Drop Height Research Articles

Prepared for landing: A simple activation strategy scales muscle force to landing height

Before landing from a jump or fall, animals preactivate muscles to stiffen their limb joints but it is unclear how muscles tune limb stiffness and how collision forcefulness is anticipated. We measured electromyography and force from the lateral gastrocnemius muscle during landings in turkeys, an animal model that allows for direct measurements of muscle force. Many studies of landings in humans and other animals have found the duration of muscle preactivation to be constant, starting approximately 100 ms before impact, irrespective of fall duration. Therefore, we hypothesized a lack of relationship between fall duration (as dictated by drop height), muscle activity onset-time, and force at toe-down. Contrary to our expectations, both muscle activity and force rose from briefly after fall initiation until toe-down. Preactivation duration was proportional to fall height, while the rate of force rise was consistent across drop heights, resulting in force at landing and leg stiffness being proportional to fall height. Onset of muscle activity lagged 22 ± 7 ms (mean ± S.E.M.) from fall initiation, consistent with a reflex response initiation of the force ramp-up. Together, our results suggest that a constant (clock-like) rate of motor unit recruitment, initiated at fall initiation provides a preactivation that is proportional to drop height. The result is a tuning of pre-landing muscle force, providing a limb stiffening that is proportional to impact intensity, possibly without using information about fall distance.

Assessing the effects of free fall conditions on damage to chickpea seeds: A comprehensive examination of seed deterioration.

Impact damage is the most destructive effect on the seeds during harvesting, handling, and storage, both on-farm and off-farm. The chickpea seeds' dicotyledonous characteristics and large mass and size make them susceptible to mechanical damage under impact loading. Tests were conducted to determine the extent of damage to chickpea seeds due to the impact caused by free fall. The extent of internal damage to the chickpea seeds was determined, which included the measurement of seed deterioration by the accelerated aging method (percentage loss in germination in the accelerated aging test) and the measurement of electrical conductivity. Three independent variables were used in the test, namely: (a) drop height (3, 6, 9, and 12 m), (b) impact surface (concrete, metal, plywood and seeds on seeds), and (c) seed moisture content (10%, 15%, 20%, and 25% w.b). The results showed that drop height, impact surface, and moisture content had significant effects (p < .01) on the loss in germination percentage and change in electrical conductivity of chickpea seeds. In terms of loss in germination, the highest damage to seeds occurred at the metal impact surface (41.96%) and the least at the seed on the seed (29.71%). The highest amount of electrical conductivity was related to the seeds dropped on the metal (36.09 μS cm-1 g-1) and the lowest was related to seed-on-seed contact (21.68 μS cm-1 g-1). By increasing the drop height from 3 to 12 m, the loss in germination and electrical conductivity of seeds increased from 27.74% to 48.08% and from 18.72 to 40.47 μS cm-1 g-1, respectively. Increasing the moisture content of chickpea seeds from 10 to 25% causes a decrease in the amount of damage to the seeds in terms of electrical conductivity (from 38.40 to 21.18 μS cm-1 g-1), but increases the damage in the form of a loss in the percentage germination in the accelerated aging test (from 29.22% to 42.88%). To reduce the impact damage to peas caused by free fall, the height of the fall should be limited to about 6 m, and they should be prevented from hitting hard and rough surfaces.

Dynamic in situ measurement of axial segregation of E-CAT particles in a bubbling fluidized bed

The present paper summarizes comprehensive in situ measurements of the temporal segregation/mixing behavior of the non-spherical Geldart B and D E-CAT particles mixture in a bubbling fluidized bed. The experiments are performed for both unsieved and sieved E-CAT particles with varying particle size distribution width and at the fluidization velocity ranging from 1.3 to 5Umf. The high-speed pressure and image data were used to provide time-resolved quantification of dynamic expanded bed height and pressure drop during the experiment. In parallel, a hybrid machine learning-aided image processing algorithm has been developed for quantifying the instantaneous particle size distribution at varying axial locations. Results reveal that the segregation exists only at low fluidization velocities (1.3 and 1.6Umf) for unsieved cases with a wider size distribution. In contrast, particles with a narrower distribution exhibited well-mixed behavior for the full range of tested gas velocities. The segregation intensity and spatial extent were found to correlate with particle size distribution width and fluidization velocity, respectively. In addition, by analyzing pressure, expanded bed height, particle size and motion, and bubble characteristics, we provided a comprehensive multi-scale dynamic view of the segregation process. This in-depth understanding of the process, coupled with the time-resolved datasets obtained, can be instrumental for benchmarking numerical models in solid–gas multiphase flows and for optimizing the design of fluidized beds.

