Martinez-Valencia, M.A., Linthorne, N.P. and Alcaraz, P.E. (2013).
Effect of lower body explosive power on sprint time in a sled-towing exercise.
Science and Sports, In press.
Introduction: This study investigated the correlation between lower body explosive power and the rate of increase in sprint time with increasing sled weight in a sled-towing exercise.
Synthesis of the facts: Eight male sprinters performed tests of lower body explosive power.
The rate of increase in sprint time showed a strong correlation with countermovement jump height (r = –0.73) and with normalized peak power in a countermovement jump (r = –0.81) and a squat jump (r = –0.80).
Conclusion: Inter-athlete differences in the rate of increase in sprint time might be due to differences in the athlete’s power-to-weight ratio.
Linthorne, N.P. (2013).
A mathematical modelling study of an athlete’s sprint time when towing a weighted sled.
Sports Engineering, 16 (2), 61–70.
This study used a mathematical model to examine the effects of the sled, the running surface, and the athlete on sprint time when towing a weighted sled.
Simulations showed that ratio scaling is an appropriate method of normalising the weight of the sled for athletes of different body size.
The relationship between sprint time and the weight of the sled was almost linear, as long as the sled was not excessively heavy.
The athlete’s sprint time and rate of increase in sprint time were greater on running surfaces with a greater coefficient of friction, and on any given running surface an athlete with a greater power-to-weight ratio had a lower rate of increase in sprint time.
The angle of the tow cord did not have a substantial effect on an athlete’s sprint time.
This greater understanding should help coaches set the training intensity experienced by an athlete when performing a sled-towing exercise.
Linthorne, N.P. and Cooper, J.E. (2013).
Effect of the coefficient of friction of a running surface on sprint time in a sled-towing exercise.
Sports Biomechanics, 12 (2), 175–185.
This study investigated the effect of the coefficient of friction of a running surface on an athlete’s sprint time in a sled-towing exercise.
The coefficients of friction of four common sports surfaces (a synthetic athletics track, a natural grass rugby pitch, a 3G football pitch, and an artificial grass hockey pitch) were determined from the force required to tow a weighted sled across the surface.
Timing gates were then used to measure the 30-m sprint time for six rugby players when towing a sled of varied weight across the surfaces.
There were substantial differences between the coefficients of friction for the four surfaces (m = 0.21–0.58), and in the sled-towing exercise the athlete’s 30-m sprint time increased linearly with increasing sled weight.
The hockey pitch (which had the lowest coefficient of friction) produced a substantially lower rate of increase in 30-m sprint time, but there were no significant differences between the other surfaces.
The results indicate that although an athlete’s sprint time in a sled-towing exercise is affected by the coefficient of friction of the surface, the relationship between the athlete’s rate of increase in 30-m sprint time and the coefficient of friction is more complex than expected.
Linthorne, N.P. and Weetman, A.H.G. (2012).
Effect of run-up velocity on performance, kinematics, and energy exchanges in the pole vault.
Journal of Sports Science and Medicine, 11 (2), 245-254.
This study examined the effect of run-up velocity on the peak height achieved by the athlete in the pole vault and on the corresponding changes in the athlete’s kinematics and energy exchanges.
Seventeen jumps by an experienced male pole vaulter were video recorded in the sagittal plane and a wide range of run-up velocities (4.5–8.5 m/s) was obtained by setting the length of the athlete’s run-up (2–16 steps).
A selection of performance variables, kinematic variables, energy variables, and pole variables were calculated from the digitized video data.
We found that the athlete’s peak height increased linearly at a rate of 0.54 m per 1 m/s increase in run-up velocity and this increase was achieved through a combination of a greater grip height and a greater push height.
At the athlete’s competition run-up velocity (8.4 m/s) about one third of the rate of increase in peak height arose from an increase in grip height and about two thirds arose from an increase in push height.
Across the range of run-up velocities examined here the athlete always performed the basic actions of running, planting, jumping, and inverting on the pole.
However, he made minor systematic changes to his jumping kinematics, vaulting kinematics, and selection of pole characteristics as the run-up velocity increased.
The increase in run-up velocity and changes in the athlete’s vaulting kinematics resulted in substantial changes to the magnitudes of the energy exchanges during the vault.
A faster run-up produced a greater loss of energy during the take-off, but this loss was not sufficient to negate the increase in run-up velocity and the increase in work done by the athlete during the pole support phase.
The athlete therefore always had a net energy gain during the vault.
However, the magnitude of this gain decreased slightly as run-up velocity increased.
