🎾 Vợt Control - Part 1¶
Giới Thiệu¶
Vợt Control - Part 1 — tài liệu 20 trang từ thư viện sách tennis.
Chủ đề chính: Thăng bằng, Racquet
Tóm tắt nội dung (trích từ tài liệu gốc): Racquet Control -- Part 1 about:reader?url=http://twu.tennis-warehouse.com/learning_center/contr... twu.tennis-warehouse.com Racquet Control -- Part 1 17-21 ph�t INTRODUCTION Racquet control is a term that is commonly used to describe the property of a racquet, but it is not a well-defined quantity like balance or swingweight. To some people, control might mean the ability to swing the racquet accurately and easily into position without having to force it to go where you want it to go. To others, control might mean that the racquet helps to control the speed and angle of the ball off the strin
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Racquet Control -- Part 1 about:reader?url=http://twu.tennis-warehouse.com/learning_center/contr...
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Racquet Control -- Part 1
17-21 ph�t
INTRODUCTION
Racquet control is a term that is commonly used to describe the
property of a racquet, but it is not a well-defined quantity like
balance or swingweight. To some people, control might mean the
ability to swing the racquet accurately and easily into position
without having to force it to go where you want it to go. To others,
control might mean that the racquet helps to control the speed and
angle of the ball off the strings. Alternatively, some might argue
that it is the player who controls the racquet and the racquet itself
does very little to improve control. Nevertheless, it is clear that a
racquet that is much too heavy for a young player will be difficult to
swing, and a racquet that is much too light will lack sufficient power
for an experienced player.
In some cases, it might be possible to quantify control in terms of
the physical properties of a racquet. For example, suppose that a
player strikes the ball near the frame rather than in the middle of
the strings. In that case, the outgoing trajectory of the ball will not
be exactly as intended, and the difference will depend mainly on
the swingweight or twistweight of the racquet. Even if the player
strikes the ball in the middle of the strings, the outgoing trajectory
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will depend on how fast the incoming ball is spinning and it will
therefore depend on how the racquet strings respond to the
incoming spin. The outgoing trajectory also depends on the
incoming ball speed and angle of incidence on the strings. The
effect of a change in the incoming speed and angle will vary,
depending on the properties of the racquet. Some racquets might
help to control or compensate for undesirable outcomes better
than others.
CONTROL EXPERIMENT
Factors that might affect racquet control were investigated by
setting up a simple experiment where a tennis ball was fired from a
ball machine to impact a hand-held racquet at rest, as shown in
Figure 1. The racquet was held vertically, with the tip resting lightly
on the floor, and the ball was fired horizontally to impact either
near the middle of the strings or closer to the frame but at the
same height (nearer the 3 or 9 o'clock positions). The racquet
wasn't swung at the ball since it is not easy to control the racquet
speed and approach angle precisely, nor is it easy to control the
impact point on the strings or even measure it. Those factors were
eliminated from the experiment by holding the racquet at rest and
varying only the incoming ball speed, incident angle, incident spin
and the impact point on the strings.
By filming the results with a video camera, we were able to
measure the effects of small changes in those quantities, as well
as large changes. Small changes happened automatically since
the ball machine was not 100% consistent. Over a period of one
week we filmed about 500 different shots using four different
racquets. In the end, we focussed on just one of those racquets
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and varied its properties by inserting two small bolts through the
strings at 3 o'clock and 9 o'clock so that we could compare a low
twistweight racquet with a high twistweight racquet. We obtained
165 shots for this racquet, and the results are described below.
3 trong 20 Figure 1 -- Ball incident on a racquet initially at rest.
Figure 1 shows the differences that arise when the incident angle
and spin are varied. If the ball is incident at right angles to the
string plane and without spin, then it bounces more or less at right
angles without spin. Nevertheless, small variations arise from
differences in string movement, and larger differences arise
depending on the impact point on the strings. The ball bounced at
low speed if it impacted near the frame rather than the middle of
the strings, and it bounced at a higher speed near the middle of
the strings or when the bolts were added.
