWORKS Premium.

Parameter	Value/Setting	Notes
Unit System	SI Metric	Adopted for consistent measurements.
Analysis Type	External	Analyzes the effect of airflow around the container.
Medium	Air (Gas)	Selected as the medium; the predefined list also includes other gases, such as CO2, ethane, etc.
Flow Type	Laminar and Turbulent	Inclusion of both regimes for realistic flow simulation.
Thermodynamic Parameters	Temperature: 293.15 K (20 °C)	Reflects typical atmospheric conditions.
	Density: 1.0 kg/m3
	Pressure: 101.325 kPa
Velocity Range	5.556 m/s (20 km/h) to 66.667 m/s (240 km/h) in 5.556 m/s (20 km/h) increments	Key velocities include 60 km/h (maximum drone speed) and higher speeds simulating VTOL usage.
Simulation Goals	Static Pressure, Total Pressure, Dynamic Pressure, Force (X), Force (Y)	Measurement of goals to analyze the effects of airflow and forces on the container.
Geometric Parameters	1 m × 1 m × 1 m	Simplified unified dimensions of the computational domain for medium-accuracy simulation. Dimensions can be adjusted based on the geometry requirements.
Discretization Settings	Global Mesh Size: Medium (Mesh Level 3)	Domain discretization with medium grid density, suitable for general-purpose simulations. The y+ value ensures accurate near-surface flow effects capture.
	Minimum Cell Size: Automatic
	y+: ~1–5
Boundary Conditions	Inlet: Air velocity starting at 20 km/h and increased iteratively based on simulation requirements.	The inlet air velocity was defined based on the simulation goals, starting at 20 km/h and increasing incrementally. Outlet and wall conditions used default settings.
	Outlet: Static Pressure = 0 Pa
	Wall: No Slip (fixed wall)
Turbulence Model	k-ε two-equation turbulence model	Used for general-purpose flow simulations, balancing accuracy and computational costs.
Numerical Scheme	Finite Volume Method	Ensures stable and accurate computation. Uses the finite volume method to solve equations and second-order accuracy for discretization.
	Second-Order Upwind Scheme
	SIMPLE Algorithm

Table 1. The simulation settings in simulation software environment Dassault Systèmes SOLIDWORKS Premium.

Parameter	Value/Setting	Notes
Unit System	SI Metric	Adopted for consistent measurements.
Analysis Type	External	Analyzes the effect of airflow around the container.
Medium	Air (Gas)	Selected as the medium; the predefined list also includes other gases, such as CO2, ethane, etc.
Flow Type	Laminar and Turbulent	Inclusion of both regimes for realistic flow simulation.
Thermodynamic Parameters	Temperature: 293.15 K (20 °C)	Reflects typical atmospheric conditions.
	Density: 1.0 kg/m3
	Pressure: 101.325 kPa
Velocity Range	5.556 m/s (20 km/h) to 66.667 m/s (240 km/h) in 5.556 m/s (20 km/h) increments	Key velocities include 60 km/h (maximum drone speed) and higher speeds simulating VTOL usage.
Simulation Goals	Static Pressure, Total Pressure, Dynamic Pressure, Force (X), Force (Y)	Measurement of goals to analyze the effects of airflow and forces on the container.
Geometric Parameters	1 m × 1 m × 1 m	Simplified unified dimensions of the computational domain for medium-accuracy simulation. Dimensions can be adjusted based on the geometry requirements.
Discretization Settings	Global Mesh Size: Medium (Mesh Level 3)	Domain discretization with medium grid density, suitable for general-purpose simulations. The y+ value ensures accurate near-surface flow effects capture.
	Minimum Cell Size: Automatic
	y+: ~1–5
Boundary Conditions	Inlet: Air velocity starting at 20 km/h and increased iteratively based on simulation requirements.	The inlet air velocity was defined based on the simulation goals, starting at 20 km/h and increasing incrementally. Outlet and wall conditions used default settings.
	Outlet: Static Pressure = 0 Pa
	Wall: No Slip (fixed wall)
Turbulence Model	k-ε two-equation turbulence model	Used for general-purpose flow simulations, balancing accuracy and computational costs.
Numerical Scheme	Finite Volume Method	Ensures stable and accurate computation. Uses the finite volume method to solve equations and second-order accuracy for discretization.
	Second-Order Upwind Scheme
	SIMPLE Algorithm

2.4. Methodology for Evaluating Results Obtained from Simulations

The evaluation of outputs from the simulations was conducted by comparing the impact of air pressure on the frontal profile of the selected shape, as illustrated in chapter 3. We monitored the minimum and maximum pressure achieved, as indicated in Table 2, Table 3, Table 4 and Table 5. To enhance clarity, we also included the pressure difference to assess the quality of air flow around the entire profile. All selected shapes were simulated at 12 basic operational flight speeds, specifically from 20 km/h to 240 km/h increments. Each conducted simulation was graphically evaluated. We compiled a measurement table for each measurement and for the final comparison of the impact of aerodynamic air resistance; we created charts number 1 to 4 for each speed separately. The comprehensive evaluation and selection of a specific shape were then conducted based on these results, which are presented in the final section of Chapter 3, where all assessments and findings are summarized. Based on these results, we then performed the final evaluation and selection of a specific shape.

Conversion to Pressure Coefficients (Cp) for Comparative Analysis

To improve the interpretability and applicability of the results, a complementary evaluation was performed by converting the pressure data to non-dimensional pressure coefficients (Cp). This approach highlights aerodynamic behavior independent of absolute pressure variations and facilitates comparisons across varying conditions.

The conversion from pressure (P) to the pressure coefficient is defined by Formula (1):

$$Cp={\displaystyle \frac{(P-P\infty )}{q\infty }}$$

(1)

where P∞ is the ambient pressure and q∞ is the dynamic pressure, calculated as (2):

$$\mathrm{q}\mathrm{\infty }={\displaystyle \frac{1}{2}}(\mathrm{\rho }{\mathrm{V}}^2)$$

(2)

Here:

• ρ: air density, set as 1.0 kg/m³ based on the simulation environment;
• V: flight speed in meters per second;
• temperature: set to 293.15 K (20 °C).

