Mechanical Differences Between Free-standing and Supported Wheat Plants, Triticum aestivum L.

The effect of wind sway on the mechanical characteristics ofthe anchorage roots and the stem was investigated in maturewinter wheat (Triticum aestivumL., cv. Hereward). Wheat plantswere field-grown, either supported by a frame, which preventedwind sway, or unsupported (free-standing) and the morphologyand mechanical properties of the stems and the anchorage, ‘coronal’, roots were measured. Wind sway had little influence on either the stem height orear weight of the plants but did affect the mechanical propertiesof the stem. Stems of supported plants were weaker and moreflexible than the stems of free-standing plants. There werealso differences in the anchorage systems between the treatments:supported plants had just under half as many ‘coronal’ anchorage roots as the free-standing plants. This reducedthe anchorage strength of supported plants by a third. These differences in mechanical structure meant that the free-standingplants were more resistant to stem buckling and more resistantto anchorage failure. However, considering the difference inthe need for mechanical strength in plants from the two regimes,these differences were small. This suggests that wheat has inherentmechanical integrity and, as a monocotyledon with no secondarythickening, it differs little structurally between environments. Triticum aestivumL.; thigmomorphogenesis; anchorage; safety factor; mechanical stimulation     

Structural development and stability of rice Oryza sativa L. var. Nerica 1

The structural development of glasshouse-grown rice Oryza sativa L. var. Nerica 1 was studied in relation to its stability against lodging. The morphology and mechanical properties of both the stem and roots were examined from tillering, 4 weeks after transplantation up to maturity, together with plant weight distribution and anchorage strength. The "factors of safety" against root and stem failure were subsequently calculated throughout development. Rice plants showed similar morphology to wheat, although they possessed around twice as many tillers per plant and 10 times as many coronal roots. The mechanics of anchorage were also similar. The strength and rigidity of individual tillers increased throughout development as the plants grew taller and heavier and were around 15 times greater than in wheat. By contrast, individual root bending strength, the number of roots, and the anchorage strength levelled off earlier, and anchorage strength was only around twice that in wheat. Consequently, while the self-weight safety factor against stem failure was much higher than in wheat, increasing until late on in development from around 30 to 150, the self-weight safety factor against root anchorage failure was similar to wheat, decreasing from around 15 to 5. Consequently, plants subjected to anchorage tests always failed in their root system rather than their shoot system. The results suggest that, in the field, rice plants would be more likely to undergo root lodging than stem lodging, and that breeding efforts to reduce the incidence of lodging should act to strengthen the rather weak coronal roots.     

Relative safety factors against global buckling, anchorage rotation, and tissue rupture in wheat.

The objective of this study was to quantify the effect of specific physical and biological factors on the relative likelihood of biomechanical failure in wheat. Wind-related crop damage is a major obstacle to wheat production that costs several billion dollars per year. The four factors varied in this study were breeding line, dwarfing gene dose, soil type, and fertilization. A theoretical model describing the dynamic structural response of living plants was used to define margins of safety against global buckling, anchorage rotation, and tissue rupture. These relative safety factors were defined for each treatment in comparison with a tall wheat variety selected from a breeding line called Seri and grown in sandy soil with low fertilization. Compared to this reference, the relative safety factor against global buckling was increased (+39%, p<0.01), and the relative safety factor against anchorage rotation was decreased (-11%, p<0.025), by one allele of the dwarfing gene. The relative safety factor against tissue rupture was unaffected by the dwarfing gene but was consistently lower (-26%, p<0.01) in a second breeding line called Kauz. Soil type and fertility did not affect the relative safety factors and this negative finding was significant at p<0.05. The key finding was that the strength of wheat was affected more by genetic rather than by environmental factors, which suggests that some varieties are intrinsically more robust than others. Also, the relative safety factor against anchorage rotation was inversely proportional to the relative safety factor against buckling, which suggests that there are competing constraints on the dynamic structural behavior of wheat.     

Structural development of the shoot and root systems of two winter wheat cultivars, Triticum aestivum L.

