Minimum Drag Research Articles

Design and analysis of an aerodynamic kit for a two wheeled race motorcycle

In this paper we discuss on what causes the limitations in aerodynamics of a two wheeled motorcycle & try to overcome them by changing its shape & altering it overall weight by adding & subtracting some of the essential & non-essential equipment in it, with considering both the rider on the vehicle as well as off it. The size and shape of a motorcycle together with the rider and any aerodynamic aids such as fairing, windscreen or leg shield induce the drag, lift, hence reduces it power capabilities. Drag is a force trying to prevent rapid movement of a motorcycle through the air. This force is generated through a difference in pressure between the front and rear of the machine. This ultimately helps to enhance the performance of the vehicle. The prototypes of the fairings are designed using 3D CAD modelling software and are compared with each other and the stock variant. Designs are refined through research using CFD (Computational Fluid Dynamics). The goal is to find the most efficient compromise between the drag values for the best handling at the highest possible speeds. Firstly, a naked version of a typical 150 cc motorcycle is used as a base to start the design of the fairings. The 2D sketch of the base motorcycle frame is traced along the outline to draw a visual teardrop structure. A teardrop is the most streamlined structure and has minimum drag coefficient. Cross sections of the motorcycle are obtained front cowl, side fairings and rear cowl are made and analysed using Ansys Fluent. These sets of designs are then compared based on Cd (co-efficient of drag) value and the best design is selected. These cross sections are used to create a wire frame model to create a 3D model using CAD software. The 3D model is then simulated using a CFD tool to study the airflow around it and the results are compared with the naked version of the motorcycle.

A Continuous Perspective on Shape Optimization via Domain Transformations

In this article we consider shape optimization problems as optimal control problems via the method of mappings. Instead of optimizing over a set of admissible shapes a reference domain is introduced and it is optimized over a set of admissible transformations. The focus is on the choice of the set of transformations, which we motivate from a function space perspective. In order to guarantee local injectivity of the admissible transformations we enrich the optimization problem by a nonlinear constraint. The approach requires no parameter tuning for the extension equation and can naturally be combined with geometric constraints on volume and barycenter of the shape. Numerical results for drag minimization of Stokes flow are presented.

TORQUE AND DRAG MEASUREMENT: A COMPARISON BETWEEN CONVENTIONAL, SLIM HOLE AND CASING DRILLING METHODS IN A DEVIATED WELL

Different locations and field conditions require various drilling methods to produce oil and gas. Three major operational methods are identified to be slim holes, conventional and casing drilling. Despite many affecting parameters, torque and drag are two highlighted factors for the determination of the best drilling method. Torque and drag play a significant role in the feasibility of drilling and its final costs. In this study, the influence of the torque and drag are investigated for the determination of optimum drilling type in consideration of the same S-shape well trajectory for all cases. Consequently, slim hole drilling showed minimum torque and drag value which meant that this method can be a good choice. Furthermore, casing drilling displayed maximum torque and drag in this study resulting in high sensitivity to the high degree of deviation. On the other hand, due to the constant weight of casing while drilling, this method showed a smooth increasing trend in terms of drag force while slim hole and conventional drilling showed significant changes in different parts of well trajectory. The number of build and drop sections significantly affect the amount of torque loss, while up to 50% to 70% of torque loss was observed in the drop or build section.Keywords: torque, drag, directional drilling, slim hole, casing while drilling, well trajectory

Aerodynamics Analysis on Wings with Winglets and Vortex Generators

This project was based on the principle of designing, simulating and developing an inexpensive, aerodynamically efficient and regular class electric powered RC aircraft. This prototype was designed to have the maximum strength to weight ratio with minimum drag coefficient (and highest lift coefficient). Moreover, all constraints provided by SAE International competition were followed. The investigation was conducted for the complete airplane and for wing optimization. The model was numerically investigated with ANSYS Fluent 16.1 through the SST K-Omega turbulence model at Reynolds number of 360,000. Once the results were obtained, model and result verification were done by wind tunnel test to validate the data. It was concluded that the airplane with 45° winglet has the highest lift force with minimal drag and 45° winglet was further modified with rectangular and triangular vortex generators in order to further enhance its aerodynamic efficiency for a range of Angle of Attacks (AOA).

