Theoretical Velocity Research Articles

Force-velocity relationship profile of elbow flexors in male gymnasts.

BackgroundThe theoretical maximum force (F0), velocity (V0), and power (Pmax) of athletes calculated from the relationship between force and velocity (F-V relationship) and the slope of the F-V relationship, reflect their competitive and training activity profiles. Evaluating the F-V relationship of athletes facilitates categorizing the profiles of dynamic muscle functions in relation to long-term sport-specific training. For gymnastics, however, no studies have tried to examine the profiles of F-V relation and power output for upper limb muscles in relation to the muscularity, while the use of the upper extremities in this sport is very unique as described earlier.PurposeIt was hypothesized that the F-V relationship of the elbow flexion in gymnasts might be characterized by low capacity for generating explosive force, notably in terms of the force normalized to muscle size.MethodsThe F0, V0, and Pmax derived from the force-velocity relationship during explosive elbow flexion against six different loads (unloaded condition, 15, 30, 45, 60, and 75% of maximal voluntary isometric elbow flexion force (MVFEF)) for 16 gymnasts (GYM) and 22 judo athletes (JD). F0 and Pmax were expressed as values relative to the cross-sectional area index (CSAindex) of elbow flexors (F0/CSAindex and Pmax/CSAindex, respectively), which was calculated from muscle thickness in the anterior upper arm. The electromyogram (EMG) activities of the biceps brachii (BB) during the maximal isometric and dynamic tasks were also determined.ResultsThere were no significant differences in CSAindex of elbow flexors between GYM and JD. MVFEF/CSAindex for GYM was significantly lower than that for JD. Force was linearly associated with velocity in the dynamic elbow flexion for all the participants (r = − 0.997 to −0.905 for GYM, r = − 0.998 to −0.840 for JD). F0, F0/ CSAindex, V0, Pmax, Pmax/CSAindex, and MVFEF were significantly lower in GYM than in JD. The activity levels of BB during the dynamic tasks tended to be lower in GYM than in JD at load of <45%MVC.ConclusionGymnasts cannot generate explosive elbow flexion force corresponding to their muscle size. This may be due to low neuromuscular activities during the maximal dynamic tasks against relatively low loads.

A beamforming-based joint estimation method for gas pipeline leak localization

This paper proposes a beamforming-based joint estimation method to improve the accuracy and robustness of the localization method that measures acoustic signals caused by gas pipeline leaks. The anti-interference capability of the new method is enhanced with the help of spatial filtering using a beamforming algorithm and a linear array. Joint estimations for leak locations and wave velocities allow the new method to ignore the requests for prior knowledge of wave velocity. The mean absolute percentage error (MAPE) of the joint estimation method using a seven-sensor linear array was reduced by 68.7% and 53.7% compared to the MAPEs of the cross-correlation method, which used the theoretical velocity of 1800 m/s and the velocity estimated through the new method, respectively. The tests also indicate that the joint estimation method has better anti-interference capabilities, of which the MAPEs remained less than 3% in the SNR range from −15 dB to 0 dB.

Sprint performance and force-velocity profiling does not differ between artificial turf and concrete

Purpose Force-velocity-power (F-v-P) profiling can illustrate an individual’s sprinting capabilities, but no study has explored the effect of different running surfaces on F-v-P outcomes. Method Twelve elite youth football players (age 16.3 ± 0.5 years, mass 67.3 ± 5.4 kg, height 176.2 ± 4.6 cm) performed two 30 m sprints on concrete and artificial turf in a randomised order on two testing days. Differences between surfaces were determined using repeated-measures ANOVA (P &lt; 0.05), whilst the coefficient of variation (CV), smallest worthwhile change and standard error of measurement were calculated to quantify reliability. Results No significant differences were found between surfaces over the average of two days. High reliability was evident for 30 m sprint time, theoretical maximum horizontal velocity and ratio of force on both surfaces (CV≤∼5%), while the remaining outputs were not reliable (CV &gt;10%). Conclusion These findings show that F-v-P profiling does not differ between concrete and artificial turf. However, higher variability on the more unfamiliar concrete surface suggests that the testing surface should match the playing surface. Since the standard error of measurement is larger than the smallest worthwhile change, the ability of this method to monitor seasonal changes may be limited in youth elite soccer players.

The Relationship Between Selected Load-Velocity Profile Parameters and 50 m Front Crawl Swimming Performance.

