Declination Angle Research Articles

Optimization of Sun Tracking Data Handling to Improve Efficiency of PV Module

The procedure of tracking the sun depends on azimuth, altitude and declination angle of sun, latitude and longitude of a location and others. The orientation of sun around the earth can be tracked by using sun tracking mechanisms to collect the maximum percentage of incidents sun ray normal to the panel. This study is conducted to meet objective i.e. optimizing data handling. Three case studies have been implemented. In the first case, a computerized sun tracking device is assumed to rotate the photovoltaic panel as per the sun movement. The output is accurate, but it is expensive as typical multiple sensors, mechanical drive and microcontroller are used. In the second scenario, the solar panel is fixed at sun azimuth (ɸ) 180° and altitude 58° angle which causes more variations in the percentage of incident sun ray normal to the panel throughout the day. Whereas, in the third case, the panel is supposed to change its direction according to the 12 paths (trajectory) of sun instead of 365 paths and each path is comprised with the monthly average of the sun azimuth and altitude angle. This procedure will reduce data handling/ sun tracking cost as compared to the first case. How to cite this article: Taheem A, Sachdeva A, Sharma VS. Optimization of Sun Tracking Data Handling to Improve Efficiency of PV Module. J Adv Res Alt Energ Env Eco 2019; 6(1&2): 1-15. DOI: https://doi.org/10.24321/2455.3093.201901

Orientation-dependent irradiation hardening in pure Zr studied by nanoindentation, electron microscopies, and crystal plasticity finite element modeling

Orientation-dependent irradiation hardening phenomena in pure Zr have been studied, and the corresponding mechanisms investigated based on the combined use of SEM, TEM, and CPFEM. Nanoindentation was conducted on ten grains at room temperature before and after ion irradiation (0.3 dpa, 250 °C). The hardness decreases as the declination angle (the angle between c-axis and sample surface normal) increases, both before and after irradiation. However, the irradiation induced maximum absolute and relative increment of hardness occur when the declination angle is about 55° and 60°, respectively. The hardness increment was found to be proportional to the relative activation of the <a> type slip with increase of declination angle, at low angles. However for angles higher than 55–60° the hardness increment was found to be reduced by the activation of deformation twinning and cross slip. A peak increment of irradiation hardening is therefore observed due to the orientation-dependent combination of different deformation mechanisms. CRSS values of all slip systems and for {10–12} <-1011> tension twinning before and after irradiation were obtained by fitting to a crystal plasticity finite element model (CPFEM). The obstacle strength of heavy ion induced <a> type dislocation loops generated at 250 °C on subsequent room temperature slip was thus calculated to be approximately 0.29 ± 0.05.

Redesigning surgical magnification loupes: effect of angle of declination, weight, and strap design on the postural ergonomics of ophthalmic surgeons

Ophthalmologists using surgical loupes often report chronic neck pain. We designed a surgical loupe and head-strap to reduce neck loading in surgeons. To quantify the effect of this new loupe design on surgeons' posture, we utilized kinematic motion capture, musculoskeletal modeling and electromyography (EMG).

Comparison-space selection to achieve efficient tracklet-to-object association

A major challenge when maintaining a space object catalog is the proper association of new measurements to already cataloged objects. Optical observations are typically associated by comparing the modeled observation to the measured one. The modeled observation is generated from cataloged object states by propagating them to the epoch of observation and transforming them from state space, e.g. orbital elements, to the observation space, e.g. right ascension and declination angles. In addition to propagating the states, their propagated uncertainty distribution is transformed to observation space as well. Statistical distance metrics, such as the Mahalanobis distance, are then evaluated to test whether the observation originated from the cataloged object or not. These distance measures often assume that the uncertainty can be represented with a normal distribution. Assuming that the catalog state uncertainty is properly represented by a normal distribution, it can still loose this property during the propagation in time and the transformation to observation space. The uncertainty of the catalog state is typically much larger than the one from new measurements (only a few arc seconds for optical telescopes) and is therefore more affected by transformation distortions. It is therefore beneficial to perform the comparison in a space advantageous for the state representation. This study will present a projection-based transformation of tracklet information into a favorable frame around the cataloged object state. The effect of the comparison-space selection on cataloguing performance is assessed, i.e. it is systematically tested if it is beneficial to directly compare angles and angular rates, or to compare in the newly proposed projected frame.

