Drag Equation Research Articles

Applicability of Drag Equation on a Dimpled Golf Ball using Changing Wind Velocities

The drag equation is commonly used to relate the resistance force experienced by an object traveling through fluids with its velocity. The pattern might vary based on the specific geometry of the objects (e.g., a dimpled golf ball). The dimples are known to reduce the amount of drag during the ball’s flight through a series of complex aerodynamic processes. To investigate the ball’s drag pattern, pressure and air velocity on the golf ball, a CFD using Ansys fluent is performed to simulate its aerodynamic features under nine different wind velocities. After the experiment, it was found that the relationship between the drag and velocity of the dimpled golf ball still generally conforms to the drag equation. The pressure and velocity distributions are consistent with the hypothesis, while the aerodynamic details are presented. The effect of dimples is also visualized, contributing to the flow demonstration. The investigation is valuable because the aerodynamic process of the dimpled sphere structure in changing wind velocities is well presented and analyzed, and it inspires further explorations on the aerodynamic effects of the dimple geometry.

Long-term field monitoring of slabs-on-ground reinforced with GFRP bars

The current design of GFRP bar-reinforced slabs-on-ground, according to ACI 440.1R-15 is based on an empirical equation derived from the design of steel-reinforced concrete slabs-on-ground, developed based on the subgrade drag equation proposed in Portland Cement Association code (1990). ACI 440.1R-15 explicitly stipulates that field performance data from the application of FRP bar-reinforced slabs-on-ground is required to validate the equation. This paper reports the experimental outcomes of a comprehensive study on the long-term field monitoring of eight large-scale slab-on-ground specimens. Slabs of plan dimensions 6000 × 1100 mm2, resting on a lean concrete subbase over a compacted soil subgrade and exposed to harsh ambient environment, were monitored for 525 days to study rebar and concrete strain development and concrete cracking. The exposed ambient environment was characterized by averages of 41.7 ℃ with RH 12.8% in summer and 9.5 ℃ with RH 87.7% in winter. The major parameters of the study are reinforcement types (ribbed GFRP, sand-coated GFRP, and ribbed steel), reinforcement spacings (200 mm and 300 mm), slab thicknesses (100 mm and 200 mm), and the presence of a contraction joint. It was observed that all GFRP bar-reinforced slabs developed a transverse mid-panel shrinkage crack within the first 18 days of casting. The maximum average crack widths over the long-term were within the ACI 440.1R-15 and AASHTO LRFD code limit of 0.7 mm, and the maximum strains in rebars in the vicinity of the cracks did not exceed 12.4% of the ultimate strains of the bars. Decreasing the slab thickness from 200 mm to 100 mm did not affect the development of cracking or strain evolution. The presence of a saw-cut contraction was effective in localizing the cracking location.

Experimental Determination of Drag Constant for Slow Moving Axisymmetric Bodies

A body moving through a fluid experiences drag, which primarily consists of two components: form drag and viscous drag. At high velocities, the form drag predominates whereas at low velocities, the viscous drag predominates. The form drag is characterized by the drag coefficient which is determined experimentally for various configurations. Similarly, the viscous drag is characterized by the drag constant which in turn is known only for specific cases and its generic governing model is not well established yet. The current study puts forward a generalized mathematical model for determination of the drag constant for frontally streamlined small axisymmetric bodies moving slowly through a fully-enclosing fluid at zero angle of attack. It has been accomplished by establishing a governing mathematical model for viscous drag, validating it via wind tunnel experiments and then comparing it with the standard linear drag equation. Conclusively, the drag constant has been determined in terms of the fluid properties and dimensions of the moving body. This paper describes the above-mentioned mathematical model followed by the process of its experimental validation and determination of drag constant.

