Single Flight Research Articles

THEORETICAL STUDY OF THE EFFECT OF GEOMETRICAL PARAMETERS AND LOCATION OF ROTOR IMPACT ELEMENTS OF AN IMPACT-CENTRIFUGAL GRINDER ON SPEED AND ANGLES OF CRUSHED PARTICLES FLIGHT

One of efficiency indicators of grain grinders is grain granulometric composition. The basis of mixed fodder is crushed grain, the particles of which must have a leveled granulometric composition for subsequent mixing and obtaining a high-quality feed mixture. In agricultural production, hammer crushers are widely used, in which the destruction of grain occurs due to the impact of a hinged hammer. The main disadvantage of these crushers is that not the entire surface of the hammers is involved in grinding, thus reduces grinding process efficiency. A slightly different principle of material destruction is laid down in the basis of the proposed design of the shock-centrifugal grinder. Main work is performed by flat impact elements located on the rotor, which serve to accelerate crushed particles with subsequent impact of them on the bump elements. An important step in the design of new constructions of shock-centrifugal grinders is to determine size and location of the impact elements on the rotor, without which the grinding process is not possible. In the calculation method presented, the dependencies for determining the velocities and angles of a single particle flight from the surface of a flat impact element for its specified dimensions are proposed. Two variants of an impact element location on the rotor are considered and analyzed: radial and at an angle in the direction of rotor rotation. As a result of research carried out, it is noted that in the case of inclined position of an impact element on the rotor an increase in flight speed and flight angles change in crushed particles, which gives the opportunity to have a positive effect on grinding process.

In-Flight UV-A Exposure of Commercial Airline Pilots.

INTRODUCTION: Understanding UV exposure is essential for the assessment of its contribution to the occupational risk of pilots developing ocular and skin pathologies. The objective of this observational study was to measure the UV exposure of pilots flying between the United Kingdom and a range of destinations at three different seasons.METHODS: The in-flight UV exposure of pilots was measured on 322 Monarch Airlines short-haul flights on the Airbus A321-231 and Airbus A320-214 to 31 destinations, mostly in Europe, from 4 UK airports in September 2016-August 2017. The erythema effective and UV-A doses were compared with the ICNIRP guidance and typical recreational weekend exposure of UK office workers.RESULTS: The erythema effective radiant doses did not exceed 0.1 SED. For most of the flights, the UV-A exposure was also low. On 27 single sector flights, UV-A exposure could have exceeded the ICNIRP guidance if eye protection was not used.DISCUSSION: The UV exposure in a cockpit is mostly governed by the presence of direct sunlight and the duration of a flight. The average monthly exposures were low and significantly below weekend recreational exposures of UK office workers over a similar period. To assess the contribution of occupational UV exposure to the risk of developing sun-related ocular and cutaneous pathologies, it is important to consider the accumulative flight time, destinations, and UV attenuation of aircraft windshields. Additionally, leisure and recreational outdoor time needs to be considered before meaningful overall risk analysis can be undertaken.Baczynska KA, Brown S, Chorley AC, O'Hagan JB, Khazova M, Lyachev A, Wittlich M. In-flight UV-A exposure of commercial airline pilots. Aerosp Med Hum Perform. 2020; 91(6):501-510.

Establishment and Application of Overbooking Model of Single Flight Departure Time Distribution

In order to put forward theoretical foundation for the airlines to strengthen the airline overbooking decision-making systems and do the best to protect the interests of both airlines and passengers. Apply mathematical statistics and probability theory. Analyzed the methods in accordance with the time line, and explains the problems of overbooking, and takes Nanjing Lukou International Airport as an example to carry out the collection and collation of single flight basic data. Based on the model hypothesis is defined. Through the MATLAB software, which verifies the correctness and effectiveness of the model. Research conclusions, according to laws operational and risk aversion mechanism, the making decision of operation method of airline passenger overbooking behavior is scientificity and feasibility.

Sublethal Effects of Diamide Insecticides on Development and Flight Performance of Chloridea virescens (Lepidoptera: Noctuidae): Implications for Bt Soybean Refuge Area Management.