The structural development of the stems and basal anchorageroots of Galahad and Hereward winter wheat cultivars (Triticumaestivum L.) were investigated and related to their mechanicalfunction. Stem and root morphology, anatomy and mechanical propertieswere examined from tillering (March) up to maturity (August),together with plant weight distribution. This allowed us tocalculate a ‘factor of safety’ against root andstem failure throughout development. As the plants grew taller the stem and the anchorage ‘coronalroots’ increased in bending strength countering the increasingmechanical demands. The bending strength, in turn, was correlatedwith the amount of lignified material around the stem and rootperimeter. Structural development ceased by ear emergence, whenthe plant was at its tallest, but because the ear weight continuedto rise the ‘self-weight’ moment pushing the plantover continued to increase. This meant that the ‘safetyfactors’ of both cultivars against both root and stemmechanical failure decreased throughout development. In bothcultivars the safety factors against root failure were lowerthan for stem failure, and Galahad had lower factors of safetythan Hereward. All these findings were consistent with resultsof field trials; failure tends to occur late in development,during grain filling, and is localized to the root system, whilstGalahad is more prone to lodging than Hereward. The pattern of mechanical development of winter wheat seemsto be one which would maximize its reproductive success, maintainingits structural integrity especially early in development whileinvesting in a minimum of structural material. Key words: Safety factor, anchorage, lodging, biomechan-ics, structural development     

Dynamic behaviour of inflorescence-bearing Triticale and Triticum stems

The mechanical response of cereal plant shoots to loads caused by wind and gravity in the field is swaying in flexure around the vertical or near vertical transient equilibrium position determined by the stationary component of the wind pressure. The aim of this work was to characterise the kinematic and dynamic attributes and their interrelations in freely swaying inflorescence-bearing stems of wheat (Triticum aestivum L.) and Triticale. The fundamental natural frequency of the stems appeared to be considerably lower than predicted from the theory of vibration using the model of a cantilever beam oscillator and assuming the spring constant to be equal to the force-deflection ratio. Because of the rate of deformation and visco-elastic behaviour of the plant material, a discrepancy of about 10% was found between the dynamic and static stem bending resistance. The presence of the tip inflorescence caused vibrating vertical stems to behave as compressed columns in which the effective spring constant was strongly biased by the apical load due to the weight of the inflorescence. At the late milk stage, in the freely swaying stems of wheat and Triticale, the resistance to dynamic lateral loads was reduced by about 30% as a result of compression exerted by the inflorescence. So the prominent effect of the tip inflorescence on the dynamic behaviour (the effective spring constant and the natural frequency) of the stem is attributed to the non-negligible magnitude of the inflorescence weight relative to the critical load producing elastic buckling in slender vertical structures. Stem softening as a consequence of increasing inflorescence weight is assumed to be one of the essential factors reducing the lodging resistance in cereal crops at the late milk stage. The feasibility of the compressed-column approach for predicting the dynamic bending performance of slender vertical plant organs is discussed. Received: 4 March 1998 / Accepted: 20 July 1998     

Stem extension and mechanical stability of Xanthium canadense grown in an open or in a dense stand

Background and Aims

Plants in open, uncrowded habitats typically have relatively short stems with many branches, whereas plants in crowded habitats grow taller and more slender at the expense of mechanical stability. There seems to be a trade-off between height growth and mechanical stability, and this study addresses how stand density influences stem extension and consequently plant safety margins against mechanical failure.

Methods

Xanthium canadense plants were grown either solitarily (S-plants) or in a dense stand (D-plants) until flowering. Internode dimensions and mechanical properties were measured at the metamer level, and the critical buckling height beyond which the plant elastically buckles under its own weight and the maximum lateral wind force the plant can withstand were calculated.

Key Results

Internodes were longer in D- than S-plants, but basal diameter did not differ significantly. Relative growth rates of internode length and diameter were negatively correlated to the volumetric solid fraction of the internode. Internode dry mass density was higher in S- than D-plants. Young''s modulus of elasticity and the breaking stress were higher in lower metamers, and in D- than in S-plants. Within a stand, however, both moduli were positively related to dry mass density. The buckling safety factor, a ratio of critical buckling height to actual height, was higher in S- than in D-plants. D-plants were found to be approaching the limiting value 1. Lateral wind force resistance was higher in S- than in D-plants, and increased with growth in S-plants.

