Aircraft Communications Addressing And Reporting System Research Articles

Real-time scale monitoring prototype of aircraft systems through wireless communication

Currently, there are aircraft tracking systems known as ACARS (Aircraft Communication Addressing And Reporting System), which are already able to provide certain information, however, this can only be used in very specific contexts, since information such as passengers or fuel used do not serve much to the maintenance area if you want to provide real-time support. Therefore, this research proposed the development of a prototype capable of real-time monitoring some of the systems of an aircraft and thus deliver the necessary information for good maintenance, monitoring, and support in real-time. For this case, the monitoring was performed on an RPAS (Remotely Piloted Aircraft System), since its acquisition or construction is more affordable; the flight prototype shed light on the behavior when acquiring and sending data frames inside the aircraft.

Specific Emitter Identification Based on a Hybrid Deep Neural Network for ACARS Authentication

With the increasing variety and quantity of aircraft, there is a potential threat to the security of the Aircraft Communications Addressing and Reporting System (ACARS) due to the lack of reliable authentication measures. This paper proposes a novel specific emitter identification (SEI) algorithm based on a hybrid deep neural network (DNN) for ACARS authentication. Our deep learning architecture is a combination of Deep Residual Shrinkage Network (DRSN), Bidirectional-LSTM (Bi-LSTM), and attention mechanism (AM), which perform the functions of local and global feature learning and feature focusing, respectively, so that the individual information hidden in the signal waveform can be thoroughly mined. We introduce soft thresholding as a nonlinear transformation in the DSRN to enhance robustness against noise and adopt a low-cost training strategy for new data using transfer learning. The proposed SEI algorithm is optimized and evaluated based on real-world ACARS signals captured in the Xianyang airport. Experimental results demonstrate that our algorithm can distinguish authorized entities from unauthorized entities and obtain an identification accuracy of up to 0.980. In addition, the design rationality and the superiority over other algorithms are verified through the experiments.

Aircarft Signal Feature Extraction and Recognition Based on Deep Learning

Radio signal recognition has a wide application in future communication systems and the vehicular communication, whose core is the extraction of signal features such as electromagnetic fingerprints. With the rapid development of artificial intelligence technology, deep learning has made amazing breakthroughs in image recognition, speech recognition and other fields. Deep learning is applied to electromagnetic fingerprint extraction in this paper. Firstly, thousands of the downlink aircraft communications addressing and reporting system (ACARS) signals used for communication between civil aircraft and airport tower are collected and generated. Then a pre-transformation network suitable for electromagnetic signals is constructed to convert one-dimensional signals into two-dimensional feature maps, and afterwards the feature maps are input into the convolutional neural network (CNN) for classification. By adopting the attention modules, the classification results were improved by a few percentage points over the baseline with a little cost. The method proposed in this paper achieves an accuracy rate of 94.1% and can obtain the aircraft type in a shorter time than traditional method. Moreover, the robustness of the proposed model in response to additive Gaussian white noise (AWGN) and phase deviation is studied and tested.

Generative adversarial network-based electromagnetic signal classification: A semi-supervised learning framework

Generative adversarial network (GAN) has achieved great success in many fields such as computer vision, speech processing, and natural language processing, because of its powerful capabilities for generating realistic samples. In this paper, we introduce GAN into the field of electromagnetic signal classification (ESC). ESC plays an important role in both military and civilian domains. However, in many specific scenarios, we can't obtain enough labeled data, which cause failure of deep learning methods because they are easy to fall into over-fitting. Fortunately, semi-supervised learning (SSL) can leverage the large amount of unlabeled data to enhance the classification performance of classifiers, especially in scenarios with limited amount of labeled data. We present an SSL framework by incorporating GAN, which can directly process the raw in-phase and quadrature (IQ) signal data. According to the characteristics of the electromagnetic signal, we propose a weighted loss function, leading to an effective classifier to realize the end-to-end classification of the electromagnetic signal. We validate the proposed method on both public RML2016.04c dataset and real-world Aircraft Communications Addressing and Reporting System (ACARS) signal dataset. Extensive experimental results show that the proposed framework obtains a significant increase in classification accuracy compared with the state-of-the-art studies.