Numerical study of longitudinal vein effects on the aerodynamic characteristics of a corrugated bio-airfoil

The purpose of the present study is to investigate the influence of cross-sectional veins topology on the flow pattern and aerodynamic performance of a pitching corrugated bio-inspired airfoil. To demonstrate the vein effects, a cross-section of Ashena Cyanea wing is modelled with three configurations. The airflow passing bio-airfoil is subjected to three Reynolds numbers of 1000, 5000, and 14000 and selected reduced frequencies (k) and angular amplitude (A). The results show that as the Reynolds number increases, the effects of veins structure become more significant. The lift coefficients of the three modelled bio-airfoils are almost identical over the range of selected Reynolds number. At the Reynolds numbers of 1000 and 5000, the thin bio-airfoil has a minimum drag coefficient, and the drag coefficients of thick and veined bio-airfoils are quite similar. The veins in the bio-airfoils increase the drag coefficient significantly for the Reynolds numbers of 14000 compared to the Reynolds number of 5000. Finally, the numerical simulations provide hysteresis of lift and drag coefficients subjected to an increment for Reynolds number, reduced frequency, and angular amplitude.

Artificial Neural Networks-Extended Great Deluge Model to predict Actuators Displacements for a Morphing Wing Tip System

Resin-based fiber composite materials have received attention in aerospace composite engineering, particularly in aircraft morphing structures, due to their high mechanical characteristics, such as stiffness, and because of their potential to highly reduce the structural mass of modern aircraft. Aircraft morphing is referred to as the ability of an aircraft’s surface to change its geometry in flight. The modelling of a dynamic morphing wing system is here studied. The morphing wing was controlled using four electric actuators situated inside of the wing model. The main role of these actuators was to modify the wing upper surface shape designed and manufactured with a flexible material, so that the laminar-to-turbulent flow transition point can move closer to the wing trailing edge, thus causing a minimum viscous drag, for various flow conditions. To determine the skin deflections in the four actuators points, both LVDT and dial indicator gages were positioned on the wing. Four Linear Variable Differential Transducers (LVDTs) were used to indicate the positions of the four actuators, and four Dial Indicators gages were positioned on the wing to measure the real deflections of the flexible composite skin in the four actuation points. The relationship between the Dial Indicators’ values and the LVDTs’ values for a same set-point command signal had a nondeterministic and unpredictable behavior (not a linear one). The values of the displacements given by the LVDTs were different than the values given by the Dial Indicators. In this paper, an Artificial Neural Network (ANN) model was investigated created with the aim to predict the displacements of the wing upper surface skin in real time using four actuators. The proposed model was trained using the Extended Great Deluge (EGD) algorithm.

Study of possibility of using axisymmetric body as heat sink for cooling machine parts

The paper presents the results of the study of possibility using a body with an optimized shape with a minimum aerodynamic drag force as a heat sink in a convective gas flow for cooling machine parts. The relevance of cooling or heat sink systems for mechanical engineering is not in doubt. Maintaining the optimum thermal state of machine parts within the specified limits is necessary to prevent heating, which can cause violations of normal operating conditions, and, as a result, increased wear, jamming and breakage of parts. To ensure the normal operation of the system, it is necessary to cool the parts contacting the hot gases, removing heat from them to the atmosphere directly, or using an intermediate body (water, low-freezing liquid). Heat sink is an aerodynamic process, a process of heat mass transfer of a substance, and aerodynamic characteristics and, in particular, the nature of streamlining of bodies of the simplest forms are of great scientific and practical interest. Bodies of complex shape can always be represented as a combination of simpler ones, for which it is easy to explore and calculate the flow paths, on the basis of which analytical methods for calculating aerodynamic characteristics are compiled. A computational experiment was conducted in the software product Ansys Fluent. The conditions of the experiment (comparison of heat removal bodies) during numerical modeling are the preservation of constants: the volume and shape of the working zone; distances from the sources, drains and centers of bodies; aerodynamic flow rates; masses of compared bodies; thermal power of the source and other parameters in addition to the shape of the surface. The resulting optimized shape of the body coincides with the current lines, which is the main advantage, since no separation from the surface is observed when streamlining the flow. Thus, the entire surface area will be the effective surface area of the heatsink as opposed to other known shapes of bodies, whereby the temperature of the heat loaded element placed in the center of the heatsink will decrease.