The purpose of the present study was to establish relationships between sprint front crawl performance and a swimming load-velocity profile. Fourteen male national-level swimmers performed 50 m front crawl and semi-tethered swimming with three progressive loads. The 50 m performance was recorded with a multi-camera system, with which two-dimensional head displacement and the beginning of each arm-stroke motion were quantified. Forward velocity (V50m), stroke length (SL) and frequency (SF) were quantified for each cycle, and the mean value of all cycles, excluding the first and last cycles, was used for the analysis. From the semi-tethered swimming test, the mean velocity during three stroke cycles in mid-pool was calculated and plotted as a function of the external load, and a linear regression line expressing the relationship between the load and velocity was established for each swimmer. The intercepts between the established line and the axes of the plot were defined as theoretical maximum velocity (V0) and load (L0). Large to very large correlations were observed between V50m and all variables derived from the load-velocity profiling; L0 (R = 0.632, p = 0.015), L0 normalized by body mass (R = 0.743, p = 0.002), V0 (R = 0.698, p = 0.006), and the slope (R = 0.541, p < 0.046). No significant relationships of SL and SL with V50m and the load-velocity variables were observed, suggesting that each swimmer has his own strategy to achieve the highest swimming velocity. The findings suggest that load-velocity profiling can be used to assess swimming-specific strength and velocity capabilities related to sprint front crawl performance.

Vertical Force-velocity Profiling and Relationship to Sprinting in Elite Female Soccer Players.

Explosive actions are integral to soccer performance and highly influenced by the ability to generate maximal power. The purpose of this study was to investigate the relationship between force-velocity profile, jump performance, acceleration and maximal sprint speed in elite female soccer players. Thirty-nine international female soccer players (24.3±4.7 years) performed 40-m sprints, maximal countermovement jumps and five loaded squat jumps at increasing loads to determine individual force-velocity profiles. Theoretical maximal velocity, theoretical maximal force, maximal power output, one repetition maximal back squat and one repetition maximal back squat relative to body mass were determined using the force-velocity profile. Counter movement jump, squat jump and maximal power output demonstrated moderate to large correlation with acceleration and maximal sprint speed (r=- 0.32 to -0.44 and -0.32 to -0.67 respectively, p<0.05). Theoretical maximal velocity and force, one repetition maximal and relative back squat demonstrated a trivial to small relationship to acceleration and maximal sprint speed (p>0.05). Vertical force-velocity profiling and maximal strength can provide valuable insight into the neuromuscular qualities of an athlete to individualize training, but the ability to produce force, maximal power, and further transference into sprint performance, must be central to program design.

Effects of Power-Oriented Resistance Training During an Altitude Camp on Strength and Technical Performance of Elite Judokas.

This study investigated the effect of a 3-week power-oriented resistance training program performed at moderate altitude on leg power output variables in a countermovement jump, a related judo technique (ippon-seoi-nage) and the relationship between them. Twenty-four elite male judokas were randomly assigned to a hypobaric hypoxia or normoxia group. Mechanical outputs from an incremental loaded countermovement jump test and the kinematic variables transferred to a dummy during an ippon-seoi-nage test (time to execution and movement accelerations) were assessed before, after, 1 and 2 weeks after training. Results indicated an increase in explosive leg capacity both at moderate altitude (2320 m.a.s.l.) and sea level. The hypoxia group showed additional benefits when compared to normoxia group for peak velocities with different percentages of the body weight, maximal theoretical velocity and jump height after the training period, and these additional benefits in jump height were maintained 2 weeks after training. The hypoxia group achieved a higher peak performance in peak velocity and jump height than normoxia group (peak velocity: 8.8 vs. 5.6%, jump height: 8.2 vs. 1.4%, respectively) and was achieved earlier in hypoxia (after training) than in normoxia (1 week after training). However, there was a detrimental effect for the hypoxia group on the times of execution and acceleration of the ippon-seoi-nage compared to the normoxia group. These results suggest that altitude training may induce faster and greater improvements in explosive leg extension capacity. Specific technique-oriented training should be included at altitude to prevent technique impairment.