Burn angle in forced and natural convection: a simplified scaling approach

The surface regression of burning solid fuels facing a forced flow has been observed and measured by several authors, because of its connection with mass burning rate and heat transfer between flame and fuel. The pyrolysis region of non-spreading flames is not uniform in space and changes in shape with time. On the contrary, for moving flames experiments showed that the competition between surface regression and spread rate causes the pyrolysis region to assume a steady-state geometry. In particular, the declination of the pyrolysis surface is constant for given burning conditions, although it is highly influenced by their variations. The geometry of the pyrolysis region is characterised by the surface declination angle, called burn angle, which can be used to study the relation between mass burning rates and flame spread rates. Despite the amount of experimental work in literature, a theoretical description of the burn angle and its dependence on burning parameters such as flow velocity is still missing. The scale analysis in this work shows an alternative approach to predict the qualitative behaviour of the burn angle and therefore of the average mass burning rate, qualitatively describing its dependence on burning conditions.

Genetic Algorithm as a Solutions Optimization of Tilt Angles for Monthly Periods of Photovoltaic Installation

Changes in the sun’s declination angle, every month for one year affect the energy received by a photovoltaic (PV). Changing the tilt angle, every month to follow changes in sun declination needs to be done so that the energy produced by PV is more optimum. Genetic algorithm (GA) was proposed in this study as the optimal PV slope solution every month of the year. GA calculates the slope angle of PV by calculating changes in sun declination, the movement of the sun from east to west, the coordinates of the location of PV installation, direct radiation and diffuse radiation. GA initializes tilt angle PV with the specified limit, then calculates to get the optimum total energy value on the inclined plane that PV can accept with the crossover, mutation and selection process. Algorithms are limited to 50 generations. The results showed that the optimization of the monthly period slope was better than the annual period. Installation with a slope angle after the monthly period optimization has increased the energy received by solar panels by 12 kWh/m2-year compared to installations with the slope of the annual period of optimization.

Making a Map of the Earth’s Magnetic Field

The Earth has a solid inner core and a liquid outer core, both made of iron and nickel. The metal carries an electrical current that is powered by the movement of the liquid. The electrical current creates a magnetic field that reaches out from the core to the surface of the Earth and beyond. The magnetic field formed by the Earth’s core is expected to align with the axis of rotation, but it deviates a bit for reasons that are not well-understood. A compass needle generally does not point to true North (the axis of rotation of the Earth), but to the magnetic North pole. The angle between true North and magnetic North at any particular position on the Earth is called the declination angle. Maps of the declination angle are very complicated and because of the flow of the outer core, the position of magnetic North moves over time.

Anatomic Considerations for a Posterior Endoscopic Approach to the Cricoarytenoid Joint.

This anatomic study considers the feasibility of a posterior endoscopic approach to the cricoarytenoid joint (CAJ) by describing relationships between readily identifiable anatomic landmarks and the posterior CAJ space in cadaver larynges. Anatomic study. Six adult cadaver larynges (2 male, 4 female) were studied. Digital calipers were used for measurements, and Image J software was used for angle calculations. All cricoarytenoid joints were injected with colored gel via a posterior approach using a 27-gauge needle. The average age of the larynges studied was 78.7 ± 10 years. The average posterior CAJ space (pCAJs) length measured 4.95 ± 0.9 mm. The average distance from the superior aspect of the midline cricoid lamina (MCL) to the center of pCAJs and the corniculate cartilage (CC) to the center of the pCAJs were 8.35 ± 1.5 mm and 14.54 ± 1.9 mm, respectively. The average pCAJs angle of declination (AD) from the horizontal plane was 54° ± 6.2°. All 12 cricoarytenoid joints were successfully injected with colored gel via a posterior approach. The posterior CAJ space can be located surgically using readily identifiable anatomic landmarks. An understanding of this posterior CAJ anatomy may allow for more consistent intra-articular injection and support the development of other CAJ procedures for a range of disorders of vocal fold motion or malposition.