On the Effect of Supplied Flow Rate to the Performance of a Tilting-Pad Journal Bearing—Static Load and Dynamic Force Measurements

Abstract Rotating machinery relies on engineered tilting-pad journal bearings (TPJB) to provide static load support with minimal drag power losses, safe pad temperatures, and ensuring a rotor-dynamic stable rotor operation. End users focus on reducing the supplied oil flow rate into a bearing to both lower operational costs and to increase drive power efficiency. This paper presents measurements of the steady-state and dynamic forced performance of a TPJB whilst focusing on the influence of supplied oil flow rate, below and above a nominal condition (50% and 150%). The test bearing has five pads, slenderness ratio L/D = 0.4, spherical pivots with pad offset = 50%, and a preload –0.40, with a clearance to radius ratio (Cr/R) ≈ 0.001 at room temperature. The bearing is installed under a load-between-pads (LBP) orientation and has a flooded housing with end seals. The test conditions include operation at various shaft surface speeds (32 m/s–85 m/s) and specific static loads from 0.17 MPa to 2.1 MPa. A turbine oil lubricates the bearing with a speed-dependent flow rate delivered at a constant supply temperature. Measurements obtained at a steady thermal equilibrium include the journal static eccentricity and attitude angle, the oil exit temperature rise, and the pads' subsurface temperatures at various locations, circumferential and axial. The rig includes measurement of the drive torque and shaft speed to produce the bearing drag power loss. Dynamic force coefficients include stiffness, damping, and virtual-mass coefficients. As expected, the drag power and the lubricant temperature rise depend mainly on shaft speed rather than on applied load. A reduction in oil flow rate to 50% of its nominal magnitude causes a modest increase in journal eccentricity, a 15% reduction in drag power loss, a moderate raise (6 °C) in pads' subsurface temperatures, a slight increase (up to 6%) in the direct stiffnesses, and a decrease (up to 7%) in direct damping coefficients. Conversely, a 1.5 times increase in oil flow rate causes a slight increase (up to 9%) in drag power loss, a moderate reduction of pads' temperatures (up to 3 °C), a maximum 5% reduction in direct stiffnesses, and a maximum 10% increase in direct damping. The paper also presents comparisons of the test results against predictions from a thermo-elastohydrodynamic (TEHD) lubrication model. In conclusion, a 50% reduced oil flow rate only causes a slight degradation in the test bearing static and dynamic force performance and does not make the bearing operation unsafe for tests with surface speed up to 74 m/s. As an important corollary, the measured bearing drag power differs from the conventional estimate derived from the product of the supplied flow rate, the lubricant-specific heat, and the oil exit temperature rise.

Assessment of robust optimization for design of rotorcraft airfoils in forward flight

The paper compares the deterministic and robust optimization approaches to improve the aerodynamic design of helicopter airfoils. The two formulations are different due to the characteristics of each approach. In the deterministic case, the objective of optimization is the minimization of drag while maintaining a level of lift that guarantees satisfaction of the trimming condition. In the case of robust design, a range of angles of attack and not a single trim condition is considered. Thus, the robust optimization takes the lift-to-drag ratio as a measure of the performance of the airfoil, imposing at the same time an inequality constraint on the lift coefficient to guarantee a sufficient level of lift, and then checking after optimization that the trimming condition can be satisfied. The two approaches are compared showing pros and cons of the robust framework. In general, the robust approach shows the capability to reach the same mean performance of the deterministic one, but with a lower degradation of performance in other conditions considered through the uncertainty. On the other hand, the difficulties in imposing the lift trim condition for the robust formulation may lead to results of limited use.

Structure of eukaryotic DNA polymerase δ bound to the PCNA clamp while encircling DNA