Rheology, bubble-particle interaction and air bubble system: A study of the influence of inorganic salts on air entrainment by bubble rising measurement

Rheological properties and the interaction between air bubbles and solid particles are important factors influencing the air bubble system in air-entrained concrete. The former may affect the bubble motion and the latter may influence the strength of bubbles. However, none of them were properly discussed by direct observation. In this study, we observe the rising behavior of various-sized bubbles in air-entrained cement paste. By a modified drag equation, the bubble-particle interaction is determined and represented by the interaction coefficient Ki. By Ki the bubble-particle interaction can be quantified and correlated with air entrainment properties. In combination with rheological properties and surface tension, the influence of inorganic salts on air entrainment is systematically studied. It is found that the content of bubbles <200 μm and the specific surface area of bubbles in the fresh mortar decrease with the increase of Ki, and the content of bubbles >1000 μm and the spacing factor increase with increasing Ki.

Development of simplified air drag models including crosswinds for commercial heavy vehicle combinations

Accurate range prediction requires good knowledge of the prevailing wind conditions and how they affect the energy consumption of the ego vehicle. A few different simplified vehicle air drag models that explicitly include the effect from crosswinds are presented and compared through some objective criteria. The models are developed from the normal air drag equation where the effect from wind is implicit and therefore often forgotten or neglected. The purpose is to find a low-complexity model complementing CFD models and wind tunnel tests, that can be used for range estimation and predictive energy management algorithms. To simplify online estimation, a requirement is that the air drag models only contain a few tuning parameters. The models are validated against CFD calculations for a few vehicle combinations and the best models show good accuracy for air attack angles up to at least 60 degrees. It is shown that the parameters of the simplified models can loosely be connected to some basic geometrical attributes of a vehicle combination so it should be possible to give at least a rough estimate of the parameters of a simplified model based on these geometrical attributes. This is useful for making a first estimate of the aerodynamic properties of a vehicle combination after major changes in the exterior, e.g. when adding a trailer. It also highlights that the size and the shape of the vehicle side may be mainly responsible for the high longitudinal air drag sensitivity to crosswinds for large vehicle combinations.

Application of ultrasonic sensor and Arduino in analysing motion of damped pendulum

An easy-to-setup experiment designed to measure the period and air drag coefficients of a damped pendulum is reported. The setup is made up of a solid metal ball and cylindrical shells of various sizes to create air drag. An ultrasonic position sensor (HC-SR04) and an Arduino Uno board were located beneath the pendulum’s lowest position. The pendulum was released from a fixed height at a small initial angle. The periods of the oscillations involving different cylindrical shells were obtained from the time series plots of the pendulum’s position when the pendulum moves back and forth above the sensor. The drag coefficients were measured from five different values of string length. The coefficient was proportional to the size of the cylindrical shells and in agreement with the drag equation for a small Reynolds number.

Soil methane emission suppression control using unmanned aircraft vehicle swarm application of biochar mulch - A simulation study

In this paper, we present a soil methane emissions suppression approach using swarms of unmanned aerial vehicles (UAVs), by spreading biochar mulch on top of the detected methane emissions area/source. Soil microorganisms can produce methane and release it into the atmosphere causing climate change such as global warming. However, people lack methods to manage soil methane emissions, especially quantification of methane emissions from the soil. Current measurement and suppression of methane methods are often limited due to the maintenance, installation, and calibration requirements of these sensing systems. To overcome these drawbacks, we present a new method called FADE-MAS2D (Fractional Advection Diffusion Mobile Actuator and Sensor) in which swarming UAVs are applied as optimal coverage control actuators to various methane release scenarios (from single to multi-source disturbances) utilizing an anomalous diffusion model with different time, and space fractional orders subject to wind fields. This strategy is based on the premise that methane diffusion can be modeled as an anomalous diffusion equation, and swarming UAVs can be applied to tackle the optimal coverage control issue. To simulate methane diffusion under the wind, we utilize the fractional calculus to solve the anomalous diffusion equation and define wind force with the drag equation. In addition, we integrated emissions control, UAV control efforts, and UAV location error in our cost function. Finally, we evaluated our approach using simulation experiments with methane diffusion and multiple methane emission sources in the time and space domain, respectively. The results show that when α ​= ​0.8 and β ​= ​1.8, the shape and emissions of methane perform well. Furthermore, our approach resulted in great control performance with multiple methane emission sources and different wind velocities and directions.