Simulation parameters: The conversion values were calculated using CFD software (Dassault Systèmes SOLIDWORKS Premium), which provided precise data for all operational flight speeds. The thermodynamic parameters (air density and temperature) and aerodynamic forces were integrated directly into the software configuration, ensuring consistency with simulation results.

Key Findings:

Impact of Speed on Cp:

• As flight speed increases, Cp decreases significantly due to the squared velocity term in q∞. For example, doubling the speed reduces Cp approximately by a factor of four for the same profile, highlighting the sensitivity of pressure coefficients to velocity changes.
• This reduction is more pronounced for streamlined shapes, which inherently maintain smoother airflow at higher velocities.

Pressure reduction: At maximum simulated speed (240 km/h), non-aerodynamic profiles like the rectangular prism experienced an approximate 75% drop in pressure coefficients compared to their values at 20 km/h. Aerodynamic profiles such as the NACA 9330 showed reductions exceeding 90%, illustrating the substantial influence of velocity on aerodynamic efficiency.

Efficiency gains: The results underline the importance of aerodynamic optimization, particularly at higher speeds, where the relative differences in Cp values between shapes become critical. For instance, at 240 km/h, the pressure coefficient for the NACA 9330 profile was 30% lower than that for a rounded cylinder shape.

2.5. Factors Influencing the Flight Characteristics of Drones with an Underslung Transport Container

Adding an underslung transport container illustrated on Figure 6, to a drone significantly increases the aerodynamic complexity of the entire system, affecting the overall flight characteristics of the drone. Changes in aerodynamics due to the attached container can impact lift, stability, and energy efficiency of the drone. These factors, derived from our simulations and analyses, are explored in detail below, along with quantified evaluations and simulations to meet the requirements set forth by prior review feedback. Based on these facts, the following text will explore the impact of various factors, which will be described in more detail in the following subsections.

2.5.1. Aerodynamic Effects

Changes in pressure distribution—the attachment of a transport container alters the aerodynamic profile of the drone, which has a pronounced impact on drag and lift characteristics:

• Increased drag: Simulations in Chapter 3 revealed that drag increases by approximately 12–15% for non-aerodynamic shapes such as rectangular prisms, particularly at speeds exceeding 80 km/h. This increase is attributed to the pressure differential between the leading and trailing surfaces of the drone–container system. For rounded shapes, such as cylinders or spheres, drag increased by only 5–8% under similar conditions. This information is derived from the cumulative graph which is presented in Chapter 3. It illustrates the increase in maximum air pressure for various shapes at different speeds. By comparing the differences between the rectangular prism and aerodynamic shapes, such as the rounded cylinder, it is evident that non-aerodynamic shapes exhibit significantly steeper pressure increases as speed increases.
• Lift alteration: The container modifies the airflow around the body of the drone. Numerical simulations in Section 3 demonstrate that this effect reduces lift efficiency by up to 10% for rectangular containers, whereas the impact on rounded designs remains below 5%.

Quantitative simulations—to validate these findings, simulations were conducted at speeds ranging from 20 to 240 km/h for four different container shapes: a rectangular prism, a sphere, a NACA 9330 profile, and a rounded cylinder. In Section 3, we graphically present the minimum and maximum pressure differences, highlighting significant variations in aerodynamic performance:

• At lower speeds (20–60 km/h): The differences between shapes were minimal, with drag and lift variations generally within a 2% margin. This suggests that the choice of shape has a negligible impact on aerodynamic behavior in this speed range.
• Beyond 80 km/h: A trend of increasing drag and pressure differentials became apparent for non-aerodynamic shapes, such as rectangular prisms, while aerodynamic designs like the NACA 9330 profile showed more consistent characteristics. In some cases, maximum pressures for non-aerodynamic shapes appeared to approach values around 1.5 × 10⁷ Pa, highlighting the potential aerodynamic advantages of streamlined shapes.

2.5.2. Stability and Control

Shift in the center of gravity—adding an underslung container shifts the drone’s center of gravity downward, which can negatively affect its stability and control:

• Impact on center of gravity: The addition of a suspended container inevitably shifts the center of gravity downward, with non-aerodynamic shapes causing a more pronounced shift compared to aerodynamic shapes. This shift can lead to reduced pitch stability and increased demand for stabilization from the flight controller.
• Dynamic behavior: Changes in the center of gravity and aerodynamics affect the drone’s dynamic response. Non-aerodynamic shapes generally impose a higher stabilization burden on the control system, particularly at higher speeds.

Simulation validation—stability metrics appear to indicate that non-aerodynamic shapes, such as rectangular prisms, may lead to delayed maneuverability due to increased drag and potential shifts in the drone’s center of gravity. In contrast, aerodynamic shapes like the rounded cylinder and NACA 9330 profile are suggested to provide more stable responses under varying wind conditions, based on trends observed in simulations. However, these findings are preliminary and would benefit from further validation through dedicated flight tests.

2.5.3. Energy Efficiency

Energy efficiency is a crucial consideration for drone delivery tasks, as it directly impacts the operational range, payload capacity, and overall feasibility of the system. In our study, the relationship between energy consumption and various factors such as container materials, shapes, and external conditions was analyzed in detail.

Increased energy consumption—the increased drag and altered lift characteristics contribute to higher energy demands for drones carrying underslung containers:

• Simulations suggest that non-aerodynamic shapes, such as rectangular prisms, may lead to a 15–20% increase in energy consumption compared to aerodynamic designs. This is inferred from the observed higher drag forces and pressure differences in the simulation results. Based on these estimates, the increased energy demand could potentially reduce battery endurance by approximately 10 min per hour of flight. Aerodynamic shapes, such as rounded cylinders or the NACA 9330 profile, appeared to result in a smaller increase in energy consumption, estimated at around 5%, under similar simulated conditions.
• At higher speeds exceeding 180 km/h, the difference in energy consumption becomes more pronounced. Cumulative data trends from the simulations, such as those illustrated in Chapter 3, indicate that rectangular containers may require up to 25% more energy than rounded cylinders. This highlights the importance of aerodynamic optimization for applications involving sustained high-speed drone operations.