Characterizing aircraft engine fuel and emission parameters of taxi phase for Shanghai Hongqiao International Airport with aircraft operational data

Aircraft engine emissions during landing and take-off cycle are commonly estimated on the basis of the International Civil Aviation Organization (ICAO) promulgated calculation model and emission parameters; however, the ICAO certified parameters are generally not applicable for an individual airport. In this study, the operation times, fuel and emission parameters of 8 aircraft models during taxi phase at Shanghai Hongqiao International Airport (SHA) are analyzed with the Aircraft Communication Addressing and Reporting System (ACARS) data, and compared with corresponding values referenced by the ICAO. The results show perceptible discrepancies between the SHA-specific and ICAO certified values. The taxi-out times at SHA are considerably overestimated (up to 35.3%) by ICAO for all the analyzed aircraft models, whereas the taxi-in durations are highly close to the ICAO referenced value with a variation within −6.3% to 9.7%. In the majority of cases, the localized fuel flows and emission indices (EIs) are overvalued by ICAO, and the extent of overestimation can be as large as 21.6% and 28.3%, respectively. Variabilities in operation times, fuel and emission parameters are also characterized depending on aircraft types. Additionally, as a novel attempt, the effect of engine aging on EIs is explored and no significant correlation has been detected, indicating that other factors may affect the EIs dominantly over engine age. The resulting SHA-specific emission parameters are significant towards a precise emission quantification and modeling of impacts on air quality and health.

Quantifying aircraft emissions of Shanghai Pudong International Airport with aircraft ground operational data

The air traffic growth at Shanghai Pudong International Airport (PVG) has attracted much concern over the potential impacts on local air quality and human health; however, the emission contributions due to aircraft activities, impact on air quality and health effects remain unclear. In this study, the ground operational data derived from the Aircraft Communication Addressing and Reporting System (ACARS) dataset are newly utilized to obtain the PVG-specific emission parameters of 10 distinct aircraft-engine combinations during the taxi-in and taxi-out phases of the landing and take-off (LTO) cycle. The resulting emission parameters, together with PVG-specific operational conditions, are applied to quantify the annual emissions in 2017 for main engines and auxiliary power units (APUs) at PVG, emission variations caused by mixing layer height, sensitivity of black carbon (BC) emissions to the estimation method and sensitivity of PM2.5 emissions to the fuel sulfur content (FSC). The results show noticeable discrepancies between the corrected fuel flows and NOx emission indices (EIs) and those certified by the International Civil Aviation Organization (ICAO). The annual emissions of hydrocarbons (HC), CO, NOx, NO, NO2, HONO, HNO3, NOy, SO2, SO42−, BC, organic carbon (OC) and PM2.5 with corrected emission parameters are 3.82 × 105 kg, 4.35 × 106 kg, 5.36 × 106 kg, 4.40 × 106 kg, 9.58 × 105 kg, 1.03 × 105 kg, 3.83 × 103 kg, 5.47 × 106 kg, 3.56 × 105 kg, 1.31 × 104 kg, 5.43 × 104 kg, 4.73 × 103 kg and 7.22 × 104 kg, respectively, while the application of the maximum height of the mixing layer contributes to emission increases as high as 16.9% (NOx). An alternative estimation of BC emissions leads to an increase of 50% compared with first-order approximation 3 (FOA3), while a reduction in PM2.5 emissions can be expected by minimizing the FSC.

Deep Learning-Based Approach for Civil Aircraft Hazard Identification and Prediction

Safety is an eternal issue in the civil aviation transportation. Once a civil aviation accident occurs, it will cause great casualties and economic losses. In order to ensure the civil aviation safety, the hazard identification and prediction of civil aircraft should be effectively and accurately realized. The civil aircraft uses Aircraft Communications Addressing and Reporting System (ACARS) to interact with the ground during flight. The data generated by ACARS has a simple structure and strong timeliness. In view of the advantages of ACARS data, a hazard identification and prediction method based on support vector machine optimized by particle swarm optimization (PSO-SVM) and long short term memory (LSTM) neural networks which uses ACARS report as analysis data is proposed. First, in order to reduce the identification and prediction time cost, the SVM-based recursive feature elimination method with cross-validation algorithm (SVM-RFECV) is used to select the characteristic parameters. Then, the SVM optimized by PSO is used to identify hazard based on the selected parameters. According to the identification results, the LSTM is used to predict the trend of the selected parameters to realize hazard prediction. An A13 report of APU generated by ACARS is selected as analysis data for hazard identification and predication in this paper. The analysis results show that the proposed identification method based on PSO-SVM and SVM-RFECV has high identification speed and accuracy. The proposed prediction method based on LSTM has the best prediction performance. The proposed method can effectively identify hazards and accurately predict the trend of parameters to improve the safety of aircraft.

