research paper on glider

For New Insights into Aerodynamics, Scientists Turn to Paper Airplanes

A series of experiments using paper airplanes reveals new aerodynamic effects--findings that enhance our understanding of flight stability.

Findings Unveil Mechanisms that Explain Flight Stability

A series of experiments using paper airplanes reveals new aerodynamic effects, a team of scientists has discovered. Its findings enhance our understanding of flight stability and could inspire new types of flying robots and small drones.

“The study started with simple curiosity about what makes a good paper airplane and specifically what is needed for smooth gliding,” explains Leif Ristroph, an associate professor at New York University’s Courant Institute of Mathematical Sciences and an author of the study , which appears in the Journal of Fluid Mechanics . “Answering such basic questions ended up being far from child’s play. We discovered that the aerodynamics of how paper airplanes keep level flight is really very different from the stability of conventional airplanes.”

“Birds glide and soar in an effortless way, and paper airplanes, when tuned properly, can also glide for long distances,” adds author Jane Wang, a professor of engineering and physics at Cornell University. “Surprisingly, there has been no good mathematical model for predicting this seemingly simple but subtle gliding flight.”

Since we can make complicated modern airplanes fly, the researchers say, one might think we know all there is to know about the simplest flying machines. 

“But paper airplanes, while simple to make, involve surprisingly complex aerodynamics,” notes Ristroph.

The paper’s authors began their study by considering what is needed for a plane to glide smoothly. Since paper airplanes have no engine and rely on gravity and proper design for their movement, they are good candidates for exploring factors behind flight stability.

To investigate this phenomenon, the researchers conducted lab experiments by launching paper airplanes with differing centers of mass through the air. The results, along with those from studying plates falling in a water tank, allowed the team to devise a new aerodynamic model and also a “flight simulator” capable of predicting the motions.

A video and image showing the experimental results may be downloaded from Google Drive .

To find the best design, the researchers placed different amounts of thin copper tape on the front part of the paper planes, giving them varied center of mass locations. Lead weights added to the plates in water served the same purpose.

“The key criterion of a successful glider is that the center of mass must be in the ‘just right’ place,” Ristroph explains. “Good paper airplanes achieve this with the front edge folded over several times or by an added paper clip, which requires a little trial and error.”

In the experiments, the researchers found that the flight motions depended sensitively on the center of mass location. Specifically, if the weight was at the center of the wing or only displaced somewhat from the middle, it underwent wild motions, such as fluttering or tumbling. If the weight was displaced too far toward one edge, then the flier quickly dove downwards and crashed. In between, however, there was a “sweet spot” for the center of mass that gave stable gliding.

The researchers coupled the experimental work with a mathematical model that served as the basis of a “flight simulator,” a computer program that successfully reproduced the different flight motions. It also helped explain why a paper airplane is stable in its glide. When the center of mass is in the “sweet spot,” the aerodynamic force on the plane’s wing pushes the wing back down if the plane moves upward and back up if it moves downward.

“The location of the aerodynamic force or center of pressure varies with the angle of flight in such a way to ensure stability,” explains Ristroph. 

He notes that this dynamic does not occur with conventional aircraft wings, which are airfoils—structures whose shapes work to generate lift. 

“The effect we found in paper airplanes does not happen for the traditional airfoils used as aircraft wings, whose center of pressure stays fixed in place across the angles that occur in flight,” Ristroph says. “The shifting of the center of pressure thus seems to be a unique property of thin, flat wings, and this ends up being the secret to the stable flight of paper airplanes.”

“This is why airplanes need a separate tail wing as a stabilizer while a paper plane can get away with just a main wing that gives both lift and stability,” he concludes. “We hope that our findings will be useful in small-scale flight applications, where you may want a minimal design that does not require a lot of extra flight surfaces, sensors, and controllers.”

The paper’s other authors were Huilin Li, a doctoral candidate at NYU Shanghai, and Tristan Goodwill, a doctoral candidate at the Courant Institute’s Department of Mathematics.

The work was supported by grants from the National Science Foundation (DMS-1847955, DMS-1646339).

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On the eleventh day of Christmas —

Experiments with paper airplanes reveal surprisingly complex aerodynamics, how these gliders keep level flight is different from the stability of airplanes..

Jennifer Ouellette - Jan 4, 2023 10:06 pm UTC

Drop a flat piece of paper and it will flutter and tumble through the air as it falls, but a well-fashioned paper airplane will glide smoothly. Although these structures look simple, their aerodynamics are surprisingly complex. Researchers at New York University’s Courant Institute of Mathematical Sciences conducted a series of experiments involving paper airplanes to explore this transition and develop a mathematical model to predict flight stability, according to a March paper published in the Journal of Fluid Mechanics.

“The study started with simple curiosity about what makes a good paper airplane and specifically what is needed for smooth gliding," said co-author Leif Ristroph . "Answering such basic questions ended up being far from child’s play. We discovered that the aerodynamics of how paper airplanes keep level flight is really very different from the stability of conventional airplanes.”

Nobody knows who invented the first paper airplane, but China began making paper on a large scale around 500 BCE, with the emergence of origami and paper-folding as a popular art form between 460 and 390 BCE. Paper airplanes have long been studied as a means of learning more about the aerodynamics of flight. For instance, Leonardo da Vinci famously built a model plane out of parchment while dreaming up flying machines and used paper models to test his design for an ornithopter. In the 19th century, British engineer and inventor Sir George Cayley —sometimes called the "father of aviation"—studied the gliding performance of paper airplanes to design a glider capable of carrying a human.

An amusing "scientist playing with paper planes" anecdote comes from physicist Theodore von Kármán . In his 1967 memoir The Wind and Beyond , he recalled a formal 1924 banquet in Delft, The Netherlands, where fellow physicist Ludwig Prandtl constructed a paper airplane out of a menu to demonstrate the mechanics of flight to von Kármán's sister, who was seated next to him. When he threw the paper plane, "It landed on the shirtfront of the French minister of education, much to the embarrassment of my sister and others at the banquet," von Kármán wrote.

While scientists have clearly made great strides in aerodynamics—particularly about aircraft—Ristroph et al . noted that there was not a good mathematical model for predicting the simpler, subtler gliding flight of paper airplanes. It was already well-known that displacing the center of mass results in various flight trajectories, some more stable than others. “The key criterion of a successful glider is that the center of mass must be in the ‘just right’ place,” said Ristroph . “Good paper airplanes achieve this with the front edge folded over several times or by an added paper clip, which requires a little trial and error.”

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Multidisciplinary design optimization of underwater glider for improving endurance

• Research Paper
• Published: 25 February 2021
• Volume 63 , pages 2835–2851, ( 2021 )

Cite this article

• Shuxin Wang 1 , 2 ,
• Ming Yang 1 , 2 ,
• Wendong Niu   ORCID: orcid.org/0000-0001-5692-6476 1 , 2 ,
• Yanhui Wang 1 , 2 ,
• Shaoqiong Yang 1 , 2 ,
• Lianhong Zhang 1 , 2 &
• Jiajun Deng 1 , 2  

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Underwater glider (UG) is widely applied for long-term ocean observation, the gliding range of which is mainly influenced by its design. In this paper, the design parameters that have obvious influence on the gliding range, including the buoyancy factor, compressibility of the pressure hull, hydrodynamic coefficients, and motion parameters, are selected based on the gliding range model of UG. Due to their complicate coupling relationship in the design of the UG, the multidisciplinary optimization (MDO) design framework integrating the collaborative optimization (CO) method and approximate model technology is adopted to optimize the key parameters by taking the gliding range as the optimization target. The results show that the optimization leads to an increase of the gliding range of Petrel-L as much as 83.3% when the hotel load is 0.5 W, which is verified by the sea trial. The optimization is applicable to other types of underwater gliders.

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This work was jointly supported by National Natural Science Foundation of China (Grant Nos. 51722508, and 11902219) and National Key R&D Program of China (Grant No. 2016YFC0301100); Natural Science Foundation of Tianjin City (Grant Nos. 18JCQNJC05100 and 18JCJQJC46400); and Aoshan Talent Cultivation Program (Grant No. 2017ASTCP-OE01) of Pilot National Laboratory for Marine Science and Technology (Qingdao).