High-dose and refuge are the most important strategies for delaying resistance evolution in Bt crops. Insecticide sprays in refuge areas could be necessary and may limit refuge effectiveness. Here, we evaluated the sublethal effects of two diamide insecticides (chlorantraniliprole and flubendiamide) on Chloridea virescens life history traits and flight performance. Sublethal concentrations of chlorantraniliprole and flubendiamide increased larval and pre-pupal development times and decreased larval weight; flubendiamide increased pupal development times. Chlorantraniliprole increased adult male longevity and reduced female fertility, while flubendiamide reduced fecundity. Overall life table parameters were negatively impacted by both treatments. Males exposed to either insecticide showed significant reductions in flight duration and distance for unsustained flights (<30 min). The duration and distance of the first flights were reduced when exposed to chlorantraniliprole. Sustained flights (>30 min) were generally unaffected by insecticide exposure and both sexes flew >6400 m in a single flight. The sublethal effects of flubendiamide and chlorantraniliprole on C. virescens’ population dynamics could lead to generation asynchrony and provide insufficient susceptible moths when sprayed on refuge crops. However, the distance and duration of flight may still be sufficient to ensure mixing of potentially resistant and susceptible populations from refuge plots.

Cost estimation for alternative aviation plans against potential radiation exposure associated with solar proton events for the airline industry

We present a systematic approach to effectively evaluate potential risk cost caused by exposure to solar proton events (SPEs) from solar flares for the airline industry. We also evaluate associated health risks from radiation, to provide relevant alternative ways to minimize economic loss and opportunity. The estimated radiation dose induced by each SPE for the passengers of each flight is calculated using ExoKyoto and PHITS. We determine a few scenarios for the estimated dose limit at 1 and 20mSv, corresponding to the effective dose limit for the general public and occupational exposure, respectively, as well as a higher dose induced an extreme superflare. We set a hypothetical airline shutdown scenario at 1mSv for a single flight per passenger, due to legal restrictions under the potential radiation dose. In such a scenario, we calculate the potential loss in direct and opportunity cost under the cancelation of the flight. At the same time, we considered that, even under such a scenario, if the airplane flies at a slightly lower altitude (from 12 to 9.5km: atmospheric depth from 234 to 365g/cm$^{2}$), the total loss becomes much smaller than flight cancelation, and the estimated total dose goes down from 1.2 to 0.45mSv, which is below the effective dose limit for the general public. In case of flying at an even lower altitude (7km: atmospheric depth 484g/cm$^{2}$), the estimated total dose becomes much smaller, 0.12 mSv. If we assume the increase of fuel cost is proportional to the increase in atmospheric depth, the increase in cost becomes 1.56 and 2.07 for the case of flying at 9.5 km and at 7 km, respectively. Lower altitude flights provide more safety for the potential risk of radiation doses induced by severe SPEs. At the same time, since there is total loss caused by flight cancelation, we propose that considering lower flight altitude is the best protection against solar flares.

Tanker Wake Effects on the Trailing UAV in Autonomous Aerial Refueling

Autonomous aerial refueling is a typical close formation flight process, in which the tanker wake has a strong aerodynamic influence to the receiver. In order to develop the accurate aerodynamic models in refueling simulations and design the control laws for autonomous aerial refueling, the tanker wake effects on an Unmanned Aerial Vehicle (UAV) are investigated through ANSYS CFX 15.0. A simplified boom-equipped tanker and a tailless delta wing UAV (named ZD-X) are used in this study. The aerodynamic characteristics of ZD-X in single flight are calculated first and the results are used as the benchmark for comparison. Then the aerodynamic characteristics of ZD-X under the effects of tanker wake are calculated, the final results are given in incremental form to facilitate comparative analysis. Numerical results are obtained from the tanker and receiver at varying lateral, vertical and longitudinal spacings. It is observed that the tanker wake effects on the receiver mostly come from wingtip vortices of the tanker wing and horizontal tail, and the lateral and vertical spacings have significant effects on the aerodynamic characteristics of the receiver, while the longitudinal spacing has almost no effect.

