Body Drag Research Articles

Wingbeat frequency and the body drag anomaly: wind-tunnel observations on a thrush nightingale (Luscinia luscinia) and a teal (Anas crecca)

A teal (Anas crecca) and a thrush nightingale (Luscinia luscinia) were trained to fly in the Lund wind tunnel for periods of up to 3 and 16 h respectively. Both birds flew in steady flapping flight, with such regularity that their wingbeat frequencies could be determined by viewing them through a shutter stroboscope. When flying at a constant air speed, the teal's wingbeat frequency varied with the 0.364 power of the body mass and the thrush nightingale's varied with the 0.430 power. Both exponents differed from zero, but neither differed from the predicted value (0.5) at the 1 % level of significance. The teal continued to flap steadily as the tunnel tilt angle was varied from -1 ° (climb) to +6 ° (descent), while the wingbeat frequency declined progressively by about 11 %. In both birds, the plot of wingbeat frequency against air speed in level flight was U-shaped, with small but statistically significant curvature. We identified the minima of these curves with the minimum power speed (Vmp) and found that the values predicted for Vmp, using previously published default values for the required variables, were only about two-thirds of the observed minimum-frequency speeds. The discrepancy could be resolved if the body drag coefficients (CDb) of both birds were near 0.08, rather than near 0.40 as previously assumed. The previously published high values for body drag coefficients were derived from wind-tunnel measurements on frozen bird bodies, from which the wings had been removed, and had long been regarded as anomalous, as values below 0.01 are given in the engineering literature for streamlined bodies. We suggest that birds of any size that have well-streamlined bodies can achieve minimum body drag coefficients of around 0.05 if the feet can be fully retracted under the flank feathers. In such birds, field observations of flight speeds may need to be reinterpreted in the light of higher estimates of Vmp. Estimates of the effective lift:drag ratio and range can also be revised upwards. Birds that have large feet or trailing legs may have higher body drag coefficients. The original estimates of around CDb=0.4 could be correct for species, such as pelicans and large herons, that also have prominent heads. We see no evidence for any progressive reduction of body drag coefficient in the Reynolds number range covered by our experiments, that is 21 600­215 000 on the basis of body cross-sectional diameter.

Simulation of the aerodynamic drag of three-dimensional star-shaped bodies at hypersonic velocities

The domain of the parameters in which the aerodynamic drag of hypersonic pyramidal bodies, whose wave component is calculated within the framework of conical flows with the boundary layer displacement thickness taken into account, agrees satisfactorily with the experimental data is found. The calculation model is also applicable in the region of minimum aerodynamic drag of star-shaped bodies in the class of conical bodies equivalent in length and mid-sectional area.

Design of minimum drag bodies in incompressible laminar flow

The problem of modifying the shape of a two-dimensional body to reduce its drag while maintaining its section area (volume per unit span) constant is addressed. Two-dimensional, incompressible, laminar flow governed by the steady-state Navier-Stokes equations is assumed about the body. In this study, a set of “adjoint” equations are solved which permits the calculation of the direction and relative magnitude of change in the body profile that leads to a lower drag. The direct as well as the adjoint set of partial differential equations are obtained for Dirichlet-type far-field conditions. Repeatedly modifying the body shape with each solution to these two sets of equations with the above boundary conditions, would lead to a body with minimum drag, for a specified section area. For such a body the product of “direct” shear and the “adjoint” shear is constant everywhere along the body. Even though viscous terms are retained in the direct and the adjoint equations, far field boundary conditions are obtained ...

Effect of the underwater torque on the energy cost, drag and efficiency of front crawl swimming.

Underwater torque (T') is defined as the product of the force with which the swimmer's feet tend to sink times the distance between the feet and the centre of volume of the lungs. It has previously been shown that experimental changes of T', obtained by securing around the swimmer's waist a plastic tube filled, on different occasions, with air, water or 2-kg lead, were accompanied by changes in the energy cost of swimming per unit of distance (Cs) at any given speed. The aim of this study was to investigate whether the observed increases of Cs with T' during front crawl swimming were due to an increase of active body drag (Db), a decrease of drag efficiency (eta /d) or both. The effect of experimental changes of T' on Cs, Db and eta /d were therefore studied on a group of eight male elite swimmers at two submaximal speeds (1.00 and 1.23 m.s-1). To compare different subjects and different speeds, the individual data for Cs, Db, eta /d and T' were normalized dividing them by the corresponding individual averages. These were calculated from all individual data (of Cs, Db, eta /d and T') obtained from that subject at that speed. It was found that, between the two extremes of this study (tube filled with air and with 2-kg lead), T' increased by 73% and that Cs, Db and eta /d increased linearly with T'. The increase of Cs between the two extremes was intermediate (approximately 20%) between that of Db (approximately 35%) and of eta /d (approximately 16%). Thus, the actual strategy implemented by the swimmers to counteract T', was to tolerate a large increase of Db. This led also to a substantial (albeit smaller) increase of r/d, the effect of which was to reduce the increase of Cs that would otherwise have occurred.