Influence of age and maturation status on sprint acceleration characteristics in junior Australian football

ABSTRACT This study aimed to investigate the influence of chronological age and maturation status on sprint acceleration characteristics in junior Australian football (AF) players. Biological maturity of 109 subjects was assessed and subjects were grouped according to predicted years from peak height velocity (PHV) (pre-, mid-, and post-PHV) and chronological age (13 years, 14 years, and 15 years). A one-way multivariate analysis of variance and magnitude-based decisions were used to determine between-group differences. Instantaneous velocity was measured during two maximal 30m sprints via radar gun with the velocity-time data used to derive the force, velocity, and power characteristics. Chronologically, the greatest differences were observed between the 13 and 14 year old groups with the latter group producing likely greater relative maximum power (Pmax) (ES[effect size]=0.44) and theoretical maximal velocity (V0) (ES=0.49). The post-PHV group likely demonstrated a greater ability to apply force at faster velocity (V0; ES=0.59) and orient the force in a horizontal direction (Drf%; ES=-0.49) than the mid-PHV group. No differences in relative theoretical maximal force (F0) were observed between groups. Considering the findings, practitioners should aim to improve relative lower limb strength through heavy sled push or sled pulls and traditional strength training exercises to improve relative F0.

Hamstring Muscle Volume as an Indicator of Sprint Performance.

Nuell, S, Illera-Domínguez, V, Carmona, G, Macadam, P, Lloret, M, Padullés, JM, Alomar, X, and Cadefau, JA. Hamstring muscle volume as an indicator of sprint performance. J Strength Cond Res 35(4): 902-909, 2021-This study aimed to compare mechanical properties and performance during sprinting, as well as thigh muscle volumes (MVs), between national-level sprinters and physically active males. In addition, the relationships between thigh MVs and sprint mechanical properties and performance were investigated. Seven male sprinters and 9 actives performed maximal-effort 40-m sprints. Instantaneous velocity was measured by radar to obtain theoretical maximum force (F0), the theoretical maximum velocity (V0), and the maximum power (Pmax). For MV assessment, series of cross-sectional images of each subject's thigh were obtained by magnetic resonance imaging for each of the quadriceps and hamstring muscles and the adductor muscle group. Sprinters were faster over 10 m (7%, effect size [ES] = 2.12, p < 0.01) and 40 m (11%, ES = 3.68, p < 0.01), with significantly higher V0 (20%, ES = 4.53, p < 0.01) and Pmax (28%, ES = 3.04, p < 0.01). Sprinters had larger quadriceps (14%, ES = 1.12, p < 0.05), adductors (23%, ES = 1.33, p < 0.05), and hamstrings (32%, ES = 2.11, p < 0.01) MVs than actives. Hamstrings MV correlated strongly with 40-m sprint time (r = -0.670, p < 0.01) and V0 (r = 0.757, p < 0.01), and moderately with Pmax (r = 0.559, p < 0.05). Sprinters were significantly faster and had greater V0 and Pmax than active males. Larger MVs were found in sprinters' thighs, especially in the hamstring musculature, and strong correlations were found between hamstring MV and sprint mechanical properties and sprint performance.

A dual‐frequency continuous wave doppler lidar for velocity measurement at far distance

AbstractA dual‐frequency continuous wave Doppler lidar for long‐distance and high‐precision velocity measurement is experimentally demonstrated in this article. The lidar system uses the optical heterodyne detection method to avoid complicated optical coherent configuration. All Phase Fast Fourier Transform and Chirp‐Z Transform are used to obtain the Doppler frequency shift. The maximum of the calculated Doppler shift was 999.83 Hz with the frequency resolution of 0.54 Hz, and the corresponding theoretical velocity was determined to be 749.87 m/s. During the experiment, the speed of the car was successfully measured in the outdoor environment, the frequency and velocity resolutions were less than 0.5 Hz and ± 0.2 m/s, respectively, and the detection distance of moving and stationary targets reached 1100 m and 2300 m. The capability of the dual‐frequency Doppler lidar system has been verified.

Full characterisation of knee extensors' function in ageing: effect of sex and obesity.