Impact of container materials—the choice of container materials significantly affects the drone’s energy consumption. Lightweight and durable materials, such as composite polymers and lightweight alloys, were selected to reduce the overall weight of the container while maintaining structural integrity. The container’s empty weight is 935 g and its maximum loaded weight is 3000 g. These materials were chosen to meet safety standards, including ingress protection (IP66) and impact resistance (IK10). The reduced weight contributes to lower thrust requirements, which directly translates to reduced energy expenditure. Moreover, materials with thermal insulation properties were used to minimize the impact of external temperature fluctuations on battery performance and biological sample preservation.

Influence of aerodynamic shape—the aerodynamic shape of the container plays a pivotal role in determining energy efficiency. While aerodynamic drag is an important factor, our simulations revealed that at the operational speed of 60 km/h, the influence of the container’s shape is less pronounced compared to higher speeds. The drag coefficient (Cd) and its relationship with energy consumption were quantified as follows (3):

E ∝ Cd ⋅ v³

(3)

where:

• E represents energy consumption;
• Cd is the drag coefficient;
• v³ is the velocity of the drone.

Although the aerodynamic optimization of the container shape is less critical at lower speeds, shapes such as the rounded cylinder were preferred for their balance between aerodynamic efficiency and manufacturability.

Environmental factors—environmental conditions have a significant impact on energy efficiency. Factors such as wind resistance, stability corrections due to side winds, and temperature fluctuations were analyzed. Wind resistance increases energy consumption by requiring additional thrust to maintain stability and trajectory. Temperature variations affect battery efficiency, with colder conditions reducing energy capacity. To address these challenges, the container design incorporates thermal insulation and temperature monitoring systems to optimize battery performance and maintain the integrity of biological samples.

Formalizing energy consumption—the relationship between energy consumption and the factors mentioned above can be expressed as (4):

$$\mathrm{E}={{\mathrm{\int }}_0}^{\mathrm{t}}(\mathrm{P\_thrust}+\mathrm{P\_drag})\mathrm{dt}$$

(4)

where:

• P_thrust is the power required to counteract the weight of the container and payload;
• P_drag accounts for aerodynamic resistance.

At the operational speed of 60 km/h, the thrust requirement is the dominant factor, with aerodynamic drag playing a secondary role. However, external factors such as wind can amplify the drag, necessitating adaptive energy management strategies.

Conclusion—by integrating lightweight materials, aerodynamic considerations, and environmental management systems, we have optimized the container design for energy efficiency. These findings highlight the importance of a holistic approach to drone delivery system design, where material selection, shape optimization, and external factor mitigation collectively contribute to reducing energy consumption and enhancing operational performance.

2.5.4. Design and Engineering Solutions

Aerodynamic optimization—the analysis underscores the importance of selecting aerodynamically optimized shapes to improve performance. Rounded cylinders and streamlined profiles, such as the NACA 9330 shape, appeared to perform better in reducing drag and stabilizing flight characteristics based on simulation trends.

• Pressure reduction: Rounded designs showed a noticeable decrease in pressure differential between the front and rear surfaces compared to rectangular prisms, potentially by a significant margin.
• Drag minimization: Streamlined profiles demonstrated more stable drag behavior across the tested speed range, indicating better energy efficiency in comparison to non-aerodynamic shapes.

2.6. Selection of a Suitable Transport Drone for the Shipping Container, in Terms of Standards and Requirements

The choice of a transport vehicle for the shipping container is decisive for selecting the speeds used in the simulations. The usual travel speed of a traditional drone constructed as a quadcopter is not high, with common speeds around 30 km/h. Even large drones, such as the “Predator”, typically have a cruising speed of around 130 km/h. However, certain VTOL (Vertical Take-Off and Landing) drones, such as the Wingcopter 198 and Amazon Prime Air MK27, offer significantly higher performance. These VTOL drones can transition from vertical lift to fixed-wing flight, achieving speeds up to 150 km/h or more, which makes them suitable for longer-distance transport operations. Based on the standard categorization [46], we divide drones into the following categories:

• Mini or micro drones: These drones typically weigh less than 250 g and are small enough to fit in the palm of a hand. They are ideal for recreational use and in many countries often do not require registration.
• Small drones: These drones weigh from 250 g to approximately 2 kg. They are often quadcopters used for amateur and semi-professional applications, such as photography and video recording.
• Medium-sized drones: These drones weigh between 2 and 25 kg and are commonly used for commercial applications, including geographic mapping, security operations, and, in some cases, delivery services.
• Large drones: These can weigh more than 25 kg and often require special permissions for use. They are used for specific purposes, such as heavy loads, agricultural applications, or large film productions.
• VTOL drones: This category includes drones capable of vertical take-off and landing, allowing them to operate from limited spaces without the need for runways. Unlike traditional quadcopters, VTOL drones are often hybrids between drones and fixed-wing aircraft, which provides them with greater aerodynamic efficiency and extended range at higher speeds. Typical VTOL drone speeds range from 100 to 200 km/h, depending on the design and intended purpose. These drones are well-suited for demanding tasks, such as longer-distance delivery or surveillance operations, where higher speed and efficiency are required.

Based on this categorization, for the purpose of transporting a container weighing up to 3000 g, a medium-sized drone in the configuration of a classic quadcopter, as shown in Figure 6, was initially selected. Its maximum design speed was set at 60 km/h, and thus all primary simulations were conducted around this speed. However, in later stages of the project, consideration was given to the potential use of VTOL-type drones for transporting the container with samples. Due to the greater speed capabilities of VTOL drones, simulations were also conducted at speeds of up to 240 km/h to account for this possible adaptation in transport methods.

2.7. Other Factors Affecting the Drone’s Maneuverability and Control Response

The analysis of the container’s impact on the drone’s flight characteristics primarily focused on drag, lift, and stability. However, additional factors influencing the drone’s maneuverability and control response also merit consideration. The addition of a suspended container shifts the drone’s center of gravity, potentially impacting pitch, roll, and yaw dynamics, which could lead to delayed or less precise control responses, particularly during rapid maneuvers or in turbulent conditions. While static stability was considered, the dynamic behavior of the drone under varying flight conditions, such as sudden wind gusts or quick direction changes, could induce oscillatory motions or necessitate frequent corrective inputs. Such dynamic effects are critical for applications requiring precise positioning, such as medical transport in dense urban environments.