The maximum drop height of high-altitude parachuting based on dynamic and thermodynamic analysis

This paper explores the maximum possible initial height for skydiving, taking into account the physical and biological constraints of the sport. It develops the dynamic and thermodynamic models of the skydiver before and after deploying the parachute, and uses numerical methods to obtain the optimal parameters for safe landing. It also examines the thermal properties of the protective suit and the maximum heat it can endure. The paper demonstrates that the initial height does not affect the landing speed, and that the heat generated by the fall is within the tolerable range of the skydiver. The paper shows that the key factor for determining the maximum skydiving height is the thermal resistance of the protective material, rather than the conventional dynamic considerations. The paper concludes that the highest height that can be skydived is 45400 meters, the opening height is 3000 meters, and the landing speed is 6.32 m/s. This paper provides a novel perspective on the physics and engineering of skydiving.

Impact response of lightweight steel foam concrete composite slabs: Experimental, numerical and analytical studies.

This paper presents a study on the low-velocity impact response of lightweight steel foam concrete (LSFC) composite slabs. The LSFC composite slab consisted of a W-shaped steel plate, foam concrete and oriented strand board (OSB). Low-velocity impact tests on the LSFC composite slabs were conducted by employing an ultra-high heavy-duty drop hammer testing machine. The tests revealed the failure mode, impact force and displacement response of LSFC composite slabs. The effects of density and thickness of foam concrete and drop height on the peak impact force and energy absorption ratio were investigated. A finite element (FE) model was set up to predict the impact resistance of the LSFC composite slabs, and a good agreement between simulation and test results was achieved. In addition, an equivalent-single-degree-of-freedom (ESDOF) model was set up to predict the displacement response of the LSFC composite slabs under impact loading.

Intra-Day and Inter-Day Reliability and Usefulness of Performance, Kinetic and Kinematic Variables during Drop Jumping in Hurling Players

The aim of this study was to estimate the intra-day and inter-day reliability and usefulness of performance (Jump height (JH), ground contact time (GCT) and reactive strength index (RSI)), kinetic (force, power, eccentric rate of force development [E-RFD] and leg stiffness [LS]) and kinematic (velocity) variables during drop jumping (DJ) in hurling players. Seventeen (n = 17; mean ± SD; age = 23.35 ± 5.78 years, height = 178.35 ± 6.30 cm, body mass = 78.62 ± 8.06 kg) male club-level hurling players completed two maximal DJs from 0.20, 0.30, 0.40, 0.50 and 0.60 m drop heights on three testing days separated by 5–9 days of rest. Reliability was assessed using the coefficient of variation percentage (CV% ≤ 15%) and intraclass correlation coefficient (ICC &gt; 0.70). For intra-day reliability, GCT (0.40 m, 0.50 m and 0.60 m), peak force (absolute and relative) (0.40 m and 0.50 m) and leg stiffness (0.40 m and 0.50 m) were found to be unreliable (ICC = 0.32–0.68 and CV% = 3.67–11.83%) from those specific drop heights. All other variables were found to be reliable (ICC = 0.72–0.98 and CV% = 1.07–14.02%) intra-day. All variables were found to be reliable (ICC = 0.72–0.96 and CV% = 2.57–14.68%) inter-day except for relative peak force and absolute and relative eccentric RFD (0.30 m and 0.40 m) (ICC = 0.68–0.90 and CV% = 7.76–16.47%). Practitioners have multiple reliable DJ performance, kinetic and kinematic variables for performance testing and training purposes.

The Mechanism behind Vibration Assisted Fluidization of Cohesive Micro-Silica

Vibro-assisted fluidization of cohesive micro-silica has been studied by means of X-ray imaging, pressure drop measurements, and off-line determination of the agglomerate size. Pressure drop and bed height development could be explained by observable phenomena taking place in the bed; slugging, channeling, fluidization or densification. It was observed that channeling is the main cause of poor fluidization of the micro-silica, resulting in poor gas-solid contact and little internal mixing. Improvement in fluidization upon starting the mechanical vibration was achieved by disrupting the channels. Agglomerate sizes were found to not significantly change during experiments.

