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System stabilizes aximuth of gondolas which are carried by high-altitude balloons as platforms for tracking telescopes. When telescopes must be constantly aimed at specific targets, control system stabilizes gondola to within 5 arc-seconds.
The first flight test of a gondola containing a Newtonian telescope with a 16 in. primary mirror is described. Bolometer tests were conducted along with gondola design studies, and changes were made in the mechanical system as a result. Parts of the system were rebuilt and tested, and it was found that the flight system had redundant data recording capabilities. In the total flight record, about 160 large signals were noted; about half of these appeared to have the correct shape for genuine signals, and the other were clearly noise spikes (they were large but the signal shape could not have been produced by the observation of a celestial object).
The design of two telescope pointing systems for remote optical sensing of the stratosphere from a balloone-borne gondola is described. The telescope pointing accuracy is + or - 0.02 deg in elevation, from a gondola which has static and dynamic tilts up to + or - 3 deg. Each system consists of a telescope, an elevation control subsystem, and a pitch-stabilized single-axis reference platform.
The Vega balloon experiment, designed to measure the dynamics of the Venus atmosphere, comprised the balloons themselves, their gondolas with on-board sensors and radio transmitters, and the radio telescope network on the earth. The structures and the physical parameters of the balloon probe are described, together with the instruments on the gondola, designed for the measurements of the atmospheric pressure, temperature, and vertical wind flows, and illumination, as well as possible flashes of lightning. Consideration is also given to the formatting of the information flow for the individual parameters measured.
A statistically significant measurement of H2O2 in the stratosphere has been obtained. The results were obtained from the 112.19/cm RQ5 branch of the torsional-rotational spectrum with a remote-sensing far-infrared Fourier transform spectrometer during the Balloon Intercomparison Campaign (BIC-2), on June 20, 1983. The concentration above the balloon gondola is unexpectedly large, corresponding to 0.68 + or - 0.21 parts per billion by volume (ppbv) at an effective altitude of 38.3 km. Below the gondola altitude the concentration of H2O2 is slightly less than expected from the model predictions at 33.2 km (0.19 + or - 0.05 ppbv) and significantly less than expected at 29.3 km (0.08 + or - 0.03 ppbv).
The scientific objectives, engineering analysis and design, results of technology development, and focal-plane instrumentation for a two-meter balloon-borne telescope for far-infrared and submillimeter astronomy are presented. The unique capabilities of balloon-borne observations are discussed. A program summary emphasizes the development of the two-meter design. The relationship of the Large Deployable Reflector (LDR) is also discussed. Detailed treatment is given to scientific objectives, gondola design, the mirror development program, experiment accommodations, ground support equipment requirements, NSBF design drivers and payload support requirements, the implementation phase summary development plan, and a comparison of three-meter and two-meter gondola concepts.
The balloon-borne instruments used in the two Balloon Intercomparison Campaigns in 1982 and 1983 to measure stratospheric HCl included five different IR spectrometers, three of which operated in the solar absorption mode and two in emission mode (at distinctly different wavelengths). This paper describes the instruments and the data reduction and analysis procedures used in each case, together with the sources and estimated magnitudes of associated errors. Comparisons are made between different techniques (absorption vs emission) used on the same gondola, as well as between the same technique used on different gondolas. The final results yield a mean profile of HCl concentration between 18 and 40 km altitude. The absolute accuracy of the final profile is estimated to be no worse than 10 percent.
A photopolarimeter designed to measure the radiance and the polarization ratio at lambda equals 0.85 microns and lambda equals 1.65 microns is set up on a gondola of a stratospheric balloon. By rotating the gondola, measurements of the diffuse solar light are obtained for a wide range of the scattering angles. An inversion scheme, based on the assumption of a log-normal size distribution, provides the relevant size parameters, the refractive index, and the slant optical thicknesses of the aerosols. Since 1983, this experiment was launched twice a year from Aire Sur Adour (S-E of France). The post-El Chichon atmospheric stratospheric aerosol proved to be quite stable in size and nature (hydratid sulfuric acid), but the abundance decreased by a factor of 10 between 1983 and 1987. The experiment was also launched to observe the stratosphere during the Arctic winter. Two flights, on January 28, 1988 and January 18, 1990, corresponded to an unperturbed atmosphere. But during a third flight, on April, 2, 1990, the temperatures were low enough for PCS formulations. A multilayer situation was observed with the standard H2SOH aerosols below 20 km; a dense layer was observed, peaked at around 23 km, with scattering coefficients about 50 times layer than in background conditions; and an upper layer was observed, rather sharp (approximately equal to 1 km), with micron sized particles.