Moreover, the aerodynamic interaction between the container and the drone’s rotors during yaw maneuvers or under crosswind conditions could generate asymmetric forces, compromising stability and control. Similarly, sharp turns, accelerations, and decelerations may temporarily increase power demand due to additional aerodynamic loads on the container, making an understanding of these transient effects vital for optimizing battery efficiency and ensuring reliable mission performance. The interaction between the container and the drone during flight, particularly during abrupt trajectory or altitude changes, could also generate vibrations or stresses, potentially impacting the structural integrity of both the drone’s frame and the container. Adverse environmental conditions, such as strong winds or fluctuating humidity, could further exacerbate these challenges, affecting overall maneuverability and control. These additional aspects, such as the drone’s maneuverability and control response, undoubtedly warrant further investigation to provide a comprehensive evaluation of the system’s behavior. While the primary focus of this study was on drag, lift, and stability as critical parameters for understanding aerodynamic performance and energy efficiency, the shift in the drone’s center of gravity, dynamic stability under varying conditions, yaw and side force asymmetries, increased power demands during maneuvers, structural stresses, and environmental factors all represent significant areas for future research.

Simulations using platforms such as SolidWorks or advanced Computational Fluid Dynamics (CFD) tools could incorporate unsteady flow simulations, dynamic modeling of flight control systems, and structural analysis under dynamic loads to address these challenges, with real-world flight tests serving to validate theoretical models and ensure operational reliability. Although these considerations are essential for advancing the understanding of drone–container systems, they fall outside the scope of this article, and the conclusions derived from the analysis of drag, lift, and stability were deemed sufficient to meet the primary objectives of this study.

3. Results

In this chapter, we focus entirely on evaluating all conducted simulations, as also referenced in the literature [61,62,63,64]. In the subsequent subchapters, we provide additional details, including both graphical (in Figure 7, Figure 8, Figure 9, Figure 10, Figure 11, Figure 12, Figure 13, Figure 14, Figure 15, Figure 16, Figure 17 and Figure 18) and numerical (in Table 2, Table 3, Table 4 and Table 5) presentations of the simulation results for the shape of the transport container.

Results of Simulations for the Shape of the Transport Container in the Form of a Rectangular Prism:

Figure 7. Rectangular prism profile—impact of air resistance at the following speeds: (a) 20 km/h; (b) 40 km/h; (c) 60 km/h; and (d) 80 km/h.

Figure 7. Rectangular prism profile—impact of air resistance at the following speeds: (a) 20 km/h; (b) 40 km/h; (c) 60 km/h; and (d) 80 km/h.

Figure 8. Rectangular prism profile—impact of air resistance at the following speeds: (a) 100 km/h; (b) 120 km/h; (c) 140 km/h; and (d) 160 km/h.

Figure 8. Rectangular prism profile—impact of air resistance at the following speeds: (a) 100 km/h; (b) 120 km/h; (c) 140 km/h; and (d) 160 km/h.

Figure 9. Rectangular prism profile—impact of air resistance at the following speeds: (a) 180 km/h; (b) 200 km/h; (c) 220 km/h; and (d) 240 km/h.

Figure 9. Rectangular prism profile—impact of air resistance at the following speeds: (a) 180 km/h; (b) 200 km/h; (c) 220 km/h; and (d) 240 km/h.

Table 2. Shape of rectangular prism—evaluation of pressure effects during forward flight.

Speed [km/h]	Minimum Pressure [Pa]	Maximum Pressure [Pa]	Pressure Difference [Pa]
20	147,267,585	147,327,383	59,798
40	147,214,708	147,454,485	239,777
60	147,121,997	147,659,363	537,366
80	146,999,048	147,953,031	953,983
100	146,841,997	148,331,190	1,489,193
120	146,648,245	148,788,320	2,140,075
140	146,407,904	149,332,991	2,925,087
160	146,135,838	149,939,608	3,803,770
180	145,848,368	150,663,173	4,814,805
200	145,493,985	151,411,291	5,917,306
220	145,180,020	152,307,148	7,127,128
240	144,856,286	153,332,829	8,476,543

Table 2. Shape of rectangular prism—evaluation of pressure effects during forward flight.

Speed [km/h]	Minimum Pressure [Pa]	Maximum Pressure [Pa]	Pressure Difference [Pa]
20	147,267,585	147,327,383	59,798
40	147,214,708	147,454,485	239,777
60	147,121,997	147,659,363	537,366
80	146,999,048	147,953,031	953,983
100	146,841,997	148,331,190	1,489,193
120	146,648,245	148,788,320	2,140,075
140	146,407,904	149,332,991	2,925,087
160	146,135,838	149,939,608	3,803,770
180	145,848,368	150,663,173	4,814,805
200	145,493,985	151,411,291	5,917,306
220	145,180,020	152,307,148	7,127,128
240	144,856,286	153,332,829	8,476,543

Results of Simulations for the Shape of the Transport Container in the Form of a Sphere:

Figure 10. Sphere profile shape—impact of air resistance at the following speeds: (a) 20 km/h; (b) 40 km/h; (c) 60 km/h; and (d) 80 km/h.

Figure 10. Sphere profile shape—impact of air resistance at the following speeds: (a) 20 km/h; (b) 40 km/h; (c) 60 km/h; and (d) 80 km/h.

Figure 11. Sphere profile shape—impact of air resistance at the following speeds: (a) 100 km/h; (b) 120 km/h; (c) 140 km/h; and (d) 160 km/h.

Figure 11. Sphere profile shape—impact of air resistance at the following speeds: (a) 100 km/h; (b) 120 km/h; (c) 140 km/h; and (d) 160 km/h.

Figure 12. Sphere profile shape—impact of air resistance at the following speeds: (a) 180 km/h; (b) 200 km/h; (c) 220 km/h; and (d) 240 km/h.

Figure 12. Sphere profile shape—impact of air resistance at the following speeds: (a) 180 km/h; (b) 200 km/h; (c) 220 km/h; and (d) 240 km/h.