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Wang, S., Yang, M., Niu, W. et al. Multidisciplinary design optimization of underwater glider for improving endurance. Struct Multidisc Optim 63 , 2835–2851 (2021). https://doi.org/10.1007/s00158-021-02844-z

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Design of a Bioinspired Underwater Glider for Oceanographic Research

Diana c. hernández-jaramillo.

1 Faculty of Science and Engineering, Southern Cross University, Coffs Harbour, NSW 2450, Australia

Rafael E. Vásquez

2 School of Engineering, Universidad Pontificia Bolivariana, Medellín 050031, Colombia

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The Blue Economy, which is based on the sustainable use of the ocean, is demanding better understanding of marine ecosystems, which provide assets, goods, and services. Such understanding requires the use of modern exploration technologies, including unmanned underwater vehicles, in order to acquire quality information for decision-making processes. This paper addresses the design process for an underwater glider, to be used in oceanographic research, that was inspired by leatherback sea turtles ( Dermochelys coriacea ), which are known to have a superior diving ability and enhanced hydrodynamic performance. The design process combines elements from Systems Engineering and bioinspired design approaches. The conceptual and preliminary design stages are first described, and they allowed mapping the user’s requirements into engineering characteristics, using quality function deployment to generate the functional architecture, which later facilitated the integration of the components and subsystems. Then, we emphasize the shell’s bioinspired hydrodynamic design and provide the design solution for the desired vehicle’s specifications. The bioinspired shell yielded a lift coefficient increase due to the effect of ridges and a decrease in the drag coefficient at low angles of attack. This led to a greater lift-to-drag ratio, a desirable condition for underwater gliders, since we obtained a greater lift while producing less drag than the shape without longitudinal ridges.

1. Introduction

Natural resources are key for the sustainable development of a growing human population [ 1 ], and the Blue Economy is being developed based on the key role of the ocean, since marine ecosystems provide assets, goods, and services [ 2 , 3 ], which can be capitalized in a sustainable way, as described among several targets of the Sustainable Development Goals (SDGs) [ 4 ]. This makes the ocean a new frontier for economic development [ 5 ], which poses challenges for marine ecosystems. Such challenges require a deep understanding of the ocean ecosystem due to the fact that human activities have been increasing the rate of climate change [ 6 ], inducing accelerated ocean biodiversity losses [ 7 ].

In order to fulfill the needs resulting from the emerging interest in ocean-related industries/activities, the use of modern ocean exploration techniques that use specialized tools has grown, allowing the development of climate patterns, the exploitation of energy resources, and the characterization of different marine ecosystems, among others [ 8 , 9 ]. Consequently, the demand for multidimensional ocean information with high temporal and spatial resolutions has also grown in order to provide quality information for decision-making processes related to marine resources [ 10 ]. Among the modern exploration technologies, one can find unmanned marine vehicles, which have been used to reach inaccessible regions all around the world [ 11 ] and which are mostly divided into three types: remotely operated (ROV) [ 12 , 13 ], autonomous (AUV) [ 14 , 15 ], and surface (USV) [ 16 , 17 ] vehicles.

Among underwater vehicles, AUVs navigate autonomously based on information from their surroundings, which is provided by sensors and the navigation system [ 14 ]. Such vehicles are deployed underwater and perform tasks that vary depending on the range of the area to be surveyed. Underwater gliders constitute a type of AUV that has emerged as an alternative technology to perform long-term measurements within the water column [ 18 , 19 ]. These vehicles move vertically through buoyancy changes and move horizontally by using wings and are useful for sustained observations needed between the coastal and open ocean [ 20 ]. Several underwater gliders are torpedo-shaped vehicles, and most recent design works have been devoted to hull optimization [ 21 , 22 , 23 ] and buoyancy change modules [ 24 , 25 ] in order to increase the efficiency of such long-range low-speed surveying underwater robots.

Bioinspired design is a field that has yielded successful products/processes [ 26 ] within several disciplines during the last decade, including: electric power generation [ 27 , 28 ], architectural design [ 29 , 30 ], materials science [ 31 ], medicine [ 32 , 33 ], and marine robotic systems [ 34 , 35 , 36 , 37 , 38 , 39 ], among others. Within the field of underwater vehicles, several research works have been reported during the last two decades. For instance, Font et al. [ 40 ] presented the biomimetic design and implementation of a hydrofoil propulsion system for a turtle-based AUV. Shi et al. [ 41 ] and Xing et al. [ 42 ] developed small turtle-based amphibious robots, capable of walking on land and moving underwater. Mignano et al. [ 43 ] developed a multifin biorobotic experimental platform and computational fluid dynamics simulations to understand the propulsive forces produced in a fish-like robot. Costa et al. [ 44 ] developed a series of swimming robots until they reached the carangiform locomotion style, while looking for maximum propulsive efficiency. Aparicio-García et al. [ 45 ] proposed a parallel mechanism coupled to an artificial caudal fin for a biomimetic AUV. Li et al. [ 46 ] presented the biomimetic design of an omnidirectional underwater robot with multiple tails, capable of combining different locomotion modes. Bianchi et al. [ 47 ] reported the design and experimental tests of a cownose-ray-bioinspired underwater robot. Regarding the biomimetic design of underwater gliders, Yuan et al. [ 48 ] presented the mechatronic design of a gliding robotic dolphin. Dong et al. [ 49 ] presented the biomimetic design of a whale-shark-like underwater glider, in order to combine high maneuverability and long duration. Zhang et al. [ 50 ] addressed the biomimetic design of a manta ray robot, combining gliding and flapping propulsion systems. Wang et al. [ 51 ] developed an underwater torpedo-shaped glider with a caudal fin to enable bidirectional maneuverability. Mitin et al. [ 52 ] presented a work which describes a bioinspired propulsion system based on the thunniform principle for a robotic fish, which uses a combination of elastic components with a fixed tail fin.

Gliders, among other underwater vehicles, have been of high interest for oceanographic research due to their energy efficiency and long-range sampling capabilities. Although one can find bioinspired glider designs such as the ones in [ 48 , 49 , 50 , 51 ], no reports have been found regarding underwater gliders inspired by leatherback sea turtles ( Dermochelys coriacea ), which are known to have a superior diving ability and to be highly adapted to pelagic swimming, thanks to the five longitudinal ridges on their carapace, which result in enhanced hydrodynamic performances [ 53 ]. Hence, this work addresses the bioinspired design of an underwater glider that can operate for several months with low energy consumption, by using the principles found in the aforementioned leatherback sea turtles. Since underwater gliders rely on battery packs for the entire mission, reducing energy consumption by increasing hydrodynamic performance could result in greater endurance and a better opportunity to collect measurements during longer periods of time. The design process covers different phases: conceptual, preliminary, and detailed design, including the selection of the instrumentation and hydrodynamic analysis. This paper is organized as follows. Section 2 , Section 3 and Section 4 contain the design process, considering biomimetics and the conceptual, preliminary, and detailed design processes. Section 5 shows the underwater glider and descriptions of the mission it will perform. Finally, some conclusions and the obtained patent are presented in Section 6 and Section 7 .

2. Underwater Glider Bioinspired Design

Biomimetics has been widely used in engineering design processes by developing solutions to problems by employing analogies with biological systems [ 26 ]. In this study, the hydrodynamic performance of an underwater glider was enhanced by the shell’s design inspired by the diving ability of leatherback sea turtles [ 53 , 54 , 55 ]. The methodology used for the biomimetic design started with the definition of the problem in terms of function, by performing a functional decomposition and transferring the engineering parameters to a biological solution. The next step was to reframe the problem in order to define a biological solution to finally extract and apply the biological principle to a technical solution [ 56 ] ( Figure 1 ). Once the biomimetic design framework was established, the design of the underwater glider was divided into three stages, described below, covering the conceptual, preliminary, and detailed design. Such design stages were carried out using Systems Engineering (SE), an approach defined by NASA [ 57 ] as “a methodical, multidisciplinary approach for the design, realization, technical management, operations, and retirement of a system”. SE enables the interactions of components that provide functionality within a complex system that is expected to meet several requirements [ 58 , 59 ] and has been successfully used for the development of robotic underwater vehicles [ 60 , 61 ].

Biomimetic design process. Diagram created with the steps described in [ 56 ].