Under the support of this grant a balloon-borne gondola containing a variety of aerosol instruments was developed and flown from Laramie, Wyoming, (41 deg N, 105 deg W) and from Lauder, New Zealand (45 deg S, 170 deg E). The gondola includes instruments to measure the concentrations of condensation nuclei (CN), cloud condensation nuclei (CCN), optically detectable aerosol (OA.) (r greater than or equal to 0.15 - 2.0 microns), and optical scattering properties using a nephelometer (lambda = 530 microns). All instruments sampled from a common inlet which was heated to 40 C on ascent and to 160 C on descent. Flights with the CN counter, OA counter, and nephelometer began in July 1994. The CCN counter was added in November 1994, and the engineering problems were solved by June 1995. Since then the flights have included all four instruments, and were completed in January 1998. Altogether there were 20 flights from Laramie, approximately 5 per year, and 2 from Lauder. Of these there were one or more engineering problems on 6 of the flights from Laramie, hence the data are somewhat limited on those 6 flights, while a complete data set was obtained from the other 14 flights. Good CCN data are available from 12 of the Laramie flights. The two flights from Lauder in January 1998 were successful for all measurements. The results from these flights, and the development of the balloon-bome CCN counter have formed the basis for five conference presentations. The heated and unheated CN and OA measurements have been used to estimate the mass fraction of the aerosol volatile, while comparisons of the nephelometer measurements were used to estimate the light scattering, associated with the volatile aerosol. These estimates were calculated for 0.5 km averages of the ascent and descent data between 2.5 km and the tropopause, near 11.5 km.
For many years scientists have been utilizing stratospheric balloons as low-cost platforms on which to conduct space science experiments. A major hurdle in extending the range of experiments for which these vehicles are useful has been the imposition of the gondola dynamics on the accuracy with which an instrument can be kept pointed at a celestial target. A significant number of scientists have sought the ability to point their instruments with jitter in the arc-second range. This paper presents the design and analysis of a stratospheric balloon borne pointing system that is able to meet this requirement. The foundation for a high fidelity controller simulation is presented. The flexibility of the flight train is represented through generalized modal analysis. A multiple controller scheme is introduced for coarse and fine pointing. Coarse azimuth pointing is accomplished by an established pointing system, with extensive flight history, residing above the gondola structure. A pitch-yaw gimbal mount is used for fine pointing, providing orthogonal axes when nominally on target. Fine pointing actuation is from direct drive dc motors, eliminating backlash problems. An analysis of friction nonlinearities and a demonstration of the necessity in eliminating static fiction are provided. A unique bearing hub design is introduced that eliminates static fiction from the system dynamics. A control scheme involving linear accelerometers for enhanced disturbance rejection is also presented. Results from a linear analysis of the total system and the high fidelity simulation are given. This paper establishes that the proposed control strategy can be made robustly stable with significant design margins. Also demonstrated is the efficacy of the proposed system in rejecting disturbances larger than those considered realistic. Finally, we see that sub arc-second pointing stability can be achieved for a large instrument pointing at an inertial target.