Table 3. Sphere profile shape—evaluation of pressure effects during forward flight.

Speed [km/h]	Minimum Pressure [Pa]	Maximum Pressure [Pa]	Pressure Difference [Pa]
20	147,228,771	147,318,228	89,457
40	147,056,667	147,416,100	359,433
60	146,773,069	147,579,304	80,6235
80	146,369,578	147,808,052	1,438,474
100	145,963,733	148,103,499	2,139,766
120	145,382,943	148,468,639	3,085,696
140	144,719,140	148,895,044	4,175,904
160	143,949,531	149,391,569	5,442,038
180	143,065,448	149,953,698	6,888,250
200	142,022,091	150,585,158	8,563,067
220	140,944,972	151,281,451	10,336,479
240	139,800,937	152,045,238	12,244,301

Table 3. Sphere profile shape—evaluation of pressure effects during forward flight.

Speed [km/h]	Minimum Pressure [Pa]	Maximum Pressure [Pa]	Pressure Difference [Pa]
20	147,228,771	147,318,228	89,457
40	147,056,667	147,416,100	359,433
60	146,773,069	147,579,304	80,6235
80	146,369,578	147,808,052	1,438,474
100	145,963,733	148,103,499	2,139,766
120	145,382,943	148,468,639	3,085,696
140	144,719,140	148,895,044	4,175,904
160	143,949,531	149,391,569	5,442,038
180	143,065,448	149,953,698	6,888,250
200	142,022,091	150,585,158	8,563,067
220	140,944,972	151,281,451	10,336,479
240	139,800,937	152,045,238	12,244,301

Results of Simulations for the Shape of the Transport Container in the Form of an Airfoil According to the NACA 9330 Profile:

Figure 13. NACA 9330 profile shape—impact of air resistance at the following speeds: (a) 20 km/h; (b) 40 km/h; (c) 60 km/h; and (d) 80 km/h.

Figure 13. NACA 9330 profile shape—impact of air resistance at the following speeds: (a) 20 km/h; (b) 40 km/h; (c) 60 km/h; and (d) 80 km/h.

Figure 14. NACA 9330 profile shape—impact of air resistance at the following speeds: (a) 100 km/h; (b) 120 km/h; (c) 140 km/h; and (d) 160 km/h.

Figure 14. NACA 9330 profile shape—impact of air resistance at the following speeds: (a) 100 km/h; (b) 120 km/h; (c) 140 km/h; and (d) 160 km/h.

Figure 15. NACA 9330 profile shape—impact of air resistance at the following speeds: (a) 180 km/h; (b) 200 km/h; (c) 220 km/h; and (d) 240 km/h.

Figure 15. NACA 9330 profile shape—impact of air resistance at the following speeds: (a) 180 km/h; (b) 200 km/h; (c) 220 km/h; and (d) 240 km/h.

Table 4. NACA 9330 profile shape—evaluation of pressure effects during forward flight.

Speed [km/h]	Minimum Pressure [Pa]	Maximum Pressure [Pa]	Pressure Difference [Pa]
20	147,253,001	147,311,841	58,840
40	147,115,421	147,412,383	29,6962
60	146,901,123	147,570,913	669,790
80	146,603,095	147,792,808	1,189,713
100	146,217,150	148,079,291	1,862,141
120	145,742,296	148,427,797	2,685,501
140	145,205,211	148,845,902	3,640,691
160	144,415,476	149,317,401	4,90,1925
180	143,639,057	149,858,161	6,219,104
200	142,765,952	150,465,921	7,699,969
220	141,794,140	151,136,304	9,342,164
240	140,728,871	151,872,598	11,143,727

Table 4. NACA 9330 profile shape—evaluation of pressure effects during forward flight.

Speed [km/h]	Minimum Pressure [Pa]	Maximum Pressure [Pa]	Pressure Difference [Pa]
20	147,253,001	147,311,841	58,840
40	147,115,421	147,412,383	29,6962
60	146,901,123	147,570,913	669,790
80	146,603,095	147,792,808	1,189,713
100	146,217,150	148,079,291	1,862,141
120	145,742,296	148,427,797	2,685,501
140	145,205,211	148,845,902	3,640,691
160	144,415,476	149,317,401	4,90,1925
180	143,639,057	149,858,161	6,219,104
200	142,765,952	150,465,921	7,699,969
220	141,794,140	151,136,304	9,342,164
240	140,728,871	151,872,598	11,143,727

Results of Simulations for the Shape of the Transport Container in the Form of a Rounded Cylinder:

Figure 16. Rounded cylinder profile shape—impact of air resistance at the following speeds: (a) 20 km/h; (b) 40 km/h; (c) 60 km/h; and (d) 80 km/h.

Figure 16. Rounded cylinder profile shape—impact of air resistance at the following speeds: (a) 20 km/h; (b) 40 km/h; (c) 60 km/h; and (d) 80 km/h.

Figure 17. Rounded cylinder profile shape—impact of air resistance at the following speeds: (a) 100 km/h; (b) 120 km/h; (c) 140 km/h; and (d) 160 km/h.

Figure 17. Rounded cylinder profile shape—impact of air resistance at the following speeds: (a) 100 km/h; (b) 120 km/h; (c) 140 km/h; and (d) 160 km/h.

Figure 18. Rounded cylinder profile shape—impact of air resistance at the following speeds: (a) 180 km/h; (b) 200 km/h; (c) 220 km/h; and (d) 240 km/h.

Figure 18. Rounded cylinder profile shape—impact of air resistance at the following speeds: (a) 180 km/h; (b) 200 km/h; (c) 220 km/h; and (d) 240 km/h.

Table 5. Rounded cylinder shape—evaluation of pressure effects during forward flight.