Conclusions

Critical buckling height increased with height growth due mainly to an increase in stem stiffness and diameter and a reduction in crown/stem mass ratio. Lateral wind force resistance was enhanced due to increased tissue strength and diameter. The increase in tissue stiffness and strength with height growth plays a crucial role in maintaining a safety margin against mechanical failure in herbaceous species that lack the capacity for secondary growth.     

小麦抗倒性状的基因效应及杂种优势分析

采用Ｈａｙｍａｎ双列分析较为系统地研究了抗倒性状的基因效应,并进行了杂种优势分析。结果表明,小麦抗倒性状的遗传以效应和显微效应为主,且以显著性效较为重要。     

The Anchorage Mechanics of Maize, Zea mays

The anchorage system of mature maize Zea mays was investigatedby combining morphological and anatomical study of the rootsystem with mechanical tests on roots and with studies in whichplants were pulled over. The root system is dominated by 20–30adventitious roots which emerge in rings from the stem basepointing radially downwards and outwards, approximately 30°from the vertical. Roots are strengthened near their base bya heavily lignified exodermis which makes them rigid in bending;distally, strength and rigidity both decrease because rootsbecome thinner and less lignified. When plants were pulled over,a maximum anchorage moment of 5–20 Nm was mobilized atangles of 8–10°, larger plants having stronger anchorage.Movement was initially centred on the leeward side of the stem,anchorage being due to the resistance of both windward and leewardroots to axial motion through the soil and to bending. At displacementsover 10°, however, leeward roots buckled under combinedbending and compression and the centre of rotation shifted tothe windward perimeter of the root system; subsequent movementof the cone of roots and soil was resisted only by the bearingstrength of the soil beneath it. The differences between anchorage failure in balsam and sunflowersand that in maize probably results from the lower angular spreadand the weakness in compression of the maize roots which preventsthe leeward side of the root system from bearing large downwardloads. The system behaves more like that of wheat; these resultssuggest that the lodging resistance of both plants may be improvedby increasing the bending strength and angle of spread of theadventitious roots. Key words: Zea mays, roots, anchorage     

不同小麦品种茎秆特性及其与抗倒性的关系

以黄淮麦区优良品种矮抗58、周麦18、豫麦49、百农418为研究对象,采用田间试验与实验室分析相结合的方法,对不同小麦品种在不同生育时期的抗倒伏性状进行研究.结果表明: 茎秆机械强度在开花期至花后20 d处于较高水平,在花后30 d明显下降;倒伏指数在开花期最小,花后30 d最大,其余两个时期处于中间水平.相关分析表明,开花期机械强度与重心高度呈显著负相关,与纤维素、木质素含量呈显著正相关,倒伏指数与节长、株高、重心高度呈显著正相关,与纤维素、木质素含量呈显著负相关;花后10 d和花后20 d机械强度与节长、株高、重心高度呈显著负相关,与茎粗、纤维素、半纤维素、木质素含量呈显著正相关,倒伏指数这段时期正好与之相反;花后30 d机械强度与株高、重心高度呈显著负相关,倒伏指数与株高、重心高度呈显著正相关,与木质素含量呈显著负相关.因此,明确各个生育时期与抗倒性相关的茎秆特性,可为黄淮麦区高产抗倒性品种的选育提供依据.     

The Mechanics of Anchorage in Wheat Triticum aestivum L.: II. ANCHORAGE OF MATURE WHEAT AGAINST LODGING

The root system of mature wheat Triticum aestivum Marts Doveis dominated by the 7 to 15 adventitious roots which emergefrom the perimeter of the stem base, pointing radially outwardsand downwards. The basal, coronal region of these roots is thickand unbranched, attached to a rhizosheath of earth by a densecovering of root hairs and stiffened in bending by lignificationof outer layers of the cortex. Root lodging of plants involves bending of the coronal rootsat their base and axial movement of leeward and windward rootsthrough the soil; their resistance to these motions providemoments resisting lodging. A model of anchorage was producedby summing the resistance of each root to both forms of motionto give two anchorage components. The model was tested in aseries of mechanical experiments in which simulated lodgingwas followed by loading of individual roots; results supportedthe anchorage model and suggested that in the experimental conditionsthe two components of anchorage were approximately equal inmagnitude. The stem was about 30% stronger than the anchoragesystem. The coronal anchorage roots made up 4.4% of total dry mass;it is suggested that anchorage could be improved either by increasinginvestment in this region or by altering root orientation. Sequentialdevelopment of seminal and adventitious root systems is relatedto the changes in anchorage requirement with age.     