Apron and macro roughness as scour countermeasures downstream of block ramps

ABSTRACT A block ramp is a grade-control structure commonly used to stabilize the river bed with a high efficiency of energy dissipation. This study investigates the effects of using macro roughness and a downstream apron as scour countermeasures on the maximum scour depth downstream of block ramps in straight rivers. All the experiments have been carried out in a horizontal channel and in clear water conditions (no sediment transport). A wide range of hydraulic conditions including densimetric Froude numbers, water drop heights, and tailwater depths for three different rough ramp slopes (1 V:3 H, 1 V:5 H, and 1 V:7 H) was tested. The results have been compared with the results from a smooth ramp (no roughness), which has been considered as a reference. Results show that both macro roughness on the ramp and downstream aprons work well as scour countermeasures while as a comparison, using macro roughness (big-size stones) on the ramp is more effective than downstream aprons to reduce the scour depth. The other finding of this study shows that increasing the downstream apron decreases the length of the scour hole, consequently decreasing the volume of eroded material.

Experimental Study on Impact Friction Damage of Sweet Potato Skin

Sweet potato skin is prone to friction damage during mechanical harvesting. To reveal the friction damage mechanism of sweet potato skin, the impact friction process between a sweet potato and a rod was theoretically analyzed. The main factors affecting the impact friction force of the sweet potato skin include the sweet potato mass, drop height, distance from the center of the pendulum to the impact center of the sweet potato, maximum elastic displacement of the sweet potato, collision contact time, curvature radius of the sweet potato collision surface, material and roughness of the collision contact surface, etc. The mass, drop height, rod direction, rod state, and rod material of the sweet potato were used as the test factors, and the critical damage acceleration of the sweet potato skin was used as the test evaluation index. The results showed that the friction force caused by the collision between the sweet potato skin and rod increased with the increase in the sweet potato mass. The minimum friction is 3.5 N. The critical damage acceleration of the sweet potato skin decreased with the increase in the sweet potato mass, and the drop height had no significant effect on the critical damage acceleration of the sweet potato skin. Compared with the vertical placement, the critical damage acceleration of the sweet potato skin was smaller when the rod was placed horizontally, and the damage was more likely to occur. Under the same conditions, the critical damage acceleration of the sweet potato skin when the rod is rolling is greater than that when the rod is fixed. The critical damage acceleration of the impact friction between the sweet potato and 65Mn rod is the smallest, and the critical damage acceleration of the impact friction with the 65Mn–leather rod is the largest.

Optimal Drop Heights for Determining Reactive Strength Performance in Youth-Is 1 Drop Height Sufficient to Generate Trustworthy Conclusions for Training Practice?

This study critically examines the suitability of using a single drop height to assess the reaction strength index in trained and active participants, a key component of athletic performance. Using a cross-sectional design, 377 trained (n = 163) and active (n = 214) participants aged 14-18years performing drop jumps from 4 different heights (24, 32, 40, and 48cm) were studied. The primary aim was to explore the individual differences in reaction strength index at these heights and to assess whether a single height can reliably represent stretch-shortening cycle capabilities. While the repeated measures analysis of variance did not reveal any significant differences, the Bland-Altmann analysis revealed significant individual discrepancies between the performance of the drop heights, resulting in a mean absolute error of 32.1 and a mean absolute percentage error of 20.6%. These results strongly suggest that a single drop height is not sufficient to determine performance in the stretch-shortening cycle. This has important practical implications as it can lead to underestimates of performance trends. The study advocates the inclusion of a range of drop heights in routine testing to accurately measure reactive power and thus improve the effectiveness of individualized training programs for young athletes/active youth.

Nonlinear finite element analysis of steel fiber reinforced concrete beams subjected to impact loads