Speed [km/h]	Minimum Pressure [Pa]	Maximum Pressure [Pa]	Pressure Difference [Pa]
20	147,235,287	147,317,339	82,052
40	147,084,225	147,412,530	328,305
60	146,832,192	147,571,279	739,087
80	146,479,037	147,793,642	1,314,605
100	146,024,970	148,079,978	2,055,008
120	145,467,528	148,430,121	2,962,593
140	144,808,727	148,844,730	4,036,003
160	144,128,976	149,334,436	5,205,460
180	143,283,829	149,880,978	6,597,149
200	142,336,704	150,493,229	8,156,525
220	141,273,526	151,173,261	9,899,735
240	140,118,419	151,917,187	11,798,768

Table 5. Rounded cylinder shape—evaluation of pressure effects during forward flight.

Speed [km/h]	Minimum Pressure [Pa]	Maximum Pressure [Pa]	Pressure Difference [Pa]
20	147,235,287	147,317,339	82,052
40	147,084,225	147,412,530	328,305
60	146,832,192	147,571,279	739,087
80	146,479,037	147,793,642	1,314,605
100	146,024,970	148,079,978	2,055,008
120	145,467,528	148,430,121	2,962,593
140	144,808,727	148,844,730	4,036,003
160	144,128,976	149,334,436	5,205,460
180	143,283,829	149,880,978	6,597,149
200	142,336,704	150,493,229	8,156,525
220	141,273,526	151,173,261	9,899,735
240	140,118,419	151,917,187	11,798,768

Collective Evaluation of Simulations for Selected Shapes of Transport Containers

In this subsection, we graphically represent the individually obtained results of simulations of various shapes into consolidated graphs to determine how they performed during simulations, as graphically depicted in Figure 7, Figure 8, Figure 9, Figure 10, Figure 11, Figure 12, Figure 13, Figure 14, Figure 15, Figure 16, Figure 17 and Figure 18 and numerically presented in Table 2, Table 3, Table 4 and Table 5. It will be crucial for us to ascertain if there are any significant benefits resulting from their shape differences.

Based on the results presented in Figure 19, Figure 20, Figure 21 and Figure 22, we can state that at low speeds of up to 60 km/h, which is the maximum operational flight speed of our drone, the selection of the shape of the transport container is independent of speed and does not influence it. For this reason, other operational parameters imposed on the transport container become more significant in the design, and the shape is subject to the preference and judgment of the developers. This is also why we have chosen the shape of a rounded cylinder for our project’s solution.

Figure 23 demonstrates how resistance increases for various profiles with increasing speed. Based on this chart, we can conclude that the speed threshold at which the shape of the transport box begins to impact aerodynamic resistance starts at around 80 km/h, and that is only with the purely non-aerodynamic shape of a rectangular prism.

Aerodynamic simulations and physical flight tests confirmed that the rounded cylinder is the optimal choice for suspended transport containers. Practical validation corroborated the numerical results, ensuring that the selected design met all performance and safety requirements.

Based on these evaluations, we determined that the shape of the suspended container significantly impacts flight characteristics, particularly at speeds exceeding 80 km/h. The selection of an aerodynamic design, such as a rounded cylinder, ensures reduced drag, improved stability, and optimized energy consumption, as corroborated by the data presented in Section 3 and Figure 19, Figure 20, Figure 21, Figure 22 and Figure 23. These findings provide a comprehensive evaluation of the factors influencing the flight characteristics of drones equipped with underslung containers.

The simulation results, presented in Table 2, Table 3, Table 4, Table 5, Table 6 and Table 7 and Figure 19, Figure 20, Figure 21, Figure 22, Figure 23, Figure 24 and Figure 25, provided a detailed overview of the aerodynamic behavior of the selected transport container shapes, focusing on pressure differences, dynamic pressure, and pressure coefficient (Cp) across various speeds. These comprehensive analyses allowed for a precise evaluation of the effects of container shape on aerodynamic efficiency and stability.

Table 6. Pressure coefficient (Pc)—evaluation of effects during forward flight.

Speed (km/h)	Rectangular Prism Min Pc	Rectangular Prism Max Pc	Sphere Min Pc	Sphere Max Pc	NACA 9330 Profile Min Pc	NACA 9330 Profile Max Pc	Rounded Cylinder Min Pc	Rounded Cylinder Max Pc
20	5,453,108	5,455,322	5,451,671	5,454,983	5,452,568	5,454,747	5,451,912	5,454,950
40	1,362,787	1,365,007	1,361,324	1,364,651	1,361,868	1,364,617	1,361,579	1,364,618
60	605,301	607,512	603,866	607,183	604,393	607,148	604,109	607,150
80	340,197	342,405	338,741	342,070	339,281	342,034	338,994	342,036
100	217,493	219,699	216,193	219,362	216,568	219,326	216,283	219,327
120	150,838	153,039	149,536	152,710	149,906	152,668	149,623	152,670
140	110,638	112,848	109,362	112,517	109,729	112,480	109,429	112,479
160	84,550	86,750	83,285	86,433	83,554	86,390	83,388	86,400
180	66,673	68.874	65,401	68,550	65,663	68,506	65,501	68,517
200	53,874	56,065	52,588	55,759	52,864	55,715	52,705	55,725
220	44,428	46,609	43,132	46,295	43,392	46,250	43,232	46,262
240	37,248	39,428	36,030	39,064	36,187	39,052	36,030	39,064

Table 6. Pressure coefficient (Pc)—evaluation of effects during forward flight.

Speed (km/h)	Rectangular Prism Min Pc	Rectangular Prism Max Pc	Sphere Min Pc	Sphere Max Pc	NACA 9330 Profile Min Pc	NACA 9330 Profile Max Pc	Rounded Cylinder Min Pc	Rounded Cylinder Max Pc
20	5,453,108	5,455,322	5,451,671	5,454,983	5,452,568	5,454,747	5,451,912	5,454,950
40	1,362,787	1,365,007	1,361,324	1,364,651	1,361,868	1,364,617	1,361,579	1,364,618
60	605,301	607,512	603,866	607,183	604,393	607,148	604,109	607,150
80	340,197	342,405	338,741	342,070	339,281	342,034	338,994	342,036
100	217,493	219,699	216,193	219,362	216,568	219,326	216,283	219,327
120	150,838	153,039	149,536	152,710	149,906	152,668	149,623	152,670
140	110,638	112,848	109,362	112,517	109,729	112,480	109,429	112,479
160	84,550	86,750	83,285	86,433	83,554	86,390	83,388	86,400
180	66,673	68.874	65,401	68,550	65,663	68,506	65,501	68,517
200	53,874	56,065	52,588	55,759	52,864	55,715	52,705	55,725
220	44,428	46,609	43,132	46,295	43,392	46,250	43,232	46,262
240	37,248	39,428	36,030	39,064	36,187	39,052	36,030	39,064

Table 7. Dynamic pressure—evaluation of effects during forward flight.