Many designs for utilizing stratospheric balloons as low-cost platforms on which to conduct space science experiments have been proposed throughout the years. A major hurdle in extending the range of experiments for which these vehicles are useful has been the imposition of the gondola dynamics on the accuracy with which an instrument can be kept pointed at a celestial target. A significant number of scientists have sought the ability to point their instruments with jitter in the arc-second range. This paper presents the design and analysis of a stratospheric balloon borne pointing system that is able to meet this requirement. The test results of a demonstration prototype of the design with similar ability are also presented. Discussion of a high fidelity controller simulation for design analysis is presented. The flexibility of the flight train is represented through generalized modal analysis. A multiple controller scheme is utilized for coarse and fine pointing. Coarse azimuth pointing is accomplished by an established pointing system, with extensive flight history, residing above the gondola structure. A pitch-yaw gimbal mount is used for fine pointing, providing orthogonal axes when nominally on target. Fine pointing actuation is from direct drive dc motors, eliminating backlash problems. An analysis of friction nonlinearities and a demonstration of the necessity in eliminating static friction are provided. A unique bearing hub design is introduced that eliminates static friction from the system dynamics. A control scheme involving linear accelerometers for enhanced disturbance rejection is also presented. Results from a linear analysis of the total system and the high fidelity simulation are given. Results from a generalized demonstration prototype are presented. Commercial off-the-shelf (COTS) hardware was used to demonstrate the efficacy and performance of the pointer design for a mock instrument. Sub-arcsecond pointing ability from a ground hang test setup is shown from the testing results. This paper establishes that the proposed control strategy can be made robustly stable with significant design margins. Also demonstrated is the efficacy of the proposed system in rejecting disturbances larger than those considered realistic. The system is implemented and demonstrates sub arc second pointing ability using COTS hardware. Finally, we see that sub arc-second pointing stability can be achieved for a large instrument pointing at an inertial target.
Recent studies have shown that progress can be made on over 20% of the key questions called out in the current Planetary Science Decadal Survey by a high-altitude balloon-borne observatory. Therefore, NASA has been assessing concepts for a gondola-based observatory that would achieve the greatest possible science return in a low-risk and cost-effective manner. This paper addresses results from the 2014 Balloon Observation Platform for Planetary Science (BOPPS) mission, namely successes in the design and performance of the Fine Pointing System. The paper also addresses technical challenges facing the new Gondola for High Altitude Planetary Science (GHAPS) reusable platform, including thermal control for the Optical Telescope Assembly, power generation and management, and weight-saving considerations that the team will be assessing in 2015 and beyond.
The Balloon Experimental Twin Telescope for Infrared Interferometry (BETTII) mission launched from Palestine, Texas in June 2017. After an exciting launch and successful cruise, the BETTII gondola suffered an anomalous event at termination. BETTII separated from its parachute and free-fell 136,000 feet into the west Texas desert. This event was classified as a "close-call" and investigated as such. We present here the recovery effort required to find the payload and extract the payload from its impact site. We also present lessons learned from the event and results from the investigation, the design for the next BETTII gondola, and a path forward for return to flight.
Venus and Earth are similar in bulk composition, size, density, and approximate distance from the Sun, yet Venus’s modern-day climate and surface geology is distinctly different [1]. Previous missions to Venus revealed unusual volcanic features, possible continental crust, widespread volcanic plains, a weak magnetic field [2], and insights into the Venusian atmosphere [3,4]. Unfortunately, data from these missions were limited in spatial and temporal resolution and global extent. A future mission to Venus is critical to address fundamental questions surrounding the chemical composition and dynamics of the Venusian atmosphere [5], its geologic history [6,7], its internal structure [8,9], and its habitability throughout time [10,11]. We present the Venus Air and Land Expedition: a Novel Trailblazer for In situ Exploration (VALENTInE) mission to meet this need. VALENTInE is a variable altitude balloon that will passively float in Venus’s atmosphere between 45 and 55 km altitude. VALENTInE will acquire atmospheric data at varying latitudes and longitudes in addition to mapping the surface geomorphology and mineralogy across multiple terrains. Mission Objectives: The VALENTInE mission concept is driven by four main science objectives: 1. Determine whether the driving force of the superrotation of Venus’s atmosphere is caused by horizontal or vertical momentum transport. 2. Determine whether the atmospheric composition and noble gas inventory of the Venusian atmosphere is a product of outgassing from the initial protoplanetary source or if there are significant contributions from exogenic sources. 3. Determine whether the tesserae regions (particularly Aphrodite Terra) are felsic and relatively older than surrounding regions. 