Alcaraz, P.E., Palao, J.M., Elvira, J.L.L. and Linthorne, N.P. (2011).
Effects of a sand running surface on the kinematics of sprinting at maximum velocity.
Biology of Sport, 28 (2), 95-100.
Performing sprints on a sand surface is a common training method for improving sprint-specific strength.
For maximum specificity of training the athlete’s movement patterns during the training exercise should closely resemble those used when performing the sport.
The aim of this study was to compare the kinematics of sprinting at maximum velocity on a dry sand surface to the kinematics of sprinting on an athletics track.
Five men and five women participated in the study, and flying sprints over 30 m were recorded by video and digitized using biomechanical analysis software.
We found that sprinting on a sand surface was substantially different to sprinting on an athletics track. When sprinting on sand the athletes tended to ‘sit’ during the ground contact phase of the stride.
This action was characterized by a lower center of mass, a greater forward lean in the trunk, and an incomplete extension of the hip joint at take-off.
We conclude that sprinting on a dry sand surface may not be an appropriate method for training the maximum velocity phase in sprinting. Although this training method exerts a substantial overload on the athlete, as indicated by reductions in running velocity and stride length, it also induces detrimental changes to the athlete’s running technique which may transfer to competition sprinting.
Linthorne, N.P. and Patel, D.S. (2011).
Optimum projection angle for attaining maximum distance in a soccer punt kick.
Journal of Sports Science and Medicine, 10 (1), 203-214.
To produce the greatest horizontal distance in a punt kick the ball must be projected at an appropriate angle.
Here, we investigated the optimum projection angle that maximises the distance attained in a punt kick by a soccer goalkeeper.
Two male players performed many maximum-effort kicks using projection angles of between 10º and 90º. The kicks were recorded by a video camera at 100 Hz and a 2-D biomechanical analysis was conducted to obtain measures of the projection velocity, projection angle, projection height, ball spin rate, and foot velocity at impact.
The player’s optimum projection angle was calculated by substituting mathematical equations for the relationships between the projection variables into the equations for the aerodynamic flight of a soccer ball.
The calculated optimum projection angles were in agreement with the player’s preferred projection angles (40º and 44º).
In projectile sports even a small dependence of projection velocity on projection angle is sufficient to produce a substantial shift in the optimum projection angle away from 45º.
In the punt kicks studied here, the optimum projection angle was close to 45º because the projection velocity of the ball remained almost constant across all projection angles.
This result is in contrast to throwing and jumping for maximum distance, where the projection velocity the athlete is able to achieve decreases substantially with increasing projection angle and so the optimum projection angle is well below 45º.
Alcaraz, P.E., Palao, J.M., Elvira, J.L.L. and Linthorne, N.P. (2008).
Effects of three types of resisted sprint training devices on the kinematics of sprinting at maximum velocity.
Journal of Strength and Conditioning Research, 23 (3), 880-897.
Resisted sprint running is a common training method for improving sprint-specific strength.
For maximum specificity of training, the athlete’s movement patterns during the training exercise should closely resemble those used when performing the sport.
The purpose of this study was to compare the kinematics of sprinting at maximum velocity to the kinematics of sprinting when using three of types of resisted sprint training devices (sled, parachute, and weight belt).
Eleven men and seven women participated in the study.
Flying sprints over 30 m were recorded by video and digitized using biomechanical analysis software.
The test conditions were compared using a two-way analysis of variance (ANOVA) with a post hoc Tukey test of honestly significant differences.
We found that the three types of resisted sprint training devices are appropriate devices for training the maximum velocity phase in sprinting.
These devices exerted a substantial overload on the athlete, as indicated by reductions in stride length and running velocity, but induced only minor changes in the athlete’s running technique.
When training with resisted sprint training devices, the coach should use a high resistance so that the athlete experiences a large training stimulus, but not so high that the device induces substantial changes in sprinting technique.
We recommend using a video overlay system to visually compare the movement patterns of the athlete in unloaded sprinting to sprinting with the training device.
In particular, the coach should look for changes in the athlete’s forward lean and changes in the angles of the support leg during the ground contact phase of the stride.
Bridgett, L.A. and Linthorne, N.P. (2006).
Changes in long jump take-off technique with increasing run-up speed.
Journal of Sports Sciences, 24 (8), 889-897.
The aim of the study was to determine the influence of run-up speed on take-off technique in the long jump. Seventy-one jumps by an elite male long jumper were recorded in the sagittal plane by a high-speed video camera.
A wide range of run-up speeds was obtained using direct intervention to set the length of the athlete’s run-up.