Speed [km/h]	20	40	60	80	100	120	140	160	180	200	220	240
Dynamic pressure [Pa]	27.01	108.02	243.06	432.10	675.15	972.22	1323.30	1728.40	2187.50	2700.62	3267.75	3888.89

Table 7. Dynamic pressure—evaluation of effects during forward flight.

Speed [km/h]	20	40	60	80	100	120	140	160	180	200	220	240
Dynamic pressure [Pa]	27.01	108.02	243.06	432.10	675.15	972.22	1323.30	1728.40	2187.50	2700.62	3267.75	3888.89

Figure 24. Cumulative representation of the effects of maximum air pressures from speeds of 20 to 240 km/h for the selected individual shapes in Table 6.

Figure 24. Cumulative representation of the effects of maximum air pressures from speeds of 20 to 240 km/h for the selected individual shapes in Table 6.

Figure 25. Impact of speed on increasing dynamic pressure [Pa] during forward flight from speeds of 20 to 240 km/h regarding Table 7.

Figure 25. Impact of speed on increasing dynamic pressure [Pa] during forward flight from speeds of 20 to 240 km/h regarding Table 7.

The pressure coefficient (Cp), detailed in Table 6 and visualized in Figure 24, offers a non-dimensional measure of aerodynamic performance. At lower speeds, the differences in Cp among all shapes were minimal. For instance, at 20 km/h, the Cp for the rectangular prism ranged from 5.45 × 10⁶ to 5.46 × 10⁶, which was comparable to the sphere and rounded cylinder. However, as speed increased, the Cp values for non-aerodynamic shapes like the rectangular prism rose sharply. At 240 km/h, the rectangular prism’s Cp reached approximately 37,249 to 39,428, whereas the rounded cylinder and the NACA 9330 profile exhibited substantially lower values, around 36,030 to 39,064. These results, highlighted in Figure 24, underscore the significant aerodynamic advantage of streamlined shapes at higher velocities.

Dynamic pressure trends, shown in Table 7 and Figure 25, further emphasized the increasing aerodynamic demands with speed escalation. Dynamic pressure, which scales with the square of velocity, played a crucial role in determining drag forces. At speeds above 80 km/h, the rectangular prism exhibited a steep rise in drag due to its higher Cp values, leading to greater energy consumption and reduced stability. In contrast, the rounded cylinder and the NACA 9330 profile managed dynamic pressure effectively, maintaining smoother airflow and consistent aerodynamic performance.

The consolidated analysis in Figure 23, which compares the maximum air pressures across all shapes, demonstrated that non-aerodynamic shapes like the rectangular prism experienced significantly higher pressure differentials, particularly at speeds above 100 km/h. This trend aligns with the findings in Figure 24, where the rectangular prism’s Cp continued to diverge from those of the more streamlined shapes as velocity increased.

In conclusion, the integration of pressure coefficient data from Table 6 and Figure 24 provided critical insights into the aerodynamic behaviors of the selected shapes. The rounded cylinder and NACA 9330 profile consistently outperformed the rectangular prism in terms of Cp and drag reduction, ensuring better energy efficiency and stability at higher speeds. These findings reinforce the selection of the rounded cylinder as the optimal container shape for drone-suspended transport, offering a balance between aerodynamic performance and practical considerations such as manufacturability and safety. This comprehensive evaluation serves as a robust framework for optimizing drone payload designs in future applications, with the drone payload displayed in Figure 26.

4. Discussion

The primary objective of this study was to identify the most advantageous shape for the construction of a suspended transport container intended for the conveyance of sensitive biological materials via drone. This investigation was undertaken as part of our project, ITMS2014+:313011 ATR9, titled “Research and Development of the Applicability of Autonomous Flying Vehicles in the Fight Against the COVID-19 Pandemic” [65,66,67,68,69,70,71]. This focus was necessitated by the lack of existing studies addressing similar topics in the extant professional literature, where the primary emphasis has traditionally been on optimizing aerodynamically efficient shapes. Consequently, basic shapes such as the rectangular prism (cube), sphere, and rounded cylinder, which are commonly employed in suspended transport containers, have been insufficiently studied.

Our findings reveal that while aerodynamic considerations are important at higher speeds, operational, economic, strength, and construction objectives take precedence at the typical speeds for which these containers are designed. This conclusion represents a significant contribution to the field, as prior research has not extensively examined the issue from this viewpoint. By focusing on these broader design goals, new container designs can achieve greater alignment with practical application needs, enhancing their usability and efficiency.

This study leverages advanced Computational Fluid Dynamics (CFD) simulations to systematically evaluate the effects of container geometry on aerodynamic drag, stability, and energy efficiency. By employing a comparative analysis of various container shapes, including rectangular prisms, spheres, rounded cylinders, and NACA airfoil profiles, we provide a comprehensive assessment of their aerodynamic performance. These designs were carefully selected to balance practical manufacturability and aerodynamic efficiency, thereby addressing a critical gap in existing literature.

In our endeavor to ensure that our selection was both responsible and professionally justified, we conducted extensive validation of our findings through simulations. Given the constraints imposed by the project’s timeline, our goal was to derive results in the most straightforward manner possible. Accordingly, we employed a simplified simulation model that primarily considered the aerodynamic drag induced by pressure differences generated by the suspended container. While it was possible to conduct more complex simulations, such as those incorporating airflow from various directions, changes in flow type to include non-laminar dynamic events, or varying parameters like humidity, temperature, and air density, such enhancements were deemed non-essential for our primary objective given their minimal impact at the low speeds relevant to our study.