Muscle function is a marker of current and prospective health/independence throughout life. The effects of sex and obesity (OB) on the loss of muscle function in ageing remain unresolved, with important implications for the diagnosis/monitoring of sarcopenia. To characterise in vivo knee extensors' function, we compared muscles torque and power with isometric and isokinetic tests in older men (M) and women (W), with normal range (NW) of body mass index (BMI) and OB. In 70 sedentary older M and W (69 ± 5 years), NW and OB (i.e. BMI < 30 kg m-2 and ≥30 kg m-2, respectively) we tested the right knee's extensor: (i) isometric torque at 30°, 60°, 75° and 90° knee angles, and (ii) isokinetic concentric torque at 60, 90, 150, 180 and 210° s-1 angular speeds. Maximal isometric T-angle, maximal isokinetic knee-extensor torque-velocity, theoretical maximal shortening velocity, maximal power, optimal torque and velocity were determined in absolute units, normalised by body mass (BM) and right leg lean mass (LLMR) and compared over sex, BMI categories and angle or angular speeds by three-way ANOVA. In absolute units, relative to BM and LLMR, sex differences were found in favour of M for all parameters of muscle function (main effect for sex, p < 0.05). OB did not affect either absolute or relative to LLMR isometric and isokinetic muscle function (main effect for BMI, p > 0.05); however, muscle function indices, when adjusted for BM, were lower in both M and W with OB compared to NW counterparts (p < 0.05). We confirmed sex differences in absolute, relative to BM and LLMR muscle function in favour of men. While overall muscle function and muscle contractile quality is conserved in individuals with class I OB, muscle function normalised for BM, which defines the ability to perform independently and safely the activities of daily living, is impaired in comparison with physiological ageing.

Relationships between Lower Limb Muscle Characteristics and Force-Velocity Profiles Derived during Sprinting and Jumping.

This study aimed to identify the relationships between lower limb muscle characteristics and mechanical variables derived from the vertical (jumping) and horizontal (sprinting) force-velocity-power (FVP) profiles. Nineteen subelite male rugby league players performed a series of squat jumps and linear 30-m sprints to derive the vertical and horizontal FVP profiles, respectively. The theoretical maximal force (F0), velocity (V0), and power (Pmax) were derived from both the vertical (i.e., vF0, vV0, and vPmax) and the horizontal (i.e., hF0, hV0, and hPmax) FVP profiles. Vastus lateralis (VL), biceps femoris long head, and gastrocnemius medialis (GM) and lateralis muscle fascicle length, pennation angle, and thickness were measured using B-mode ultrasonography. Magnetic resonance imaging was used to calculate volumes of major lower limb muscles, whereas proton magnetic resonance spectroscopy was used to quantify the carnosine content of the GM to estimate muscle fiber typology. Variation in vPmax was best explained by GM muscle fiber typology (i.e., greater estimated proportion of Type II fibers) and VL volume (adjusted r2 = 0.440, P = 0.006), whereas adductor and vastus medialis volume and GM muscle fiber typology explained the most variation in hPmax (adjusted r2 = 0.634, P = 0.032). Rectus femoris and VL volume explained variation in vF0 (r2 = 0.430, P = 0.008), whereas adductor and vastus medialis volume explained variation in hF0 (r2 = 0.432, P = 0.007). Variations in vV0 and hV0 were best explained by GM muscle fiber typology (adjusted r2 = 0.580, P < 0.001) and GM muscle fiber typology and biceps femoris short head volume (adjusted r2 = 0.590, P < 0.001), respectively. Muscle fiber typology and muscle volume are strong determinants of maximal muscle power in jumping and sprinting by influencing the velocity- and force-oriented mechanical variables.

Intraday and Inter-day Reliability of Sprinting Kinetics in Young Female Athletes Measured Using a Radar Gun

ABSTRACT The radar gun is a valid and practically feasible tool to measure sprinting speed and kinetics among athletes. However, its reliability in youth populations, particularly females, is unknown. Therefore, this study aimed to evaluate the intraday and inter-day reliability of sprinting kinetics using a radar gun to measure force (Fo), theoretical velocity (Vo), maximal velocity (Vmax), power max (Pmax) and split times (0–30 m) in young female athletes. Twenty-nine young female athletes aged 13.7 0.89 years (height 1.62 0.06 m; weight 51.7 8.41 kg) from sports teams at a private girl’s college participated. The assessment included four sprints over 30 m (separated by 7 days) for inter-day analysis and two sprints over 30 m on the same day for intraday analysis. Moderate to strong intraclass correlation coefficient 0.74 to 0.98 with a coefficient of variation ranging from 1.70% to 12.70% across all kinetic variables were reported for both intraday and inter-day reliability. The smallest worthwhile change ranged from 1.17% to 6.89%. All tests were identified as having acceptable reliability.

Determination of ASI and THIV parameters based on the results of experimental and numerical research in relation to EU standards

Determining the values of ASI (Acceleration Severity Index) and THIV (Theoretical Head Impact Velocity) parameters during tests allows you to assign an appropriate class for a given type of object to determine the safety level and to give the CE marking. The paper presents the methodology for determining these parameters based on the EN 1317-1 and EN 12767 standards. The paper also presents a tool created with the use of the Python programming language, which, based on the results of experimental tests or the results of numerical calculations, allows to determine the ASI and THIV values. The values of key parameters from the point of view of normative tests were calculated based on the results of experimental tests of the road sign supporting mast and numerical analysis carried out for the same case using the Finite Element Method and LS-Dyna software, following the EN 12767 standard.

