Fasbender, P., Korff, T. J., Baltzopoulos, V. M., and Linthorne, N. P.
(2020). Optimal mass of the arm segments in throwing: A two-dimensional
computer simulation study. European Journal of Sport Science,
Producing a high release speed is important in throwing sports such as
baseball and the javelin throw. Athletes in throwing sports might be
able to achieve a greater throwing speed by improving the effectiveness
of the kinetic chain. In this study a two-dimensional computer
simulation model of overarm throwing was used to examine the effect of
changes in forearm mass and upper arm mass on the release speed of a
lightweight (58 g) projectile. The simulations showed that increasing
the mass of the forearm decreases release speed, whereas increasing the
mass of the upper arm initially increases release speed. For a given
forearm mass there is an optimal upper arm mass that produces the
greatest release speed. However, the optimal upper arm mass
(5–6 kg) is substantially greater than that of an average
adult (2.1 kg). These results suggest that athletes might be able to
throw faster if they had a stronger tapering of segment mass along the
length of their arm. A stronger taper could be readily achieved by
attaching weights to the upper arm or by using hypertrophy training to
increase the mass of the upper arm. High-speed overarm throwing is a
complex three-dimensional movement and this study was a preliminary
investigation into the effect of arm segment mass on throwing
performance. Further simulation studies using three-dimensional
throwing models are needed to generate more accurate insights, and the
predictions of the simulation studies should be compared to data from
experimental intervention studies of throwing sports.
Linthorne, N. P., Heys, M. E. R., Reynolds, T. J., and Eckardt, N.
Attaching mass to the upper arm can increase throw distance in a
modified javelin throw. Acta of Bioengineering and
Purpose: The effectiveness of the whip-like coordination in throwing
might be influenced by the inertial properties of the
athlete’s arm. This preliminary study investigated the acute
effect of attaching mass to the upper arm on the distance achieved in a
modified javelin throw. The aim was to identify the optimum upper arm
mass that maximizes throw distance. Methods: Three well-trained adult
male athletes performed maximum-effort throws with an 800-g javelin
training ball. A wide range of masses (0–1.5 kg) were
attached to the upper arm and a 2D video analysis was used to obtain
measures of the projection variables for each attached mass. Results:
All three athletes showed an effect of attached arm mass on throw
distance, and with the optimum mass the athlete’s throw
distance was increased by 2.2 m, 1.2 m, and 0 m (7%, 4%, and 0%)
respectively. The optimum mass was specific to the athlete (0.6 kg, 0.2
kg, and 0 kg) and changes in throw distance were mostly due to changes
in release velocity rather than changes in release angle or release
height. The experimental results were broadly similar to those obtained
from a simple 2D mathematical model of throwing. Conclusions: These
results indicate that some javelin throwers might see an increase in
throwing performance when a mass is attached to their upper arm.
However, the relationship between upper arm mass and throwing
performance should be investigated further with studies on more
athletes, projectiles of different mass, and other throwing events.
Linthorne, N.P. (2020). The correlation between jump height and
mechanical power in a countermovement jump is artificially inflated. Sports
The countermovement jump is commonly used to assess an
neuromuscular capacity. The aim of this study was to identify the
mechanism behind the strong correlation between jump height and
mechanical power in a countermovement jump. Three athletes each
performed between 47 and 60 maximal-effort countermovement jumps on a
force platform. For all three athletes, peak mechanical power and
average mechanical power were strongly correlated with jump height (r
0.54–0.90). The correlation between jump height and peak
was largely determined by the correlation between jump height and the
velocity at peak power (r = 0.83–0.94) and
was not related to
correlation between jump height and the ground reaction force at peak
power (r = 0.20–0.18). These results
confirm that the strong
correlation between jump height and power is an artefact arising from
how power is calculated. Power is a compound variable calculated from
the product of instantaneous ground reaction force and instantaneous
velocity, and application of statistical theory shows that the
correlation between jump height and power is artificially inflated by
the near-perfect correlation between jump height and the velocity at
peak power. Despite this finding, mechanical power might still be
useful in assessing the neuromuscular capacity of an athlete.
Martinez-Valencia, M.A., Linthorne, N.P.,
González-Ravé, J.M., Alcaraz, P.E. and Navarro
Valdivielso, F. (2017). Effect of strength-to-weight ratio on the time
taken to perform a sled-towing exercise. Journal
of Human Sport and Exercise, 12
Sled-towing exercises are effective at developing sprint acceleration
in sports. In a sled-towing exercise the time taken by an athlete to
tow the sled over a given distance is affected by the weight of the
sled, the frictional properties of the running surface, and the
physiological capacities of the athlete. To accurately set the training
intensity for an athlete, the coach needs a detailed understanding of
the relationships between these factors. Our study investigated the
relationship between the athlete’s strength-to-weight ratio
and the rate of increase in sled-towing time with increasing sled
weight. Twenty-two male athletes performed a one-repetition maximum
(1RM) half-squat and sled-towing exercises over 20 m with sleds of
various weights. The strength of the correlation between 1RM half-squat
performance (normalized to body weight) and the rate of increase in
sled-towing time with increasing sled weight was interpreted using the
Pearson product-moment correlation coefficient. As expected, we found
substantial inter-athlete differences in the rate of increase in time
with increasing sled weight, with a coefficient of variation of about
21% and 17% for sled-towing times over 10 and 20 m, respectively.