4. Determine if there is any evidence of a recent dynamo preserved in the rock record of Venus. Mission Overview: A balloon architecture provides a robust system that can survive long-term in the Venusian environment while taking accurate measurements of the lower cloud deck and surface. Two prior balloon missions to Venus, VEGA 1 and VEGA 2 in 1984, have demonstrated the potential for such planetary exploration; however, these missions were short-lived (46 hr), with limited range (54 km). Our spacecraft concept consists of a battery powered balloon with a gondola and flyby carrier stage (Fig. 1). Our novel design allows for at least 15 days of atmospheric exploration, including multiple ascents and descents in the Venus atmosphere. VALENTInE is baselined to launch in 2032, cruise on solar power for 128 days, enter, descend, and inflate (EDI) into Venus’s atmosphere above Aphrodite Terra, and float in Venus’s atmosphere for a total nominal mission duration of 15 days. The balloon, able to control its altitude by changing its buoyancy, will make one full circumnavigation every 4–8 days and move poleward ~1 o latitude per day; it will be passively directed by the horizontal air currents on Venus. The balloon can only be controlled in the z direction, and the expected latitude range is ±10° from EDI. The balloon itself will be a tracer for atmospheric structures such as zonal winds [5, 12]. During the 15-day operational period, there will be five dips to 45 km for a compositional study of the lower atmosphere and geological and magnetic mapping of the surface. Dips are used to take images and measurements closer to the surface and to obtain in situ vertical atmospheric profiles between 45 and 55 km. Instruments: The VALENTInE instrument payload will allow for extensive study of the geology, atmosphere, and interior of Venus. The instrument suite consists of six instruments. The mission profile for each instrument is shown in Fig. 2. Lower Atmosphere Meteorology Analyzer (LAMA) is an atmospheric structure instrument consisting of a thermometer, barometer, and accelerometer to continuously measure temperature and pressure as a function of altitude, longitude, and latitude. TracE and Noble Gas Investigator (TENGI) is aneutral mass spectrometer used to sample the dense atmosphere. TENGI will operate continuously at 45 km and 55 km and will measure D/H ratios, as well as Ne, Ar, and O isotopic ratios. Kilometer Scale Spectral Imager (KSSI) is amultispectral imager (850-1150 nm) used to resolve surface features on the order of km. Near InfraRed Multispectral Photometer (NIRMP) is an Infrared (IR) photometer used to image the surface through the clouds to characterize mineral assemblages at five different areas of the surface. NIRMP will be operated during dwell. ELevation REConnaissance (ELREC) is a light detection and ranging (LIDAR) instrument used for measuring topography at five different areas of the surface. The ELREC data will be combined with those of NIRMP to determine mineral assemblages and how they correlate to topography. Magnetic Exploration and Interior Detective (MEID) is a magnetometer used to detect any near-surface magnetic anomalies. The magnetometer will continuously operate at all altitudes. Mission Design: The spacecraft’s propulsion system will have a wet mass of 930 kg and will be launched on an Atlas V rocket. The spacecraft will jettison the payload upon arrival in Venus’s atmosphere before decelerating to orbital velocity. Figure 2. Notional power-dip profile while the balloon is on the dayside. Risks and Challenges: Raising and lowering the spacecraft to dip beneath the haze layer require a large amount of energy. This issue was partly compensated by limiting the number of dips over the 15 day prime mission. Power needs for pumping helium are reduced by slowing the descent speed, which consequently increases spatial resolution of in situ measurements between 45 and 55 km. The main limitation for the duration of the mission is the need to carry 15 days’ worth of batteries. The bus experiences external Venusian temperatures ranging from ~27°C at 55 km altitude to ~110°C at 45 km altitude. These high atmospheric temperatures require thermal protection for the bus (instruments, electronics, and flight systems) during its descent, dwell at 45 km, and ascent. The bus is maintained at a mechanically safe temperature range of -10°C to 50°C using white external paint, multi-layer insulation (MLI), mechanical/thermal isolation (e.g. Ti, composites), and ~57 kg of Phase Change Materials (PCM). Images and spectra taken below the haze dominate the available data transmission regardless of the time spent at 45 km. Therefore, less time at the lower altitude mainly reduces the coverage of in situ measurements there. Further, we assumed an unrealistically low-density material for the helium storage tanks on the gondola. However, this issue is partially resolved if we were to jettison 75% of the spent helium storage tanks. After the entry process, the balloon volume remains mostly inflated and storage tanks are required only for reducing balloon volume in dipping to 45 km. This mission was planned against an expected New Frontiers 5 (NF5) cost cap of $1B, as the NF5 call had not yet been released. The mission we describe fits within the predicted cost cap if the flyby carrier stage, responsible for powering the spacecraft during cruise and for relaying in situ measurements back to Earth, can be contributed by another space agency. Acknowledgments: We thank the JPL Planetary Science Summer School, especially A. Nash, J. Scully, K. Mitchell, L. Lowes, and J. Armijo, and our mentors from JPL Team X. Thank you to our review panel for their insightful review. References: [1] Kane, S. et al. (2019) JGR:Ps, 124 , 2015–2028. [2] Phillips, J. L., & Russell, C. T. (1987). JGR: Space Physics , 92 (A3), 2253-2263. [3] Nakamura, M. et al. (2018) Earth Planets Space, 70 (1), 144. [4] Svedhem, H. et al. (2009) JGR:P 114 (E5). [5] Limaye et al. (2009) Decadal Survey White Paper . [6] Ivanov, M. and Head, J. (2011) PSS, 59 (13) , 1559-1600. [7] Smrekar, S. et al. (2018) Space Sci Rev, 214 (5), 88. [8] O’Rourke, J. et al. (2018) EPSL, 502 , 46-56. [9] O’Rourke J. et al. (2019) GRL , (46), 5768–5777 [10] Way, M. et al. (2016) GRL, 43 (16), 8376-8383. [11] Way, M. et al. (2020) JGR:P, 125 (5), e2019JE006276. [12] Preston, R. A. et al. (1986) Science, 231 (4744), 1414-1416.