Body drag control in supersonic gas flows by injection of liquid jets

Body drag control in supersonic gas flows by injection of liquid jets

Effect of swimming suit design on the energy demands of swimming.

Eight competitive male swimmers completed a standardized 365.8 m (400 yd) freestyle swimming trial at a fixed pace (approximately 90% of maximal effort) while wearing a torso swim suit (TOR) or a standard racing suit (STD). Oxygen uptake (VO2), blood lactate, heart rate (HR), and distance per stroke (DPS) measurements were obtained. In addition, a video-computer system was used to collect velocity data during a prone underwater glide following a maximal leg push-off from the side of the pool while wearing the TOR and STD suits. These data were used to calculate the total distance covered during the glides. VO2 (3.76 +/- 0.16 vs 3.92 +/- 0.18 l.min-1) and lactate (8.08 +/- 0.53 vs, 9.66 +/- 0.66 mM) were significantly (P < 0.05) lower during the TOR trial than the STD trial. HR was not different (P > 0.05) between the TOR (170.1 +/- 5.1 b.min-1) and STD (173.5 +/- 5.7 b.min-1) trials. DPS was significantly greater during the TOR (2.70 +/- 0.066 m.stroke-1) versus STD (2.58 +/- 0.054 m.stroke-1) trial. A significantly greater total distance was covered during the prone glide while wearing the TOR (2.05 +/- 0.067 m) compared to the STD (2.00 +/- 0.080 m) suit. These findings demonstrate that a specially designed torso suit reduces the energy demand of swimming compared to a standard racing suit which may be due to a reduction in body drag.

The motion of a rigid body in viscous fluid bounded by a plane wall

The boundary-integral method is used to calculate the hydrodynamic force and torque on an arbitrary body of revolution whose axis of symmetry is oriented at an arbitrary angle relative to a planar wall in the zero-Reynolds-number limit. The singular solution of the Stokes equations in the presence of a planar wall is used to formulate the integral equations, which are then reduced to a system of linear algebraic equations by satisfying the no-slip boundary conditions on the body surface using the boundary collocation method or weighted residual technique.Numerical tests for the special case of a sphere moving parallel or perpendicular to a planar wall show that the present theory is accurate to at least three significant figures when compared with the exact solutions for gap widths as small as only one-tenth of the particle radius. Higher accuracy can be achieved and solutions can be obtained for smaller gap widths at the expense of more computation time and larger storage requirements.The hydrodynamic force and torque on a spheroid with varying aspect ratio and orientation angle relative to the planar wall are obtained. The theory is also applied to study the motion of a toroidal particle or biconcave shaped disc adjacent to a planar wall. The coincidence of the drag and torque of a biconcave-shaped body and a torus having an aspect ratio b/a = 2 with the same surface area shows that in this case the hole of a torus has little influence on the flow field. On the other hand, for an aspect ratio b/a = 10, the effect of the hole is significant. It is also shown that when the body is not very close to the wall, an oblate spheroid can be used as a good approximation of a biconcave-shaped disc.

Dependence of the drag of a conical axisymmetric cavitation body on the cone angle and the cavitation number

Numerical investigations of flow past axisymmetric conical captation bodies have shown that the drag coefficient of the cavitation body, calculated from the maximum cross-sectional area of the cavity (midsection), depends on the cavitation number and the cone angle.

Measurement of drag using a momentum balance

SummaryThis note presents the results of the application of a momentum control surface analysis to the estimation of the drag of bodies and surfaces placed in the test section of a windtunnel. The assumptions of the method are stated and accuracy of the method considered with particular reference to the drag of riblet surfaces at high subsonic speeds, the drag of two-dimensional cavities at both high subsonic and low supersonic speeds, and the drag of manipulators at high subsonic speeds.

