Note on the Numerical Evaluation of the Wave Drag of Smooth Slender Bodies Using Optimum Area Distributions for Minimum Wave Drag

1956 ◽  
Vol 60 (541) ◽  
pp. 61-63 ◽  
Author(s):  
E. Eminton ◽  
W. T. Lord
Keyword(s):  
Numerical Evaluation ◽  
Practical Method ◽  
Wave Drag ◽  
The Body ◽  
Cross Sectional ◽  
Area Distribution ◽  
Slender Bodies ◽  
Kinetic Pressure ◽  
Image Position ◽  
Sectional Shape

The linearised theory value of the wave drag D at zero lift of a smooth slender body of arbitrary cross-sectional shape was shown by Ward to be given bywhere S (x), 0 ⩽ x ⩽ 1, is the cross-sectional area distribution of the body and q is the kinetic pressure. The development of this result has aroused interest in two problems: the derivation of the optimum area distribution for minimum wave drag under certain specified conditions and the numerical evaluation of the wave drag of a specified area distribution. These apparently distinct problems have hitherto been treated separately, but it is shown here how an attempt to solve the first problem has led to a practical method of solving the second.

Note on the Evaluation of the Integral

1954 ◽  
Vol 58 (527) ◽  
pp. 787-788 ◽  
Author(s):  
N. A. Routledge ◽  
W. T. Lord ◽  
E. Eminton
Keyword(s):  
Logarithmic Singularity ◽  
Wave Drag ◽  
Cross Sectional Area ◽  
Sectional Area ◽  
Direct Evaluation ◽  
Cross Sectional ◽  
Numerical Work ◽  
Singular Form ◽  
Area Distribution ◽  
Kinetic Pressure

The Integral I occurs frequently in aerodynamics. To cite a particular case, Ward has shown that ifS(x)is the cross-sectional area distribution of a slender body its wave dragDis given to a first approxition by D = qI/(2π), whereqis the kinetic pressure. In this case,S(x)is often defined numerically, and the direct evaluation of I is then complicated by the presence of the logarithmic singularity. Several methods may be employed to avoid this complication. Legendre has recently suggested rewriting I in a non-singular form, which unfortunately is not well suited to numerical work. Here, a method for the evaluation of the unmodified integral is presented.

Supersonic Flow Past Slender Bodies With Discontinuous Profile Slope

1955 ◽  
Vol 6 (2) ◽  
pp. 114-124 ◽  
Author(s):  
L. E. Fraenkel ◽  
H. Portnoy
Keyword(s):  
Internal Flow ◽  
Leading Edge ◽  
Rate Of Change ◽  
The Body ◽  
Cross Sectional ◽  
Slender Body Theory ◽  
Bodies Of Revolution ◽  
Slender Bodies ◽  
External Forces ◽  
Sectional Shape

SummaryWard’s slender-body theory is extended to derive first approximations to the external forces on slender bodies of general cross section with discontinuous profile slope. Two classes of body are considered: bodies whose profile (typified by the local radius) is continuous between the nose and base, and certain bodies whose profile is discontinuous, such as bodies with annular or side air intakes and wing-bodies on which the wing has an unswept leading edge. (Where air intakes are concerned, it is assumed that they are sharp-edged and that there is no “ spillage ” of the internal flow).The following conclusions apply to the former class of bodies. The variation of drag with Mach number is found to depend only on the discontinuities in the longitudinal rate of change of the cross-sectional area, and is thus independent of cross-sectional shape. The drag itself is unchanged if the direction of the flow is reversed. The expressions for lift and moment assume the same forms as for smooth pointed bodies, the lift depending only on conditions at the base of the body.The general theory is applied to winged bodies of revolution with an unswept wing leading edge: the results bear a marked resemblance to those obtained by Ward. The results for wings alone are seen to be applicable, with one modification, to subsonic as well as to supersonic speeds.