New insights into real-time detection of tephra grainsize, settling velocity and sedimentation rate

Characterizing the size and settling velocity of pyroclastic fragments injected into the atmosphere during volcanic eruptions (i.e., tephra) is crucial to the forecasting of plume and cloud dispersal. Optical disdrometers have been integrated into volcano monitoring networks worldwide in order to best constrain these parameters in real time. Nonetheless, their accuracy during tephra fallout still needs to be assessed. A significant complication is the occurrence of particle aggregates that modify size and velocity distributions of falling tephra. We made the first use of the Thies Clima Laser Precipitation Monitor (LPM) for tephra-fallout detection at Sakurajima volcano (Japan), which is characterized by a lower size detection window with respect to more commonly used disdrometers (e.g., Parsivel2) and can more easily distinguish different falling objects. For the first time, individual particles have been distinguished from most aggregates based on disdrometer data, with the potential to provide useful grain-size information in real time. In case of negligible aggregation, LPM and collected sample-based estimates are in agreement for both grain-size and sedimentation rate. In case of significant aggregation, particle shape analyses and a dedicated drag equation are used to filter out aggregates from LPM data that also provide good agreement with collected tephra samples.

Physical properties of the superbolide of Tajikistan based on combined satellite and ground-based observations

In this paper we present the study of the photometric mass and density for the Tajikistan superbolide of 23 July 2008. Using the combined data from satellite and ground-based observations the mass was calculated by three approaches: photometric (based on the light intensity at the height of maximum brightness), graphics (using published data of cars) and using the kinetic energy of the superbolide. As a result, the calculated values of the mass are 25.3, 19.9 and 18.9 tons, respectively (with average value of 21.3 ± 2.1 tons). The superbolid density was evaluated using the drag equation, the equation density of atmosphere at the heights of the maximum luminosity and beginning of the train and criterion-PE. The densities calculated by these three methods are equal to 1.1, 0.53 and 0.95 g/cm3 (with the average superbolide density as 0.86 ± 0.15 g/cm3).

A model for rigid asymmetric ellipsoidal projectiles penetrating into metal plates

A theoretical model is presented for penetration of asymmetric ellipsoidal projectiles which are proposed to fit the lift-generating outline of hypersonic vehicles. The projectile is composed of two triaxial quarter ellipsoids with one different semiaxis, and four geometric parameters are required to decide the shape. The model is based on two-term drag equation and a stress distribution relation of elliptical boundary with hole enlargement mechanism. Verification of the model is completed by simulation cases of six different projectiles with initial velocity between 600 m/s to 1000 m/s. Ballistic characteristics of asymmetric ellipsoidal projectiles including acceleration and residual velocity are derived from the model and analyzed to acquire the effects of geometric parameters on penetration results. Two decisive factors of cross section shapes, asymmetry and flatness, are specially discussed in contributions to residual velocity. Comparations with traditional circular cross-sectional cases are also presented, which indicates that same penetration capacity could be retained in the asymmetric ellipsoidal projectiles as in the circular cross-sectional one by selecting the shape controlling factors.

Learning the Resistance Coefficients of Pendulum Motion Using Balls of Various Sizes

In order to obtain the damping and resistance coefficients of a pendulum, we constructed an optical system containing a photogate for measuring the speed of the pendulum at the lowest point of motion. The photogate consisted of a photoresistor, a laser, a mechanical body, and a pendulum ball. A 3D printer was used to produce the mechanical body and pendulum balls of various sizes. Furthermore, we used Arduino to automate measurement of the speed at the lowest point of motion and increase the precision. We found that the resistance coefficient was proportional to the size of the balls, regardless of the ball mass, in agreement with the drag equation for a small Reynolds number.