Supersonic, turbulent flow computation and drag optimization for axisymmetric afterbodies

The compressible, turbulent flow about an axisymmetric body was numerically studied using the MacCormack unsplit explicit algorithm applied to the mass-average Navier-Stokes equations solved in conjunction with the k-ϵ turbulence model of Jones and Launder. Numerical predictions of total body drag (pressure drag, skin friction drag, and base drag) were made for an axisymmetric body six diameters in length, with and without a boattail. Surface pressures and viscous layer profiles are compared with available wind tunnel data and are found to be in good agreement for both geometries. The Golden Section optimization method was used to optimize the body boattail angle for minimum drag. The solution method can serve as a tool for preliminary design analysis where the relative merits of utilizing boattails on axisymmetric afterbodies is being considered.

A subaerial arthropod trackway from the Upper Silurian Clam Bank Formation of Newfoundland

Trackways are reported for the first time from Silurian rocks in Newfoundland. They occur in the Clam Bank Formation of the Port au Port Peninsula. At least one of the trackways represents one of the earliest known occurrences of a large subaerial arthropod trace fossil. It is preserved in hyporelief in a red fine-grained sandstone. The trackway, Diplichnites Dawson, 1873, consists of two parallel series of clearly defined imprints. It is attributed to a myriapod similar to the Lower Devonian Eoarthropleura. The sandstone contains halite pseudomorphs that indicate that the sediment horizon had been subject to desiccation immediately prior to the formation of the trackway. The arthropod walked on a red siltstone deposited in an alluvial flats environment. Analysis of the trackway suggests that the arthropod was approximately 23 cm long and had 17 pairs of walking appendages. It appears that a high-geared gait with a ratio of forestroke:backstroke of 8:2 was used in walking across the substrate, that is, approximately 20% of walking appendages were in contact with the substrate at any one time. This rapid gait, and the lack of a body drag mark, indicates that the arthropod was well adapted to subaerial locomotion. Knowledge of modern myriapod gaits has been used to extrapolate a theoretical trail, which compares well with the fossil trackway. Smaller, less well preserved trackways occur elsewhere in the Clam Bank Formation and may have been made by a similar arthropod.

Amphibian footprints from the mid-Carboniferous of Northumberland, England: Sedimentological context, preservation and significance

Abstract A trackway and footprints produced by a large amphibian have been discovered in Namurian strata on the coast of Northumberland, near Howick, in northeastern England. They occur on a thin layer of mud upon the surface of a sandstone bed deposited by a small delta on a coastal plain. They were preserved by subsequent deposition of a thin sandstone from the flooding of a nearby channel. Abandonment of the area led to the growth of plants and the formation of a thin coal seam, so that the footprint sandstone was rootleted to form a seatearth. The Howick footprints average 18 cm in length and 14 cm in width. The trackway is poorly preserved and appears to consist of at least five footprints arranged either side of a groove 0.19 m in width which is interpreted as a body drag trace. The external trackway width is 0.7 m, and the stride is 1.4 m. At Howdiemont Bay 3 km south of Howick Bay, more footprints occur of about the same size, but also poorly preserved, upon the surface of a fluvial sandstone. These footprints are some of the earliest occurring in Carboniferous strata in Europe. Although preservation of both sets of footprints is now poor, the Howick footprints can be compared to the ichnogenus Baropezia.

Effect of local energy supply to a hypersonic flow on the drag of bodies with different nose bluntness

Parameters of the axisymmetric flow around bodies with different bluntness are compared in the case of constant energy supply to the main hypersonic flow. Flow structures, drag coefficients, and expenditure of energy on overcoming drag are analyzed with the effect of thermal energy on the flow taken into account for different bodies with equal volume.

Numerical investigation of supersonic flows around a spiked blunt body

In supersonic flow, a spike attached to the nose reduces the drag of a blunt body. In this paper, supersonic flows around a spiked blunt body are numerically simulated to examine the effects of the spike length, Mach number, and angle of attack. Three-dimensional thin-layer compressible Navier-Stokes equations are solved using a highresolution upwind scheme with LU-ADI time-integration algorithm. The computed results show that the drag of the spiked blunt body is significantly influenced by the spike length, Mach number, and angle of attack. Scales of the separated region are not significantly influenced by the freestream Mach number. For the spiked blunt body at angle of attack, the flowfield becomes complex with spiral flows. The computed results are in reasonable agreement with experimental data.

