Static Stability Concept Research Articles

STABILITAS PARAMETRIK HASIL 14 GENOTIPE TOMAT (Solanum lycopersicum L.) DI EMPAT LINGKUNGAN DATARAN RENDAH

This study aimed to obtain information stability results 14 tomato genotypes grown in four lowland locations using multiple methods of parametric stability analysis. The experiments were conducted at four locations, namely Purwakarta, Lombok, Tajur and Leuwikopo. Experiments at each location using Randomized Complete Block Design (RCBD) with three replications which replicates nested within location. The method used were Francis and Kannenberg, Wrickle ekovalens, Finlay and Wilkinson, Eberhart and Russel, Wrickle ekovalens and AMMI .
 Research carried out shows based on the concept of static stability using the method of Francis and Kannenberg and Russell Eberhart, who declared stable genotype were IPBT3, IPBT53 and IPBT78. Based on the concept of dynamic stability using Wrikle ekovalens and Finlay & Wilkinson methods, stable genotype were IPBT3, IPBT8, IPBT33, IPBT34, IPBT57, IPBT60, IPBT64 and Intan. IPBT3, IPBT33, IPBT34, IPBT60 and Intan as stable genotypes under AMMI methods.

Stability analysis of fat and polyphenol content of five cocoa clones grown in different environment in Indonesia.

Fat and polyphenols are functional compounds in cocoa beans that determine product quality and are highly influenced by environmental factors. Informationregarding the stability of the character of the polyphenol and fat content of the cocoa plant is still limited, therefore it needs further study. This study aimed todetermine the stability of fat and polyphenol content in several cocoa clones at three different growing locations. The study used a nested design with a randomized block design with field design consisting of five cocoa clones, three different growing locations and each combnation treatment was repeated three times. The cocoa clones used were ICCRI 09, MCC 02, Sulawesi 1, KW 516, and KW 562, planted in three different growing locations namely, Kaliwining Experimental Station, Jember, East Java; Sekampung Udik, East Lampung, Lampung; and Harapan Jaya, Pesawaran, Lampung. The combined analysis of variance indicated that there was a genetic interaction with the environment for the character of fat and polyphenol content. Based on the stability analysis, it is known that all cocoa clones fall into the stable category according to the concept of static stability. Furthermore, based on addtive main effect and multiplicative interaction (AMMI) analysis, the clones that can be recommended for Jember, East Lampung and Pesawaran locations for the character of fat content are clone KW 516, while for the characters of high and stable polyphenol levels at the three locations are clones MCC 02, KW 516, and KW 562. In addition, the most recommended clone based on fat content at Jember was the MCC 02 clone, KW 562 at East Lampung, and KW 516 clone at Pesawaran. The existence of the phenomenon of genetic interaction and the growing environment for the characters of fat and polyphenols in cocoa plants provides important information, especially in considering the development of cocoa for specific purposes, namely parameters of fat and polyphenols.

Nonparametric Analysis of Genotype Grain Yield Performance of Barley Trials Based on Ranks

Plant breeding has been concerned with genotype by environment (GE) interaction and high yielding genotypes with stable performance are desirable while this target is difficult to achieve due to high environmental variations and unpredictable GE interaction. Stability of grain yield performance of 18 barley genotypes was evaluated at 5 locations for 3 years in the rainfed conditions and it was studied through 25 nonparametric stability methods. Four nonparametric tests indicated highly significant GE interaction due to differential performance of genotypes across fifteen environments. Regarding mean yield and six Hühn’s statistics, genotype G12 (1946 kg ha-1) was the most favorable genotype while based on the RN1, G4, G10 and G11 were the most stable genotypes. Genotypes G4, G8 and G10 were the most favorable genotypes according to rank-sum while genotypes G2, G13 and G18 were the most favorable genotypes based on nonparametric superiority. The relative interactivity index identified G4, G16 and G8 as the most stable genotypes while the genotypic classification identified G1, G2, G13 and G18 as the most stable genotypes. Clustering of the nonparametric stability methods indicated that there were two groups with different static and dynamic characteristics. In this study, five nonparametric stability methods as GC, FM, PA, RN2 and KR2 were associated with high grain yield and reflected the dynamic concept of stability, but the other twenty nonparametric stability methods were not positively correlated with yield and characterized a static concept of stability. Finally, genotypes genotype G13 (2114.13 kg ha-1) and G18 (2062.69 kg ha-1) were found to be the most favorable genotypes and are thus recommended for commercial release in semiarid areas of Iran.