PIV measurements using refraction at a solid–fluid interface

Laser light sheet refraction at the fluid flow–window interface is proposed to perform fluorescent particle image velocimetry (PIV) measurements, in particular for cases in which optical access limits the possibilities of illuminating a flow with a planar collimated light sheet. The study of laser sheet propagation in the present measurement method is led by ray tracing to quantify the illumination intensity. To describe the limitations of this developed PIV version (refracted PIV (R-PIV)), we proposed a cross-correlation model (CCM) for analyzing image pairs that is an extension of the models used in the cases of µ-PIV or planar PIV (P-PIV) techniques. This CCM accounts for the R-PIV optical constraints of (1) in-depth and longitudinal inhomogeneities of the light sheet refraction at the location of the object plane or (2) integration in depth of the fluorescence from seeding particles. This R-PIV and the P-PIV techniques are further compared in the case of an academic pipe flow for which the analytic solution is known. Our extended CCM function is finally applied, given the theoretical flow velocity, the flow illumination and the seeding flow parameters, to analyze error levels in determining the real flow velocity field.

Propagation characteristic of axial and circumferential interface waves and detection of the interlaminar defect in multilayered pipes

This paper focuses on the dispersion characteristic of interface waves and the detection of interlaminar defects in multilayered pipes. The interface waves propagating along axial and circumferential directions are simplified as strain problems of planes (r, z) and (r, θ), respectively. The axial interface wave is well suited to axial localization of the defect, just as the circumferential interface wave is to circumferential localization. The dispersion curves and wave structures in generalized forms are built based on double- and treble-layered examples. Both interface waves converge to the Stoneley wave velocity at high frequency, while energy is concentrated on the interface. An experimental system is built. Theoretical and experimental group velocities are compared. The results indicate that the average relative errors of these two interface waves are 0.47% and 0.53%, respectively. An interlaminar crack is detected effectively both in axial and circumferential directions, revealing that interface waves hold great potential for non-destructive evaluation.

The Effect of Different Cathode Configurations of the Plasma Cell on the Ion Velocity Distribution Function

The ion velocity distribution in a plasma source was investigated through a comparison between two different configurations of the cathode of the plasma cell, namely, the one mesh system electrodes (OMSE), and the one mesh and three system electrodes (OMTSE). The velocity ranged from 1 to 3.5 km/s for OMSE and from 4 to 22 km/s for OMTSE. The comparison between the experimental and theoretical ion velocity distribution function (IVDF) of OMSE and OMTSE under the same applied conditions shows a better agreement for OMSE than for OMTSE due to the difference in plasma cell construction, cathode mesh wire configuration, and cathode edge. Even though the velocity and density of ions for the OMTSE reactor are higher than those for the OMSE reactor, the OMSE reactor was found to be the best system to avoid dusty plasma defects through the etching process.

Low-Frequency Distributed Acoustic Sensing for Early Gas Detection in a Wellbore

An unexpected and unwanted influx of gas or “kick” into the wellbore during hydrocarbon drilling can cause catastrophic blowout incidents, resulting in human casualties, ecological damage, and asset losses. The ability of the oil and gas industry to control gas kick depends on our ability to accurately detect and monitor gas migration in a borehole in real-time. This study demonstrates the application of optical fiber-based Distributed Acoustic Sensors (DAS) for early detection and monitoring of gas in wellbore. Multiphase flow experiments conducted in a 5000 ft. deep test-well are analyzed for different injection, circulation, and pressure conditions. In each case, the low-frequency component of DAS demonstrates a superior capability to detect gas signatures both inside the tubing and the annulus of the well, even at small gas volumes. In comparison, the high-frequency DAS data seems limited in detail. The gas influx velocity was calculated using the frequency-wavenumber analysis of the gradient of the low-frequency DAS phase with respect to time, which shows good agreement with theoretical velocity estimates using flow models and surface gauge measurements. This study demonstrates a novel workflow to analyze low-frequency DAS to qualitatively and quantitatively map gas influx in a wellbore.