A Solar Time Based Analog Ensemble Method for Regional Solar Power Forecasting

This paper presents a new analog ensemble method for day-ahead regional photovoltaic (PV) power forecasting with hourly resolution. By utilizing open weather forecast and power measurement data, this prediction method is processed within a set of historical data with similar meteorological data (temperature and irradiance), and astronomical date (solar time and earth declination angle). Furthermore, clustering and blending strategies are applied to improve its accuracy in regional PV forecasting. The robustness of the proposed method is demonstrated with three different numerical weather prediction models, the North American mesoscale forecast system, the global forecast system, and the short-range ensemble forecast, for both region level and single site level PV forecasts. Using real measured data, the new forecasting approach is applied to the load zone in Southeastern Massachusetts as a case study. The normalized root mean square error has been reduced by 13.80% to 61.21% when compared with three tested baselines.

Outcomes of the calcaneo-stop procedure for the treatment of juvenile flatfoot in young athletes.

PurposeFlexible flatfoot (FFF) is a widespread condition in juvenile patients. If symptomatic, FFF can require surgical treatment. The calcaneo-stop procedure has shown excellent clinical and radiographic outcomes and low rates of complications. The aim of the present study was to assess the sport practice of young athletes affected by FFF having undergone the calcaneo-stop procedure.MethodsBetween 2008 and 2016, 68 sport practitioners were bilaterally treated by the calcaneo-stop procedure, for a total of 136 FFF cases. Clinical evaluation, including the American Orthopedic Foot and Ankle Score (AOFAS), the Yoo et al score and The Foot & Ankle Disability Index (FADI) and FADI Sport scores were assessed. Radiographic evaluation was based on measurement of talar declination, Costa-Bertani’s angle and calcaneal pitch.ResultsMean follow-up was 57.6 months (sd 16.8). The AOFAS score mean increased from 79.3 (sd 5.7) to 97.3 (sd 4.5) three years after surgery. The Yoo score improved from 3.1 (sd 1.0) preoperatively to 11.7 (sd 0.6) three years after surgery. The FADI Sport subscale mean improved from 74.1 (sd 10.4) preoperatively to 95.9 (sd 4.9) three years after surgery.Costa-Bertani’s angle decreased from 156.1° (sd 4.2°) to 135.8° (sd 7.3°) at three years postoperatively; mean talar declination angle decreased from 44.2° (sd 6.3°) to 30.6° (sd 3.2°) at three years postoperatively and mean calcaneal pitch increased from 12.6° (sd 2.3°) to 16.3° (sd 1.3°) at three years postoperatively.ConclusionAdolescent patients who underwent the calcaneo-stop procedure reported satisfactory outcomes in terms of clinical and radiological evaluations. Moreover, our results showed an improvement of sport activity levels, with patients recovering sports activity within three months of surgery and without limitation in the execution of preferred activities.Level of Evidence:IV

Dynamic Error Analysis of Measurement While Drilling Using Variable Geomagnetic In-Field Referencing

Summary The safe and economical determination of a wellbore trajectory in directional drilling is traditionally achieved by measurement-while-drilling (MWD) methods, which implement magnetic north-seeking sensor packages. Inaccuracies in the determination of well path arise because of random and systematic errors in the measurements of the sensors. Multistation analysis (MSA) and magnetic in-field referencing (IFR) have already demonstrated the potential to decrease the effects of errors because of magnetization of drillstring components along with variable errors caused by irregularities in the magnetization of crustal rocks in the vicinity of wells. Advanced MSA methodologies divide a borehole into several sections and use the average reference values of the total magnetic field, declination, and dip angle for analysis of errors in each section. Our investigations indicate that the variable-reference MSA (VR-MSA) can lead to a better determination of errors, specifically in areas of high magnetization. In this methodology, magnetic reference values are estimated at each station using forward and inverse modeling of surface-magnetic observations from IFR surveys. The fixed errors in magnetometer components are then calculated by minimizing the variance of the difference between the measured and unique estimated reference values at each station. A Levenberg-Marquardt algorithm (LMA) is adopted to solve the nonlinear optimization problem. Examination of this methodology using MWD data confirms more than 20% improvement in well-path-determination accuracy by comparing the results with the corrected path from the conventional MSA method and gyro surveys.