Angle-of-Attack Command Longitudinal Control for Supersonic Advanced Trainer Aircraft

This paper details the design procedure of developing an angle-of attack command longitudinal control system for the relaxed static stability aircraft in power approach mode. An advanced method of relaxed static stability is utilized for improving aerodynamic performance of a supersonic advanced trainer aircraft. The trainer aircraft adopts the relaxed static stability concept to improve the aerodynamic performance and to guarantee the aircraft stability. The longitudinal control law of the aircraft uses the dynamic inversion and proportional-plus-integral control methods. This paper addresses the analysis of the aircraft characteristics such as damping ratio, natural frequency, and gain and phase margins about the state variables for the longitudinal inner loop feedback design. In numerical simulations, the flight control performance of the developed angle-of-attack command longitudinal control system is compared with that of the existing pitch rate command longitudinal control system.

Comparison of Non-parametric Stability Statistics for Selecting Stable and Adapted Soybean Genotypes under Different Environments

The objectives of this study were to investigate the comparison among non-parametric stability statistics and to evaluate seed yield stability of the sixteen soybean genotypes across four locations during the 2016, 2017 and 2018 growing seasons in Egypt. All trials were laid down in a randomized complete block design (RCBD) with three replications. The AMMI analysis showed ahighly significant effect of genotype (G), environment (E) and G x E interaction (GEI). The major contributions to treatment sum of squares were GEI, followed by G and E. The AMMI analysis also partitioned the total GEI component into eleven PCAs and Residual. The first eight PCAs were highly significant and accounted for about 99.56% of the total GEI. Based on the static and dynamic concepts, the results of spearman’s rank correlation and PCA showed that stability measures could be classified into three groups. The non-parametric stability statistics i.e., YSi, KR, TOP, RSM and δgy related to the dynamic concept and strongly correlated with mean seed soybean yield of stability. While, the other non-parametric stability statistics (Si(1) ,Si(2) ,Si(3) and Si(6),NPi(1) ,NPi(2) ,NPi(3) and NPi(4) , δr, MID, LOW) represented the concept of static stability, which were influenced simultaneously by both yield and stability. The non-parametric stability statistics in each the groups I, II, and III were positively and significantly correlated with each other, thus; any of these parameters could be considered as appropriate alternatives for each other. According to cluster analysis, soybean genotypes G6, G4, G8, G11, G9, G1, G7 and G2 were more stable varieties on the basis of mean seed yield and non-parametric stability statistics. In conclusion, both yield and stability should be considered simultaneously to exploit the useful effect of GEI and to make the selection of genotypes more precise and refined. Thus, the YSi, KR, TOP, RSM and δgy were more useful statistics in soybean breeding programmes and could be useful alternatives to parametric stability statistics. According to most non-parametric stability statistics, the genotypes G6 and G11 were more stable coupled with high seed yield; therefore, these genotypes might be used for genetic improvement of soybean and they must be released in studied regions and other regions in Egypt.