Figure 1(a) shows a typical result where the ball is incident without
spin, at 30� to the normal, and impacts towards the frame. The ball
bounces with reduced speed (compared with the incoming speed),
and with topspin. If the same ball is incident with backspin, as in
Figure 1(b), the outgoing topspin is reduced, and so is the
outgoing angle to the normal. Figure 1(c) shows an example
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where the ball is incident at right angles to the string plane, with
backspin, with the result that the ball bounces away from the
normal and with reduced speed and spin compared with the
incoming ball.
EXPERIMENTAL CONDITIONS
The ball launcher contained two counter-rotating wheels that could
be rotated at the same speed to launch balls without spin, or at
different speeds to launch balls with backspin onto the racquet.
Without spin, the incident ball speed was 16.5 +/- 1 m/s, and 74
shots were fired at the racquet at right angles or at 30 +/- 1
degrees away from the normal, with and without the bolts
connected. Each bolt weighed 13.4 g, adding 26.8 g to the 291 gm
racquet. An additional 91 shots were filmed with backspin at -270
+/- 20 rad/s and at an incident speed 13.5 +/- 0.5 m/s. In both
cases, the impact point was varied from x = -80 mm to x = 60 mm,
that is from near 9 o'clock to near 3 o'clock.
BOUNCE SPEED
Suppose that a ball is incident at speed 60 mph at right angles to
the string plane, and the racquet is initially at rest and hand held
as shown in Figure 2(a). If the ball bounces at 18 mph, at right
angles to the string plane, then the ratio of those two speeds is
18/60 = 0.3, a number known as the Apparent Coefficient of
Restitution, or ACOR. It is given the symbol eA when used in
formulas. The ACOR for a racquet depends on the impact point
and is typically about 0.4 in the middle of the strings and about 0.1
or 0.2 near the frame, regardless of the speed of the incoming ball.
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The significance of the ACOR is that if a racquet approaches the
ball at speed V , and if the ball is at rest instead of the racquet (as
in a serve), then the outgoing ball speed is v = (1 + eA)V . For
example, if eA = 0.4 and V = 70 mph then v = 1.4 x 70 = 98 mph.
Figure 2(b) shows a different situation where the ball is incident at
40� to the string plane and bounces at 30�. The speed of the
incident ball is again 60 mph, and its speed in a direction
perpendicular to the string plane is 60 x cos 40 = 46 mph. The ball
bounces at 16 mph, and its speed perpendicular to the string plane
is 16 x cos 30 = 13.8 mph. In that case, ACOR = 13.8/46 = 0.3.
That is, the ACOR is the same, provided the ball bounces off the
same spot on the strings.
5 trong 20 Figure 2 -- Definition of ACOR (eA).
Measurements of ACOR showing all 165 shots are shown in
Figure 3, both with the added bolts and without the bolts. The main
points of interest are that (a) the ball bounces best near the middle
of the strings and not so well near the frame, (b) adding extra
mass to the frame results in an increase in ACOR, and (c) the
value of ACOR at any given impact point does not depend very
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much on the speed, spin or angle of the incident ball. Similar
results have been observed many times before, with many
racquets. The fact that all the data points do not lie on two
perfectly smooth curves means that no two bounces are exactly
the same and that ACOR depends slightly on the spin of the ball
and whether the ball lands on two, three or four strings and
whether the strings move sideways in the string plane.
Figure 3 -- Measurements of ACOR vs distance from the long axis
(x). Smooth curves are fitted to the data points for impacts with
and without added mass.
Effective mass (Me), also known as hittingweight, is another
helpful measurement for measuring performance. Each impact
location behaves "as if" it were a localized point having the
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calculated effective mass. Typically, Me is about one-third the
actual racquet weight in the tip, one-half in the center, and equal
near the balance point, or center of mass. At any location, the
hittingweight (as well as ACOR) will depend on the swingweight
and twistweight. The higher the hittingweight, the less the racquet
will twist, rotate, and translate and both control and power will
increase. Figure 4 shows how ACOR (power) depends on
hittingweight.
Figure 4 -- ACOR vs hittingweight for all 165 bounces, both with
and without added bolts.