Factors Controlling the Change of Shape of Certain Nemertean and Turbellarian Worms

1958 ◽  
Vol 35 (4) ◽  
pp. 731-748 ◽  
Author(s):  
R. B. CLARK ◽  
J. B. COWEY
Keyword(s):  
Water Conservation ◽  
Ecological Factors ◽  
Longitudinal Axis ◽  
The Body ◽  
Cross Sectional ◽  
Ciliary Action ◽  
Theoretical Predictions ◽  
Observed Behaviour ◽  
Body Wall Musculature ◽  
Sectional Shape

1. Nemerteans and turbellarians have an inextensible fibre system around them in the form of a lattice of left- and right-handed spirals. The effect of this system on the change of shape on these worms has been analysed theoretically and compared with the observed behaviour of nine species of turbellarian and nemertean from widely differing habitats. 2. The following theoretical relationships have been studied: (a) Variation of the angle between the geodesics and the longitudinal axis of the worm during changes in length, and the role of the fibre system in limiting changes in length of the animal. (b) The change in cross-sectional shape during changes in length. (c) The extension of the fibres and the extensibility of the worms, assuming the fibres of the lattice to be elastic. 3. The species investigated conform with the theoretical predictions to varying degrees and have been grouped accordingly: (a) Geonemertes dendyi and Rhynchodemus bilineatus have low extensibilities and fit the prediction well. They are nearly circular in cross-section at all lengths as a result of their low extensibility and this is related to their terrestrial habit and need for water conservation. (b) Amphiporus lactifloreus, Lineus gesserensis and L. longissimus are moderately flattened in the relaxed position and have extensibilities between 6 and 10. They are marine crawling forms using cilia for locomotion and so must present a fairly large ciliated surface to the substratum. The fibre system does not limit contraction; the compression of the epithelial cells causes the observed extensibilities to fall a little short of the theoretical values. (c) Cerebratulus lacteus, Malacobdella grossa, Polycelis nigra and Dendrocoelum lacteum are very flattened forms and have very high theoretical extensibilities, but very low observed ones. The factors causing this are the thickness of the body-wall musculature (Cerebratulus), the limiting effect of longitudinal and circular reticulin fibres in the muscle layers, and the presence of dorso-ventral and diagonal muscles. Their flattened form is correlated with ecological factors (with swimming in Cerebratulus, with its parasitic life in the mantle of bivalves in Melacobdella) or with physical ones in turbellarians where a permanently flattened form is necessary for these worms to move by ciliary action.

The Structure and Function of the Basement Membrane Muscle System in Amphiporus lactifloreus (Nemertea)

1952 ◽  
Vol s3-93 (21) ◽  
pp. 1-15
Author(s):  
J. B. COWEY
Keyword(s):  
Basement Membrane ◽  
Cross Section ◽  
Circular Cross Section ◽  
The Body ◽  
Minimum Length ◽  
Muscle Fibres ◽  
Body Volume ◽  
Cross Sectional ◽  
Elliptical Cross ◽  
Sectional Shape