Integrating different stability models to investigate genotype × environment interactions and identify stable and high-yielding barley genotypes

Barley is the fourth largest grain crop globally with varieties suited to temperate, subarctic, and subtropical areas. The identification and subsequent selection of superior varieties are complicated by genotype-by-environment interactions. The main objective of this study was to use parametric and non-parametric stability measures along with a GGE biplot model to identify high-yielding stable barley genotypes in Iran. Eighteen barley genotypes (16 new genotypes and two control varieties) were evaluated in a randomized complete block design with four replications at five locations over three growing seasons (2013–2014, 2014–2015, 2015–2016). The combined analysis of variance indicated that the environment main effect accounted for > 69% of all variation, compared with < 31% for the combined genotype (G) and genotype-by-environment interaction effects. The mean grain yield of each genotype across the five test sites and three seasons ranged from 1900 to 2302 kg ha−1. Using Spearman’s rank correlation and principal component analyses, the stability measures were divided into three groups: the first included mean yield, TOP and b, which are related to the dynamic concept of stability, the second comprised θi, W 2 , σ 2 , CVi, $$S_{di}^{2}$$ , KR, and the non-parametric measures, S(i) and NP(i), which are related to the static concept of stability, and the third included θi and R2. The GGE biplot analysis indicated that, of the five test locations, Gonbad and Moghan had the most discriminating and representative environments. Hence, these locations are recommended as ideal test locations in Iran for the selection of superior genotypes. The numerical and graphical methods both produced similar results, identifying genotypes G12, G13, and G17 as the best material for rainfed conditions in Iran; these genotypes should be promoted for commercial production.

Graphic analysis of yield stability in new improved lentil (Lens culinaris Medik.) genotypes using nonparametric statistics

Yield stability is an interesting feature of today’s lentil breeding programs, due to the high annual variation in mean yield, particularly in the arid and semi-arid areas. The genetic effects including genetic main and genotype × environment (GE) interaction effects for grain yield of eighteen lentil (Lens culinaris Medik.) genotypes were studied with fourteen nonparametric stability statistics. Results of five distinct nonparametric tests of GE interaction and combined ANOVA showed there were both additive and crossover interaction types and genotypes varied significantly for grain yield. According to most of the nonparametric stability statistics, genotypes G5, G6, G8 and G18 were the most stable genotypes. Considering mean yield versus stability values via their plotting, indicates that genotypes G2, G11 and G14 following to G5, G16 and G18 were the most favorable genotypes. None of the nonparametric stability statistics were correlated with mean yield and so had static concept of stability. Our results confirmed that rankings of genotypes within environments and using mean yield information permit ease of interpretation of nonparametric results. Finally genotypes G2 (FLIP 92-12L), G11 (Gachsaran) and G14 (ILL 6206) were found to be the most stable and high mean yielding genotype and thus recommended for commercial release. Such an outcome could be used to delineate predictive, more rigorous recommendation strategies as well as to help define stability concepts for lentil and other crops.

English

This study aims to acquaint breeders of the need to use statistical tools that will help resolve the identification of consistently better performing genotypes across various environmental conditions. It also aim to reveal the relationship among the various statistical methods used to describe genotype × environment interaction (GEI) and cultivar stability. A mixed model with fixed genotypes and random environments were used for the analysis of variance (ANOVA). In the present study, twenty released bread wheat cultivars were evaluated during the 2009 main cropping season using a randomized complete block design (RCBD) with three replications at seven different environments. The combined ANOVA revealed the presence of a highly significant GEI (p < 0.01) for grain yield indicating its influence on cultivar selection and recommendation. Spearman’s rank correlation coefficient revealed a perfect correspondence between Wricke’s ecovalence (Wi) and Shukla’s statbility variance (s2). These stability measures also showed a highly significant positive rank correlation with deviation from regression (S2di), coefficient of determination( ri2), AMMI stability value (ASV), variance of ranks (Si(2)), rank sum (R-sum), and mean absolute rank difference (Si(1)) indicating their similarity in cultivar ranking. The principal component analysis (PCA) clearly showed three groupings of the statistical methods as the static concept of stability, the dynamic concept of stability and yield performance measures. Therefore, it is imperative to consider one stability measure from the dynamic concept and one from the yield performance measures for efficient cultivar recommendation. Key words: Bread wheat, genotype × environment interaction (GEI), principal component analysis (PCA), rank correlation, stability measures.