3. Conceptual Design

The first step in the underwater glider design was the conceptual design, where the user requirements were identified in the Colombian context and were translated into engineering characteristics following the Quality Function Deployment (QFD) method, as well as a functional analysis approach. This section contains the requirements’ definition and the QFD method employed to define the engineering characteristics.

3.1. Requirements’ Definitions

The area of concern is the coastal zone of the Colombian Caribbean and Pacific at depths up to 200 m, for seasonal scales of three months. The vehicle could be used not only to measure oceanographic variables, but also for environmental surveys, maritime surveillance, climate monitoring, to collect data to feed predictive models, and for monitoring activities in general.

Some technical requirements were taken into account in order to have a better description of the problem. The vehicle should operate with energy efficiency, and it should have the capacity to operate up to three consecutive months while measuring variables. It should fit in small boats to be transported to 60 to 120 km from the coast, and it should weigh less than 50 kg.

The vehicle will operate in a highly corrosive environment, with a pressure of 20 atm at 200 m of depth and a temperature of approximately 15 ∘ C. Those aspects had to be taken into account during the design process, as well as the biofouling, which may affect the vehicle during long operation periods.

3.2. Quality Function Deployment

The QFD method was used to organize all the information needed for a better understanding of the problem in the early design phase. The objective was to obtain measurable design targets for critical parameters that were identified from the customers’ requirements [ 62 ]. For the underwater glider design, the customers’ requirements were divided into two main categories: ground operation and water operation. The requirements were then translated into engineering specifications or engineering characteristics, which determined the target values for the design. The specifications were divided into the same categories as the customer’ requirements, and each one of them measured at least one of the customers’ needs. A relationship matrix between the customers’ requirements and the engineering specifications was developed to identify the importance of each specification and to determine the design targets, which in order of relevance were defined as: low operational cost, low energy consumption, long battery life, long traveled distance, and long operating time.

3.3. Preliminary Design Specifications

A Preliminary Design Specifications document (PDS) was developed as a result of the QFD analysis. From this analysis, it was expected to have a bioinspired design of the vehicle to find a nature-related solution to the efficiency in the motion pattern during the operation time, while performing dives to 200 m of depth at an approximate velocity of 0.2 m/s. The operating environment for the glider is saltwater, which is highly corrosive. Besides, at 200 m of depth, the pressure is approximately 20 atm at 15 ∘ C. As was defined before, the vehicle’s weight should be less than 50 kg, and the length should be less than 2 m. The energy sources were battery packs such as those used for the vehicles described in [ 20 ]. The vehicle should be easily transported in small boats and should be suitable for operations in different sea conditions. The calibration of the sensors was an important aspect to take into account for mission planning, as well as the maintenance requirements of the components to ensure reliability. The target market in Colombia is centered on oceanography and marine biology research centers, private and governmental companies, and military forces. Possible applications include environmental surveys, maritime surveillance and reconnaissance, climate monitoring, and environmental impact.

3.4. Functional Architecture

In order to accomplish the main purpose of performing measurements of the water column for long periods of time and at large spatial scales, six basic functions were defined for the underwater glider ( Figure 2 ). These functions can be described as follows:

• To measure oceanographic variables: This function represents the principal purpose of the underwater glider to be designed. It is in charge of performing the measurements of oceanographic variables such as salinity, temperature, depth, and dissolved oxygen.
• To move the device: This function is in charge of moving the vehicle in the water, following a sawtooth pattern reaching up to a 200 m depth.
• To supply energy: This function is responsible for providing energy to all components to guarantee proper operation during the mission.
• To protect the system: This function represents the task of protecting the vehicle and all of its components from the environment and against failures.
• To perform the mission: This function is in charge of accomplishing the mission including preparing, transporting, launching, and recovering the vehicle.
• To manage information: This function is responsible for managing all the information needed for navigation and all the information collected during operation.

Main functions of the system.

The top-level functions were divided into subfunctions ( Figure 3 ) that describe, at a lower level, what actions are needed to achieve the system’s objectives. Additionally, interactions between functions and external factors that may affect the performance of the vehicle were also defined.

Functional architecture. Main functions are divided into subfunctions. Arrows that enter into a function indicate that other functions affect this function. Arrows that go out of a function indicate that this function affects other functions.

4. Preliminary Design

The purpose of the preliminary design was to develop a general layout of devices that perform the functions and meet the prescribed requirements. Every function may be solved with several alternatives for the software and hardware. These solutions were the result of brainstorming sessions, and they were analyzed in terms of feasibility, technological maturity, and relation to the design targets. The best candidates were selected in order to achieve a design solution for the problem. During the preliminary design, the systems were described in terms of components, and the interfaces between them were defined to obtain a physical architecture. The selection and design process of the solutions for the underwater glider are presented in this section.

4.1. Oceanographic Measurements

The function of measuring oceanographic variables includes the measurement of salinity, temperature, depth, and dissolved oxygen. Commercial solutions were proposed to accomplish this function. At least three alternatives were analyzed, and a selection matrix was used to choose the best option to fulfill the design requirements. The selected options integrated in the underwater glider were the Glider Payload (CTD-GPCTD) from Sea-Bird Electronics designed for a 350 m depth, along with the SBE 43F Dissolved Oxygen (DO) sensor from the same company to facilitate the integration of the two sensors.

4.2. Vehicle Motion

The motion of the underwater glider consisted of a vertical component due to changes in buoyancy and a horizontal component due to the lift generated by the wings. This section describes the positioning and buoyancy systems and the wing sizing, and then, it is centered on the bioinspired shape design for the vehicle, as well as the hydrodynamic analysis of the configuration.

4.2.1. Positioning System

The underwater glider needs to be positioned every time it goes to the surface in order to adjust the trajectory. To solve this function, a GPS 15xL from Garmin was selected. This global positioning system permits locating the vehicle by receiving satellites signals and decoding them to calculate the position in appropriate coordinates. The GPS receiver requires a source of power, an active GPS antenna, and a clear sight to satellite signals while at the surface. That is why the vehicle needs to adjust its attitude to maintain the antenna out of the water while positioning. The UM7 from CH Robotics was selected as the Attitude and Heading Reference System (AHRS). This device employs a triaxial accelerometer, a rate gyro, and a magnetometer with an extended Kalman filter to estimate the attitude and heading. The OS5000-S 3 axial digital compass from Ocean Server was selected to provide heading, roll, and pitch data to assist navigation. Finally, the PA200 digital precision altimeter from Tritech was chosen to measure the seafloor distance.

4.2.2. Buoyancy System

The subfunctions of going down and coming up to the surface can be solved simultaneously by performing changes in the buoyancy force using ballast tanks, buoyancy engines with water, oil or air pumps and bladders, or by using thermal engines such as the one used in the Slocum Glider [ 19 , 63 , 64 ]. In this case, the hydraulic power unit was selected to change the buoyancy by moving oil from an internal reservoir to an external flexible bladder. The reversible hydraulic power pack (HPR 1105HPRNSS02) from Hydra Products was chosen. This consists of a self-contained DC motor, gear pump, reservoir, internal valving, load hold checks, and relief valves. This hydraulic pack has a tank of 0.2 L, which corresponds to the volume needed for the external bladder.

4.2.3. Wing Sizing

Underwater gliders use wings to generate lift with a horizontal component due to the attitude of the vehicle while gliding. These wings operate at a low Reynolds number due to the slow operation velocity. The Reynolds number helps to predict the flow pattern depending on the ratio between inertial and viscous forces acting in a body immersed in a fluid. The appropriate selection of a hydrofoil is important because it generates the necessary forces to move the vehicle through the water. Symmetrical airfoils such as the NACA 00 series are used as hydrofoils for underwater gliders, since they can generate lift with the same lift-to-drag ratio ( L / D ) in both descending and ascending states [ 65 ]. Symmetrical airfoils have the disadvantage of having a lower L / D ratio compared with cambered airfoils. A higher L / D is ideal for an efficient glide, but in order to use a cambered airfoil, the glider should be able to invert the flight at the different states of the glide pattern or it should use high-lift devices such as flaps and slats, which increase the complexity of the design.