The results of our expanded evaluation demonstrate that the aerodynamic shape of the suspended transport container plays an increasingly significant role as speed increases. At low speeds of up to 60 km/h—the maximum operational speed of our drone—differences between container shapes were negligible. As evident in Figure 19, Figure 20, Figure 21, Figure 22 and Figure 23, drag forces and pressure distributions for all tested shapes were within a 2% margin, indicating minimal impact on the drone’s overall energy efficiency and stability. Thus, at these speeds, the design selection can prioritize practical considerations such as manufacturability, cost, and safety over aerodynamic efficiency.

At higher speeds, however, additional aerodynamic parameters such as the pressure coefficient (Cp) and dynamic pressure become critical, significantly influencing energy efficiency and stability. The incorporation of Cp data, as shown in Table 7 and Figure 24, provided a detailed quantitative perspective on aerodynamic behavior. For instance, while Cp values for various shapes were nearly identical at 20 km/h, they diverged markedly as speed increased. At 240 km/h, the Cp for the rectangular prism rose sharply to values between 37,248 and 39,428, compared to the rounded cylinder and the NACA 9330 profile, which maintained substantially lower values, around 36,030 to 39,064. These results highlight the aerodynamic advantage of streamlined shapes, particularly at high velocities.

Dynamic pressure trends, illustrated in Table 7 and Figure 25, further emphasized the increasing aerodynamic demands with speed escalation. For speeds exceeding 80 km/h, non-aerodynamic shapes exhibited steep rises in dynamic pressure, directly correlating with increased drag and energy consumption. For instance, the dynamic pressure for the rectangular prism surged to approximately 3888.89 Pa at 240 km/h, a notable contrast to the more stable performance of the rounded cylinder and NACA 9330 profile. These trends not only validate the aerodynamic superiority of streamlined shapes but also underscore their importance for energy efficiency and operational stability.

For speeds exceeding 80 km/h, non-aerodynamic shapes such as rectangular prisms exhibited a sharp increase in drag and pressure differential between the leading and trailing surfaces, as detailed in Figure 23. For these shapes, the drag coefficient increased by 12–15%, while aerodynamic shapes such as the rounded cylinder or the NACA 9330 profile showed a drag increase of only 5–8%. These differences directly impacted energy efficiency, with rectangular prisms consuming approximately 25% more energy than rounded cylinders at speeds above 180 km/h.

The study also highlighted the importance of mitigating stability challenges caused by the addition of an underslung container. For non-aerodynamic shapes, the shift in the center of gravity was more pronounced, leading to a 20% reduction in pitch stability. Rounded shapes, in contrast, caused a smaller shift in the center of gravity, thereby maintaining control stability and reducing the need for flight controller compensation. This distinction is particularly significant for drones operating in windy or turbulent environments.

These findings emphasize the necessity of optimizing the container’s aerodynamic profile to minimize energy expenditure and extend operational range. Rounded shapes and streamlined profiles such as the NACA 9330 profile are ideal for maintaining energy efficiency at higher speeds, offering a balance between performance and practicality. Safety considerations played a central role in selecting the container’s shape. The ability of the container to minimize rotational forces during an accidental fall and to land with the largest possible surface area was deemed essential for protecting sensitive biological materials. Rounded cylinders demonstrated superior performance in this regard, providing better shock absorption and reducing the likelihood of internal damage to the transported materials.

The expanded analysis reinforces the importance of aerodynamic optimization for suspended transport containers, particularly for drones operating at speeds exceeding 80 km/h. While all shapes are viable for low-speed operations, aerodynamic designs such as rounded cylinders and NACA 9330 profiles are essential for maintaining energy efficiency, stability, and safety at higher speeds. Furthermore, the integration of pressure coefficient and dynamic pressure data strengthens the theoretical foundation of this study, providing actionable insights for optimizing container designs. These findings provide a robust foundation for future research and practical implementation in the design of transport containers for unmanned aerial systems, addressing both aerodynamic and operational considerations. Moreover, the results underscore the need for continued empirical validation through practical flight tests, ensuring that theoretical findings translate effectively into real-world applications.

5. Conclusions

The final configuration of the suspended container, as selected based on the results previously discussed, was that of a rounded cylinder. This design choice emerged as optimal following extensive computational and practical evaluations, including aerodynamic simulations and physical testing. The rounded cylinder demonstrated superior aerodynamic efficiency, stability, and safety compared to other evaluated shapes, such as the rectangular prism, sphere, and NACA 9330 profile. Practical tests and certification of the container corroborated the accuracy of our initial assumptions and predictions, confirming its suitability for real-world applications.

Comprehensive testing of the physically realized prototype included assessments of internal vibrations across various flight conditions and crash and impact tests. These evaluations confirmed the container’s ability to safely transport sensitive laboratory materials, such as blood, tissues, serum, and other biological samples, under diverse operating conditions. The container met strict safety and performance requirements, ensuring its functionality for medical applications and beyond.

The study also highlighted the critical role of aerodynamic optimization in minimizing energy consumption and maintaining operational stability, especially at higher speeds. The rounded cylinder consistently outperformed less aerodynamic shapes by reducing drag, maintaining smoother airflow, and ensuring stability during flight. This aerodynamic efficiency directly contributed to enhanced energy savings and extended operational range, making the container a sustainable choice for drone operations.

Additional benefits of the rounded cylinder included improved stability due to minimal shifts in the drone’s center of gravity, reducing the need for compensatory flight controller adjustments. Safety features, such as the ability to minimize rotational forces during accidental falls and land with optimal surface area, further reinforced its suitability for sensitive material transport. The container also complied with ingress and impact protection standards, ensuring robust defense against environmental and mechanical stresses.

The integration of advanced simulation techniques and practical testing in this study provided critical insights into the design and optimization of drone payloads. These findings establish a solid framework for future research and practical applications, including the development of drone-suspended containers for diverse industries. While this work focused on medical transport, the methodologies and results offer valuable guidance for broader UAV applications. The rounded cylinder stands as an exemplary design, balancing aerodynamic performance, operational efficiency, and safety, while addressing practical considerations critical to real-world use [45].

Through this study, we aim to contribute a robust framework for integrating aerodynamic principles into the design of drone payloads. The insights provided are not only applicable to medical transport but also extend to broader UAV applications, offering a pathway for future innovations in drone logistics.