Aerodynamic characteristics of external store configurations at low speeds

Aerodynamic characteristics of external store configurations used on interceptor aircraft were investigated experimentally and computationally. Balance measurements, flow visualization, and static pressure measure- ments were made in a low-speed wind tunnel. The experimental and computational data revealed the global structure of the flow around a basic configuration. Six groups of models were used in the present study. This article discusses the results for the first and second group of models. The incompressible flow over a limited number of models was computed by solving the Navier-Stokes equations. The solution method is based on the Galerkin finite element discretization of space and the fractional step discretization of time. Reasonably good agreement was observed between the experimental and computational static pressure distributions on a basic geometry. The computational data, which revealed details of reverse flow regions, supported and supplemented the experimental data. using the code employed in the present study are presented in Refs. 5-7. The scope of the study was limited to the aero- dynamic characteristics of the isolated carriage, i.e., inter- ference with the aircraft body was not investigated. The experimental and computational data revealed the global structure of the flow around the carriage. Balance measure- ments showed that aerodynamically more suitable forms of the carriage geometry could be obtained by modifying its major drag-producing features. Surface flow visualization in- dicated locations of vortical flow regions whose existence was also supported by contour plots of the measured static pres- sure. Despite differences in the Reynolds numbers of the computed and measured flows, reasonably good agreement was observed between the experimental and computational static pressure distributions on the basic carriage geometry. The computations also exhibited details of reverse flow re- gions and, thus, both supported and supplemented the ex- perimental data that did not include velocity measurements. The geometry of the basic carriage used in the present study is not axisymmetric. There is a lack of data in the literature on studies of external stores that have nonaxisymmetric ge- ometries. References 8 and 9 present data for bodies having square and rectangular cross sections. Studies of the flow around axisymmetric bodies show that there exist four char- acteristic flow regimes1012: vortex-free, symmetric vor- tex, asymmetric vortex, and wake-like flow regimes are observed with increasing angle of attack. Crossflow separation of the boundary layer on an axisymmetric body gives rise to formation of vortices on the lee side. Reference 10 states that the nonlinear lift force due to these vortices can be much larger than the lift predicted by the linear (small perturbation) theory. References 13-15 describe studies that investigate the effect of afterbody modifications on the drag of axisymmetric bodies. Interference between the flowfields of stores and air- craft bodies is investigated by Refs. 1 and 2.

Optimum design of minimum drag bodies in incompressible laminar flow using a control theory approach

The problem of modifying the shape of a two-dimensional body to reduce its drag while maintaining its section area (volume per unit span) constant is addressed. Two-dimensional, incompressible, laminar flow governed by the steady-state Navier-Stokes equations is assumed about the body. In this paper, a set of “adjoint” equations is obtained, the solution to which permits the calculation of the direction and relative magnitude of change in the body profile that leads to a lower viscous drag. The direct as well as the adjoint set of partial differential equations are obtained for Dirichlet-type far-field conditions. Repeatedly modifying the body shape with each solution to these two sets of equations with the above boundary conditions, would lead to a body with minimum drag, for a specified section area. For such a body it is shown that the product of shear and the “adjoint” shear is constant everywhere along the body. Even though the viscous terms are retained in the direct and the adjoint equations, in order to determine farfield boundary conditions, the characteristics of the adjoint set of equations are examined in the absence of the viscous terms. This is done in order to obtain computationally tractable boundary conditions at far-field instead of the Dirichlet type conditions required by analysis. Numerical solutions to the direct and the adjoint equations are obtained using these modified boundary conditions. Preliminary results obtained using an ellipse as the initial body shape demonstrate that the approach does provide meaningful shape modification information.

The Minimum Drag Profile in Laminar Flow: A Numerical Way

It would be of interest to engineers and scientists to know the shape of the body of a given volume that will have minimum drag when moving through a viscous fluid at constant speed. It would be extremely useful if one could devise an evolution procedure that can evolve the minimum drag body in a logical and an orderly manner. Such a procedure was suggested by Pironneau for laminar flow wherein optimality conditions derived using optimal control theory were used in a non-linear gradient algorithm. The literature cites an attempt of the procedure at high Reynolds number where for each iteration in the evolution process, the flow field required an outer and an inner solution and the calculation of the gradient optimality condition required the solution of the co-state equation, a type of boundary layer equation. This paper addresses the direct simulation of the governing elliptic partial differential equations, viz., the Navier-Stokes and the co-state equations. Even though the latter has no simple mechanical interpretation, capitalizing on its resemblance to the former, this paper shows how the solution to the co-state equation could be obtained by simply adapting an existing Navier-Stokes code. Solution of the flow field and the calculation of the necessary criteria required in the evolution process are also discussed. The novelty of this direct approach is to make the evolution process more general, arbitrary and less complex. The profile evolution is demonstrated for flows at different Reynolds numbers.