The Mechanics of Anchorage in Wheat Triticum aestivum L.: I. THE ANCHORAGE OF WHEAT SEEDLINGS

Model of the mechanics of uprooting lead to the identificationof ‘optimal’ anchorage systems which can withstanda given upward force at a minimum construction cost. Such systemshave many downward-pointing fibrous roots which are strengthenedprogressively towards the base. A study of the anchorage systemof 7- and 21-d-old wheat (Triticum aestivum L.) plants showedthat the plants possessed five seminal roots, of which onlythree pointed vertically. Each root was well suited for anchorage,being convered in root hairs and strengthened progressivelytowards the base by lignification of the stele. Strength andstiffiness of roots but not their mass per unit length increasedwith age. There was little interaction between roots when plantswere uprooted; the three vertical roots broke while the twohorizontal ones pulled out, as occurred when roots were pulledout singly, Uprooting forces increased with age and the rootsystem could withstand uprooting forces greater than those requiredto pull out upper leaves, so reducing the chances of the plantbeing uprooted by a herbivore, By 3 weeks a stiff adventitiousroot system, which would later help prevent the wheat lodging,was developing.     

The theory of tree bole and branch form

Summary Working from the general postulate that natural selection of plant form operates so as to maximize the survival potential of a species, this paper examines the hypothesis that the mechanical support of tree foliage must approach optimality in the use of wood, i.e., that tree stems and branches will have optimal form with respect to the amount of support tissue. Mathematical models of bole and branch form are presented, based on the proposition that either wind or gravity are the primary limiting factors for tree size and shape. Predictions of trunk and branch diameter as a function of tree size were tested with dimensional measurements ofPopulus tremuloides. The individual stems were selected from close-grown stands of differing ages. For small and intermediate trees, trunk diameter is such that stems have only 1.6 times as much wood as the minimum required to keep the tree from buckling under its own weight due to elastic instability. Branch diameters are shown to be close to the minimum required to maintain the spatial position of growing branches, as well as withstand wind forces. This minimal branch cost not only reduces the load which the stem must support against elastic instability, but allows the crown to flex in high winds. The flexing, in turn, reduces the drag force exerted by the wind on the trunk. Thus, the hypothesis that the observed tree form is an optimal design cannot be rejected on the basis of these results. Additional studies are planned with respect to optimal foliage distribution.     

The criteria for biomass partitioning of the current shoot: water transport versus mechanical support

In this study, we determine the theoretical criteria for biomass partitioning into the leaf and stem of the current shoot, using two quantitative models. The water transport model, based on the biochemical model of CO(2) assimilation, predicts the relationship between the water transport capacity per biomass investment in the stem (stem mass specific conductivity) and the partitioning of biomass that maximizes shoot productivity. The mechanical support model, based on Euler's buckling formula, predicts the relationship between the mechanical strength per biomass investment in the stem (the inverse relationship of stem mass density) and the partitioning of biomass to avoid mechanical failures such as lodging. These models predict the stem properties of mass specific conductivity and stem mass density that result in optimum partitioning just sufficient to provide adequate water transport and static mechanical support. In reality, the stem properties of plants differ from those predicted for optimum partitioning: the partitioning of biomass in the current shoot of both angiosperms and gymnosperms is mainly governed by the mechanical support criterion, although gymnosperms are probably more affected by the water transport criterion. This tendency is supported by actual measurements of biomass partitioning in plants.     