Drag coefficient and frontal area of a solitary mature tree

Trees are important natural wind engineering elements in both the urban and the agricultural contexts, but their aerodynamic description has been limited by its focus on young, flexible trees. Here, we provide a reformulation of the classical drag equation, which is also suitable for mature and wind-adapted trees. The new formulation is based on results from a full-scale experiment with focus on a solitary oak tree, for which we determined all terms in the drag equation experimentally. We also present a new photographical method for the accurate quantification of the tree’s frontal area under highly variable outdoor lighting conditions. We used a database of images from a surveillance camera, from which a high-quality subset was automatically selected with machine learning algorithms. Compared to previous work on younger and smaller trees, the mature tree has a lower absolute value of the Vogel exponent, which indicates a relatively low degree of reconfiguration. The presented results underline the high efficiency of mature trees in reducing the momentum of the wind. The results can be used to quantify the effect of similar trees in wind simulations, and the new method for determining the frontal area can be applied in other tree measurement campaigns.

Characteristics of Breaking Wave Forces on Piles over a Permeable Seabed

Most offshore wind turbines are installed in shallow water and exposed to breaking waves. Previous numerical studies focusing on breaking wave forces generally ignored the seabed permeability. In this paper, a numerical model based on Volume-Averaged Reynolds Averaged Navier–Stokes equations (VARANS) is employed to reveal the process of a solitary wave interacting with a rigid pile over a permeable slope. Through applying the Forchheimer saturated drag equation, effects of seabed permeability on fluid motions are simulated. The reliability of the present model is verified by comparisons between experimentally obtained data and the numerical results. Further, 190 cases are simulated and the effects of different parameters on breaking wave forces on the pile are studied systematically. Results indicate that over a permeable seabed, the maximum breaking wave forces can occur not only when waves break just before the pile, but also when a “secondary wave wall” slams against the pile, after wave breaking. With the initial wave height increasing, breaking wave forces will increase, but the growth can decrease as the slope angle and permeability increase. For inclined piles around the wave breaking point, the maximum breaking wave force usually occurs with an inclination angle of α = −22.5° or 0°.

Energy consumption and conversion efficiency for a micromotor under DC voltage

A water droplet works as a novel kind of micromotor exhibiting back-and-forth motion between two needle-shaped electrodes in an oil phase under a stationary direct-current voltage. In the present study, a quantification method was adapted to estimate the kinetic energy output of back-and-forth motion of a water droplet, together with the electric energy input to this system. It was observed that the volume of the droplet gradually decreased accompanied by the periodic motion, which is attributed to electrolysis. Energy consumption owe to the electrolysis vs. the generation of kinetic energy of the moving droplet experimentally evaluated. The kinetic energy was deduced based on Stokes’ drag equation. Electric current was measured at the pA level. Then, the energy conversion efficiency of this micromotor system was able to be calculated. As far as we aware, this is the first report on the conversion efficiency for the autonomous motion under stationary DC voltage. Until now, various kinds of micromotor systems have been individually developed by different study group, and the comparison was difficult due to the lack of universal reliable index of the efficiency. The quantification method reported here evaluates micromotor system on its energy conversion efficiency, irrespective of experiment conditions. This quantification method can be a universal tool for micromotor system comparison, and is expected to play the role as the guidelines for future developments.