Aircraft engine fault detection based on grouped convolutional denoising autoencoders

Many existing aircraft engine fault detection methods are highly dependent on performance deviation data that are provided by the original equipment manufacturer. To improve the independent engine fault detection ability, Aircraft Communications Addressing and Reporting System (ACARS) data can be used. However, owing to the characteristics of high dimension, complex correlations between parameters, and large noise content, it is difficult for existing methods to detect faults effectively by using ACARS data. To solve this problem, a novel engine fault detection method based on original ACARS data is proposed. First, inspired by computer vision methods, all variables were divided into separated groups according to their correlations. Then, an improved convolutional denoising autoencoder was used to extract the features of each group. Finally, all of the extracted features were fused to form feature vectors. Thereby, fault samples could be identified based on these feature vectors. Experiments were conducted to validate the effectiveness and efficiency of our method and other competing methods by considering real ACARS data as the data source. The results reveal the good performance of our method with regard to comprehensive fault detection and robustness. Additionally, the computational and time costs of our method are shown to be relatively low.

Undermining Privacy in the Aircraft Communications Addressing and Reporting System (ACARS)

Abstract Despite the Aircraft Communications, Addressing and Reporting System (ACARS) being widely deployed for over twenty years, little scrutiny has been applied to it outside of the aviation community. Whilst originally utilized by commercial airlines to track their flights and provide automated timekeeping on crew, today it serves as a multi-purpose air-ground data link for many aviation stakeholders including private jet owners, state actors and military. Such a change has caused ACARS to be used far beyond its original mandate; to date no work has been undertaken to assess the extent of this especially with regard to privacy and the various stakeholder groups which use it. In this paper, we present an analysis of ACARS usage by privacy sensitive actors-military, government and business. We conduct this using data from the VHF (both traditional ACARS, and VDL mode 2) and satellite communications subnetworks. Based on more than two million ACARS messages collected over the course of 16 months, we demonstrate that current ACARS usage systematically breaches location privacy for all examined aviation stakeholder groups, explaining the types of messages used to cause this problem.We illustrate the challenges with three case studies-one for each stakeholder group-to show how much privacy sensitive information can be constructed with a handful of ACARS messages. We contextualize our findings with opinions on the issue of privacy in ACARS from 40 aviation industry professionals. From this, we explore recommendations for how to address these issues, including use of encryption and policy measures.

Nocturnal Relative Humidity Maxima above the Boundary Layer in the U.S. Midwest: A Diagnostic for the Mountain–Plains Solenoidal Circulation

Measurements from the Aircraft Communications, Addressing, and Reporting System (ACARS) dataset between 2005 and 2014 are used to construct diurnal vertical cross sections of relative humidity in the lower troposphere at six airports in the U.S. Midwest. In summer, relative humidity maxima occur between 2 and 3 km during the overnight hours of 0300–0900 local solar time (LST). These maxima coincide with negative anomalies in temperature and positive anomalies in specific humidity. Vertical winds from the Modern-Era Retrospective Analysis for Research and Applications, version 2 (MERRA-2), reanalysis dataset show that the height and diurnal timing of these positive relative humidity anomalies are consistent with the regional diurnal pattern of vertical motion. During the day, there is rising motion over the Rocky Mountains and subsidence over the Midwest, while conversely at night, there is sinking motion over the mountains and rising motion over the Midwest. The nocturnal relative humidity maxima over the Midwest are the strongest direct observational evidence to date of this mountain–plains solenoidal circulation, and provide a useful diagnostic for testing the strength of this circulation in climate and reanalysis models. There is significant interannual variability in the strength of the nocturnal relative humidity maxima. In 2011, the relative humidity maxima are very pronounced. In 2014, however, they are almost nonexistent. Finally, the relative humidity maxima are discussed in relation to the low-level jet (LLJ). The LLJ appears to be too low to directly contribute to the nocturnal relative humidity maxima.