Simulation of gait and gait initiation associated with body oscillating behavior in the gravity environment on the Moon, Mars and Phobos

 A double-inverted pendulum model of body oscillations in the frontal plane during stepping [Brenière and Ribreau (1998) Biol Cybern 79: 337–345] proposed an equivalent model for studying the body oscillating behavior induced by step frequency in the form of: (1) a kinetic body parameter, the natural body frequency (NBF), which contains gravity and which is invariable for humans, (2) a parametric function of frequency, whose parameter is the NBF, which explicates the amplitude ratio of center of mass to center of foot pressure oscillation, and (3) a function of frequency which simulates the equivalent torque necessary for the control of the head-arms-trunk segment oscillations. Here, this equivalent model is used to simulate the duration of gait initiation, i.e., the duration necessary to initiate and execute the first step of gait in subgravity, as well as to calculate the step frequencies that would impose the same minimum and maximum amplitudes of the oscillating responses of the body center of mass, whatever the gravity value. In particular, this simulation is tested under the subgravity conditions of the Moon, Mars, and Phobos, where gravity is 1/6, 3/8, and 1/1600 times that on the Earth, respectively. More generally, the simulation allows us to establish and discuss the conditions for gait adaptability that result from the biomechanical constraints particular to each gravity system. Received: 15 February 1999 / Accepted in revised form: 9 October 2000     

The anchorage mechanics of deep rooted larch, Larix europea L. japonica

The anchorage of deep rooted 16-year-old larch trees, Larixeuropea japonica, has been studied by combining winching testswith analyses of strain around the base of the trunk and rootsystem and mechanical tests on individual roots. These showedthat anchorage is provided by the laterals which emerge fromaround the stem base, sinker roots which emerge along theirlength, and tap roots positioned directly underneath the bole.During anchorage failure the leeward laterals are bent and eventuallybreak close to their base, whilst the windward laterals arepulled out of the ground, with their sinker roots intact. Afterinitially being confined by the soil and bending, the tap rootrotates in the soil. Anchorage failure is similar when the soilis dry as when it is wet, but failure occurs closer to the trunk.Strain measurements along the lateral roots revealed that thestresses were highest close to the trunk and that these regionsof the roots contribute most to tree stability. The two major components of anchorage were found to be the resistanceof leeward laterals to bending and the resistance of tap rootsand windward sinkers to uprooting. Bending tests on leewardlaterals revealed that they provide around 25% of tree anchorage.Almost 75% of the anchorage strength must, therefore, be providedby the windward sinkers and tap roots. Anchorage strength ofroots was positively correlated to their cross-sectional area.The vertical orientation of the sinkers makes the anchoragesystem of larch more efficient than the plate system formedby Sitka spruce on waterlogged soils and means that no root-soilplate is formed. Key words: Anchorage, root architecture, sinker roots, root bending strength, windthrow     

Oscillation frequencies of tapered plant stems

Free oscillations of upright plant stems, or in technical terms, slender tapered rods with one end free, can be described by considering the equilibrium between bending moments in the form of a differential equation with appropriate boundary conditions. For stems with apical loads, where the mass of the stem is negligible, Mathematica 4.0 returns solutions for tapering modes α = 0, 0.5, and 1. For other values of α, including cases where the modulus of elasticity varies over the length of the stem, approximations leading to an upper and a lower estimate of the frequency of oscillation can be derived. For the limiting case of ω = 0, the differential equation is identical with Greenhill's equation for the stability against Euler buckling of a top-loaded slender pole. For stems without top loads, Mathematica 4.0 returns solutions only for two limiting cases, zero gravity (realized approximately for oscillations in a horizontal orientation of the stem) and for ω = 0 (Greenhill's equation). Approximations can be derived for all other cases. As an example, the oscillation of an Arundo donax plant stem is described.     

Effects of shade on root characters associated with lodging in wheat (Triticum aestivum)

Previous work has shown that as the density of wheat plants increase, the spread of the root plate, root length and root number per plant decrease, leading to reduced anchorage strength and increased lodging susceptibility. The aim of this study was to determine which aspect of mutual plant shading [reduction of photosynthetically active radiation (PAR) or the ratio of red to far red light (R : FR)] is associated with this reduction in anchorage strength. Field experiments were conducted at Sutton Bonington, Leicestershire, UK, in two seasons using a range of plant densities in conjunction with shading materials to manipulate PAR and R : FR independently. The spread of the root plate, which has been linked most strongly with anchorage strength, was almost exclusively influenced by PAR intercepted per plant at the beginning of stem extension. Root number and root length were influenced by both PAR and R : FR. When structural roots (defined as thicker than 0.5 mm) and nonstructural roots were considered separately, it was discovered that increasing plant density and PAR shading reduced the length of both structural and nonstructural roots. However, reducing R : FR only reduced the length of structural roots without affecting the length of nonstructural roots.     