Sound Source Omnidirectional Positioning Calibration Method Based on Microphone Observation Angle

To get source azimuth from microphone observation angle of view in a complex real environment, this article, on the basis of the analysis of geometric positioning method, established a seven-element microphone array model and proposed a sound source omnidirectional positioning calibration method based on microphone observation angle. By using a seven-element array to invert the position and angle of a sound source, the relative time delay value of a pair of microphones on the vertical axis of the coordinate system is used to determine the elevation angle polarity and realize the omnidirectional sound source positioning. The array parameters, sound velocity, array size, horizontal deflection angle, elevation angle, and sound source are analyzed, and the error method is proposed. The sound source data was measured using the microphone array perspective, and a new Cartesian coordinate system was established based on the observation angle of view for omnidirectional positioning calibration of the sound source. The simulation results show that the position error of the method is about 0.01% and the angle error is about 0.005%, with high calibration accuracy. The actual measurement results show that this method can effectively calibrate the sound source azimuth, the error rate of the source coordinates is around 10%, the horizontal declination angle error is less than 5%, and the elevation angle error is less than 8%. Appropriately increasing the spacing of the array will have a better calibration effect in an actual complex experimental environment.

Solar tracker development based on a POF bundle and Fresnel lens applied to environment illumination and microalgae cultivation

Although within the group of countries with the highest solar irradiation index in the world, Brazil still underuses its natural power. Brazil’s hydropower energy today makes up 68,5% of the total energy produced, in contrast however, photovoltaic energy production is still only 0.01%. As an effort to open up new frontiers for solar energy uses, the main objective of this project was to use solar energy in form of light to reduce the power consumption required for continuously lighting any kind of environment as well as to propose a new technology for illuminating a conventional window-type photobioreactor (PBR) in the cultivation of microalgae for biofuel production in order to reduce their associated costs. The system is composed by a solar tracker, an electromechanical control, a Fresnel lens and a plastic optical fiber (POF) bundle, in which tip the lens concentrates the solar radiation. Therefore, at the other end of the bundle, the POFs can be distributed homogeneously in any local where one wants to illuminate. The solar tracker is able to track the Sun from sunrise to sunset using an algorithm whose function is to calculate the Sun position according to the local time and latitude using an equatorial mount structure. In addition, some sensors are employed for monitoring relevant parameters, for instance, the light intensity inside the POF bundle, the right ascension and declination angles of the tracker and the solar radiation. These parameters can be downloaded in real time through a specially designed mobile application. As application of the solar tracker, two projects were developed and described in this paper: two kinds of solar luminaires for illumination of internal ambiences and a closed photobioreactor by POF illumination, with nontransparent material, free of outside contamination with low cost and the study of the produced biomass through the lipid content. Both applications were compared in performance with their conventional counterparts and, as a conclusion, it is shown that in both cases they can substitute their conventional counterparts with advantages.

GPS availability and positioning issues when the signal paths are aligned with ionospheric plasma bubbles

The propagation paths of signals through equatorial ionospheric irregularities are analyzed by evaluating their effects on Global Navigation Satellite System (GNSS) positioning and availability. Based on observations during 32 days by a scintillation monitor at Sao Jose dos Campos, Brazil, it was noted that there is a dominance of enhanced scintillation events for Global Positioning System (GPS) ray paths aligned with the azimuth angle of 345° (geographic northwest). This azimuth corresponds to the magnetic meridian that has a large westward declination angle in the region (21.4oW). Such results suggest that the enhanced scintillation events were associated with GPS signals that propagated through plasma bubbles aligned along the direction of the magnetic field. It will be shown that, under this alignment condition, the longer propagation path length through plasma bubbles can result in more severe scintillation cases and more losses of signal lock, as supported by proposed statistics of bit error probability and mean time between cycle slips. Additionally, large precise positioning errors are also related to these events, as demonstrated by precise point positioning experiments.

Numerical simulation of Rayleigh-Bénard convection in an inclined enclosure under the influence of magnetic field

Two-dimensional numerical simulations are performed on the Rayleigh-Bénard convection using the finite element method, and the effect of the magnetic field on a thermally driven flow of a conducting fluid in a rectangular enclosure is studied. The simulations are performed on liquid Sodium with a Rayleigh number of 6 × 106 in a rectangular enclosure (aspect ratio – 4). The effects of the angle of declination of the enclosure and the influence of magnetic field in horizontal and vertical direction are examined. It is observed that the angle of declination of the enclosure (7°–28°) influenced the convection configurations with larger angles restraining the fluid velocity and hampering the formation of vortices. The applied magnetic field (0.001 T–0.003 T) too affected the formation of Bénard cells, and is dependent on the direction and the magnitude of the external field. In the presence of a horizontal magnetic field, a suppression of multiple vortices in favor of a singular cell structure is seen, and the degree of suppression is directly proportional to the magnitude of the field. Higher magnitudes of magnetic field suppressed convection with the isotherms showing lesser irregularities. However, vertical magnetic fields at smaller declination angles improved the circulation inside the enclosure leading to multiple well-defined parallel structures, which caused severe distortions in the temperature distributions. At large declination angles, the vertical magnetic field too suppressed the formation of well-defined Bénard cells.