As the athlete’s run-up speed increased the jump distance and take-off speed increased, the leg angle at touchdown remained almost unchanged, and the take-off angle and take-off duration steadily decreased.
The predictions of two previously published mathematical models of the long jump take-off are in reasonable agreement with the experimental data.
Linthorne, N.P. and Everett, D.J. (2006).
Release angle for attaining maximum distance in the soccer throw-in.
Sports Biomechanics, 5 (2), 243-260.
We investigated the release angle that maximizes the distance attained in a long soccer throw-in.
One male soccer player performed maximum-effort throws using release angles of between 10 and 60º, and the throws were analysed using two-dimensional videography.
The player’s optimum release angle was calculated by substituting mathematical expressions for the measured relationships between release speed, release height and release angle into the equations for the flight of a spherical projectile.
We found that the musculoskeletal structure of the player’s body had a strong influence on the optimum release angle.
When using low release angles the player released the ball with a greater release speed and, because the range of a projectile is strongly dependent on the release speed, this bias toward low release angles reduced the optimum release angle to about 30°.
Calculations showed that the distance of a throw may be increased by a few metres by launching the ball with a fast backspin, but the ball must be launched at a slightly lower release angle.
Wakai, M. and Linthorne, N.P. (2005).
The optimum take-off angle in the standing long jump.
Human Movement Science, 24 (1), 81-96.
The aim of this study was to identify and explain the optimum projection angle that maximises the distance achieved in a standing long jump.
Five physically active males performed maximum-effort jumps over a wide range of take-off angles, and the jumps were recorded and analysed using a 2-D video analysis procedure.
The total jump distance achieved was considered as the sum of three component distances (take-off, flight, and landing), and the dependence of each component distance on the take-off angle was systematically investigated.
The flight distance was strongly affected by a decrease in the jumper’s take-off speed with increasing take-off angle, and the take-off distance and landing distance steadily decreased with increasing take-off angle due to changes in the jumper’s body configuration.
The optimum take-off angle for the jumper was the angle at which the three component distances combined to produce the greatest jump distance.
Although the calculated optimum take-off angles (19–27º) were lower than the jumpers’ preferred take-off angles (31–39º), the loss in jump distance through using a sub-optimum take-off angle was relatively small.
Linthorne, N.P., Guzman, M.S., and Bridgett, L.A. (2005).
Optimum take-off angle in the long jump.
Journal of Sports Sciences, 23 (7), 703-712.
In this study, we found that the optimum take-off angle for a long jumper may be predicted by combining the equation for the range of a projectile in free flight with the measured relations between take-off speed, take-off height and take-off angle for the athlete.
The prediction method was evaluated using video measurements of three experienced male long jumpers who performed maximum-effort jumps over a wide range of take-off angles.
To produce low take-off angles the athletes used a long and fast run-up, whereas higher take-off angles were produced using a progressively shorter and slower run-up.
For all three athletes, the take-off speed decreased and the take-off height increased as the athlete jumped with a higher take-off angle.
The calculated optimum take-off angles were in good agreement with the athletes’ competition take-off angles.
Linthorne, N.P. (2001).
Analysis of standing vertical jumps using a force platform.
American Journal of Physics, 69 (11), 1198-1204.
A force platform analysis of vertical jumping provides an engaging demonstration of the kinematics and dynamics of one-dimensional motion.
The height of the jump may be calculated (1) from the flight time of the jump, (2) by applying the impulse-momentum theorem to the force-time curve, and (3) by applying the work-energy theorem to the force-displacement curve.
Linthorne, N.P. (2001).
Optimum release angle in the shot put.
Journal of Sports Sciences, 19 (5), 359-372.
The aim of the study was to assess the accuracy of a method of calculating the optimum release angle in the shot put.
Using the proposed method, the optimum release angle is calculated by combining the equation for the range of a projectile in free flight with the relations between release speed, release height and release angle for the athlete.
The method was evaluated using measurements of five college shot-putters who performed maximum-effort throws over a wide range of release angles.
When the athletes threw with high release angles, the shot was released from a greater height above the ground and with a lesser release speed.
For all five athletes, the calculated optimum release angle was in good agreement with the athlete’s preferred release angle.
Each athlete had his own specific optimum release angle because of individual differences in the rate of decrease in release speed with increasing release angle.
Simple models of shot-putting were developed to explain the relations between release speed, height and angle in terms of the anthropometric and strength characteristics of the athlete.
Linthorne, N.P. (2000).
Energy loss in the pole vault take-off and the advantage of the flexible pole.