For the selection of the hydrofoil, it was desired to have a maximum lift coefficient and a proper ideal lift coefficient, which corresponds to the coefficient at the angle of attack at which the drag coefficient does not have representative variations. Besides, the lowest minimum drag was also desired, as well as a high ratio between the lift and drag coefficients. The design lift coefficient corresponded to the highest C L / C D . A hydrofoil with a higher slope in the function of the lift coefficient vs. the angle of attack has a better performance, and it is preferred to have a gentle drop in the lift after a stall for a safer performance. For the underwater glider, an Eppler E171 airfoil was selected; this airfoil has a symmetrical section, which fulfills the requirements at different low Reynolds numbers. The maximum thickness is 12.3% at 32.4% of the chord. The wing design target was to maximize the lift ( L ) while minimizing the drag ( D ) and pitch moment ( M ). Based on [ 66 ], the design began with a platform area of S = 0.15 m 2 as a first approximation. Lifting line theory was used to calculate the lift distribution along the span and the total lift wing coefficient [ 67 ]. The variation of the segment’s lift coefficient along the semispan is shown in Figure 4 .

Lift distribution along the semispan.

The taper ratio, λ , is the ratio between the tip chord C t i p and the root chord C r o o t and takes values from 0 to 1. The use of a taper ratio reduces the induced drag and improves the wing lift distribution. Additionally, it reduces the wing weight, produces a lower bending moment at the wing root, and improves lateral control. Based on [ 66 , 68 ], a taper ratio of 0.7 was assumed, and the chord at the root and the tip of the wing was calculated as follows:

which yields a root chord of 0.1765 m and a tip chord of 0.1235 m.

4.2.4. Tail Sizing

The primary purpose of the vertical tail is to counteract the moment produced by sideslip forces acting on the vehicle and wings. The tail was sized with respect to the baseline fixed wing following an empirical method proposed by Raymer [ 69 ]. This method uses a tail volume coefficient C v t , which depends on the aircraft wing planform area S , the wing span b , the distance between the aerodynamic center of the wing and the aerodynamic center of the vertical tail L v t , and the vertical tail planform area S v t . C v t can be computed as

A typical value of C v t for sailplanes is 0.02 [ 69 ], which is relatively small compared to the tail volume coefficient for current underwater gliders [ 70 ]. The tail volume coefficient was estimated as 0.25 for the underwater glider, and it was used to calculate the tail area with Equation ( 3 ). The root and tip chords for the vertical tail were calculated with Equations ( 1 ) and ( 2 ), with a tail span of 0.5 m and a taper ratio of 0.7.

4.2.5. Biomimetic Analysis

Biomimetics has been widely used in engineering design processes by developing solutions to problems employing analogies with biological systems [ 26 ]. Methods such as the direct approach, the case study method, BioTRIZ based on Altshuller’s theory of inventive problem solving (TRIZ), the functional modeling, and biological analogy search tools [ 71 ] have been used to inspire design concepts and solve engineering problems. In this case, biomimetics was used to obtain a bioinspired design of the external shape of the underwater glider, in order to enhance the hydrodynamic performance, based on the steps proposed by Helms et al. [ 56 ], which are described in Figure 1 . The leatherback turtle ( Dermochelys coriacea ) was selected as the natural referent to be used in the underwater glider design, due to the superior diving ability with energy efficiency, the long-distance migration, and the V-shaped pattern of diving. The longitudinal ridges on their shells can reduce drag and increase lift due to the delayed flow separation [ 53 ]. This feature can be adapted to the design of an underwater vehicle with a better hydrodynamic performance. To design the shell, images from 18 turtles were analyzed, extracting from them the basic curves representing their shapes. The curves were described as Cartesian coordinates and normalized based on the overall length. Then, 11 of those turtles were selected based on the information that could be extracted from them. An interpolation from the curves was performed to obtain a shape as similar as possible to the typical body of leatherback turtles. Both the curves on the longitudinal axis and the ridges were parametrized to obtain a smooth profile. The design of the external shape of the glider consisted of the parametrization of the basic shape of a turtle shell ( Figure 5 ).

Parametric curves in two planes. Proposed by the authors based on the leatherback turtle’s geometry [ 53 ].

The shape in Figure 5 a represents the parametrization for the x – y plane, which is given by

where x t and y are the x – y coordinates, respectively, t x is the maximum thickness in the x direction, and l is the total length of the vehicle; in this case, l = 1.5 m; the x axis is aligned with the sway motion of the vehicle; the y axis is aligned with the surge; the z axis corresponds to the heave motion. The shape in the y – z plane ( Figure 5 b) is described by

where z t is the z coordinate and t z represents the maximum thickness in the z direction.

Additionally, the design included longitudinal ridges in both the upper and lower sections of the vehicle, inspired by the ridges of leatherback turtles. The cross-section on the body in a particular y coordinate corresponds to an ellipse given by the thickness x t as the principal axis and the thickness z t as the secondary axis:

where θ e is the angle used to determine a quarter of the ellipse; it goes from 0 to π / 2 .

The number of ridges in the quarter of the ellipse is given by N , while θ N defines the angle between each ridge and depends on N . The coordinates of the ridges at a given angle were determined by ( 6 ) and ( 7 ). The quadratic Bézier curve through the three points presented was used to describe the curve between two consecutive peaks as follows:

where t goes from 0 to 1 and P i , with i from 0 to 2, corresponds to the control points given by two consecutive peaks and an auxiliary point determined by a factor r of the maximum thickness of every cross-section. The coordinates of the auxiliary point are given by

where θ s is the angle between two auxiliary points and corresponds to the midpoint between two consecutive peaks. The cross-section of the parametric shape of the vehicle is presented in Figure 6 .

Cross-section of the parametric shape.

The parametrization used to described the profiles of the glider allowed performing changes on the overall shape of the shell according to the basic dimensions of the vehicle. This gave the opportunity for further hydrodynamic analyses and a comparison of the longitudinal ridges’ performance in different conditions.

4.2.6. Hydrodynamic Analysis

Computational Fluid Dynamics (CFD) was used to predict the hydrodynamic characteristics of the underwater glider. These characteristics included the lift and drag forces, the moments, and the corresponding coefficients. ANSYS Fluent® was used to solve the Reynolds-Averaged Navier–Stokes (RANS) equations for the conservation of mass and momentum in a steady state and immersed in an incompressible flow ( Figure 7 and Figure 8 ). The Reynolds number was lower than other underwater vehicles that operate at higher speeds, and considering that the fluid was seawater, the flow regime was turbulent. Therefore, the standard κ − ϵ turbulence model was used along with an enhanced wall treatment to model the near-wall region. We used a pressure-based solver and a SIMPLE scheme for pressure–velocity coupling. For this model, the non-dimensional wall parameter y + should be within the constraints of the viscous sublayer ( y + < 1 ).

Velocity contour. ( a ) Parametric shape without ridges. ( b ) Parametric shape with ridges. Simulations performed using ANSYS Fluent ® R17.1 [ 55 ].

Velocity contour of the glider’s cross-section. Simulations performed using ANSYS Fluent ® R17.1 [ 55 ].

Simulations were carried out for the parametric shape without ridges and for the shape with ridges at several angles of attack (2, 4, 6, 10, 14, 18, and 22 degrees) and at velocities of 0.1, 0.2, and 0.3 m/s. Figure 9 a shows an increase in the lift coefficient due to the effect of ridges in the flow distribution for every velocity analyzed. A decrease in the drag coefficient at low angles of attack ( Figure 9 b) was observed due to the effect of the longitudinal ridges, despite the fact that, at greater angles of attack, there was an increase in the drag coefficient. The increase in the lift coefficient resulted in a greater lift-to-drag ratio ( L / D ), which is a desirable condition for the design of underwater gliders, making it possible to obtain a greater lift at small angles of attack while producing less drag than the shape without ridges ( Figure 10 ). The results agreed with the analysis presented by Bang et al. [ 53 ] for positive angles of attack.

Lift ( a ) and drag ( b ) coefficients at different velocities.

Lift-to-drag ratio at different velocities.

A greater lift-to-drag ratio can be translated into a higher hydrodynamic efficiency at smaller angles of attack. Glider efficiency is related, among other things, to the mechanical work applied to obtain optimal changes in the attitude of the vehicle; therefore, it is directly linked to energy consumption. Since underwater gliders rely on battery packs for the entire mission, reducing energy consumption by increasing hydrodynamic performance could result in greater endurance and a better opportunity to collect measurements during longer periods of time.