Application of 3D energetic metal-organic frameworks containing Cu as the combustion catalyst to composite solid propellant

Abstract Using traditional metallic combustion catalysts in composite solid propellant (CSP) can lead to sharp energy losses of CSP due to the non-energetic properties of the catalysts. In the current study, the energetic ligands based 3D [Cu(atrz)3(NO3)2]n metal-organic frameworks (MOF(Cu)) were first used as the combustion catalysts to study their effects on the performance of CSP. It was found that the variation of MOF(Cu) content in the range of 0–5% had no significant effects on the theoretical specific impulse (Isp) and characteristic velocity (C*) of CSP. MOF(Cu) reduced the high decomposition temperature of AP to 344 °C and the complete decomposition temperature of CSP to 358 °C. It also decreased the thermal decomposition activation energy of CSP from 74.1 kJ mol−1 to 63.3 kJ mol−1. The CSP containing MOF(Cu) exhibits higher burning rates, particular flame structure and lower pressure index, as compared with that with CuO as the catalyst. The mechanical sensitivity test results reveal that MOF(Cu) can reduce the friction sensitivity and impact sensitivity of CSP from 40% and 39.4 cm to 32% and 63.5 cm, respectively. The current study is promising to develop a new kind of energetic combustion catalysts for CSP.

Determining strength training needs using the force-velocity profile of elite female handball and volleyball players

The aim of this study was to assess the vertical jump performance and the force-velocity profile of elite female handball and volleyball players. Forty-one female athletes were measured, 28 handball players (age: 24.0 ± 3.6 years, body height: 1.75 ± 0.05 m, body mass: 69.0 ± 7.3 kg) and 13 volleyball players (age: 24.1 ± 5.2 years, body height: 1.83 ± 0.07 m and body mass: 74.9 ± 7.9 kg). All players performed unloaded and loaded countermovement jumps (CMJ) on a force platform. The theoretical maximal force ( F0), the theoretical maximum velocity ( v0), the theoretical maximal power ( Pmax), the slope of the F-v relationship ( Sfv) and the force-velocity imbalance ( FVimb) were calculated. Mean value of vertical jump height was 0.33 ± 0.03m, with no difference between handball and volleyball players. Mean values of F0, v0, Pmax, Sfv and FVimb for all players were 31.2 ± 2.6 N/kg, 3.10 ± 0.50 m·s−1, 24.2 ± 3.2 w/kg, -10.32 ± 2.09 Ns/m/kg and 28.1 ± 13.3% respectively. Two players had a low magnitude velocity-deficit, whereas most of the players exhibited a low to high force-deficit. A strong correlation was found between the ratio of measured to optimal F-v slope with the change in the proportion of net force to total force during unloaded and loaded conditions. The findings suggest that it would be beneficial for these athletes to first decrease their force deficit through mainly maximal strength training before implementing training to further maximize power output. Establishment of the F-v profile could be a useful diagnostic tool for coaches to optimize strength training and to design training intervention based on the individual need of each athlete.

Love-Wave Phase-Velocity Estimation from Array-Based Rotational Motion Microtremor

ABSTRACTThe most popular array-based microtremor survey methods estimate velocity structures from the phase velocities of Rayleigh waves. Using the phase velocity of Love waves improves the resolution of inverted velocity models. In this study, we present a method to estimate the phase velocity of Love waves using rotational array data derived from the horizontal component of microtremors observed using an ordinal nested triangular array. We obtained discretized spatial derivatives from a first-order Taylor series expansion to calculate rotational motions from observed array seismograms. Rotational motions were obtained from a triangular subarray consisting of three receivers using discretized spatial derivatives. Four rotational-motion time histories were calculated from different triangular subarrays in the nested triangular arrays. Phase velocities were estimated from the array of the four rotational motions. We applied the proposed Love-wave phase-velocity estimation technique to observed array microtremor data obtained using a nested triangular array with radii of 25 and 50 m located at the Institute for Integrated Radiation and Nuclear Science, Kyoto University. The phase velocities of rotational and vertical motions were estimated from the observed data, and results showed that the former were smaller than those of the latter. The observed phase velocities obtained from vertical and rotational components agreed well with the theoretical Rayleigh- and Love-wave phase velocities calculated from the velocity structure model derived from nearby PS logs. To show the ability of the rotation to obtain Love wave, we estimated apparent phase velocities from north–south or east–west components. The apparent velocities resulted in between the theoretical velocities of Rayleigh and Love waves. This result indicates that the calculated rotation effectively derived the Love waves from a combination of Love and Rayleigh waves.