The effect of nitrogen and growth regulators on stem and root characteristics associated with lodging in two cultivars of winter wheat

The effects of nitrogen and plant growth regulators (stem shorteners)on root and shoot characteristics associated with lodging resistancewere investigated in two winter wheat (Triticum aestivum L.)cultivars of contrasting lodging resistance: the susceptibleGalahad and the resistant Hereward. The morphology and mechanicalstrength of the stems and anchorage systems grown at two levelsof nitrogen and with or without growth regulators were measuredand related to the incidence of lodging recorded in a fieldtrial. In both cultivars high levels of nitrogen increased theheight of the stem, thereby increasing the ‘self-weight’moment transmitted into the ground and weakened both the stemsand the anchorage coronal roots. As a result, the anchoragestrength was also reduced, plants failing in the root systemin simulated lodging tests. Growth regulators, in contrast,had little effect on the bending strength of the shoots androot systems, but reduced plant height so that the over turningmoments generated by the weight of the shoot were less. Therewere also differences between cultivars: Galahad plants hadweaker anchorage due to the smaller number and lower strengthof the coronal roots. The morphological and mechanical measureswere used to calculate a safety factor against both stem androot lodging. Five factors were found to influence the safetyfactors, these were: cultivar type, the type of lodging, therate of nitrogen and growth regulator application, and time,being lowest in Galahad plants at high levels of nitrogen andwithout growth regulators and at grain filling when the earswere heaviest. This was consistent with the observed patternof lodging: root lodging occurred at grain filling and onlyin Galahad which had been treated with high nitrogen rates,most strongly in plants without growth regulators. Key words: Lodging, safety factors, anchorage, ‘self-weight’ moment     

The effect of wind exposure on the tree aerial architecture and biomechanics of Sitka spruce (Picea sitchensis, Pinaceae)

This paper reports on the effect of wind loading below damaging strength on tree mechanical and physical properties. In a wind-exposed Sitka spruce stand in western Scotland, 60 trees at four different levels of wind exposure (10 m, 30 m, 50 m, 90 m from edge) were characterized for stem and crown size and shape and mechanical properties, including structural Young's modulus (E(struct)), natural frequency, and damping ratio. E(struct) increased from the stand edge to the mid-forest, but with a large inter-tree variation. Swaying frequency and damping ratio of the trees also increased with distance from edge. Wind-exposed edge trees grew shorter, but more tapered with an overall lower E(struct), allowing for greater flexural stiffness at the stem base due to the larger diameter and for higher flexibility in the crown region of the stem. The trees at the middle of the stand compensated for their increased slenderness with a higher E(struct). Thus, for the different requirements for wind-firmness at stand edge and mid-forest, an adapted combination of tree form and mechanical properties allows the best withstanding of wind loads. The results show the requirement to understand the different strategies of trees to adapt to environmental constraints and the heterogeneity of their growth reactions in response to these strategies.     

Kelvin-Helmholtz instability on the magnetopause, magnetohydrodynamic waveguide in the outer magnetosphere, and Alfvén resonance deep in the magnetosphere

Oscillations of the “magnetosphere-solar wind” system are studied analytically in the framework of a plane-stratified model of the medium. The properties of oscillations are determined by three phenomena: Kelvin-Helmholtz instability on the tangential discontinuity (magnetopause) separating the magnetosphere and the solar wind, the presence of a waveguide for fast magnetosonic waves in the magnetosphere, and the Alfvén resonance—a sharp increase in the amplitude of oscillations having the properties of Alfvén waves—in the inner magnetosphere. The oscillations of the system form a discrete spectrum of eigenmodes. Analytical expressions are obtained for the frequency and growth rate of instability of each mode, as well as for the functions describing the spatial structure of these modes. All these characteristics of the eigenmodes are shown to depend on the velocity of the solar wind as a parameter. The dependences of the main mode characteristics (such as the instability thresholds, the points of the maximum and minimum growth rate, and the spatial distributions of the oscillation energy) on this parameter are determined for each eigenmode.