Small Multicopter-UAV-Based Radar Imaging: Performance Assessment for a Single Flight Track

This paper deals with a feasibility study assessing the reconstruction capabilities of a small Multicopter-Unmanned Aerial Vehicle (M-UAV) based radar system, whose flight positions are determined by using the Carrier-Phase Differential GPS (CDGPS) technique. The paper describes the overall radar imaging system in terms of both hardware devices and data processing strategy for the case of a single flight track. The data processing is cast as the solution of an inverse scattering problem and is able to provide focused images of on surface targets. In particular, the reconstruction is approached through the adjoint of the functional operator linking the unknown contrast function to the scattered field data, which is computed by taking into account the actual flight positions provided by the CDGPS technique. For this inverse problem, we provide an analysis of the reconstruction capabilities by showing the effect of the radar parameters, the flight altitude and the spatial offset between target and flight path on the resolution limits. A measurement campaign is carried out to demonstrate the imaging capabilities in controlled conditions. Experimental results referred to two surveys performed on the same scene but at two different UAV altitudes verify the consistency of these results with the theoretical resolution analysis.

Insect Target Classes Discerned from Entomological Radar Data

Entomological radars employing the ‘ZLC’ (zenith-pointing linear-polarized narrow-angle conical scan) configuration detect individual insects flying overhead and can retrieve information about a target’s trajectory (its direction and speed), the insect’s body alignment and four parameters that characterize the target itself: its radar cross section, two shape parameters and its wingbeat frequency. Criteria have previously been developed to distinguish Australian Plague Locusts Chortoicetes terminifera, large moths, medium moths and small insects using the target-character parameters. Combinations of target characters that occur frequently, known as target ‘classes’, have also been identified previously both through qualitative analyses and more objectively with a 4D peak-finding algorithm applied to a dataset spanning a single flight season. In this study, fourteen years of radar observations from Bourke, NSW (30.0392°S, 145.952°E, 107 m above MSL) have been used to test this approach and potentially improve its utility. We found that the previous criteria for assigning targets to classes require some modification, that classes identified in the previous studies were frequently present in other years and that two additional classes could be recognized. Additionally, by incorporating air-temperature information from a meteorological model, we have shown that different classes fly in different temperature ranges. By drawing on knowledge concerning migrant species found in the regional areas around the radar site, together with morphological measurements and radar cross-section data for proxy species, we have made tentative identifications of the insect taxa likely to be contributing to each class.

First use of radio telemetry to assess behavior of red palm weevil, Rhynchophorus ferrugineus (Olivier) (Coleoptera: Dryophthoridae) in the presence and absence of pheromone traps

The red palm weevil, Rhynchophorus ferrugineus (Olivier) (RPW) is a destructive insect pest of palm trees, destroying thousands of date palm trees in Kingdom of Saudi Arabia (KSA) and other countries. Radio telemetry has provided beneficial knowledge on the movements, the habitat preference, and reproductive behaviors of numerous species of animals. In this study, we tracked the movements and habitat preferences of RPW in date palm orchards in KSA using radio telemetry with and without the use of pheromone traps. This study is the first to track individual adult RPW using radio telemetry in production date palm orchards. Small radio transmitters (LB-2X, HOLOHIL) were glued on wild-caught adults and released in date palm orchard in late April and early May 2019. Our results indicated that wild-caught adult RPW with attached dummy transmitters were able to fly normally, whereas laboratory-reared adults were unable to fly successfully with attached transmitters. The flight behavior of the RPW adults was influenced by pheromone traps. The average flight of the RPW was 69.1 m (7.7–213 m) in the presence of pheromone traps and only 24.4 m (10–90 m) without pheromone traps. The mean distances females and males covered were 95.80 m and 42.40 m in the presence of pheromone traps and 32.47 m, 16.30 m in the absence of pheromone traps, respectively. The percentages of tagged adults that dispersed more than 50 m were 50% and 8.3% in the presence and absence of pheromone traps, respectively. Time required for taking-off from the release point was 5–20 min and 0.5–6 h in the presence and absence of pheromone traps, respectively. The aggregation rate was 33.3% and 75.0%, in the presence and absence of pheromone traps, respectively. Only a single flight was taken by each adult in the presence or absence of pheromone traps. Adults showed high preference in selecting habitats. RPW adults were attracted to infested or previously infested male palm trees, surface water of drip irrigation systems, and pheromone traps. In conclusion, radio telemetry appears to be a suitable technique to track RPW in date palm orchards when wild-caught adults are used.