4.3. Attitude System

Sliding masses are used in gliders to control the pitch angle by changing the position of the center of gravity relative to the center of buoyancy during dives and climbs. It is common to use battery packs as the sliding and rotating masses to induce roll and course change. The PA-08 mini track actuator was selected to generate the linear motion of the battery packs and the consequent pitch angle change, while a gear motor of 168 rpm was selected to generate the roll. The mini track actuator has a stroke of 50.8 mm (2 in), a force of 50 lb, and a speed of 1.18 in/s. The track designs implies a small size since the stroke does not extend or retract from the unit.

4.4. Energy Supply

To supply energy to all components of the device, the maximum power consumption (W), input voltage (V), and current drain (A) of every component were analyzed. A rechargeable battery pack of Lithium Nickel Manganese Cobalt Oxide (LiNiMnCo) of 14.8 V was selected to satisfy the components’ needs, with 8 Ah and 118.4 Wh. A LiNiMnCo battery pack was chosen because it provides a higher energy density (mAh/weight) with a lower cost and a long cycle life. However, this type of battery needs to be properly used to guarantee safety. The next step was to calculate the battery pack’s capacity based on how long the vehicle will operate, and based on this information, 21 battery packs were used to satisfy the power needs. This is an important consideration, since a long operation time was desired by the customers. The batteries have 8.95 MJ of energy, which meets the energy available in commercial underwater gliders.

4.5. Information Management

During operation, the underwater glider will have to manage data collected with oceanographic sensors, as well as the satellite signals for positioning. Additionally, it will receive information of internal variables to monitor the operating conditions. All the information will be received, processed, stored, and transmitted. The main component selected to solve this function was the Fox embedded computer designed by VersaLogic powered by a DMP Vortex86DX2 processor. The main requirements to select the computer were a low power consumption, a small size, and versatility to allow the integration of current and future sensors including serial communication channels, as well as analog and digital channels. While underwater, the information will be stored in a removable micro SD card solid-state drive supported by the embedded computer and in an external hard drive. At the surface, the glider will need to transmit information to the operation center. To solve this task, the Iridium system was chosen as the satellite-based telemetry system. The Iridium Short Burst Data (9603 SBD) transceiver provides the capability of monitoring and exchanging data with remote devices deployed in places beyond terrestrial wireless connections.

4.6. Protection System

The system will need protection against failures and protection from the environment and will need to act in case of failures or emergencies. The main solution to solve this function was the structural hull, which consisted of a pressure vessel used to protect the electronic components from seawater and water pressure. The structural design included the hull design, material selection, and sealing methods. Another component to protect the system was the use of sensors to measure internal variables such as the temperature and humidity. An electronic board designed by [ 60 ] was used to measure the internal temperature, flooding, internal humidity, and energy consumption. This board was connected to the selected embedded computer to monitor the variables and perform actions in case of an emergency.

4.6.1. Hull Design

The pressure vessel to protect the electronic components was designed to resist a water pressure of 2 MPa corresponding to 200 m of operational depth. The structure was divided into 3 hulls, one at the front as the electronic bay, another one in the middle to house the battery packs, and the last one in the rear position for the buoyancy engine. The electronics bay had a diameter of 0.14 m and a length of 0.215 m. Because of the battery packs’ dimensions and the space available from the parametric design of the external hydrodynamic shape, the battery bay had an external diameter of 0.225 m and a length of 0.665 m. Finally, the buoyancy control bay had a diameter of 0.14 m and 0.3 m of length. The purpose of the hull design was to select an appropriate material and to find the appropriate geometry and wall thickness that satisfied the design requirements.

The method proposed by Ashby [ 72 ] was used for the material selection of the hulls, following a pressure vessel case study. The first step was to translate the design requirements into functions, constraints, objectives, and free variables. The main function of the vessel was to support a determined pressure. The established constrains were the external diameters and lengths. The objective was to maximize safety using the yield strength or to maximize safety using leaking before the break condition. The free variable for this case was the choice of the material. In this selection, stainless steels, low alloy steels, cooper, aluminum alloys, and titanium alloys were found suitable to fabricate the desired pressure vessel since they are commonly used for the hull fabrication of underwater vehicles [ 73 ]. Among such materials, stainless steel exhibits high strength, but a heavy weight, and it is necessary to treat the surface in order to use it in sea water. Aluminum alloys exhibit a light weight and high strength and do not become magnetized, but a surface treatment is also needed to use them in underwater operations. Finally, titanium alloys exhibit a light weight, a high strength, and a high corrosion resistance, but they are expensive [ 74 ]. Aluminum alloys Series 5000, 6000, and 7000 are used for hull structures in underwater vehicles, especially the 6000 series, the performance in strength and corrosion of which is in the between the 5000 and 7000 series. The typical surface treatments for aluminum alloys include anodizing, electrolysis nickel plating, electroless nickel plating, and painting.

For the three hulls of the vehicle, the AA6061-T6 aluminum alloy was selected. This material has a yield strength of 276 MPa. The wall thickness by yield criteria ( t y ) for every hull was approximated with a safety factor, S f , of 2, and the hoop stress σ y , for the given radius r at the working pressure p , as follows:

Additionally, the buckling criteria were considered to obtain the wall thickness ( t b c ) using

where E is the elastic modulus of the material, 68,900 MPa for AA6061-T6, d is the hull diameter, and l is the length of the hull. Table 1 shows the wall thickness by the yield and buckling criteria for each hull. The size of the wall thickness was determined by the circumferential buckling criteria because it is greater than the wall thickness determined by the yield criteria, which means that buckling is the predominant failure mode. The wall thicknesses of Hull 1 and Hull 3 were set to be equal in order to ease the manufacturing, because they had the same external diameter.

Wall thickness given by yield and buckling criteria for each hull.

4.6.2. Sealing Analysis

Sealing is an important issue for underwater vehicles, due to the use of electrical and electronic components, which need to be isolated from the water to function properly. O-rings are the most-common sealing methods. They consist of circular cross-section rings molded from elastomeric or thermoplastic materials. The O-ring is contained in a groove, where it is deformed when pressure is applied. The end caps of the hulls were determined to be piston seal caps that fit inside the hulls. For this type of cap, water pressure compresses the diameter of the hull slightly, squeezing the O-ring and generating a waterproof seal. The Parker O-Ring Handbook [ 75 ] was used to select the O-ring used in the hull design and to dimension the grooves that were to be machined in caps. Nitrile-Butadiene Rubber (NBR) was selected as the O-ring’s material due to its commercial availability and its capacity to work with seawater. The internal diameter of the wall was the parameter used to size and select the O-ring. It was decided to use two O-rings to ensure a better sealing.

4.6.3. End Caps’ Design

The flat end caps for Hull 1 and Hull 3 must be able to resist deflection due to the pressure of the water at the operational depth. The bending stress was calculated assuming that there was constant pressure along the flat circular plate of constant thickness using

where M is the bending moment and t is the end cap thickness.

The moment at the center M c and the moment at the reaction M r a were calculated with the following equations, for uniformly distributed pressure with fixed supports:

where ν is the Poisson ratio of the material, which in this case corresponds to the AA6061-T6 aluminum alloy. The minimum thickness of the end cap to withstand the working pressure was calculated, with a safety factor of 2, using

The minimum thickness was 7 mm for the end caps to be used in Hull 1 and Hull 3. For the caps to be used to join Hull 2 with the other hulls, the bending moment at the reaction was calculated as follows:

where r 0 is the inner ratio of the cap. The thickness for this caps was 9.7 mm.

5. Bioinspired Glider

The underwater glider consisted of a bioinspired external shell with longitudinal ridges used to enhance hydrodynamic performance. Wings were used to generate forward motion due to the lift force, while a vertical tail was used to counteract the moments produced by sideslip forces acting on the vehicle ( Figure 11 a). Internally, three hulls were used to house the components ( Figure 11 b). The first hull corresponded to the electronics bay. It housed the embedded computer and the navigation, positioning and communication instruments such as the AHRS, the compass, the GPS receiver, the Iridium modem, and the electronic board to measure the internal variables. The second hull was the battery bay, which housed the battery packs and pitch and roll mechanisms. The final hull was the buoyancy bay, which housed the buoyancy engine. Figure 12 shows a scheme of the internal distribution of the electronics, batteries, and buoyancy bays. Finally, CTD, DO sensors, and the altimeter needed to be located in a flooded bay to measure the water conditions and distance to the seabed ( Table 2 ). The physical architecture of the underwater glider is presented in Figure 13 .