Adding extra mass to the frame improves the bounce, but then the
racquet is harder to swing, so the outgoing ball speed might be
about the same in practice. However, it is clear that if the ball is
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struck near the frame rather than in the middle of the strings, then
the outgoing ball speed will be reduced. In that respect, it is the
player's fault. Nevertheless, a racquet with extra mass in the head
does help slightly, since ACOR does not decrease as much near
the frame as it does with a head light racquet. For example, in
Figure 3, ACOR is about 0.3 near the frame for the heavier
racquet but it is only about 0.2 for the lighter racquet.
When you graph any result against both ACOR and hittingweight,
the results look very similar. That is because they both depend on
swingweight and twistweight. They are somewhat different ways of
looking at the impact however. ACOR measures a result of the
bounce and hittingweight is a calculated property that explains the
ACOR result. Hittingweight is perhaps the most intuitive parameter
for understanding performance results. We will use both below in
the discussions on bounce angle and spin.
BOUNCE ANGLE
Unlike the bounce speed, the bounce angle depends strongly on
both the angle of incidence and the incident spin. Figure 5 shows
the geometry and incident parameters of interest (future figures
will reference the impact conditions of Figure 5 -- letters "A", "B",
"C", and "D").
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9 trong 20 Figure 5 -- Incident geometry and parameters (velocity units are
m/s). Friction acts opposite the tangential speed of the ball relative
to the racquet (Vc) where Vc = vx1 + R1, where vx1 is tangential
component of v1 and R1 is the tangential spin speed.
In Figure 5, vx1 is the incident velocity component tangent to the
strings, R1 is the tangential speed of the spinning ball, where R
is the radius, and Vc is the contact velocity tangent to the strings
where Vc = vx1 + R1. Friction acts opposite the direction of Vc
and its duration depends on the magnitude of Vc. Under most
circumstances, friction acts both to slow the ball and to change the
spin in the direction opposite that of the incident spin. However,
friction can sometimes act to increase incident tangential speed
(as in the bounce of a topspin lob) and spin (as in any slice shot).
Slowing the tangential speed of the ball decreases (makes closer
to the perpendicular) the rebound angle. In Figure 5A, there is no
friction, so there is no change in spin or direction of the rebound. In
Figure 5B, friction decreases vx1 and turns it into topspin. In Figure
5C, the ball has no linear tangential incident velocity (vx1 = 0), but
it does have tangential spin speed. Friction acts to decrease the
spin and push the ball backwards, thus the negative rebound
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angle. And in Figure 5D, Vc is large due to both vx1 and R1 being
in the same direction. Friction slows the ball and reverses spin
until vx and R are equal and opposite so Vc = 0, sliding stops,
and the friction force drops to zero.
Figure 6 displays the rebound angle vs ACOR. For impact group A
(30�, no spin) and D (0�, -270 rad/s spin), as ACOR increases both
due to impact location and to the addition of the bolts, the rebound
angle is closer to the perpendicular, indicating more control. When
a player strikes a ball, he or she normally expects the ball to head
off in a direction perpendicular to the string plane, or at least in the
same direction that the racquet head is moving. If it doesn't then
that indicates poor control. Surprisingly, the bounce for group D
with both incident angle and spin is almost the same as in group A
where there was no tangential speed or spin. Since VC is relatively
large in D, the friction force acts for a long time while the ball slides
across the strings. As a result, the horizontal speed of the ball
drops almost to zero, so the ball rebounds almost perpendicular to
the string plane.
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Figure 6 -- Bounce angle 2 vs ACOR for all 165 bounces, both
with and without added bolts.
Figure 7 shows the dependency of rebound angle on hittingweight.
This is essentially the same result as in Figure 6 but displayed in
units that are more familiar to most readers -- grams. Here again
we see that adding bolts decreases the rebound angle, except for
groups A and D which are effectively zero angle, zero spin
incidence and rebound.
Figure 7 -- Bounce angle 2 vs hittingweight (impact conditions A
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and D have here been fit to one curve since the results are so
similar).
Figure 8 is another equivalent view of the same results. This graph
plots the rebound angle vs the impact distance from the
longitudinal axis. The efficacy of the bolts for minimizing rebound
angle is apparent.
12 trong 20 Figure 8 -- Bounce angle 2 vs impact distance from longitudinal
axis.