Early detection of Agrilus planipennis: investigations into the attractive range of the sex pheromone (3Z)‐lactone

AbstractThe emerald ash borer (EAB), Agrilus planipennis Fairmaire (Coleoptera: Buprestidae), is a highly destructive primary pest of ash (Fraxinus sp., Oleaceae) trees outside of its native range. Ash is an important component of many ecosystems and its loss would be detrimental to both the economy and the environment. The present study aimed to improve our understanding of the effectiveness of green sticky prism traps baited with host kairomone and insect pheromone lures for A. planipennis and to collect data for modelling the range of attraction of the pheromone (3Z)‐dodecen‐12‐olide [(3Z)‐lactone]. Traps were deployed over a single flight season in urban locations of Ontario, Canada, with low densities of EAB. Traps were placed in pairs of trees separated by not more than 25 m. All traps contained the host kairomone, (3Z)‐hexenol, with the remaining half in each pairing additionally baited with (3Z)‐lactone pheromone. Both lure types were highly effective in capturing EAB, with &gt;90% detection rates overall. However, traps baited with the lactone pheromone and host volatile lures doubled trap captures of EAB over distances of at least 25 m from the nearest traps baited with only host volatiles. Although the baseline detection rate of traps containing (3Z)‐hexenol alone is not significantly reduced compared with traps containing (3Z)‐lactone, the overall trap effectiveness is significantly increased when (3Z)‐lactone is present. The implications for the use of (3Z)‐lactone at 3 mg per septum dose in an early warning trapping system are discussed. Trap layout methods and risk‐based analysis models can now be further refined by including these data about the attractive range of lures and their behaviour in different plot environments.

Optimal Design of Cooperative Penetration Trajectories for Multiaircraft

At present, two kinds of shortages exist in the research on cooperative combat. One is that radar detection threat (which cannot be ignored) is rarely considered. The other is that limited efforts have been made on the cooperative penetration trajectories under the conditions of long distance, vast airspace, and wide speed range. In order to offset the shortages of the research on cooperative combat, the penetration trajectory optimization method considering the influence of aircraft radar cross-section (RCS) and the cooperative penetration strategy is proposed in this study. Firstly, the RCS data are calculated by the physical optics (PO) method. The radar detection threat model is established considering the influence of the aircraft RCS. Then, a trajectory optimization framework with the dynamic model, constraint conditions, and optimal objectives is formed. Using the hp-adaptive Radau pseudospectral method, the optimal control problem for a single aircraft flight is solved. Finally, a cooperative penetration strategy is proposed to solve the cooperative penetration problem of multiaircraft. The impact time and angle constraints are given, and the virtual target point is introduced for terminal guidance. Two cases are simulated and verified. Simulation results demonstrate that the proposed method is effective. The single aircraft can effectively penetrate, and the multiaircraft can fulfill the requirement of cooperative impact time and angle under the condition of meeting the minimum threat of radar detection.

Micro-X Sounding Rocket: Transitioning from First Flight to a Dark Matter Configuration

The Micro-X sounding rocket flew for the first time on July 22, 2018, becoming the first program to fly Transition-Edge Sensors and multiplexing SQUID readout electronics in space. While a rocket pointing failure led to no time on-target, the success of the flight systems was demonstrated. The successful flight operation of the instrument puts the program in a position to modify the payload for indirect galactic dark matter searches. The payload modifications are motivated by the science requirements of this observation. Micro-X can achieve world-leading sensitivity in the keV regime with a single flight. Dark matter sensitivity projections have been updated to include recent observations and the expected sensitivity of Micro-X to these observed fluxes. If a signal is seen (as seen in the X-ray satellites), Micro-X can differentiate an atomic line from a dark matter signature.

Assessment of degradation equivalent operating time for aircraft gas turbine engines

ABSTRACTThis paper presents a novel method for quantifying the effect of ambient, environmental and operating conditions on the progression of degradation in aircraft gas turbines based on the measured engine and environmental parameters. The proposed equivalent operating time (EOT) model considers the degradation modes of fouling, erosion, and blade-tip wear due to creep strain, and expresses the actual degradation rate over the engine clock time relative to a pre-defined reference condition. In this work, the effects of changing environmental and engine operating conditions on the EOT for the core engine booster compressor and the high-pressure turbine were assessed by performance simulation with an engine model. The application to a single and multiple flight scenarios showed that, compared to the actual engine clock time, the EOT provides a clear description of component degradation, prediction of remaining useful life, and sufficient margin for maintenance action to be planned and performed before functional failure.