Steel fiber reinforced concrete, compared to the conventional concrete; is a composite building material that performs much better in terms of parameters such as ductility, energy absorption capacity, fracture toughness, fatigue resistance, and the use of steel fiber reinforced concrete (SFRC) in structures has become widespread. In this study, a nonlinear finite element model (FEM) has been developed that can represent the behavior of beams produced by using steel fiber concrete subjected to impact load. For this purpose, a finite element model of beam series produced with fiber-reinforced concrete obtained from the literature was created. The ABAQUS package program was used to create models simulating the behavior. Numerical results showed that the model could successfully capture the experimental results of beams selected from the literature. In addition to simulation, a parametric study was also performed to investigate the effect of stirrups, reinforcement ratio, and drop height on the behavior of SFRC beams under impact loads. The results of the parametric study showed that increasing the fiber ratio and reinforcement ratio positively affected the behavior of SFRC beams in terms of displacement recovery.Steel fiber reinforced concrete, compared to the conventional concrete; is a composite building material that performs much better in terms of parameters such as ductility, energy absorption capacity, fracture toughness, fatigue resistance, and the use of steel fiber reinforced concrete (SFRC) in structures has become widespread. In this study, a nonlinear finite element model (FEM) has been developed that can represent the behavior of beams produced by using steel fiber concrete subjected to impact load. For this purpose, a finite element model of beam series produced with fiber-reinforced concrete obtained from the literature was created. The ABAQUS package program was used to create models simulating the behavior. Numerical results showed that the model could successfully capture the experimental results of beams selected from the literature. In addition to simulation, a parametric study was also performed to investigate the effect of stirrups, reinforcement ratio, and drop height on the behavior of SFRC beams under impact loads. The results of the parametric study showed that increasing the fiber ratio and reinforcement ratio positively affected the behavior of SFRC beams in terms of displacement recovery.

Cavity flow characteristics of a curved hull section impacting a free surface with inclined postures

The water entry of structures is a complex gas–liquid flow. This paper studies the asymmetrical flow characteristics of a curved hull section entering water through numerical and experimental methods. The free-falling test from drop heights of 250–900 mm and inclination angles from 0° to 20° is carried out. Compared to a smooth hull section (cutting the bottom appendage), the experimental results observe some special asymmetrical flow phenomena (i.e., flow separation, jet impact, bubble flows, and bubble expansion). The physical mechanisms behind these flows are explained through combing the free surface flow and pressure distribution obtained by the numerical method. The effects of the inclination angle and impact velocities on these flow phenomena are further discussed, and they increase the degree of flow separation, bubble volume, and fragmentation. The load characteristics before and after cavity formation are analyzed based on a volume-of-fluid method. The high pressure caused by bubble closure can produce an instantaneous impulse pressure that even be 34% larger than the conventional impact pressure and is worth noting. This study clarifies some complex asymmetrical impact flow characteristics of curved hull sections and thus reveals the evolution mechanism of gas–liquid flows for complex geometries during oblique water entry.

Effect of Impactor's Taper Angle on the Response of a Square Slab to a Falling Mass

Reinforced concrete (RC) slabs during their service life experience falling mass impacts which are significantly different from quasi-static loading on account of short-term load transference and higher strain rate. Slab being a thin flexural member is prone to short-term dynamic loadings susceptible to irreparable damage or even collapse. Considerable research has been done with round impacting mass, however, the impacting mass needs not necessarily be round and may have a different geometry such as a rolling boulder or fragmented rock mass. To simulate the practical impacting geometries of the falling mass, eight different variations of the geometries varying from flat of 300mm diameter followed by 40mm flat with tapering from 90° to 0° in increments of 15° keeping the material characteristics and drop height of the falling mass constant across all the eight cases, have been considered herein to investigate the influence of impactor’s taper angle on the anti-impact response of the validated square slab in Abaqus Explicit package program. A comparison of several response parameters including displacement, damage, stress distribution, and plastic dissipation energy has been done with the validated model, and the geometries of the impactor causing the maximum and minimum damages are identified. A key finding from this study is that all considered impacting geometries lead to bond failure in the lower layer of the re-bars, however, the impactors having the geometry with taper angles below 45° possess the capacity to induce bond failure in the re-bars of the upper layer too, beyond the impacted region.

Effects of 10KM run on foot morphology and bilateral symmetry in male recreational runners.