Derivation of phenomenological turbulence theory in liquid with small additives of drag reducing agents

Paper considers the issue of deriving the phenomenological turbulence theory in liquids treated with small additives of drag reducing agent. It also proposes the concept that for practical purposes, it is the phenomenological theory, which is relevant, since it determines the parameters of the phenomenon in question in the absence of detailed knowledge of the mechanisms of additives action, which, despite many years of intensive studies, remain either unknown or not fully understood. Different additives have different effects on shear turbulence in pipes and channels and, accordingly, change the integral characteristics of the turbulent flow in different ways. Some additives affect only the narrow wall-bounded areas of the flow without changing the turbulent viscosity in the flow core, while others act throughout the entire flow volume and significantly change the turbulent viscosity. Additives of the first type affect a turbulent flow by changing the boundary conditions in known models without changing the model coefficients. Additives of the second type change both the boundary conditions and the coefficients of the model itself. It is shown that the von Karman modified theory (model) of shear turbulence is equally suitable for describing the turbulent flow of a liquid with additives of the both first and second types. The universal drag equation with experimentally determined transfer coefficients that follows from this model enables calculating the hydraulic drag coefficient depending on the properties of the drag reducing agent used.

Estimating the 3D shape of volcanic ash to better understand sedimentation processes and improve atmospheric dispersion modelling

The sedimentation rate of volcanic ash through the atmosphere influences its travel distance, with important implications for aviation and health. The fall velocity of a particle depends on its size and density, but also shape, and volcanic ash is not spherical. To capture the sedimentation of ash, atmospheric dispersion models use empirical drag equations calibrated using geometric shape descriptors. However, particle shape data are scarce and there is no standard method of shape measurement. In addition, shape measurements are not always available during an eruption, when dispersion models are used operationally to forecast ash hazard. We assess the variability in the shape of volcanic ash from Icelandic eruptions using X-ray computed tomography. To consider how good different drag equations and shape descriptors are at representing the sedimentation of volcanic ash we compare calculated fall velocities to measured fall velocities of volcanic ash in air in a settling column. We then suggest the best drag equations and shape descriptors for use in atmospheric dispersion models. We find that shape-dependent drag equations produce more accurate results than a spherical approximation. However, accurate drag calculations based on the shape descriptor sphericity, which is a function of surface area, require the imaging resolution to be within the range of 102 - 105 voxels per particle (where a voxel is a volumetric pixel) as surface area is sensitive to imaging resolution. We suggest that the large-scale form of the particle impacts sedimentation more than small-scale surface roughness. Shape descriptors based on ratios between principal axis lengths are more practical as they are less variable among particle size classes and much less sensitive to imaging resolution. Finally, we use particle shape data from this study and literature sources to make recommendations on default values for use with atmospheric dispersion models where no shape data are available.

A buoyancy–shear–drag-based turbulence model for Rayleigh–Taylor, reshocked Richtmyer–Meshkov, and Kelvin–Helmholtz mixing

A phenomenological turbulence model for Rayleigh–Taylor, reshocked Richtmyer–Meshkov, and Kelvin–Helmholtz instability-induced mixing is developed using a general buoyancy–shear–drag model. Analytic solutions to the simplified model equations corresponding to each instability are derived separately, which are then used to calibrate the model coefficients to predict specific values of the mixing layer growth parameters and exponents. The buoyancy–shear–drag equations for the bubble and spike mixing layer widths are then solved numerically, and a turbulent diffusivity (or viscosity) is constructed dimensionally as the product of the mixing layer width, h, and its time-derivative, dh/dt. Surrogate turbulent fields are then constructed by multiplying a presumed, approximate self-similar spatial profile by appropriate functions of h and dh/dt. Using several simplifying approximations, the turbulent diffusion equations satisfied by the mean mass fraction and mean shear velocity are solved analytically in a reference frame moving with the mean advection velocity, and it is shown that the mean fields evolve in space and time as expected. The explicit modeling and solution of turbulent transport equations (e.g., for the turbulent kinetic energy and its dissipation rate or a lengthscale) are not required. By using separate equations for the bubble and spike evolution, the model naturally captures the asymmetry induced by an increasing density contrast between the heavy and light fluids. The model also includes molecular dissipation and diffusion, and therefore, can describe transition to fully-developed turbulence if the initial turbulent diffusivity/viscosity is much smaller than the molecular diffusivity/viscosity. This model is applied to constant-acceleration Rayleigh–Taylor, impulsively reshocked Richtmyer–Meshkov, and variable-density Kelvin–Helmholtz mixing layers to demonstrate its utility. It is shown that the numerical solutions of the model calibrated using specific values of the instability growth parameters and exponents: (1) produces mixing layer widths in agreement with the expected self-similar growth power laws; (2) gives spatiotemporal profiles of turbulent fields that are expected and consistent with previous results; (3) predicts the expected power-law growths and decays of the spatially-integrated turbulent fields, and; (4) gives spatiotemporal profiles of the mean fields that are expected and consistent with previous results. This relatively simple model can be implemented numerically, and is expected to be useful for fundamental as well as astrophysical and inertial confinement fusion applications.