Genotype × environment interactions for seed yield in rainfed winter safflower (Carthamus tinctorius L.) multi-environment trials in Iran

Evaluation of genotype × environment interaction (GEI) is an important component of the variety selection process in multi-environment trials. The objectives of this study were first to analyze GEI on seed yield of 18 spine safflower genotypes grown for three consecutive seasons (2008–2011) at three locations, representative of rainfed winter safflower growing areas of Iran, by the additive main effects and multiplicative interaction (AMMI) model, and second to compare AMMI-derived stability statistics with several stability different methods, and two stability analysis approaches the yield-stability (Ysi) and the GGE (genotype + genotype × environment) biplot that are widely used to identify high-yielding and stable genotypes. The results of the AMMI analysis showed that main effects due to genotype, environment, and GEI as well as first six interaction principle component axes (IPCA1 to 6) were significant (P < 0.01). According to most stability statistics of AMMI analyses, genotypes G5 and G14 were the most stable genotypes across environments. According to the adjusted stability variance (s2), the high-yielding genotype, G2, was unstable due to the heterogeneity caused by environmental index. Based on the definition of stable genotypes by regression method (b = 1, S d 2 = 0), genotypes G11, G9, G14, G3, G12 and G13 had average stability for seed yield. Stability parameters of Tai indicated that genotype G5 had specific adaptability to unfavorable environments. The GGE biplot and the Ysi statistic gave similar results in identifying genotype G2 (PI-209295) as the best one to release for rainfed conditions of Iran. The factor analysis was used for grouping all stability parameters. The first factor separated static and dynamic concepts of stability, in which the Ysi and GGED (i.e., the distance from the markers of individual genotypes to the ideal genotype) parameters had a dynamic concept of stability, and the other remaining parameters had static concept of stability.

Mediciones no paramétricas corregidas y sin corregir en ensayos multiambientales de estabilidad con trigo duro

Se estudió la estabilidad del rendimiento de 20 genotipos mejorados (G1-G20) de trigo duro en un diseño en bloques completos al azar con 4 repeticiones de 3 años en 5 ambientes diferentes. Los datos fueron analizados con las cinco medidas de estabilidad no paramétricas de Thennarasu (NP), de acuerdo a los rangos de los procedimientos corregidos y sin corregir. El análisis de varianza combinado para los ambientes (E), los genotipos (G) y la interacción GE fue significativo, lo que sugiere una respuesta diferencial de los genotipos y la necesidad de analizar el rendimiento de la estabilidad. En este estudio, se asociaron valores bajos de NP no corregidos (UNP2, UNP3 y UNP4) con un elevado rendimiento medio, pero las otras medidas no paramétricas de estabilidad no se correlacionaron positivamente con el rendimiento medio y se consideraron como concepto estático de estabilidad. Sin embargo, de acuerdo con los parámetros de estabilidad, tanto corregidos como sin corregir, los genotipos G7, G8, G13 y G14 se mantuvieron estables, pero solamente G7 y G8 tuvieron un elevado rendimiento medio. Los resultados del análisis factorial, de la correlación de Spearman y del procedimiento bootstrap de nuevo muestreo de las mediciones de estabilidad no paramétricas y la media de rendimiento, indicaron que sería útil utilizar datos incorrectos no corregidos para seleccionar de forma simultánea elevados rendimientos y estabilidad. En conclusión, de acuerdo con los resultados de las diferentes mediciones de estabilidad no paramétricas, se recomienda el genotipo G7 de trigo duro para su uso comercial como el más favorable en Irán.