BOUNCE SPIN
The rebound spin, 2 is shown in Figure 9 vs ACOR and Figure
10 vs Me. The spin does not depend strongly on either, although
the spin does decrease as ACOR and Me increase when the ball is
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incident without spin at 1 = 30�.
Figure 9 -- Bounce spin 2 vs ACOR for all 165 bounces, both
with and without added bolts.
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Figure 10 -- Bounce spin 2 vs Me for all 165 bounces, both with
and without added bolts.
COEFFICIENT OF FRICTION
A surprising result is that the coefficient of friction (COF) between
the ball and the strings varies over a wide range, depending on the
incident ball spin and angle. The results are shown in Figure 11
(COF vs ACOR) and Figure 12 (COF vs Hittingweight). Usually,
the coefficient of friction is defined as the ratio of the horizontal
force to the vertical force acting on an object moving along a
horizontal surface. When a ball impacts the strings, the forces
perpendicular and parallel to the strings vary with time, and the
ball can also slide on the strings or grip the strings. A more
convenient definition of the COF in that case is COF = (change in
parallel speed)/(change in perpendicular speed), which is the ratio
plotted in Figures 11 and 12.
If the ball is incident at right angles to the string and bounces at
right angles then the parallel speed is zero so COF = 0. If the ball
is incident with backspin at an angle away from the normal, then
the ball will tend to slide on the strings and the COF will be
relatively large, about 0.4 in the figures. Otherwise, the ball will
slide for a short time then grip the strings, in which case the COF
is smaller.
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Figure 11 -- Coefficient of friction COF vs ACOR for all 165
bounces, both with and without added bolts.
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Figure 12 -- Coefficient of friction COF vs Me for all 165 bounces,
both with and without added bolts.
CONTACT VELOCITY
As much as hittingweight and ACOR might influence the rebound,
the incident parameters matter more. Incident speed, spin, and
angle combine to determine the contact velocity tangential to the
stringbed (Vc = R1 + vx1). Friction acts opposite Vc and its
duration will in part depend on the magnitude of Vc. Friction acts to
slow the ball and to reverse the direction of spin. The spin is
changed at a faster rate than is the linear ball speed. This is
shown in Figures 13 and 14. Figure 13 shows that for a given
contact velocity, the rotational contact velocity component is
changed a little more than 1.5 times as much as the linear contact
velocity component. Figure 14 makes this clear by plotting the
change in the rotational component to the change in the linear
component.
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Figure 13 -- Change in linear and rotational tangential velocity vs
contact velocity.
Figure 14 -- Change in rotational tangential velocity vs change in
linear tangential velocity.
Figure 15 shows the dependence of COF on contact velocity. The
greater is Vc, the longer friction will act before the ball grips the
string and the greater will be the change in linear and rotational
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speed. In other words, a larger Vc is associated with more sliding
on the strings.
Figure 15 -- Coefficient of friction (COF) vs contact velocity.
The change in rebound spin (2 - 1) is strongly dependent on
contact velocity (Figure 16). Change in spin is used instead of the
actual rebound spin because it shows the direction and magnitude
of work done by friction independent of the final sign of 2. The
positive change in spin for all impacts indicates that friction acted
in the topspin direction. The final bounce may have been spinning
with topspin, or if it still had backspin, it would be greatly reduced.
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Figure 16 -- Change in spin (2 - 1) during impact vs contact
velocity (Vc).
The change in rebound angle (2 - 1) is not as dependent on
contact velocity (Figure 17).
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Figure 17 -- Change in angle (2 - 1) during impact vs contact
velocity (Vc).
CONCLUSION
This experiment has shown that both control and power are
increased by adding mass to the racquet in order to increase the
hittingweight at the impact point. A higher hittingweight can be
obtained by either selecting a racquet that has a high swingweight
and twistweight or by customizing an existing racquet by adding
lead or tungsten tape to the frame. A racquet with a high
hittingweight at the impact point will twist, rotate, and translate less
than a racquet with a lower hittingweight. That means a truer,
faster bounce -- in otherwords, more power and control.
However, the two factors that most contribute to power and control
are the angle and spin of the incident ball and the swing of the
player. The incoming parameters can't be changed except
choosing to take the ball on the rise, descent, or top of the bounce,
but the player can alter the speed and angle of swing to affect a
desired outcome.
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