Toward reduced transport errors in a high resolution urban CO2 inversion system

We present a high-resolution atmospheric inversion system combining a Lagrangian Particle Dispersion Model (LPDM) and the Weather Research and Forecasting model (WRF), and test the impact of assimilating meteorological observation on transport accuracy. A Four Dimensional Data Assimilation (FDDA) technique continuously assimilates meteorological observations from various observing systems into the transport modeling system, and is coupled to the high resolution CO2 emission product Hestia to simulate the atmospheric mole fractions of CO2. For the Indianapolis Flux Experiment (INFLUX) project, we evaluated the impact of assimilating different meteorological observation systems on the linearized adjoint solutions and the CO2 inverse fluxes estimated using observed CO2 mole fractions from 11 out of 12 communications towers over Indianapolis for the Sep.-Nov. 2013 period. While assimilating WMO surface measurements improved the simulated wind speed and direction, their impact on the planetary boundary layer (PBL) was limited. Simulated PBL wind statistics improved significantly when assimilating upper-air observations from the commercial airline program Aircraft Communications Addressing and Reporting System (ACARS) and continuous ground-based Doppler lidar wind observations. Wind direction mean absolute error (MAE) decreased from 26 to 14 degrees and the wind speed MAE decreased from 2.0 to 1.2 m s–1, while the bias remains small in all configurations (< 6 degrees and 0.2 m s–1). Wind speed MAE and ME are larger in daytime than in nighttime. PBL depth MAE is reduced by ~10%, with little bias reduction. The inverse results indicate that the spatial distribution of CO2 inverse fluxes were affected by the model performance while the overall flux estimates changed little across WRF simulations when aggregated over the entire domain. Our results show that PBL wind observations are a potent tool for increasing the precision of urban meteorological reanalyses, but that the impact on inverse flux estimates is dependent on the specific urban environment.

Aviation Cyber Security: A Constructive Look at the Work of ICAO

The Economist of 4 November 2014 speaks of ‘cyberjacking’ – a phenomenon that refers to the equivalent of hijacking an aircraft with the use of cyber technology. This could happen from outside the aircraft or from the inside. The catalyst in this instance is the increasing popularity with passengers of internet connectivity on board for work, games, movies et al. The article also mentions that internet signals are routed through existing communications architecture, such as the Aircraft Communications Addressing and Reporting System (ACARS), or the Automatic Dependent Surveillance-Broadcast (ADS-B), which is an anti-collision system, which, both being information communications systems can, in theory be targets of cyber-attacks. In its later edition of 21 May 2015 the same journal highlighted that a hacker had identified a weakness with the in-flight entertainment (IFE) systems on Boeing 737-800, 737-900, 757-200 and Airbus A320 aircraft. He had demonstrated this fact by accessing the systems by plugging a laptop into one of the electronic boxes usually found under the seats either side of the aisle. Once connected, the hacker claims to have accessed other systems on the aircraft. None of these claims have been validated by the scientific community nor have they been put into practice by terrorists or criminals against civil air transport. Nonetheless, this may be a sign of things to come, particularly when one considers that the National Aeronautics and Space Administration’s computers have been hacked in the past and that all computer systems of SONY were hacked in the recent past, allegedly by a foreign State sponsored hacking exercise. As this article discusses, there has been at least one confirmed cyber-attack on a computer system of a commercial airline. The International Civil Aviation Organization(ICAO) has been active in the field of prevention of cyber terrorism, which this article will elaborate on, with some constructive suggestions.

An Improved Method of Demodulation for Air-Ground Data Link Communication System

The Aircraft Communication Addressing and Reporting System (ACARS) is playing an increasingly important role to guarantee the safety and the efficiency of aircraft, so more effective method of receiving is necessary. The modulation of the ACARS system is MSK, the aim of this paper is to find a better demodulation method for the signal of ACARS. The characteristic of mapping relationship between code-element and the signal of waveform is analyzed. A new demodulation method is proposed based on the characteristic. Compared to the traditional demodulation method, it has a more simple structure. A simulation is made to verify its performance in the background of Gaussian noise. The comparison with traditional methods is also be made. Finally the benefit and weakness of this method is discussed.