Using Huehn’s Nonparametric Stability Statistics to Investigate Genotype × Environment Interaction

Genotype × environment interaction (GEI) is of special interest in breeding programs to identify adaptation targets and test locations as well as to determine the most favorable genotypes. There are several nonparametric procedures used to interpret the GEI in multi-environmental trials. The purposes of this investigation were (i) to compare the effect of correction on Huehn’s nonparametric stability statistics and (ii) to use nonparametric statistics for a GEI study on lentil. Nine improved lentil genotypes and one local cultivar were grown in 5 sites during two consecutive years. Results of the nonparametric analysis demonstrated both additive and crossover GEIs. According to uncorrected nonparametric statistics, genotypes G8 and G9 were the most stable and based on corrected nonparametric statistics of Huehn, genotypes G1, G2 and G10 were the most stable. In this investigation, mean of ranks (MR) and coefficient of variation of ranks (CV) with (6)iSwere associated with high mean yield (within the dynamic concept of stability), but the other nonparametric statistics were not positively correlated with mean yield and were identified within a static concept of stability. Results also indicated that corrected nonparametric statistics were not suitable for simultaneous selection of mean yield and stability. Such an outcome could be used to delineate predictive, more rigorous recommendation strategies as well as to help define stability concepts to identify recommendations for lentil and other crops.

Voronoi languages: Equilibria in cheap-talk games with high-dimensional types and few signals

We study a communication game of common interest in which the sender observes one of infinite types and sends one of finite messages which is interpreted by the receiver. In equilibrium there is no full separation but types are clustered into contiguous cells. We give a full characterization of the strict Nash equilibria of this game as Voronoi languages. As the strategy set is infinite static stability concepts for finite games such as ESS are no longer sufficient for Lyapunov stability in the replicator dynamics. We give examples of unstable strict Nash equilibria and stable inefficient Voronoi languages. We derive efficient Voronoi languages with a large number of words and numerically illustrate stability of some Voronoi languages with large message spaces and non-uniformly distributed types.

English

Analysis of multienvironment trials (METs) of crops for cultivar evaluation and recommendation is an important issue in plant breeding research. Evaluating both stability of performance and high yield is essential in MET analyses. The objectives of this study were to assess interrelationship among these measures and to identify high-yield and stable barley (Hordeum vulgare&nbsp;L.) cultivars in 11 environments during 2001 - 2003 in the central Black Sea region of Turkey. Significant differences were observed among barley cultivars for grain yield, thousand-grain weight, hectoliter weight, plant height and heading date.&nbsp;In this study, high values of TOP (proportion of environments in which a genotype ranked in the top third) was associated with high mean yield,&nbsp;but the other methods were not positively correlated with mean yield and instead characterized a static concept of stability. The results of principal component (PC) analysis and correlation analysis of parametric and nonparametric stability statistics and yield indicated that only TOP method would be useful for simultaneously selecting for high yield and stability. This method recommended Fahrettinbey and Sladoran as stable and Balkan 96 and Erginel as unstable genotypes. A biplot of the first two PCs also revealed that the stability statistic methods grouped as three distinct classes that corresponded to different dynamic (agronomic) and static (biological) concepts of stability. &nbsp; Key words:&nbsp;Barley,&nbsp;genotype x environment interaction, parametric and nonparametric measures, dynamic and static stability.

Study of Genotype × Environment Interaction for Chickpea Yield in Iran

Plant breeders aim to select genotypes with stable phenotypes across environments. Multienvironment trials (METs) including 3 yr and six locations for 17 genotypes of chickpea (Cicer arietinum L.) were performed in Iran. Bartlett's test of homogeneity of variances was not significant and so the combined analysis was done. This analysis indicated that the environment (E), genotype (G), and the genotype by environment (GE) interaction were significant. Thus, stability analysis was necessary, and so additive main effects and multiplicative interaction (AMMI) stability parameters and some regression methods were used for a stability analysis. According to regression method, the high‐yielding genotype, G8, was more responsive (bi &gt; 1) to improved environmental conditions than the other genotypes. Stability parameters of Tai indicated that genotypes G3 and G17 and stability statistics of AMMI analyses showed that G2 and G3 were the most stable genotypes. The first and the second factors (F1 and F2) of factor analysis explained 73.84% total variance of stability parameters, and F1 separated the Di2 and αi from the other parameters. The F2 separated static and dynamic concepts of stability, in which the mean yield, regression coefficient, EVF, SIPCF, and AMGEF parameters had a dynamic concept of stability, and the other remaining parameters had static concept of stability. Finally, according to all stability statistics and regarding the high mean yield, genotype G8 (Flip 93‐93) was recommended for national release in Iran, as it adequately demonstrated wide adaptation across environments.