Custom 3D-printed Total Talar Prostheses Restore Normal Joint Anatomy Throughout the Hindfoot

Category: Hindfoot Introduction/Purpose: Third generation total talar prostheses (TTP) are viable options for talar avascular necrosis (AVN) in the absence of neighboring joint pathology. The use of modern three-dimensional (3D) printing allows for the production of custom implants that exactly mimic the patient’s anatomy. The aim of this study is to determine the accuracy of 3D printing in reproducing a synthetic talus, and in doing so, restoring more normal anatomic relationships. We hypothesize that this mode of replication will restore and maintain normal radiographic alignment of the ankle, subtalar, and forefoot joints in the setting of talar AVN. Methods: A retrospective analysis was performed on all patients undergoing TTP implantation for the treatment of talar AVN between 2016 and 2017. Pertinent demographic and operative factors were recorded. Radiographic measurements were taken pre- and post-operatively to determine native talar dimensions, TTP implant dimensions, and the corresponding radiographic alignment about the forefoot, hindfoot, and ankle. Results: Fourteen patients, treated for AVN between 2016-2017, were identified in our cohort. Talar arc length and width were not found to be significantly changed, however talar height was significantly increased with use of TTP. Five alignment dimensions were measured (tibiotalar alignment, talar tilt angle, Boehler’s angle, talar declination angle, and Meary’s Angle), of which, only talar tilt angle was significantly changed. Instances of Meary’s angle correction were observed in cavus and planus foot deformity. Conclusion: This study represents the largest case series of TTP performed in the United States, and is the first to investigate the 3D printed TTP. As a proof-of-concept, 3D printed TTP was successful in restoring talar height and talar tilt in the setting of AVN. Additionally, the procedure maintained normal alignment in non-pathologic joints. Total talar prosthesis, based on our cohort, is a viable option to restore more normal anatomic alignment.

Reconstruction of Calcaneal Fracture Malunion With Osteotomy and Subtalar Joint Salvage

Category: Hindfoot Introduction/Purpose: The goal of this study was to discuss the outcomes of treating calcaneal fracture malunion by restoring the subtalar joint with a reconstructive osteotomy. Methods: From May 2005 to November 2016, 85 patients (88 feet) with calcaneal malunions after a displaced intraarticular calcaneal fracture were treated by osteotomy and autogenous bone graft. The subtalar joint was preserved. The mean time from initial injury to reconstructive operation was 8.9 months (95% confidence interval, 4.5-11.6 months). The displaced posterior facet was restored through a reconstructive osteotomy, whereas the bone defect in the calcaneus after reduction was filled with the lateral exostosis that had been removed, iliac bone graft was used if necessary. All patients were evaluated clinically and radiographically at a minimum of 24 months. Sixty two patients (63 feet) were followed for a mean of 45.4 months (29.0-52.3 months). Results: According to American Orthopaedic Foot &amp; Ankle Society (AOFAS) ankle and hindfoot score, the average score was 81.6 points (95% confidence interval, 78.5-90.4 points), which was significantly higher than the preoperative assessment. Radiographs showed that Böhler’s angle, Gissane’s angle, talus declination angle, and width and height of calcaneus were improved to a great extent. Eight patients had wound edge necrosis, and 4 had superficial infection. Two patient required a subtalar fusion for subtalar arthritis at 2 years after surgery. Conclusion: Restoring the subtalar joint with a reconstructive osteotomy and autogenous bone graft was an effective treatment method for selected calcaneal fracture malunions. It reconstructed calcaneal morphology and preserved the subtalar joint.