The body wall of A. lactifloreus has the following structure from the outside inwards. (i) A basement membrane of five to six layers immediately underlying the epithelium. Each layer consists of right-hand and left-hand geodesic fibres making a lattice, whose constituent parallelograms have a side length of from 5 to 6µ. The fibres are attached to one another where they cross; so there can be no slipping relative to one another. (ii) A layer of circular muscle-fibres running round the animal containing two systems of argyrophil fibres--one of fibres at intervals of 10µ. running parallel to the muscle-fibres and the other of fibres running radially through the layer from the basement membrane to the myoseptum. (iii) A myoseptum which is identical in structure with a single layer of the basement membrane (iv) A layer of longitudinal muscle, whose fibres are arranged in layers on each side of a series of longitudinal radial membranes. Membranes identical in structure with the basement membrane invest the nerve cords, the gut, the gonads, and the proboscis. The interrelations of argyrophil and muscle-fibres in the muscle layers is described and their functioning discussed. The system of inextensible geodesic fibres is analysed from a functional standpoint. The maximum volume enclosed by a cylindrical element (cross-section circular), of such a length that the geodesic makes one complete turn round it, varies with the value of the angle θ between the fibres and the longitudinal axis. When θ is 0° the volume is zero; it increases to a maximum when θ is 54° 44' and decreases again to zero when θ is 90°. The length of the element under these conditions varies from zero when θ is 90° to a maximum (the length of one turn of the geodesic) when θ is 0°. The body-volume of the worm is constant. Thus it has a maximum and minimum length when its cross-section is circular, and at any length between these values its cross-section becomes more or less elliptical. It is maximally elliptical when θ is 54° 44', i.e. when the volume the system could contain, at circular cross-section, is maximal. From measurements of the ratio of major to minor axes of this maximally elliptical cross-section, the maximum and minimum lengths of the worm relative to the relaxed length and values of θ at maximum and minimum length are calculated. The worm is actually unable to contract till its cross-section is circular; but measurements of its cross-sectional shape at the minimum length it can attain, permit calculation of the theoretical length and value of θ for this cross-sectional shape. Calculated values of length and the angle 6 agree well with the directly observed values.

Correlation between body condition score and hormone level of Bali cattle with postpartum anestrus

2018 ◽  
Author(s):  
Desak Nyoman Dewi Indira Laksmi ◽  
I Gusti Ngurah Bagus Trilaksana ◽  
Rai Jaine Darmanta ◽  
Megawati Darwan ◽  
Wayan Bebas ◽  
...  
Keyword(s):  
Body Condition ◽  
Hormone Level ◽  
Body Condition Score ◽  
Practical Method ◽  
Assessment Method ◽  
The Body ◽  
Direct Role ◽  
Cross Sectional ◽  
Condition Score ◽  
Bali Cattle

Body Condition Score (BCS) is a simpler and more practical method to evaluate the body’s energy and fat reserves in cows. Nutrition play a direct role both in the hypothalamus by synthesizing and releasing GnRH, as well as on the anterior pituitary by controlling the synthesis and release of Leptin, FSH, LH and Estrogen. The purpose of this study was to determine the relationship between the body condition score with the activation of hormones in the hypothalamic–pituitary–gonadal axis on Bali cattle that experienced postpartum anestrus. This research was an observational analytic study with Cross-Sectional Study design. The samples used were Bali cattle that have given birth and have not shown estrus for more than three months. BCS assessment method is qualitatively conducted through visual and tactile techniques. Measurements of Leptin, FSH, LH and estrogen hormone levels were performed using the ELISA Double Antibody Sandwich method. The results showed a correlation between body condition score to hormone level i.e. Leptin level of 0.861; LH level of 0.960; FSH level of 0.799; and Estrogen level of 0.761. These data demonstrated that BCS significantly affects Leptin hormone concentrations. It takes Leptin with a certain concentration to trigger the release of LH in follicle maturation and ovulation, thus achieving a threshold that causes the activation of the hypothalamic–pituitary–gonadal axis.

Axisymmetric control of large tokamak devices

1984 ◽  
Vol 32 (3) ◽  
pp. 399-412 ◽  
Author(s):  
T. H. Jensen ◽  
F. W. McClain
Keyword(s):  
Magnetic Field ◽  
Control Problem ◽  
Vacuum Chamber ◽  
Practical Method ◽  
Chamber Wall ◽  
Power Supplies ◽  
Cross Sectional ◽  
Resistive Wall ◽  
Sectional Shape ◽  
The Magnetic Field

The problem of controlling the position and cross-sectional shape of plasmas is addressed for circumstances relevant to large tokamaks. A principle for, as well as a practical method of analysis of, this control problem is presented. The relevant elements of the tokamak system included in the analysis are the plasma, a resistive wall (vacuum chamber wall) surrounding the plasma, toroidally wound coils which also surround the plasma, as well as their associated external circuitry and a number of monitors of properties of the magnetic field in the vicinity of the plasma; the signals obtained from these monitors are used for control of power supplies which are part of the external circuits.

scholarly journals IMPLEMENTATION OF TRANSONIC AREA RULE AND SWEPT BACK DELTA WING DESIGN ON AN AIRCRAFT.