Nonparametric stability methods for interpreting genotype by environment interaction of bread wheat genotypes (Triticum aestivum L.)

Evaluation of performance stability and high yield is essential for yield trials conducted in different environments. We determined the stability of 10 bread wheat (Triticum aestivum L.) genotypes (5 cultivars and 5 advanced lines) using nonparametric stability measures and compared nonparametric stability statistics across 19 environments in the Central Anatolian Region of Turkey. Experiments were setup in a randomized complete block design with four replications. Nonparametric stability measures revealed that AL-2, Karahan-99 and Altay-2000 were the most stable and well adapted genotypes across the 19 environments. In addition, it was concluded that graphs of mean grain yield (t ha-1) vs. nonparametric measures (Si(¹), Si(²), S(³), Si(6) and σgy) values and kr vs. σr values could enhance visual efficiency of genotype selection based on genotype by environment interaction. Furthermore, high TOP values, Si(³) and Si(6) were associated with high grain yield, but the other nonparametric stability measures were not positively correlated with grain yield and instead characterized a static concept of stability. Choice of genotype for increased grain yield in bread wheat would, therefore, be expected to change yield stability by increasing the values of the Si(³), Si(6) and TOP nonparametric stability statistics.

Comparison of parametric and non-parametric methods for selecting stable and adapted durum wheat genotypes in variable environments

Twenty parametric and non-parametric measures derived from grain yield of 15 advanced durum genotypes evaluated across 12 variable environments during the 2004–2006 growing seasons were used to assess performance stability and adaptability of the genotypes and to study interrelationship among these measures. The combined ANOVA and the non-parametric tests of Genotype × environment interaction indicated the presence of significant crossover and non-crossover interactions, and of significant differences among genotypes. Principal component analysis based on the rank correlation matrix indicated that most non-parametric measures were significantly inter-correlated with parametric measures and therefore can be used as alternatives. The results also revealed that stability measures can be classified into three groups based on static and dynamic concepts of stability. The group related to the dynamic concept and strongly correlated with mean grain yield of stability included the parameters of TOP (proportion of environments in which a genotype ranked in the top third), superiority index (P i) and geometric adaptability index. The second group reflecting the concept of static stability included, Wricke’s ecovalence, the variance in regression deviation (S 2 di), AMMI stability value, the Huehn’s parameters [S i (1) , S i (2) ], Tennarasua’s parameter [NP i (1) ], Kang’s parameter (RS) and yield reliability index (I i) which were not correlated with mean grain yield. The third group influenced simultaneously by grain yield and stability included the measures S i (3) , S i (6) , NP i (2) , NP i (3) , environmental variance (S 2 xi), coefficient of variability and coefficient of regression (b i). Based on the concept of dynamic stability, genotypes G6, G4, and G3 were found to be the most adapted to favorable environments, whereas genotypes G8, G9, and G12 were more stable and are related to the concept of static stability.

Interpreting genotype × environment interactions for durum wheat grain yields using nonparametric methods

The objective of this study was to compare nonparametric stability procedures and apply different nonparametric tests for genotype × environment (G × E) interactions on grain yields of 15 durum wheat genotypes selected from Iran/ICARDA joint project grown in 12 environments during 2004–2006 in Iran. Results of nonparametric tests of G × E interaction and a combined ANOVA across environments indicated the presence of both crossover and noncrossover interactions, and genotypes varied significantly for grain yield. In this study, high values of TOP (proportion of environments in which a genotype ranked in the top third) and low values of sum of ranks of mean grain yield and Shukla’s stability variance (rank-sum) were associated with high mean yield. The other nonparametric stability methods were not positively correlated with mean yield but they characterized a static concept of stability. The results of correlation analysis indicated that only TOP and rank-sum methods would be useful for simultaneous selection for high yield and stability. These two methods identified lines Mrb3/Mna-1, Syrian-4 and Mna-1/Rfm-7 as genotypes with dynamic stability and wide adaptation. According to static stability parameters, the genotypes 12A-Mar8081 and 19A-Mar8081 with lowest grain yield were selected as genotypes with the highest stability.