Foot morphology and arch integrity do not remain constant during a running bout. Previous studies have reported inconsistent changes in foot sizes and arch parameters and this discrepancy may be related to the variation in their test duration, e.g., 15-min treadmill run vs. 30KM trial. Hence, this study sought to evaluate the change in foot morphology, arch integrity and bilateral symmetry after a 10KM run among 19 male recreational runners. Before and after the run, a portable foot scanner was used to capture the 3-dimensional foot images and measure foot dimensions in both weight-bearing and non-weight-bearing conditions. Foot arch integrity was quantified by arch height ratio, arch height index, and arch stiffness index (ASI). Bilateral symmetry was evaluated by calculating the symmetry index. Increased foot length (p = 0.007; = 0.18) and decreased ball girth (p = 0.038; = 0.11) were demonstrated following the run with absolute differences of less than 2mm. Navicular height, dorsum height, arch height ratio and arch height index significantly decreased after the run (p < 0.001; ≥0.30) whereas ASI increased (p < 0.001, = 0.33) and navicular height drop reduced (p < 0.001, = 0.37). Significances of symmetry index were only demonstrated for navicular height (p = 0.019, effect size = 0.37) and arch height ratio (p = 0.019, effect size = 0.42). A few changes in foot morphology were detected but a reduction in foot arch height was demonstrated, which may give shoe manufacturers insights into shoe design. Male recreational runners were recommended to choose shoes with arch support for maintaining foot arch function during a 10KM run.

Review of World Rugby’s Test Method 01 head injury criteria: Procedure analysis and optimisation

Rugby is a close-contact sport in which players occasionally fall headfirst to the ground during scrums and tackles. Because head impacts represent an obvious threat to players’ integrity and safety, World Rugby, Rugby’s International Governing Body, developed a test method named Test Method 01 to evaluate the capacity of the playing surface to mitigate head impacts by determining the critical fall height (CFH). The aim of this study is to analyse World Rugby’s current Test Method 01 head injury criteria (HIC), which consider a field as unsafe if the CFH is below 1.3 m. To make this analysis, a pilot study was performed on seven artificial turf rugby fields. At each field, a three-drop procedure was performed to estimate the initial CFH (CFH0). Subsequently, the procedure was repeated on each surface at 50-mm intervals, from 0.6 m below to 0.6 m above CFH0. All possible combinations of four height–HIC data pairs with two height values below and above 1000 HIC were obtained. A comparison was performed between the linear adjustment, currently prescribed in Test Method 01 to calculate the CFH0, and the quadratic adjustment. In particular, the percentage of outliers obtained when applying both the linear and quadratic adjustment and the robustness of the regressions were investigated. The results show that the current Test Method 01 can be improved by applying two main modifications: first, replacing the linear adjustment with a quadratic adjustment, and second, adapting the current test restrictions by maintaining the maximum difference between the highest and the lowest drop heights in 1.00 m, increasing the minimum difference between consecutive drop heights from 0.15 to 0.20 m and removing the current prohibition on obtaining HIC values close to 1000.

Enhanced anti-impact resistance of polyurethane foam composites with multi-phase shear thickening fluids containing various carbon nanofillers

Polyurethane (PU) foams are commonly used as impact-absorbing materials in various applications. However, the anti-impact performance of PU foams can be improved by incorporating non-Newtonian based smart fluids in their strudture. This study enhanced a open-cell based PU foam with multi-phase shear thickening fluids (M-STFs) containing three types of carbon nanofillers (carbon nanotubes, carbon nanofibers, and their mixture). M-STFs were prepared by adding 0.5, 1.0, 1.5, and 2.0 wt% of carbon nanofillers to the STF (55 wt% SiO2) and subsequently impregnating them into the structure of PU foams. Various configurations of PU foam composites were designed and evaluated for their impact resistance performance using a low-velocity drop tower system. The rheological behavior of fabricated suspensions were characterized using a rotational two plate-based system. The chemical structure and morphology of M-STF-treated PU foams were characterized by FTIR spectroscopy and SEM, respectively. The peak deceleration values in terms of G were measured after subjecting the designed samples to impacts at three different heights of 0.1, 0.2, and 0.3 m. The results indicated that the addition of nanofillers enhaced the initial and peak viscosity of the STF, and carbon nanotube had the most significant effect. The PUF-STF/CNT(1.5) sample exhibited approximately 62.7% to 73.0% reduction at different heights in peak deceleration compared to the clean PU foam sample. Moreover, to investigate the impact of filler content, drop height, and type of fillers on the peak deceleration of M-STF-treated PU foams, a response surface methodology analysis was utilized and the model provided insight into the optimal conditions for minimizing peak deceleration. This study highlights the potential of using M-STFs to enhance the anti-impact performance of PU foams.