Aircraft rerouting and rescheduling in multi-airport terminal area under disturbed conditions

The disturbances, caused by resource competition, weather changes, and demand uncertainties, frequently occur and result in obvious fluctuations (e.g., the increase or decrease of demand and capacity) in demand and capacity. This work addresses the problem of aircraft rerouting and rescheduling in presence of disturbances, characterized by the increase or decrease of demand and capacity, at a multi-airport terminal maneuvering area (TMA). A multi-objective optimization model is proposed to minimize the total flight delays and total extra flying time, considering the aircraft wake turbulence separation, runway operation rules, air traffic control regulations, scheduling time windows, and airport/airspace capacity, etc. Based on the non-dominated sorting genetic algorithm (NSGA-II), we designed an efficient evolutionary algorithm to solve the proposed model and search the Pareto solutions. Five scenarios are designed to analyze and compare the operation performance under normal and disturbed conditions, using the classic First-Come-First-Served (FCFS) and optimized scheduling (OPTS) methods. A case study is conducted for Shanghai Pudong and Hongqiao Airports, and the computational results show that, compared with the FCFS method, the proposed OPTS method significantly performs a overall better performance in minimizing total flight delay and total extra flying time, while slightly inferior in optimizing the delay and extra flying time of one single flight.

Simulation of Giesekus fluid flow in extruder using helical coordinate system

In the present work, it is proposed to use a helical coordinate system for mathematical modeling of non-isothermal Giesekus fluid flow in the extruder in the metric zone. The convenience of using a helical coordinate system is to reduce the three-dimensional problem to two-dimensional without the use of additional assumptions. The helical coordinate system is applicable only for steady flow conditions. Particular results of the numerical implementation of the use of a helical coordinate system are presented on the example of a Giesekus fluid flow in an extruder with a single flight, the results are compared with the flow of Newtonian fluid.

Direct-imaging of light-driven colloidal Janus particles in weightlessness.

We describe a highly integrated automated experiment module that allows us to investigate the active Brownian motion of light-driven colloidal Janus-particle suspensions. The module RAMSES (RAndom Motion of SElf-propelled particles in Space) is designed for the sounding rocket platform MAPHEUS (MAterialPHysikalische Experimente Unter Schwerelosigkeit). It allows us to perform experiments under weightlessness conditions in order to avoid sedimentation of the Janus particles and thus to study the spatially three-dimensional dynamics in the suspension. The module implements a newly developed strong homogeneous light source to excite self-propulsion in the Janus particles. The light source is realized through an array of high-power light-emitting diodes and replaces the conventional laser source, thus reducing heat dissipation and spatial extension of the experiment setup. The rocket module contains ten independent sample cells in order to ease the systematic study of the effect of control parameters such as light intensity or particle concentration and size in a single sounding-rocket flight. For each sample cell, transmitted light intensities are stored for postflight analysis in terms of differential dynamical microscopy.

Decision-making in migratory birds at stopover: an interplay of energy stores and feeding conditions

Migrating birds make stopovers to rest and fuel to prepare for their next flight. The decision when to continue migration significantly affects total duration of migration and thus arrival timing at the migratory destination. Departure decisions of migrants are therefore important to understand variation in arrival timing. Since the amount of energy can limit flight duration, feeding conditions and energy stores have a significant effect on the departure decisions. Unexpectedly though, various fasting-refuelling experiments controlling for these two parameters and using migratory restlessness as a proxy for departure probability did not find consistent patterns within and across different songbird species of departure decisions. Here we performed a fasting-refuelling experiment on four actively migrating songbird species during autumn, to assess the significance and consistency of the feeding conditions and energy stores on the bird’s departure decision. We found no differences in the departure probability between low and favourable feeding conditions in all species. During the low food phase, however, birds with higher energy stores were more likely to depart than leaner birds. When fasted individuals encountered improved feeding conditions, they significantly increased their energy stores and showed a significant drop in migratory restlessness. This is tantamount to the decision of staying at stopover. The consistency of the patterns seems to be generalizable across species. Additionally, the results highlight the importance of the interplay of feeding conditions, changes in these and the bird’s current energy stores for the stopover decision-making process. Many migratory songbirds travelling thousands of kilometres do so by making several single nocturnal flights interrupted by resting periods on the ground. To decide when to continue migration, birds seem to follow general departure rules. Fat birds continue migration when they do not find food during their rest, while lean birds stay until the feeding conditions have improved. In this study, we show for the first time a generalizable consistent pattern that feeding conditions, changes in food availability and the current energy stores jointly influence the departure decisions of migratory songbirds at stopovers. This is in contrast to former studies showing inconsistent patterns on the reaction of a low food phase regarding the departure probability. Our experiment, therefore, advances our knowledge about the decision-making process of bird migrants and demonstrates the importance of favourable feeding conditions for migratory birds resting at a stopover site.