The DNA polymerase (Pol) δ of Saccharomyces cerevisiae (S.c.) is composed of the catalytic subunit Pol3 along with two regulatory subunits, Pol31 and Pol32. Pol δ binds to proliferating cell nuclear antigen (PCNA) and functions in genome replication, repair, and recombination. Unique among DNA polymerases, the Pol3 catalytic subunit contains a 4Fe-4S cluster that may sense the cellular redox state. Here we report the 3.2-Å cryo-EM structure of S.c. Pol δ in complex with primed DNA, an incoming ddTTP, and the PCNA clamp. Unexpectedly, Pol δ binds only one subunit of the PCNA trimer. This singular yet extensive interaction holds DNA such that the 2-nm-wide DNA threads through the center of the 3-nm interior channel of the clamp without directly contacting the protein. Thus, a water-mediated clamp and DNA interface enables the PCNA clamp to "waterskate" along the duplex with minimum drag. Pol31 and Pol32 are positioned off to the side of the catalytic Pol3-PCNA-DNA axis. We show here that Pol31-Pol32 binds single-stranded DNA that we propose underlies polymerase recycling during lagging strand synthesis, in analogy to Escherichia coli replicase. Interestingly, the 4Fe-4S cluster in the C-terminal CysB domain of Pol3 forms the central interface to Pol31-Pol32, and this strategic location may explain the regulation of the oxidation state on Pol δ activity, possibly useful during cellular oxidative stress. Importantly, human cancer and other disease mutations map to nearly every domain of Pol3, suggesting that all aspects of Pol δ replication are important to human health and disease.

Obtaining the Practical Formula for the Trim-tab Dimensions to Reach the Minimum Drag for Planing Boat

Trim-tab is a device for controlling and stabilizing planing boats in different sea conditions. This paper presents to find dimensions of the trim-tab at various speeds of the boat to reach the minimum drag. The speed of the boat is from15 m/s to 30m/s. Drag of the boat is calculated by Stavisky’s method. The minimum drag is found based on the optimum the trim angle. A Matlab program code is prepared for these calculations and all the all results such as drag, dimensions of the trim-tab, longitudinal center of pressure and time angle at different speeds of the boat are presented and discussed.

Internal Shocks in Supersonic Flows past the Contours of Optimal Bodies and Nozzles

The problems of designing the contours of two-dimensional and axisymmetric bodies of minimum wave drag and maximum-thrust nozzles, such that flow past them can contain internal shocks, are considered within the ideal (inviscid and non-heat-conducting) gas model. These shocks may occur in flows past internal breaks in the optimal contours or on intersection of characteristics of the same family proceeding from these breaks. The submerged shocks occurring in the latter case are named internal, if their initial points lie within the domain of determinacy of the flowed-over optimal contour region. Further downstream the domain of determinacy is bounded by the characteristic coming to the end point of this contour. The internal submerged shocks can appear, when the optimal contour includes an interval of an isobaric streamline. The appearance of internal breaks in the optimal contours is possible due to the reflection of the pressure waves induced by them from the bow shock (for body noses) or, as might be expected, from tangential discontinuities (for afterbodies). In the case of supersonic freestreams having a tangential discontinuity the search for optimal two-dimensional afterbodies with an internal concave break flowed-over with an oblique shock is performed using the direct method with the representation of the required contours by the Bernstein—Bezier curves, a genetic algorithm, and a rapid and accurate marching scheme for calculating steady supersonic flows. While the optimal two-dimensional afterbodies with a convex internal break designed earlier using the general method of Lagrange multipliers could be reliably reproduced using the above-mentioned method, the expected optimal configurations with a concave break and an internal shock were not found. Instead, optimal contours with centered compression and expansion waves with the common focus on a tangential discontinuity and an “external” oblique shock proceeding from it were discovered. Then the new “discontinuous shock-free” solutions were constructed in the exact formulation, within the framework of the method of indefinite control contours and the method of characteristics. The solutions are generalized to include the contours of the afterbodies of revolution and supersonic parts of nozzles. In the case of a uniform freestream the flow past optimal afterbodies never includes internal shocks.

Genetic enhancement of essential amino acids for nutritional enrichment of maize protein quality through marker assisted selection.

Maize grain protein is deficient in two essential amino acids, lysine and tryptophan, defining it as of low nutritive value. The discovery of opaque2 (o2) gene has led to the development of quality protein maize (QPM) that has enhanced levels of essential amino acids over normal maize. However, the adoption of QPM is still very limited. The present study aims at improving the quality of normal four maize inbred lines (LM11, LM12, LM13 and LM14) of single cross hybrids; Buland (LM11 × LM12) and PMH1 (LM13 × LM14) released in India for different agro-climatic zones by introgressing o2 allele along-with modifiers using marker assisted backcross breeding. Both foreground and background selection coupled with phenotypic selection were employed for selection of o2 specific allele and maximum recovery of the recurrent parent genome (87-90%) with minimum linkage drag across the crosses. The converted QPM lines had <25% opaqueness which isclose to the respective recurrent parents. The QPM versions showed high level of tryptophan content ranging from 0.72 to 1.03 across the four crosses. The newly developed best QPM lines were crossed in original combinations to generate QPM hybrids. The grain yield of improved QPM hybrids was at par and there was significant increase in tryptophan content over the original hybrids.The integrated marker assisted, and phenotypic selection approach holds promise to tackle complex genetics of QPM. The dissemination and adoption of improved QPM versions may help to counteract protein-energy malnutrition in developing countries.