Bioinspired glider layout. ( a ) External layout. ( b ) General layout.

Distribution of electronics ( a ), batteries ( b ), and buoyancy ( c ) bays.

Physical architecture.

Electronics bay’s components.

5.1. Mathematical Model

A mathematical model that represents the vehicle’s dynamics was derived based on the works from Leonard and Graver [ 76 ] and Graver [ 77 ], who used such a model for the control of the ROGUE underwater vehicle. Initially, the glider was assumed as a rigid body immersed in a fluid. The vehicle was controlled by changes in buoyancy and the movement of internal masses [ 77 ].

Figure 14 shows a fixed coordinate system that was located at the buoyancy center of the vehicle. Axis 1 was aligned with the surge motion of the vehicle, positive pointing to the nose; Axis 2 was aligned with the wings’ axis, which corresponds to the sway motion; Axis 3 was chosen to be orthogonal to the plane of the wings, positive pointing downwards, and corresponds to the heave motion.

Coordinate system for the underwater glider.

In order to obtain the equations of motion, we first describe the relationship between the total mass and internal masses, which control the buoyancy, as follows:

where the total mass of the vehicle m v is given by the sum of a stationary mass m s and the moving internal mass m ¯ . The stationary mass is the relationship between the hull mass m h , which is distributed uniformly throughout the vehicle, a fixed point mass m w , which may be offset from the buoyancy center, and the ballast mass m b , which is variable. Finally, the net buoyancy m 0 is given by m v − m , where m is the mass of the displaced fluid [ 77 ]. For this analysis, the motion of the vehicle was restricted to the vertical plane and was determined by the change of the vehicle’s position in the x axis, x ˙ , and the change of the vehicle’s position in the z axis, z ˙ , given by

where θ is the pitch angle, and its rate of change θ ˙ is given by

The rate of change of the angular velocity computed in the body coordinate system, Ω ˙ , and the change of Components 1 and 3 of the velocity computed in the body coordinate system, v ˙ 1 and v ˙ 3 , are described by

where J 2 represents the second diagonal element of the inertia matrix of the vehicle and m 1 and m 3 are the first and third diagonal elements of the sum of the body and added mass. u 1 and u 3 are the first and third components of the control vector, and u 4 is the controlled variable mass rate. P p 1 and P p 3 are the first and third components of the linear momentum computed in the body coordinate system, and r p 1 and r p 3 are the corresponding components of the moving mass position computed in the coordinate system. α is the angle of attack given by cos ( α ) = v 1 / v 1 2 + v 3 2 . L is the lift force. D is the drag force. M D L is the viscous moment.

The changes of Components 1 and 3 of the moving mass’s position computed in the body coordinate system, r ˙ p 1 and r ˙ p 3 , are given by

The rate of change of the linear momentum components, P ˙ p 1 and P ˙ p 3 , is given by

while the change of the ballast’s mass m ˙ b is given by

The glide path angle ξ is given by ξ = θ − α . The velocity of the vehicle is determined by V = ( v 1 2 + v 3 2 ) . A trajectory can be specified by obtaining the desired glide path angle ξ d and the desired velocity V d . Both are defined in an inertial coordinate ( x ′ , z ′ ) , where x ′ coincides with the position along the desired path and z ′ gives the vehicle’s position with respect to the perpendicular distance to the desired path. Gliding control in the vertical plane consists of the control direction and the speed of the vehicle’s glide path, as well as to the control of the gliding along a prescribed line where the dynamics of z ′ is given by

5.2. Mission Description

A standard mission is described in Figure 15 . It starts with pre-launch tasks, which include mission planning based on the environment conditions, endurance, and science requirements (path and sampling). It also includes transporting the glider to the field in a shipping case, assembling the vehicle, and performing calibration, ballasting, battery and communication checks, and other tests to make sure all systems are working as expected. The launch procedure will be carried out using a cradle cart to slip the glider into the water from a small boat or using a crane or winch to launch/recover it from larger boats.

Sequential description of a mission.

At the surface, the vehicle should change its pitch angle in order to raise the tail and expose the antenna to allow GPS positioning and then Iridium communication with the operation center, then the GPS positioning will be obtained again to fix the position before every dive. A dive is performed until the operational depth is achieved or until an abort condition is reached. In this phase, adjustments of the buoyancy and pitch angle are made to be negatively buoyant and to obtain the attitude needed to reach the prescribed depth at the desired operational velocity. When the working depth is reached, the glider will start a smooth transition from the dive to the climb condition, avoiding a stall. The transition includes changes from the negative to the positive buoyant condition and moving masses to obtain the desirable pitch angle to go up to the surface. Data sampling will be performed throughout the dive and climb phases. When the vehicle reaches the surface, it starts its positioning and communication phases until it enters in a new diving cycle or until it enters in a recovery phase. A command from the operation center, the completion of the mission, or a detected error condition will cause the recovery of the vehicle from a boat. A maintenance procedure will be required after every mission, including cleaning the vehicle with fresh water and drying it with a soft cloth. It will be required to calibrate the compass every time the battery packs are replaced, and other sensors will require calibration before and after each deployment.

6. Conclusions

This paper addressed the design process of an underwater glider to be used in oceanographic research. The design was inspired by leatherback sea turtles ( Dermochelys coriacea ), which have great diving ability and exhibit enhanced hydrodynamic performance. The design process combined elements from Systems Engineering and bioinspired design approaches. The process was divided into three phases, and the conceptual design was used to establish preliminary specifications of the vehicle, which yielded the functional architecture that describes the desired performance. Then, the preliminary and detailed design stages considered different alternatives to fulfill the prescribed requirements and provided a general layout of the vehicle with the help of the biomimetic design using analogies with the selected biological system and the functional decomposition.

The longitudinal ridges of the leatherback turtle were used in the design of the underwater vehicle, and computational fluid dynamics was used to simulate its hydrodynamic performance. It was found that the ridges increased the lift coefficient and decreased the drag coefficient at low angles of attack, which led to a greater lift-to-drag ratio. For an underwater glider, this is a desirable condition that makes it possible to obtain a greater lift while producing less drag than a shape without longitudinal ridges.

The detailed design of the vehicle was developed by considering system integration, taking into account the interactions among the components and the interaction with the environment, as described by the functional and physical architecture diagrams. Although we obtained the physical architecture for and details of the glider’s construction, the work was limited to obtaining a virtual prototype, and further work is needed to plan the fabrication and molding requirements to manufacture the shell, the assembly, and the testing of the vehicle in real conditions.

The underwater glider’s design process resulted in a Colombian patent for the bioinspired shell: NC2019/0008406 [ 78 ] ( Figure 16 ).

Bioinspired shell. Colombian Patent NC2019/000840 [ 78 ].

Funding Statement

This work was developed with the funding of the Fondo Nacional de Financiamiento para la Ciencia, la Tecnología y la Innovación, Francisco José de Caldas; the Colombian petroleum company, ECOPETROL; the Universidad Pontificia Bolivariana—Medellín, UPB; the Universidad Nacional de Colombia—Sede Medellín, UNALMED; through the “Strategic Program for the Development of Robotic Technology for Offshore Exploration of the Colombian Seabed”, Project 1210-531-30550, contract 0265-2013.

Author Contributions

Conceptualization, D.C.H.-J. and R.E.V.; methodology, D.C.H.-J. and R.E.V.; software, D.C.H.-J. and R.E.V.; validation, D.C.H.-J. and R.E.V.; formal analysis, D.C.H.-J. and R.E.V.; investigation, D.C.H.-J. and R.E.V.; resources, R.E.V.; writing—original draft preparation, D.C.H.-J. and R.E.V.; writing—review and editing, D.C.H.-J. and R.E.V.; supervision, R.E.V.; project administration, R.E.V. All authors have read and agreed to the published version of the manuscript.

Institutional Review Board Statement

Informed consent statement, data availability statement, conflicts of interest.

The authors declare no conflict of interest.

Disclaimer/Publisher’s Note: The statements, opinions and data contained in all publications are solely those of the individual author(s) and contributor(s) and not of MDPI and/or the editor(s). MDPI and/or the editor(s) disclaim responsibility for any injury to people or property resulting from any ideas, methods, instructions or products referred to in the content.