However, the rate of increase in sled-towing time showed no correlation
with normalized 1RM half-squat performance (r =
confidence interval = –0.45 to 0.26; and r
90% confidence interval = –0.38 to 0.34, for sled-towing
times over 10 and 20 m, respectively). These results indicate that
inter-athlete differences in the rate of increase in sled-towing time
with increasing sled weight are not likely to be due to differences in
strength-to-weight ratio. Instead, we recommend the weight of the sled
be scaled according to the athlete’s power-to-weight ratio.
Wickington, K.L. and Linthorne, N.P. (2017). Effect of ball weight on
speed, accuracy, and mechanics in cricket fast bowling. Sports,
(1), 18 1–14.
The aims of this study were 1) to quantify the acute effects of ball
weight on ball release speed, accuracy, and mechanics in cricket fast
bowling; and 2) to test whether a period of sustained training with
underweight and overweight balls is effective in increasing a
player’s ball release speed.
Ten well-trained adult male cricket players performed maximum-effort
deliveries using balls ranging in weight from 46% to 137% of the
standard ball weight (156 g).
A radar gun, bowling target, and 2D video analysis were used to obtain
measures of ball speed, accuracy, and mechanics.
The participants were assigned to either an intervention group, who
trained with underweight and overweight balls, or to a control group,
who trained with standard-weight balls.
We found that ball speed decreased at a rate of about 1.1 m/s per 100 g
increase in ball weight.
Accuracy and bowling mechanics were not adversely affected by changes
in ball weight.
There was evidence that training with underweight and overweight balls
might have produced a practically meaningful increase in bowling speed
(> 1.5 m/s) in some players without compromising accuracy or
increasing their risk of injury through inducing poor bowling
In cricket fast bowling, a wide range of ball weight might be necessary
to produce an effective modified-implement training program.
Linthorne, N.P. (2016). Improvement in 100-m sprint performance at an
altitude of 2250 m. Sports, 4
(2), 29 1–9.
A fair system of recognizing records in athletics should consider the
influence of environmental conditions on performance.
The aim of this study was to determine the effect of an altitude of
2250 m on the time for a 100-m sprint.
Competition results from the 13 Olympic Games between 1964 and 2012
were corrected for the effects of wind and de-trended for the
historical improvement in performance.
The time advantage due to competing at an altitude of 2250 m was
calculated from the difference between the mean race time at the 1968
Olympic Games in Mexico City and the mean race times at the
low-altitude competition venues.
The observed time advantage of Mexico City was 0.19 (±0.02)
s for men and 0.21 (±0.05) s for women (±90%
These results indicate that 100-m sprinters derive a substantial
performance advantage when competing at a high-altitude venue and that
an altitude of 1000 m provides an advantage equivalent to a 2 m/s
assisting wind (0.10 s).
Therefore, the altitude of the competition venue as well as the wind
speed during the race should be considered when recognizing record
Linthorne, N.P. and Stokes, T.G. (2014). Optimum projection angle for
attaining maximum distance in a rugby place kick. Journal of
Sports Science and
Medicine, 13 (1), 211–216.
This study investigated the effect of projection angle on the distance
attained in a rugby place kick. A male rugby player performed 49
maximum-effort kicks using projection angles of between 20 and
50°. The kicks were recorded by a video camera at 50 Hz and a 2
D biomechanical analysis was conducted to obtain measures of the
projection velocity and projection angle of the ball. The
player’s optimum projection angle was calculated by
substituting a mathematical expression for the relationship between
projection velocity and projection angle into the equations for the
aerodynamic flight of a rugby ball. We found that the
player’s calculated optimum projection angle (30.6°,
95% confidence limits ±1.9°) was in close agreement
with his preferred projection angle (mean value 30.8°, 95%
confidence limits ±2.1°). The player’s
calculated optimum projection angle was also similar to projection
angles previously reported for skilled rugby players. The optimum
projection angle in a rugby place kick is considerably less than
45° because the projection velocity that a player can produce
decreases substantially as projection angle is increased. Aerodynamic
forces and the requirement to clear the crossbar have little effect on
the optimum projection angle.
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, 28
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
Conclusion: Inter-athlete differences in the rate of increase in sprint
time might be due to differences in the athlete’s
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
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),
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
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
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
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
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
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
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
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
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
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
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
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
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
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
Veitch, P.J., Blair, D.G., Linthorne, N.P., Mann, L.D. and Ramm, D.K.
Development of a 1.5 tonne niobium gravitational radiation antenna. Review
of Scientific Instruments, 58 (10),
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.