Sports Engineering, 3 (4), 205-218.
A model of pole vaulting with a flexible pole was developed with the aim of predicting the optimum take-off technique and pole characteristics for a typical world-class pole vaulter.
The key features of the model are that it includes the interdependence of the take-off angle and the take-off velocity, and that it accounts for the energy losses in the pole plant and take-off phases of the vault.
A computer simulation programme was used to systematically investigate the effect of different combinations of take-off velocity, take-off angle, grip height, and pole stiffness on the performance of a world-class male vaulter.
For the highest vault with this model, the vault height and the corresponding optimum combination of take-off velocity, take-off angle, grip height, and pole stiffness were in good agreement with measured values for world-class vaulters using fibreglass poles.
The results from the model were compared with those from a model of vaulting with a rigid pole.
There was a clear performance advantage to vaulting with a flexible pole.
The flexible pole produced a 90 cm higher vault by allowing a 60 cm higher grip and by giving a 30 cm greater push height.
There are two main advantages of a flexible fibreglass pole over a rigid pole made of steel or bamboo.
A flexible pole reduces the energy dissipated in the vaulter’s body during the pole plant, and it also lowers the optimum take-off angle so that the athlete loses less kinetic energy when jumping up at take-off.
Tobar, M.E., Blair, D.G., Ivanov, E.N., van Kann, F., Linthorne, N.P., Turner, P.J., and Heng, I.S. (1995).
The University of Western Australia’s resonant-bar gravitational wave experiment.
Australian Journal of Physics, 48 (6), 1007-1025.
The cryogenic resonant-mass gravitational radiation antenna at the University of Western Australia (UWA) has obtained a noise temperature of <2 mK using a zero order predictor filter.
This corresponds to a 1 ms burst strain sensitivity of 7 ´ 10-19.
The antenna has been in continuous operation since August 1993.
The antenna operates at about 5 K and consists of a 1.5 tonne niobium bar with a 710 Hz fundamental frequency, and a closely tuned secondary mass of 0.45 kg effective mass.
The vibrational state of the secondary mass is continuously monitored by a 9.5 GHz superconducting parametric transducer.
This paper presents the current design and operation of the antenna.
From a two-mode model we show how we calibrate, characterise and theoretically determine the sensitivity of our detector.
Experimental results confirm theory.
Linthorne, N.P. (1994).
Mathematical model of the takeoff phase in the pole vault.
Journal of Applied Biomechanics, 10 (4), 323-334.
A mathematical model is presented of the takeoff phase in the pole vault for an athlete vaulting with a rigid pole.
An expression is derived that gives the maximum height that the vaulter may grip on the pole in terms of the takeoff velocity, the takeoff angle, the athlete's vertical reach, and the depth of the takeoff box.
Including the dependence of the vaulter's takeoff velocity on the takeoff angle reveals that there is an optimum takeoff angle which maximizes the vaulter's grip height.
It is also shown that taller and faster vaulters are able to grip higher on the pole.
The results of the investigation compare favourably with data for vaulters using bamboo and steel poles.
Linthorne, N.P. (1994).
The effect of wind on 100-m sprint times.
Journal of Applied Biomechanics, 10 (2), 110-131.
The effect of wind on the race times of international standard 100-m sprinters was determined using statistical information from official competitions.
A time adjustment curve derived from mathematical models was fitted to performances by the finalists at the U.S. Olympic Trials and TAC Championships over the last 10 years, and to multiple performances by individual athletes at recent Olympic Games and World Championships.
Consistent results were obtained from the two studies.
The rate of improvement in race time gradually decreased with increasing wind velocity, and so the disadvantage of a head wind was greater than the benefit of a tail wind of the same magnitude.
The advantage of a 2-m/s following wind was 0.10 ± 0.01 s for the male sprinters and 0.12 ± 0.02 s for the female sprinters.
These results indicated that the altitude of Mexico City (2,250 m) provides an advantage of about 0.07 s.
Time adjustment versus wind velocity curves are presented that allow comparison of the merit of 100-m sprint times achieved under diverse wind conditions.
The curves supersede those derived by previous investigators.
Mittoni, L.J., Linthorne, N.P., Mann, A.G. and Blair, D.G. (1993).
Optimization of superconducting re-entrant cavities for transducer applications.
Journal of Physics D: Applied Physics, 26 (5), 804-809.
We report a study of the effects of geometry and surface preparation in 10 GHz superconducting niobium re-entrant cavities for use as ultra-sensitive transducers.
The balance between surface dielectric losses, radiative losses, and magnetic losses is analysed.