Research on cracking and mechanical responses of semi-rigid base under falling weight impact

Disadvantages of semi-rigid materials bring a significant challenge to the maintenance of the semi-rigid base pavement. The micro-cracking treatment employs the falling weight to break the semi-rigid base into interlocking blocks to create a new base material to regenerate the old base. To study the micro-cracking mechanism, the cracking patterns and mechanical responses of the semi-rigid base under different types of falling weights and drop heights were obtained in field tests. The DEM-FDM coupling model was established to investigate the cracking distribution further. The results showed that as the impact contact area of the falling weight decreases, the depth of the groove progressively deepens, and the resilient modulus of the semi-rigid base decreases. Besides, the flat-bottomed falling weight produced the highest compressive stress, while the big convex points falling weight caused the most vertical displacement. Combined with simulation analysis, the flat-bottomed falling weight almost exclusively caused shear cracking on the contact edge. The small convex points falling weight mainly generated the shear cracking on the surface, and the big convex points falling weight induced more extensive tensile cracking within the semi-rigid base. Therefore, the big convex points falling weight is more recommended for micro-cracking treatment, which creates a greater cracking degree in semi-rigid base and is conducive to breaking the semi-rigid base into interlocking small blocks.

Development of alginate beads for precise environmental release applications: A design of experiment based approach and analysis

Controlled release of active ingredients are important for drug delivery and more recently environmental applications including modulated dosing of chemical and biological controls. This study demonstrates the importance of investigating various material science factors that can influence the diffusion rates of alginate beads to improve and tune their performance for marine environmental applications. This investigation aimed to design a rational workflow to aid in leveraging alginate bead use as a carrier matrix for releasing a specific active agent into water. Experiments were conducted to focus on the narrow a large list of relevant material formulation parameters, which included chitosan molecular weight, chitosan concentration, calcium concentration, drop height, and bead size. Once the most relevant material preparation methods were screened, a more robust statistic Design of Experiments approach was performed and results determined the important (and unimportant) factors for increasing dye release kinetics in marine water. The process was further streamlined by narrowing the critical experimental factors to a three-level based on the prior analysis: chitosan MW, chitosan concentration, and bead size. Analysis of the collected data indicated that while chitosan MW had a negligible impact (Fstatistic = 0.22), bead size (Fstatistic = 60.33) significantly influenced the diffusion rates based on surface area. However, chitosan MW had minor effects where lower chitosan MW enabled higher product release rates. This case investigation was a novel application of the design of experiment approach towards environmental applications to understand differences in release rates to marine waters for the first time and the workflow provided also serve as the basis for researchers to optimize other environmental applications requiring optimization when it is unknown how a large number of formulation variables will impact performance in different environmental scenarios.

İnce Kenarlı Savaklardaki Havalandırma Verimliliğinin Deneysel Olarak İncelenmesi: Debi Etkisi

In this experimental study, the aeration performance of weirs was investigated by means of the discharge effect. For this purpose, experiments were performed at a 90º V-notch weir with drop heights ranging from 0.35-0.535 m and unit discharges ranging from 3x10-2 to 6.33x10-2 m2/s and E20 varied in the range of 0.13-0.23. A positive correlation was found between the unit discharge and aeration efficiency and the resulting relationship was defined by a power function in terms of drop height and unit discharge. It was found that aeration efficiency is in proportion to the 3/4 power of drop height and 1/3 power of unit discharge. The proposed empirical formula prediction capacity has been compared with the other empirical formulas in terms of their average relative error values. Additionally, by assuming a drop height equal to head loss, it was observed that hydraulic jump aeration efficiency dependence on head loss continued for weirs indicating the free-surface macro turbulence's main role in the process.

Высота микро- и нанокапли в модели, учитывающей толщину поверхностного слоя капли

A hanging drop of a fixed volume with axial symmetry is considered. The forming line of drop surface depends on a natural parameter. The B.V. Deryagin&amp;#x27;s model is used taking into account the interphase transition from liquid to gas. The total energy functional is used which takes into account the wedging energy of the surface layer component of the second order of smallness in the decomposition of the potential energy of the drop over the dimensionless width of the potential well. It is found the equation of the dependence of the drop height on the radius of the sticking spot. The value of the Lagrange multiplier is determined, at which an equilibrium drop is found among hanging drops of a fixed volume, a fixed area of adhesion to a horizontal surface and the wetting angle determined by Young&amp;#x27;s formula. A comparison with other models determining the relationship between the height of the drop, the radius of the spot of adhesion of the drop and the wetting angle is carried out.