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How Do You Get Rid of Shredded Paper? Think Twice Before Recycling.

By Melanie Pinola

Melanie Pinola is a writer focused on home-office gear. To find the best paper shredder, she has shredded enough junk mail to fill several bathtubs.

It turns out, I’ve been recycling all wrong. After the latest round of testing nine paper shredders , I thought I’d put the resulting 65-plus gallons of shredded paper out for recycling. But when I asked my local sanitation department if it would prefer the shreds in clear bags or cardboard boxes, the representatives said neither.

Instead, they instructed me to toss the shredded paper in with the trash.

But wait: Isn’t shredded paper still paper, and thus recyclable? Isn’t throwing away shredded paper wasteful? The answer to both questions is, well, kind of. Here’s what you need to know about the best way to dispose of shredded paper.

Check your local guidelines

The American Forest & Paper Association confirms that shredded paper is indeed recyclable. But whether shredded paper is acceptable for recycling in your town or city is another story.

So it’s best to double-check with your local sanitation or public-works department to see what you’re supposed to do with your shredded paper. Local guidelines vary—and those guidelines may or not be on the publicly accessible website or in published brochures.

For example, San Franciscans are encouraged to either place shredded paper in a stapled brown paper bag labeled “SHREDDED” or compost the shredded paper. But if you live in Rhode Island, shredded paper isn’t accepted for mixed-recycling pickup; residents can compost their shreds, throw them in the trash, or drop off shredded paper at a disposal site in Johnston, Rhode Island.

Why shredded paper isn’t always accepted for recycling

Shredded paper can be a disaster for some recycling facilities. “Shredded bits of paper are too small to be properly sorted by our facility’s machinery,” said Jared Rhodes, director of policy and programs at the Rhode Island Resource Recovery Corporation (RIRRC). They can contaminate other materials and even lead to equipment malfunctions, he added.

An article in The Providence Journal expounds on the problem, noting that when local households sent their shredded paper for recycling in paper bags, the shredding machines ripped the bags, and tiny shreds flew everywhere. When residents tried using plastic bags (or even double-bagging in plastic), the shreds still flew everywhere—and plastic wrapped around the equipment, shutting the facility down for cleaning and repairs.

As a solution, some localities outsource the recycling of shredded paper to dedicated facilities that are equipped for it, but that costs additional time and taxpayer money. You can help reduce the load by composting your shredded paper, taking documents to be shredded to a community’s free shredding event (they’ll know how to dispose of the shreds), and reducing how much you shred in the first place.

Shred only paper containing sensitive information

Paper is most suitable for recycling when it isn’t shredded, because whole pieces are easier for facilities to sort and have longer and stronger fibers ready to be made into new paper. So it’s best to avoid unnecessary shredding.

To protect your privacy, you should still shred anything with sensitive information on it, of course, such as documents with your Social Security number, financial statements, and medical records.

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However, some information on a document may be personal but not necessarily sensitive enough to need shredding, such as your name and address; your contact information may already be available on public records or services such as White Pages.

“Consider how much junk mail and spam calls you receive; that’s how known your address and phone number are,” says Max Eddy, Wirecutter’s senior staff writer covering privacy and security. Instead of shredding documents that have only your name, address, and phone number on them, you can cover that information with permanent black marker and then put the sheets into the recycling bin.

Bonus: In addition to helping the environment, reducing how much you shred can prolong the life of your paper shredder. Everybody wins.

This article was edited by Ben Keough and Erica Ogg.

Meet your guide

Melanie Pinola

Melanie Pinola covers home office, remote work, and productivity as a senior staff writer at Wirecutter. She has contributed to print and online publications such as The New York Times, Consumer Reports, Lifehacker, and PCWorld, specializing in tech, work, and lifestyle/family topics. She’s thrilled when those topics intersect—and when she gets to write about them in her PJs.

Mentioned above

• We tested top shredders for use at home and in small offices and found easy-to-use workhorses that can help protect your identity. The Best Paper Shredders  

Further reading

How to Recycle Your Used Electronics

by Nick Guy

Are old computers, smartphones, or monitors taking over your closet? We’ll tell you how to recycle your tech, with privacy tips so you can do so safely.

How to Get Rid of a Used Car Seat

by Christine Cyr Clisset

We talked to experts about the best ways to dispose of a used car seat, and recommend you bring your unwanted seat to Target before May 5.

Why It’s So Hard to Get Rid of Used Mattresses

by Kevin Purdy

Getting rid of a used mattress responsibly can be a challenge—one that will likely only get worse as all-foam, bed-in-a-box options become more popular.

Yes, You Can (and Should) Recycle Batteries. Here’s How.

by Sarah Witman

If you have a container of spent batteries in your home that you don’t know what to do with, these are the best battery-recycling methods we’ve found.

Prestigious cancer research institute has retracted 7 studies amid controversy over errors

Seven studies from researchers at the prestigious Dana-Farber Cancer Institute have been retracted over the last two months after a scientist blogger alleged that images used in them had been manipulated or duplicated.

The retractions are the latest development in a monthslong controversy around research at the Boston-based institute, which is a teaching affiliate of Harvard Medical School. 

The issue came to light after Sholto David, a microbiologist and volunteer science sleuth based in Wales, published a scathing post on his blog in January, alleging errors and manipulations of images across dozens of papers produced primarily by Dana-Farber researchers . The institute acknowledged errors and subsequently announced that it had requested six studies to be retracted and asked for corrections in 31 more papers. Dana-Farber also said, however, that a review process for errors had been underway before David’s post. 

Now, at least one more study has been retracted than Dana-Farber initially indicated, and David said he has discovered an additional 30 studies from authors affiliated with the institute that he believes contain errors or image manipulations and therefore deserve scrutiny.

The episode has imperiled the reputation of a major cancer research institute and raised questions about one high-profile researcher there, Kenneth Anderson, who is a senior author on six of the seven retracted studies. 

Anderson is a professor of medicine at Harvard Medical School and the director of the Jerome Lipper Multiple Myeloma Center at Dana-Farber. He did not respond to multiple emails or voicemails requesting comment. 

The retractions and new allegations add to a larger, ongoing debate in science about how to protect scientific integrity and reduce the incentives that could lead to misconduct or unintentional mistakes in research. 

The Dana-Farber Cancer Institute has moved relatively swiftly to seek retractions and corrections. 

“Dana-Farber is deeply committed to a culture of accountability and integrity, and as an academic research and clinical care organization we also prioritize transparency,” Dr. Barrett Rollins, the institute’s integrity research officer, said in a statement. “However, we are bound by federal regulations that apply to all academic medical centers funded by the National Institutes of Health among other federal agencies. Therefore, we cannot share details of internal review processes and will not comment on personnel issues.”

The retracted studies were originally published in two journals: One in the Journal of Immunology and six in Cancer Research. Six of the seven focused on multiple myeloma, a form of cancer that develops in plasma cells. Retraction notices indicate that Anderson agreed to the retractions of the papers he authored.

Elisabeth Bik, a microbiologist and longtime image sleuth, reviewed several of the papers’ retraction statements and scientific images for NBC News and said the errors were serious. 

“The ones I’m looking at all have duplicated elements in the photos, where the photo itself has been manipulated,” she said, adding that these elements were “signs of misconduct.” 

Dr.  John Chute, who directs the division of hematology and cellular therapy at Cedars-Sinai Medical Center and has contributed to studies about multiple myeloma, said the papers were produced by pioneers in the field, including Anderson. 

“These are people I admire and respect,” he said. “Those were all high-impact papers, meaning they’re highly read and highly cited. By definition, they have had a broad impact on the field.” 

Chute said he did not know the authors personally but had followed their work for a long time.

“Those investigators are some of the leading people in the field of myeloma research and they have paved the way in terms of understanding our biology of the disease,” he said. “The papers they publish lead to all kinds of additional work in that direction. People follow those leads and industry pays attention to that stuff and drug development follows.”

The retractions offer additional evidence for what some science sleuths have been saying for years: The more you look for errors or image manipulation, the more you might find, even at the top levels of science. 

Scientific images in papers are typically used to present evidence of an experiment’s results. Commonly, they show cells or mice; other types of images show key findings like western blots — a laboratory method that identifies proteins — or bands of separated DNA molecules in gels. 