Optimization of UAS‐based high‐throughput phenotyping to estimate plant health and grain yield in sorghum

AbstractHigh‐throughput phenotyping (HTP) has enabled the acquisition of vast amounts of data. Therefore, finding the most informative phenological stage(s) and high‐throughput traits could lead to significant optimization of HTP‐assisted selection. An investigation as to when phenotypic data should be collected and how it should be processed from unmanned aerial system (UAS) imagery for the optimization and assessment of two primary traits in grain sorghum [Sorghum bicolor (L). Moench], namely, grain yield and plant health (based on anthracnose scores) was conducted. By evaluating multiple flight dates across the growing season via multispectral UAS‐based imagery, a set of scenarios composed of combinations of flight dates and vegetation indices were constructed for analysis. In this sense, results showed no increase in predictive ability when combining multiple vegetation indices. Hence, using only an index with a higher predictive ability (e.g., normalized difference vegetation index (NDVI) or modified simple ratio (MSR) for plant health with 0.75; and any tested index but chlorophyll index (CIg) for grain yield with ∼0.55) is recommended. Likewise, the combining of multiple flights did not result in a significant increase in predictive ability for either primary trait. Thus, we observed that a single flight for each trait (e.g., 121 d after sowing with 0.81 for plant health; 104 d after sowing with 0.59 for grain yield) was optimal. Concerning, the predictive algorithms examined, partial least squares regression (PLSR) and neural network, results were similar, with PLSR generally outperforming. In addition, we discuss our findings from an application standpoint of a field‐based breeding program and suggest additional optimization options.

Evidence for male genitalia detachment and female mate choice in the Australian stingless bee Tetragonula carbonaria

Mating systems are poorly understood for the majority of the world’s estimated 600 stingless bee species (Meliponini). It is assumed that in most species, a virgin queen takes a single nuptial flight, mates with a single drone and returns to the nest, using the stored sperm from this one event for the remainder of her life. Multiple genetic studies focused on stingless bee species from around the world have supported the hypothesis of single mating—monandry—by demonstrating shared paternity of workers within colonies. One possible mechanism for monandry is through male genitalia detachment during mating, which forms a residual mating plug inside the queen. Despite being thought to be the norm for stingless bees, male genitalia detachment has only been observed in a small number of species from the neotropics. Here I report on detailed observations of mating interactions for four queens of the Australian stingless bee Tetragonula carbonaria. Male genitalia detachment was observed in each case of copulation, providing the first evidence of male genitalia detachment in any Asian–Australian stingless bee lineage. Observations of the behaviour of queens also provide possible evidence for female mate choice in T. carbonaria. To more fully understand the mating system of T. carbonaria, further observations must be made of wild, natural copulation events, and the behaviour of the queen and the workers within the nest upon her return from the nuptial flight.

Multiscale multifractal analysis on air traffic flow time series: A single airport departure flight case

Multiscale multifractality of air traffic flow volume time series characterizes the operation and the evolution characteristics of the air traffic system in the temporal dimension, which are helpful in gaining a better understanding of the dynamical evolution mechanism of this system. We identify the airport departure air traffic flow volume time series is of multiscale multifractality via the investigation on the Hurst surface obtained by the multiscale multifractal analysis. The resulting Hurst surface is of distinct local fluctuation characteristics and shows distinct fractal characteristics on different scales. We confirm that the two types of multifractality both present in the time series, with the long-range correlation being the main cause of the multifractality. We extend multifractal spectra to multifractal spectrum surfaces to provide a common multiscale framework for exploring the multifractal strength, the dominant fluctuation type and the insensitivity of the multifractality. Furthermore, we find that we can use the time series of only 101 days, saving us 116 days, to obtain a quite similar Hurst surface whose difference to the original one is only 2.11662−7.