On modeling Richtmyer–Meshkov turbulent mixing widths

We present several observations concerning the Richtmyer–Meshkovmixing widths after a shock or reshock passes through the interface between two fluids. The mixing evolves with two oppositely-moving fronts: A bubble (b) side into the heavier fluid and a spike (s) side into the lighter fluid. Our first observation concerns the reference surface used to partition the total mix width, hb+s, into separate hb and hs widths. Next, we point out that if and when hb and hs obey power-laws tθ with separate θb and θs, then hb+s cannot be given, except as an approximation, by a single θb+s. Finally, we describe a fully continuous model for hit, i=b,s, or b+s, as the solution to the “drag equation” with a time-dependent θi(t).

Hydrodynamic performance of bottom trawls with different materials, mesh sizes, and twine thicknesses

Nowadays, the fishing industry faces several constraints such as continuous increase infuel price and decrease in fish stocks. Bottom trawl efficiency is mainly affected by the drag force of trawl net and sweep area during fishing operations. This study focuses on the drag of bottom trawl models constructed from traditional and new materials. A nylon net panel, a traditional material, was used in two model trawl nets, namely, trawl nets 1 and 4; the geometric shape ofwing net on trawl net 4 was a triangle. Considering the physical characteristics of the new materials such as Dyneema and nylon monofilament, net panels with a large mesh size and small twine stiffness were used, respectively. The trawl nets were named as trawl nets 2 and 3, respectively. The drag forces provided by the standard trawl (trawl net 1) were 57%, 56.2%, and 47% less than those of trawl nets 2,3, and 4 respectively. The drag coefficient of trawl net 1 was 40.68%, 30.35%, and 33.96% greater than those of trawl nets 2, 3, and 4, respectively. The results also show that these three trawl net models are geometrically efficient in terms of net mouth height than a standard trawl net. This indicates that the drag force of bottom trawl net with a new material was much lower than those made with a traditional material. The developed equations in this study provide the basis for a drag and geometry prediction model for a bottom trawl. The advantage of this predicted drag equations over previous net drag formulas is that it can be evaluated using only information available from a net drawing (mesh size and twine diameter), so that the net drag of bottom trawl net of a reasonably standard shape can be estimated at the design stage.

Influence of drag equations on computational fluid dynamic modeling of fluidization behavior of loblolly pine wood grinds

Abstracts The drag equations used in computational modeling of particulate materials were developed with fundamental assumptions on shapes, size distribution and densities that are different from biomass. This study evaluated the applicability of drag equations available in popular Computational Fluid Dynamics modeling software having material with properties that are like loblolly pine wood grinds. The models were validated using a bench scale fluidized bed system. The result showed that non-spherical drag equations predicted the minimum fluidization velocity (Umf) better than other drag equations with mean relative deviation that was less than 5%. All the model predicted bed entrainment at 2 s simulation time. The body force correlation applied improved the non-spherical drag equations fluidization behavior but with minimal impact when other drag equations were evaluated.