Backscatter Lidar Observations of Lower Tropospheric Dynamics during Southern California Wildfires

Abstract Wavelike features suggesting gravity waves were revealed by lidar observations (from El Segundo, California) of smoke layers produced by large wildfires in the Southern California region during a Santa Ana event. Unique features of the observations were multiple thin layers that enabled precise determinations of wave frequency, amplitude, and vertical structure. The data revealed persistent wavelike oscillations that showed no phase variation with altitude, an amplitude of 20 m, and a period near 12 min. The observations were averaged over 1.5 min with a vertical resolution of 3 m and were obtained over a period of 5 h on 25 October and 8 h on 26 October 2007. Vertical profiles of temperature and winds from the Aircraft Communication Addressing and Reporting System (ACARS) of commercial aircraft departing Los Angeles International Airport (LAX) were selected for temporal and spatial coincidence with the lidar observations. In addition, satellite images of the smoke distribution over the Los Angeles Basin and the coastal areas (including coastal waters) to the south were obtained from Moderate Resolution Imaging Spectroradiometer (MODIS) data from overflights 5.5 h prior to the lidar observation window. The images show wavelike features with horizontal wavelengths of ∼10 km or less. The temperature data showed an inversion layer topped at 500-m altitude. The wind data were consistent with a residual sea breeze near the surface and Santa Ana easterlies above. A simple model of wave ducting showed that the observed features were the evanescent extension of resonant waves ducted in the lower stable inversion layer. These are the first detailed observations, including vertical structure, of ducted waves associated with Santa Ana conditions. It is suggested that such waves should be a common feature in conditions occurring during Santa Ana events.

Performance Characteristics of a Pseudo-Operational Ensemble Kalman Filter

The 2-yr performance of a pseudo-operational (real time) limited-area ensemble Kalman filter (EnKF) based on the Weather Research and Forecasting Model is described. This system assimilates conventional observations from surface stations, rawinsondes, the Aircraft Communications Addressing and Reporting System (ACARS), and cloud motion vectors every 6 h on a domain that includes the eastern North Pacific Ocean and western North America. Ensemble forecasts from this system and deterministic output from operational numerical weather prediction models during this same period are verified against rawinsonde and surface observation data. Relative to operational forecasts, the forecast from the ensemble-mean analysis has slightly larger errors in wind and temperature but smaller errors in moisture, even though satellite radiances are not assimilated by the EnKF. Time-averaged correlations indicate that assimilating ACARS and cloud wind data with flow-dependent error statistics provides corrections to the moisture field in the absence of direct observations of that field. Comparison with a control experiment in which a deterministic forecast is cycled without observation assimilation indicates that the skill in the EnKF’s forecasts results from assimilating observations and not from lateral boundary conditions or the model formulation. Furthermore, the ensemble variance is generally in good agreement with the ensemble-mean error and the spread increases monotonically with forecast hour.

Mesoscale FDDA Experiments with WTM and ACARS Data

This is a real-data Four Dimensional Data Assimilation (FDDA) study using MM5 in conjunction with West Texas Mesonet surface observations and ACARS (Aircraft Communications Addressing and Reporting System) profile data collected by commercial aircraft during both en route and ascent/descent phases of their flights. The high-frequency mesonet data and ACARS wind and temperature profiles are ideal for testing the effects of FDDA on short-term mesoscale numerical weather prediction. The mesonet experiments involved 35 sites with an average horizontal spacing of about 30 km, while in the ACARS case ninety five profiles were used. Results indicated that nudging the MM5 model with the surface-based data over the relatively small area of the mesonet domain had limited impact on the model’s performance. In the ACARS runs, FDDA had long-lasting impact throughout the entire model atmosphere. FDDA appeared to improve the quantitative precipitation forecasting skill of MM5 and reduce slightly the model’s warm bias at the surface. The study suggests that ACARS has potential to significantly enhance our expertise in short-term mesoscale modeling and to support the need to rapidly and accurately adjust high-resolution meteorological model forecasts to real-time observations.