2022 ◽  
pp. 20-25
Author(s):  
S. Rajat Singh ◽  
Y.D. Dwivedi
Keyword(s):  
Delta Wing ◽  
Wave Drag ◽  
Wing Design ◽  
Cross Sectional ◽  
Ansys Fluent ◽  
Area Distribution ◽  
Area Rule ◽  
Drag Ratio ◽  
Commercial Aircrafts ◽  
Lift To Drag Ratio

The transonic area rule was first implemented in the 1950s. It is an important concept related to the drag on an aircraft or other body in transonic and supersonic flight which states that two airplanes with the same longitudinal cross-sectional area distribution have the same wave drag, independent of how the area is distributed laterally. A swept back delta wing increases the critical Mach number of the wing and performs well at low speeds, as a result of unique swirling vortices that form on the upper surface of the wing. BOOM Supersonic plans to bring back Supersonic Commercial aircrafts by implementing these modifications in the famous Concorde. In this paper two aircraft designs inspired by Concorde and BOOM Overture are compared using ANSYS Fluent. These were designed in CATIA with changes in fuselage dimensions, wing configuration and engine configuration. The lift to drag ratio of both the designs are calculated and compared. Pressure contours, velocity vectors, vector pathlines, turbulence pathlines and pressure pathlines are also compared. The results show that the design with the implementation of transonic area rule and swept back delta wing has a better Lift to Drag ratio when compared to the design with a wide fuselage and a delta wing design.

scholarly journals Pilot study about the micro hydropower generation by use of flow induced vibration phenomenon

2018 ◽  
Vol 180 ◽  
pp. 02122
Author(s):  
Yoshifumi Yokoi
Keyword(s):  
Power Generation ◽  
The Body ◽  
Flow Induced Vibration ◽  
Cross Sectional ◽  
Generation Characteristic ◽  
Micro Power ◽  
Power Generation System ◽  
Sectional Shape ◽  
Body Section ◽  
Piezo Electric

In order to construct a micro power generation system using a piezo-electric element, power generation was tried using excitation oscillation of the bluff cylinder by the vortex shedding from the bluff cylinder. The bluff cylinder consists of a board spring section in which the piezo-electric element was attached, and a body section. The bluff cylinder was inserted into the water flow, the shape and the submersion depth of the bluff cylinder, and the flow velocity were varied, and the power generation characteristic was investigated. As a result, it was found that it can generate electricity by vortex excitation. It was found that the length and the submersion depth of the body section influence power generation. It was shown that the power generation characteristic changes with cross-sectional shape of the bluff cylinder. The most suitable state was the case where the submersion depth was set to 140 mm with a circular cylinder with a span length of 250 mm. It is important to choose the power generation object which suited the use purpose.

Inertia effects on the motion of long slender bodies

1989 ◽  
Vol 209 ◽  
pp. 435-462 ◽  
Author(s):  
R. E. Khayat ◽  
R. G. Cox
Keyword(s):  
Reynolds Number ◽  
Asymptotic Expansion ◽  
Body Length ◽  
Unit Length ◽  
The Body ◽  
Total Force ◽  
Cross Sectional ◽  
Inertia Effects ◽  
Slender Bodies ◽  
Valid Solution

A solid long slender body with curved centreline is held at rest in a fluid undergoing a uniform flow. Assuming that the Reynolds number Re based on body length is fixed, the force per unit length on the body is obtained as an asymptotic expansion in terms of the ratio κ of the cross-sectional radius to body length. In the limit of large Re, this result is no longer valid and an asymptotic expansion in κRe is necessary. A uniformly valid solution is obtained from these two expansions. The total force and torque acting on a body with a straight centreline are explicitly determined. The limiting cases of small and large Re are studied in detail.

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