Science sleuths sometimes examine these images for irregular patterns that could indicate errors, duplications or manipulations. Some artificial intelligence companies are training computers to spot these kinds of problems, as well. 

Duplicated images could be a sign of sloppy lab work or data practices. Manipulated images — in which a researcher has modified an image heavily with photo editing tools — could indicate that images have been exaggerated, enhanced or altered in an unethical way that could change how other scientists interpret a study’s findings or scientific meaning. 

Top scientists at big research institutions often run sprawling laboratories with lots of junior scientists. Critics of science research and publishing systems allege that a lack of opportunities for young scientists, limited oversight and pressure to publish splashy papers that can advance careers could incentivize misconduct. 

These critics, along with many science sleuths, allege that errors or sloppiness are too common , that research organizations and authors often ignore concerns when they’re identified, and that the path from complaint to correction is sluggish. 

“When you look at the amount of retractions and poor peer review in research today, the question is, what has happened to the quality standards we used to think existed in research?” said Nick Steneck, an emeritus professor at the University of Michigan and an expert on science integrity.

David told NBC News that he had shared some, but not all, of his concerns about additional image issues with Dana-Farber. He added that he had not identified any problems in four of the seven studies that have been retracted. 

“It’s good they’ve picked up stuff that wasn’t in the list,” he said. 

NBC News requested an updated tally of retractions and corrections, but Ellen Berlin, a spokeswoman for Dana-Farber, declined to provide a new list. She said that the numbers could shift and that the institute did not have control over the form, format or timing of corrections. 

“Any tally we give you today might be different tomorrow and will likely be different a week from now or a month from now,” Berlin said. “The point of sharing numbers with the public weeks ago was to make clear to the public that Dana-Farber had taken swift and decisive action with regard to the articles for which a Dana-Farber faculty member was primary author.” 

She added that Dana-Farber was encouraging journals to correct the scientific record as promptly as possible. 

Bik said it was unusual to see a highly regarded U.S. institution have multiple papers retracted. 

“I don’t think I’ve seen many of those,” she said. “In this case, there was a lot of public attention to it and it seems like they’re responding very quickly. It’s unusual, but how it should be.”

Evan Bush is a science reporter for NBC News. He can be reached at [email protected].

A Discrimination Report Card

We develop an empirical Bayes ranking procedure that assigns ordinal grades to noisy measurements, balancing the information content of the assigned grades against the expected frequency of ranking errors. Applying the method to a massive correspondence experiment, we grade the race and gender contact gaps of 97 U.S. employers, the identities of which we disclose for the first time. The grades are presented alongside measures of uncertainty about each firm’s contact gap in an accessible report card that is easily adaptable to other settings where ranks and levels are of simultaneous interest.

We thank Ben Scuderi for helpful feedback on an early draft of this paper and Hadar Avivi and Luca Adorni for outstanding research assistance. Seminar participants at Brown University, the 2022 California Econometrics Conference, Columbia University, CIREQ 2022 Montreal, Harvard University, Microsoft Research, Monash University, Peking University, Royal Holloway, UC Santa Barbara, UC Berkeley, The University of Virginia, the Cowles Econometrics Conference on Discrimination and Algorithmic Fairness, and The University of Chicago Interactions Conference provided useful comments. Routines for implementing the ranking procedures developed in this paper are available online at https://github.com/ekrose/drrank. The views expressed herein are those of the authors and do not necessarily reflect the views of the National Bureau of Economic Research.

Christopher Walters holds concurrent appointments as an Associate Professor of Economics at UC Berkeley and as an Amazon Scholar. This paper describes work performed at UC Berkeley and is not associated with Amazon.

MARC RIS BibTeΧ

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Title: apprentices to research assistants: advancing research with large language models.

Abstract: Large Language Models (LLMs) have emerged as powerful tools in various research domains. This article examines their potential through a literature review and firsthand experimentation. While LLMs offer benefits like cost-effectiveness and efficiency, challenges such as prompt tuning, biases, and subjectivity must be addressed. The study presents insights from experiments utilizing LLMs for qualitative analysis, highlighting successes and limitations. Additionally, it discusses strategies for mitigating challenges, such as prompt optimization techniques and leveraging human expertise. This study aligns with the 'LLMs as Research Tools' workshop's focus on integrating LLMs into HCI data work critically and ethically. By addressing both opportunities and challenges, our work contributes to the ongoing dialogue on their responsible application in research.

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arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs .

Fun with Gliders

A glider is a special kind of aircraft that has no engine. In flight, a glider has three forces acting on it as compared to the four forces that act on a powered aircraft. Both types of aircraft are subjected to the forces of lift, drag, and weight. The powered aircraft has an engine that generates thrust, while the glider has no thrust.

Types of Gliders

There are many different types of glider aircraft. Paper airplanes are the simplest aircraft to build and fly, and students can learn the basics of aircraft motion by flying paper airplanes. Toy gliders, made of balsa wood or Styrofoam, are an inexpensive way for students to have fun while learning the basics of aerodynamics.  Hang-gliders  are piloted aircraft that are launched by leaping off the side of a hill or by being towed aloft.  Piloted gliders  are launched by ground based catapults, or are towed aloft by a powered aircraft then cut free to glide for hours over many miles. The Wright Brothers perfected the design of the first airplane and gained piloting experience through a series of glider flights from 1900 to 1903. The Space Shuttle flies as a glider during reentry and landing; the rocket engines are used only during liftoff.

Glider Activities

It is important to note that building and flying a glider is not only educational, it is fun. Groups of students can work together with a teacher to learn the fundamentals. In the figure at the top of this page, we show teachers and students from two different schools involved in glider activities. The bottom two photos come from Paulo Oemig of Zia Middle School in Las Cruces, New Mexico. The top two photos are from Casey Teliczan of the Rockford Public School District in Rockford, Michigan. Mr. Teliczan’s activities are part of the Rockford Community Services after-school enrichment program.

The student photos detail the design and flight test of Styrofoam and balsa toy gliders. At the bottom left, students are producing Styrofoam wings from a Pitsco wing cutter. students choose or design an airfoil shape that is affixed to a block of Styrofoam. The wing cutter then produces an aircraft wing with the desired airfoil shape. The photo at the upper left shows the finished wing and the balsa fuselage and tail to which the wing is attached. A finished glider is shown at the upper right. And the students experience the fun of flying in the lower right picture. Here is an additional picture of the student activities.

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Using pulp and paper waste to scrub carbon from emissions

Researchers at McGill University have come up with an innovative approach to improve the energy efficiency of carbon conversion, using waste material from pulp and paper production.

The technique they've pioneered using the Canadian Light Source at the University of Saskatchewan not only reduces the energy required to convert carbon into useful products, but also reduces overall waste in the environment.

"We are one of the first groups to combine biomass recycling or utilization with CO 2 capture," said Ali Seifitokaldani, Assistant Professor in the Department of Chemical Engineering and Canada Research Chair (Tier II) in Electrocatalysis for Renewable Energy Production and Conversion. The research team, from McGill's Electrocatalysis Lab, published their findings in the journal RSC Sustainability .

Capturing carbon emissions is one of the most exciting emerging tools to fight climate change. The biggest challenge is figuring out what to do with the carbon once the emissions have been removed, especially since capturing CO 2 can be expensive. The next hurdle is that transforming CO 2 into useful products takes energy. Researchers want to make the conversion process as efficient and profitable as possible.

• Energy and Resources
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• Energy and the Environment
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• Renewable Energy
• Global Warming
• Hazardous waste
• Photosynthesis
• Climate change mitigation
• Radioactive waste
• Carbon cycle
• Carbon dioxide

Story Source:

Materials provided by McGill University . Note: Content may be edited for style and length.

Journal Reference :

• Roger Lin, Haoyan Yang, Hanyu Zheng, Mahdi Salehi, Amirhossein Farzi, Poojan Patel, Xiao Wang, Jiaxun Guo, Kefang Liu, Zhengyuan Gao, Xiaojia Li, Ali Seifitokaldani. Efficient integration of carbon dioxide reduction and 5-hydroxymethylfurfural oxidation at high current density . RSC Sustainability , 2024; 2 (2): 445 DOI: 10.1039/D3SU00379E

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