A Design Method of HTS Bulks Array for Decreasing Rotation Loss in a Superconducting Maglev Microthrust Stand

Rotation losses at low frequency is very crucial to the microthrust stand depending on high temperature superconductors (HTS) maglev. HTS bulks arrays are sources of levitation forces and have an influence on declination angle of the levitation platform during rotation. Changes of declination angle can lead to variation of external magnetic field on HTS bulk arrays, which then affect rotation losses of the microthrust stand. An experimental setup has been established to investigate influence of HTS bulk arrays and eccentric loads on rotation losses. Space ratio is applied to describe the dispersion degree of HTS bulk arrays with different geometrical configurations. Experimental results show that Arrays with smaller space ratio help diminish rotation losses of the HTS maglev stand. Presetting eccentric loads with proper amount and initial circumferential angle could decrease rotation losses for arrays with smaller space ratio. For microthrust measurement using HTS maglev stand, HTS bulk arrays should be optimized to achieve lower rotation losses and better adjustability.

PRIMARY TESTING OF AUTOMATED DUAL-AXIS SOLAR TRACKER IN THE CLIMATIC CONDITIONS OF THE ORENBURG REGION AS THE PROSPECTS FOR THE ESTABLISHMENT OF A HARDWARE-SOFTWARE COMPLEX

One of the reasons for the high cost of electricity generated by statically located solar power plants is the low efficiency of photoelectric converters. Using high-precision solar tracking system will solve this problem. The paper provides a detailed description of the developed modernized structure of an autonomous solar power station with statically and dynamically located modules of solar batteries and a physical model of an automated dual-axis solar tracker. The presented development allows us to increase energy efficiency of solar batteries by precision pointing dynamically located solar modules on the Sun in two coordinates (azimuth and declination angle) during the day. In addition, it is shown that another feature of this photovoltaic system is that statically and dynamically located photoelectric modules are equipped with two types of solar cells – monocrystalline and polycrystalline that leads to an additional gain in the generation of electrical power regardless of the clouds. The ways of increasing the reliability of the autonomous solar power plant operation are mentioned. We have considered the solar tracking systems in the Russian Federation (Orenburg, Tomsk, Chelyabinsk regions) and abroad (United States of America, India, Iran, Turkey, Taiwan), and have justified the necessity of using photovoltaic systems with solar trackers. Moreover, we have successfully tested the developed autonomous solar power plant; the essence of the tests is in an experimental comparison of power generation using statically and dynamically located solar cell modules. The results of the experiments have showed that the use of a solar module with a precision dual-axis solar tracking system, in comparison with a statically located module, makes it possible to increase the efficiency of a photovoltaic installation by 50 %. Thus, experimental evidence of the effectiveness of the automate d tracking system application has been obtained. The work can be useful in the design of energy-efficient photovoltaic installations with the solar tracking system.

Metatarsus Primus Elevatus Resolution After First Metatarsophalangeal Joint Arthroplasty.

Hallux limitus (HL) is the second-most common pathology associated with the first metatarsophalangeal joint. A common etiology believed to be associated with HL is metatarsus primus elevatus (MPE), although causation has been unsubstantiated by evidence. Historically, correction of MPE is surgically addressed with an osteotomy. However, some believe MPE is a secondary manifestation of HL due to retrograde pressure and lack of dorsiflexion at the first metatarsophalangeal joint. This study sought to determine whether MPE resolves spontaneously after first metatarsophalangeal joint arthroplasty and reinstitution of normal joint dorsiflexion. Twenty-seven weightbearing lateral radiographs from patients with HL were reviewed before and after nonimplant first metatarsophalangeal joint arthroplasty. Radiographs were taken preoperatively and at postoperative visits 1 (mean, 2 weeks) and 2 (mean, 10 weeks). Measurements included first to second metatarsal elevation, Seiberg Index, first to fifth metatarsal distance, sagittal plane first to second metatarsal angle, Meary's angle, metatarsal declination angle, and hallux equinus angle. Statistically significant improvement was seen at both postoperative visits in all of the previously mentioned measurements except first to fifth metatarsal distance, which was reduced but was not statistically significant. Metatarsus primus elevatus was reduced significantly after first metatarsophalangeal joint arthroplasty. Resolution occurred rapidly and was maintained at the final postoperative visit. This could be due to MPE being a manifestation of HL and not a cause. Based on the results of this study, osteotomies may be unnecessary to surgically address MPE because it can spontaneously correct after reinstitution of first metatarsophalangeal joint motion.