Nonparametric Methods for Interpreting Genotype × Environment Interaction of Lentil Genotypes

ABSTRACTAnalysis of multienvironment trials (METs) of crops for cultivar evaluation and recommendation is an important issue in plant breeding research. Evaluating both stability of performance and high yield is essential in MET analyses. The objective of this investigation was to compare 10 nonparametric stability methods and apply nonparametric tests (which do not require distributional assumptions) for genotype‐by‐environment (G × E) interaction to 11 lentil (Lens culinaris Medik) genotypes. Nine improved lentil genotypes and two local cultivars were grown in 20 semiarid environments in Iran from 2002 to 2004. Results of nonparametric tests of G × E interaction and a combined ANOVA across environments showed there were both crossover and noncrossover G × E interactions and genotypes varied significantly for yield. In this study, high values of TOP (proportion of environments in which a genotype ranked in the top third) and low values of rank‐sum (sum of ranks of mean yield and Shukla's stability variance) were associated with high mean yield, but the other nonparametric methods were not positively correlated with mean yield and instead characterized a static concept of stability. The results of principal component (PC) analysis and correlation analysis of nonparametric stability statistics and yield indicated that only rank‐sum and TOP methods would be useful for simultaneously selecting for high yield and stability. These methods recommended FLIP 92–12L as stable and FLIP96–6L as unstable genotypes. A biplot of the first two PCs also revealed that the nonparametric methods grouped as three distinct classes that corresponded to different agronomic and biological concepts of stability.

Definition System and Criteria Related to the Static Stability of Airplanes. (First Report). Definition System, Static Flight Speed Stability, and Static Angle of Attack Stability.

This paper discusses the static stability concepts of airplanes. The definition of static stability has not been systematically discussed. For example, although “Cmα 0” are merely the aerodynamic criteria corresponding to each static stability, they are used just like the definition of static stability. Moreover, “flight path stability” is well known as the static stability concept on one translational motion, but the stability concepts in regard to the heaving and sliding motions of an airplane are indefinite. And though “tuck under” and “flight path divergence” are also static stability problems, they are treated not systematically but individually as special problems. So, this paper proposes a definition system consisting of six static stability concepts. Moreover, in the first report of this paper, “static flight speed stability” and “static angle of attack stability” are discussed in detail, and their stability criteria in terms of the aerodynamic characteristics of an airframe are obtained.

Definition System and Criteria Related to the Static Stability of Airplanes. (Third Report). Static Sideslip Stability, Static Roll Stability, and Static Yaw Stability.

To systematically study the static stability for airplanes, we proposed the system of definitions of six static stability concepts. The details of “static flight speed stability” and “static angle of attack stability” were discussed in the first report of this paper, and “static pitch stability” was studied in the second. In this third report, the static stability concepts of lateral and directional motions are discussed, and their stability criteria are obtained in terms of the aerodynamic characteristics of an airframe. They are “static sideslip stability,” “static roll stability,” and “static yaw stability,” and their fundamental definitions are respectively “dY⁄dβ<0,” “dR⁄dΦ<0,” and “dN⁄dΨ<0,” where R denotes rolling moment. The general criteria are deduced from these definitions. Moreover, they give “CYβ<0” for static sideslip stability, “Clβ⁄CYβ>0” for static roll stability, and “Cnβ>0” for static yaw stability, respectively, as the criteria in normal and low subsonic flights. As a conclusion, a summary of this entire paper is given.