A Novel Control Allocation Method for Yaw Control of Tailless Aircraft

Tailless aircraft without vertical stabilisers typically use drag effectors in the form of spoilers or split flaps to generate control moments in yaw. This paper introduces a novel control allocation method by which full three-axis control authority can be achieved by the use of conventional lift effectors only, which reduces system complexity and control deflection required to achieve a given yawing moment. The proposed method is based on synthesis of control allocation modes that generate asymmetric profile and lift induced drag whilst maintaining the lift, pitching moment and rolling moment at the trim state. The method uses low order models for aerodynamic behaviour characterisation based on thin aerofoil theory, lifting surface methodology and ESDU datasheets and is applied to trapezoidal wings of varying sweep and taper. Control allocation modes are derived using the zero-sets of surrogate models for the characterised aerodynamic behaviours. Results are presented in the form of control allocations for a range of trimmed sideslip angles up to 10 degrees optimised for either maximum aerodynamic efficiency (minimum drag for a specific yawing moment) or minimum aggregate control deflection (as a surrogate observability metric). Outcomes for the two optimisation objectives are correlated in that minimum deflection solutions are always consistent with efficient ones. A configuration with conventional drag effector is used as a reference baseline. It is shown that, through appropriate allocation of lift based control effectors, a given yawing moment can be produced with up to a factor of eight less aggregate control deflection and up to 30% less overall drag compared to use of a conventional drag effector.

Drag reduction through shape optimisation for satellites in Very Low Earth Orbit

Operating satellites at altitudes in Very Low Earth Orbit (VLEO) has many advantages. However, due to the higher atmospheric density of this region, satellites encounter significantly higher atmospheric drag. Depending on the mission, this may require a propulsive system to maintain the orbit which costs both fuel mass and volume. It is therefore desirable to reduce the drag in order to either reduce these costs or to extend the operational life. In this paper a series of viable aeroshell profiles are identified for satellites operating in VLEO using a Radial Basis Function-based surrogate model with data generated using both Panel Methods and Discrete Simulation Monte Carlo simulations. It was demonstrated that a maximum drag reduction of between 21% and 35% was achievable for the profiles when optimising a bi-conic profile for minimum drag based on Discreet Simulation Monte Carlo simulations with an energy accommodation coefficient of 0.95. Accounting for the loss of internal volume and assuming the reduction in fuel mass results in an equally proportioned reduction in fuel system volume it was observed that only a 13% to 27% reduction was achieved.

Numerical study of the effect of aspect ratio on the flow characteristics of the Ground Transportation System

The effect of varying the aspect ratio of a 1:8 scaled Ground Transportation System (GTS) was numerically investigated using the steady formulation of the RANS k−ω SST model. Cases of different aspect ratios (defined as the ratio of the varying width to the baseline width (Eq. (1)), with and without a boat-tail, were considered. For the GTS without boat-tail, a quasi-linear decline in the drag coefficient was found with increasing aspect ratio, resulting from a variation in the strength of the side shear layers, and the consequent change in the vertical symmetry of the near-wake. The average length of the wake was found to increase with increasing aspect ratios, resulting from an increase in the size of high Reynolds shear stress regions in the wake. For the GTS with boat-tail, variation of aspect ratio was found to have no effect on the critical boat-tail angle, albeit the magnitude of reduction in the drag coefficient differed between low and high aspect ratio configurations. Variation of the ground clearance (G∗) of the GTS (without boat-tail) concluded a G∗ value corresponding to minimum drag coefficient (G∗=0.083), while retaining of vertical quasi-symmetry was observed for G∗≥0.29.