Introduction: The three Venus missions that were recently selected for upcoming flight (VERITAS, DAVINCI+, and EnVision) will be incredibly valuable to our understanding of Venus’ history, geology, and atmosphere. However, even once completed, key gaps in our knowledge of Venus, and more generally the formation and active processes on rocky, Earth-like planets, will still persist. Remaining questions include 1) how global intrinsic magnetic fields might be maintained on rocky worlds, and how they could then go extinct, and 2) what role atmospheric sulfur chemistry plays in climates of Earth-like planets, which is an increasingly timely subject as Earth’s own atmospheric sulfur content is climbing due to human activity. These questions require in-situ observations from Venus’ cloud deck, at the altitudes at which the UV absorber exists. The Venus Environment Research and Novel Exploration (VERNE) mission will address these questions with an aerial platform that will drift around the equatorial region of the planet for 9 days. VERNE will collect data to determine the identity of the mysterious UV absorber, while also taking magnetic field measurements over the tesserae, the regions on Venus that are most likely to retain remanent crustal magnetization, in order to understand the potential role of a past intrinsically-generated global magnetic field on Venus. Mission Objectives: The two major science objectives that drive the VERNE mission are: 1) Determine the identity of the Venusian unknown ultraviolet absorber(s). First observed approximately a century ago [1], the composition of Venus’ ultraviolet (UV) absorber is one of the oldest mysteries in Venus atmospheric chemistry [2,3]. While several candidate UV absorbers (mostly sulfur species) have been proposed, no consensus has been reached on its composition and its specific interactions with the atmosphere. Determining the identity of the UV absorber will aid climate models by showing how and where incident solar energy is absorbed by the atmosphere and make progress towards understanding the chemical and energetic processes taking place above Venus’ upper cloud deck [4]. 2) Determine if Venus retains evidence of a past, internally-generated magnetic field. While Venus does not currently have an intrinsically-generated magnetic field, evidence for the existence of a past field on Venus and a timeline of its decay will fill in a more holistic picture of the evolution of Venus’ geological record and atmosphere. As the oldest geologic units on the surface, Venus’ tesserae may still have remanent crustal magnetization signatures within the rocky composition [5]. In any case, the signatures detected will provide insight into Venus’ past geological and core dynamo activity. Mission Summary: VERNE includes a 3-part flight system made up of 1) an entry system with a HEEET (Heatshield for Extreme Entry Environment Technology) aeroshell, 2) an orbiter for data relay, and 3) an in-situ balloon and gondola. After entry into Venus’ atmosphere, the balloon will be deployed within the upper cloud deck, at an altitude of 62 km, over a tesserae region. The in-situ data collection will last for the duration of 2 full circumnavigations of the planet, which will take ~9 days. Instrumentation Suite: The four instruments that comprise VERNE’s instrument payload will enable the identification of the unknown UV absorber and the detection of remanent crustal magnetization if it exists in the tesserae. The proposed instrument suite cycle during mission operations is shown in Fig. 1. The four instruments are described below: 1) Adams (ion neutral mass spectrometer) has a range of 18-257 AMU and will detect and distinguish the mixing ratios of O₂, H₂O, H₂SO₄, S, S₂, S₃, S₄, S₅, S₆, S₇, S₈, SO, SO₂, OSSO, SO₃, Cl₂, FeCl₃ and other trace sulfur and organic species. The spatial (longitudinal) and temporal (day/night) variations will be observed throughout 2 circumnavigations with a sample cadence of 12 minutes. 