Characteristics and Capacity of VDL Mode 2, 3, and 4 Subnetworks

In the current National Airspace System (NAS), voice communications for Air Traffic Services (ATS) are transmitted by analog VHF radios. Aeronautical Operational Communications (AOC) use a character-oriented system operating in the VHF band known as Aircraft CommunicationsAddressing and Reporting System (ACARS). These radios are neither capable of supporting the growth in air traffic expected in the near future, nor are they capable of enabling new services under development. Three bit-oriented digital VHF radios, VDL Modes 2, 3, and 4, have been proposed as solutions to frequency congestion in the aeronautical VHF band. In this paper each mode is investigated through simulations which explore their individual characteristics under variable loads. The three modes are also tested in realistic terminal and en route domain scenarios. The capacity of each mode is estimated based on the subnetwork delays specified in the standards. The results indicate that VDL Mode 2 can support the highest traffic load, but cannot provide deterministic delays for critical applications. Mode 3 supports the least load due to large downlink delays, but provides the required mechanisms for critical information transfer. Mode 4 has a marginally higher capacity than Mode 3 with similar prioritization capabilities.

Use and Impact of Automated Aircraft Data in a Global 4DVAR Data Assimilation System

Abstract The use of automated aircraft data [Aircraft Meteorological Data Relay (AMDAR) and Aircraft Communication Addressing and Reporting System (ACARS)] has recently been extended in ECMWF's operational 4DVAR data assimilation system. Herein, a modified data selection procedure is reported on that allows the use of more aircraft profiling data during the aircraft's ascending and descending phase, and more of the most frequent reports at cruise level. It is shown that the accuracy of analyzed jet streams is improved through these changes, as verified against independent (non–real time) aircraft data that had not been used in the experiments. The modifications are shown to have a clear positive impact on the short- and medium-range forecast performance. The revised aircraft usage was implemented operationally in January 2002. The impact in 4DVAR of profiles from American and European automated aircraft in ascending and descending phase has been tested in a data denial impact study, for January and July 2001. This particular impact study was run partly on the request of the WMO/Commission for Basic Systems (CBS) Expert Team on data requirements and the redesign of the global observing system. Their interest is in testing whether a modern data assimilation system (such as 4DVAR) obtains substantial benefit from the aircraft profiles, which sample very irregularly in space and time, given that America and Europe are relatively well covered by radiosondes and wind profilers. The results show a substantial positive impact of the profiling aircraft data on analysis and forecast accuracy. The short-range forecast performance is improved over North America, the North Atlantic, and Europe. In the medium range a clear positive impact is found in the North Atlantic, the European, and Arctic areas in the winter period, and beyond day 6 in the summer period. These results are statistically significant and support the ongoing WMO initiative for further expansion of the AMDAR/ACARS coverage. The results also illustrate the effectiveness of 4DVAR with respect to observations that are irregularly distributed in space and time.

Analytical Studies of Low-Level Internal Gravity Waves over the Kanto Plain Associated with a Stationary Front

Abstract An observational analysis of the low-level internal gravity waves over the Kanto Plain in Japan on 17 October 1998 was performed. The data from the Doppler Radar for Airport Weather (DRAW), as well as Aircraft Communications Addressing and Reporting System (ACARS) data of wind and temperature, provided unique observations with high spatial and temporal resolutions and were used to analyze detailed wave structures and environmental conditions, especially the wave-trapping mechanism. According to the data analysis, the horizontal wavelength was approximately 7 km, the ground-relative phase speed of the waves was approximately 1 m s−1, and the direction of propagation was toward 50° (NE). The profiles from ACARS revealed that the Scorer parameter decreased rapidly with height above 1500 m AGL and became less than the horizontal wavenumber near 2600 m AGL. These results indicate that the atmosphere acts as a duct and the waves were trapped vertically and reflected downward. The observed horizontal wa...

Accuracy of RUC-1 and RUC-2 Wind and Aircraft Trajectory Forecasts by Comparison with ACARS Observations

Abstract As part of an investigation into terminal airspace productivity sponsored by the NASA Ames Research Center, a study was performed at the Forecast Systems Laboratory to investigate sources of wind forecast error and to assess differences in wind forecast accuracy between the 60-km Rapid Update Cycle, version 1 (RUC-1), and the newer 40-km RUC-2. Improved knowledge of these errors is important for development of air traffic management automation tools under development at NASA Ames and elsewhere. This information is also useful for operational users of RUC forecast winds. To perform this study, commercial aircraft reports of wind reported through Aircraft Communications, Addressing, and Reporting System (ACARS) were collected in a region over the western and central United States for a 13-month period, along with RUC-1 and RUC-2 wind forecasts. Differences between forecasts and ACARS observations and estimates of ACARS wind observation error itself were both calculated. It was found that rms vector...