An unloaded electrical Q of 6.5 ´ 105 was obtained at 4.2 K.
Compared with conventional designs, a wide re-entrant post produces almost an order of magnitude increase in the electromechanical coupling.
Linthorne, N.P. and Blair, D.G. (1992).
Superconducting re-entrant cavity parametric transducer for a resonant bar gravitational radiation antenna.
Review of Scientific Instruments, 63 (9), 4154-4160.
A 10 GHz superconducting niobium re-entrant cavity parametric transducer was developed for use in a cryogenic 1.5-tonne Nb resonant bar gravitational radiation antenna.
The transducer has a very high electrical Q (6 ´ 105 at 4.2 K), and was operated at high cavity fields without degrading the Q.
A very high electromechanical coupling between the antenna and the transducer was therefore achieved.
The highest coupling attained, constrained by the available pump power, was 0.11.
If the transducer were to be operated in conjunction with a wideband impedance matching element, an antenna bandwidth comparable to the frequency of the antenna would be attained.
The temperature dependence of the Q of the transducer was in good agreement with theory.
At temperatures above about 6 K the Q was degraded by the increase in the BCS surface resistance, while at lower temperatures the Q was limited by radiative losses.
Linthorne, N.P., Veitch, P.J. and Blair, D.G. (1990).
Interaction of a parametric transducer with a resonant bar gravitational radiation detector.
Journal of Physics D: Applied Physics, 23 (1), 1-6.
It is shown that a microwave parametric transducer for a resonant bar gravitational radiation antenna can achieve high electromechanical coupling without degrading the acoustic Q of the antenna.
The reactive coupling of the transducer to the antenna leads to both cold-damping and modification of the antenna's resonant frequency.
These effects are examined in a 1.5 tonne niobium resonant bar antenna.
At low coupling the observed behaviour is found to be in good agreement with theory. At higher coupling, the behaviour is complicated by other effects.
We discuss how these parametric effects may be used to advantage when suitably controlled.
Moore, G.I., Stacey, F.D., Tuck, G.J., Goodwin, B.D., Linthorne, N.P., Barton, M.A., Reid, D.M. and Agnew, G.D. (1988).
Determination of the gravitational constant at an effective mass separation of 22 m.
Physical Review D: Particles and Fields, 38 (4), 1023-1029.
A vacuum balance that compares the weights of 10-kg stainless-steel masses suspended in evacuated tubes at different levels in a hydroelectric reservoir is being used to measure the gravitational attractions of layers of lake water up to 10 m in depth.
The mean effective distance between interacting masses in this experiment is 22 m, making it the largest-scale measurement of G using precisely controlled moving masses.
The experiment extends laboratory-type measurements into the range previously explored only by geophysical methods.
Assuming purely Newtonian physics the value of the gravitational constant determined from data obtained so far is G = 6.689(57) ´ 10-11 m3kg-1s-2, which agrees with laboratory estimates.
The data admit at a 0.6 standard deviation level the parameters of non-Newtonian gravity inferred from geophysical measurements in mines and a tower.
These measurements push the estimated ranges of non-Newtonian forces down to a scale accessible to our reservoir experiment, so that experimental improvements now at hand may provide a critical test of non-Newtonian effects.
Veitch, P.J., Blair, D.G., Linthorne, N.P., Mann, L.D. and Ramm, D.K. (1987).
Development of a 1.5 tonne niobium gravitational radiation antenna.
Review of Scientific Instruments, 58 (10), 1910-1916 (1987).
A 1.5-tonne Nb gravitational radiation antenna is described.
Problems associated with a noncontacting magnetically levitated parametric upconverter transducer are discussed, and a system using a bonded microwave reentrant cavity and bonded mechanical impedance transformer is described and analyzed in detail.
It is shown that such an antenna can be expected to achieve a noise temperature of ~ 1 mK.
An ultralow phase noise tunable microwave source for the transducer pump signal is described, as well as precision bonding techniques which yield a mechanical positioning accuracy of 10-6 m, and a reproducibility of 10-8 m.
Veitch, P.J., Ferreirinho, J., Blair, D.G. and Linthorne, N.P. (1987).
Low temperature acoustic loss of pure and alloyed niobium and titanium with application to gravitational radiation detectors.
Cryogenics, 27 (10), 586-589.
Low acoustic loss cryogenic materials are required for various high precision experiments, resonant-bar gravitational radiation antennae in particular.
We report here cryogenic acoustic loss measurements of various commercially pure and alloyed Nb and Ti samples.