2) Shelley (nephelometer) will determine the size distribution of the aerosols (0.4 to 36 um) in the atmosphere. With a size resolution of <0.7 um, it can determine which mode of H2SO4 is present and characterize the large (>30 um) organic particles previously detected by the Venera and Galileo missions [6,7]. 3) Herbert (UV imager) will measure UV radiance at 283 nm (the wavelength of SO2 absorption) and 365 nm (the unknown part of the absorber). UV images will be taken concurrently with the INMS and nephelometer to correlate UV absorption with abundances of the UV absorber species. 4) Vonnegut (magnetometer) has a range of >600 nT and a precision and accuracy of 1 nT. If magnetized by a past field, the crust may have retained a magnetization of up to 3 A/m2 [5]. With a noise floor of 10 nT, the magnetometer will be able to detect RCM from an altitude of 62 km, even if the thickness of the magnetized crust is just 1 km (Fig. 2). Mission Concept Design: VERNE will be launched with a mass of 3300 kg in an intermediate-high performance class vehicle with a 4-m fairing. The 475-day mission includes 466 days for the cruise, coasting, and orbit initialization phases before entry, descent, and balloon deployment. During the 9-day science phase, the aerial platform will make 2 circumnavigations of the planet at an altitude of 62 km. The INMS and the nephelometer will acquire data for 2 hours during the daytime and nighttime during each circumnavigation, while the UV imager will be on for the duration of the daytime, and the magnetometer will be operational throughout the entirety of the science phase. Data will be stored and processed with the JPL-designed Sphinx command and data handling system. Data will be sent from the balloon to the orbiter using an S-band relay link, stored on the orbiter, and then forwarded to Earth where it will be received by the DSN. Conclusion: VERNE will fill key gaps in our understanding of the history and ongoing processes related to the geology and atmosphere of Venus and rocky worlds in general. Even with adequate flight system contingencies and expected costs below the $900M New Frontiers cost cap, VERNE is not without its risks and challenges. Further trade spaces to explore include 1) using solely battery power vs. including solar panels to increase the mission duration and 2) investigating the use of lightweight materials and 3D-printed structures to reduce the gondola mass, among others. Acknowledgments: We would like to thank the JPL Planetary Science Summer School, especially our mentors Troy Hudson, Karl Mitchell, and Leslie Lowes, as well as our Team-X study lead Al Nash and the members of Team-X. We’d additionally like to thank our review panel for asking insightful questions and providing valuable feedback. References: [1] Ross, F. E. (1928) Astrophysical J., 68, 57-92. [2] Rossow, W. B. et al. (1980) J. Geophysical Research, 85, 8107-8128. [3] Pinto, J. P. et al. (2021) Nature Communications, 12, 175. [4] Titov, D. V. et al. (2007) Cosmic Research, 21, 401. [5] O’Rourke, J. et al. (2019) Geophysical Research Lett., 46, 5768–5777. [6] Limaye, S. S. et al. (2018) Astrobiology, 18(9), 1181-1198. [7] Grinspoon, D. H. et al. (2013) Planetary and Space Sci., 41(7), 515-542. [8] Parker, R. L. (2003) J. Geophysical Research, 108, 5006. *The cost information contained in this document is of a budgetary and planning nature and is intended for informational purposes only. It does not constitute a commitment on the part of JPL and/or Caltech.
Polarimetric observations in UV range by high altitude balloon-borne equipment, discussing development and operation of balloon gondolas
Radiometric measurements of earth reflectance patterns of solar radiation from high altitude balloons, discribing balloon gondola and instrumentation
This paper describes the design, calibration, and operation of a magnetic spectrometer for particle astronomy. The spectrometer consists of a superconducting magnet, optical spark chambers, scintillation detectors, and associated electronics. The instrument has been flown in a balloon gondola to 4.8 g/sq cm residual atmosphere, where it was used to analyze the charge and differential rigidity spectra of primary nuclei from 5 to 100 GeV/c.