Wind loading of a finite prism: aspect ratio, incidence and boundary layer thickness effects

A systematic set of low-speed wind tunnel experiments was performed at Re = 6.5x104 and 1.1x105 to study the mean wind loading experienced by surface-mounted finite-height square prisms for different aspect ratios, incidence angles, and boundary layer thicknesses. The aspect ratio of the prism was varied from AR = 1 to 11 in small increments and the incidence angle was changed from α = 0° to 45° in increments of 1°. Two different boundary layer thicknesses were used: a thin boundary layer with δ/D = 0.8 and a thick boundary layer with δ/D = 2.0–2.2. The mean drag and lift coefficients were strong functions of AR, α, and δ/D, while the Strouhal number was mostly influenced by α. The critical incidence angle, at which the prism experiences minimum drag, maximum lift, and highest vortex shedding frequency, increased with AR, converged to a value of αc = 18° ± 2° once AR was sufficiently high, and was relatively insensitive to changes in δ/D. A local maximum value of mean drag coefficient was identified for higher-AR prisms at low α. The overall behaviour of the force coefficients and Strouhal number with AR suggests the possibility of three flow regimes.

Properties and numerical solution of an integral equation system to minimize airplane drag for a multiwing system

We consider an open multiwing system, composed of N ≥ 2 disjoint open plane curves, not necessarily symmetric, and examine the corresponding (constrained) induced drag minimization problem. To this end, we first derive the associated Euler‐Lagrange system of equations, which is then reduced to an equivalent system of Cauchy singular integral equations. By generalizing a previous approach of ours for the case of a single open wing, we obtain existence and uniqueness results for the problem solution in a product of weighted Sobolev type spaces. This system is then solved by applying to it a collocation‐quadrature method. For this, we prove stability and derive corresponding error estimates. Finally, to test the efficiency of the proposed numerical method, we apply it to some multiwing systems.

A reduced-order model for gradient-based aerodynamic shape optimisation

This work presents a reduced order model for gradient based aerodynamic shape optimization. The solution of the fluid Euler equations is converted to reduced Newton iterations by using the Least Squares Petrov-Galerkin projection. The reduced order basis is extracted by Proper Orthogonal Decomposition from snapshots based on the fluid state. The formulation distinguishes itself by obtaining the snapshots for all design parameters by solving a linear system of equations. Similarly, the reduced gradient formulation is derived by projecting the full-order model state onto the subspace spanned by the reduced basis. Auto-differentiation is used to evaluate the reduced Jacobian without forming the full fluid Jacobian explicitly during the reduced Newton iterations. Throughout the optimisation trajectory, the residual of the reduced Newton iterations is used as an indicator to update the snapshots and enrich the reduced order basis. The resulting multi-fidelity optimisation problem is managed by a trust-region algorithm. The ROM is demonstrated for a subsonic inverse design problem and for an aerofoil drag minimization problem in the transonic regime. The results suggest that the proposed algorithm is capable of aerodynamic shape optimization while reducing the number of full-order model queries and time to solution with respect to an adjoint gradient based optimisation framework.

Gradient-Limiting Shape Control for Efficient Aerodynamic Optimization

Local shape control methods, such as B-spline surfaces, are well-conditioned such that they allow high-fidelity design optimization; however, this comes at the cost of degraded optimization convergence rate as control fidelity is refined due to the resulting exponential increase in the size of the design space. Moreover, optimizations in higher-fidelity design spaces become ill-posed due to high-frequency shape components being insufficiently bounded; this can lead to nonsmooth and oscillatory geometries that are invalid in both physicality (shape) and discretization (mesh). This issue is addressed here by developing a geometrically meaningful constraint to reduce the effective degrees of freedom and improve the design space, thereby improving optimization convergence rate and final result. A new approach to shape control is presented using coordinate control () to recover shape-relevant displacements and surface gradient constraints to ensure smooth and valid iterates. The new formulation transforms constraints directly onto design variables, and these bound the out-of-plane variations to ensure smooth shapes as well as the in-plane variations for mesh validity. Shape gradient constraints approximating a continuity condition are derived and demonstrated on a challenging test case: inviscid transonic drag minimization of a symmetric NACA0012 airfoil. Significantly, the regularized shape problem is shown to have an optimization convergence rate independent of both shape control fidelity and numerical mesh resolution, while still making use of increased control fidelity to achieve improved results. Consequently, a value of 1.6 drag counts is achieved on the test case, the lowest value achieved by any method.