Drag and wake modification of axisymmetric bluff bodies using Coanda blowing

This work investigates the ability of Coanda jet blowing to modify the base pressure of a cylindrical body aligned axially in a flow, and thereby, produce overall drag reduction. It is found that blowing through one or two slot jets concentric to the outer body circumference can significantly influence the entire base flow region. The recirculating wake is eliminated and is replaced by freestream fluid entrained by the Coanda blowing. Base pressure rises significantly and leads to drag reduction of up to 30% beyond the thrusting action of the Coanda jet. A comparison between the power savings through drag reduction and the power requirement of the Coanda jet demonstrates that net benefits are attainable at certain body geometries and flow conditions. By judiciously selecting the jet blowing velocity, it is possible to produce a nearly flat wake velocity profile requiring little net power. RAG reduction of immersed bodies is a subject with a long history, leading to the early concept of streamlining. The net drag force on a body may be considered the sum of viscous drag and pressure drag forces. For streamlined aero- dynamic and hydrodynamic bodies, the pressure drag is small, and current research is directed towards the application of laminar flow control (e.g., suction), turbulent viscous drag reduction (e.g., riblets and large eddy breakup devices (LEBUs)), and the use of nonlinear aerodynamics for induced drag reduction (e.g., winglets or crescent wing planforms). For bluff bodies, on the other hand, streamlining is usually not an option for reducing drag because the bluff shape is often dictated by other constraints. This situation is particu- larly true for trucks, buses, and most automobiles. For bluff bodies then, where pressure drag dominates, drag reduction is primarily through base flow modification, including flow separation control using airfoils, the use of plates, cavities, base bleed, and suction/blowing. Bluff bodies may be considered of two general classifica- tions—high and low aspect ratio. The former may be modeled as bodies of large span relative to a characteristic height, and are generally two-dimensional in nature. Examples would be the classic cylinder in crossflow, or a symmetric airfoil with a thick, blunt trailing edge. Drag reduction for such bodies has been performed13 with drag reductions of up to 64% reported in the literature. Low aspect ratio bodies have also been studied. Such bodies are characterized by three-dimensionality or axisymmetry, with a sphere being the classic example. Other examples would be cylinders of rectangular or circular cross section aligned axially in the flow direction. Work on drag reduction of such bodies has been reported in Refs. 4-12. A variation of these studies would include inclined base regions such as fast-back auto- mobiles and cargo transport aircraft. During the energy crisis of the seventies, renewed interest in vehicle drag led to many important new findings which are summarized in the books

Numerical investigation of the effects of base slant on the wake pattern and drag of three-dimensional bluff bodies with a rear blunt end

A computational model has been developed to help the automotive design engineer to optimize the body shape with minimum wind tunnel testing. Unsteady, Reynolds-averaged, Navier-Stokes equations have been solved numerically by a finite-volume method and have been applied to study the flow around Ahmed's vehicle-like body. The standard k— ε model has been employed to model the turbulence in the flow. The finite volume equations have been formulated in a strong conservative form on a three-dimensional, unstructured grid system. The resulting equations have been solved then by an implicit, time marching pressure-correction based algorithm. The steady state solution has been obtained by taking sufficient time steps until the flow field ceases to change with time within a prescribed tolerance. For the pressure-correction equation, a preconditioned conjugate gradient method has been employed to obtain the solution. Most of the essential features of the flow field around a bluff body in ground proximity, such as the formation of trailing vortices and the reverse flow region resulting from separation, could be well predicted. In addition, the variation of the drag coefficient with the back slant angle agreed reasonably well with the experimentally observed values.

General methodology of measurements of drag or drift of a solid body by a continuous medium

An ensemble of methods is considered for measuring the drag or drift acceleration of oriented and nonoriented, stationary and nonstationary solid bodies by a continuous medium. A new treatment is proposed for real-time instrumental identification of the characteristics of a moving object in a continuous medium and the pertinent mathematical relations are presented.