Biophysics of somersault and arm sets in trampolining

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Biophysics of somersault and arm sets in
trampolining

• John Mitchell
• Thanks to Lisa Withey Jack Mitchell for
  performance

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Introduction
In depth calculations are not included in this
presentation. These are available on request. The
data presented is approximately 50 from direct
video measurement and 50 from calculation.
Where calculations have been used a number of
body weight and size approximations have been
used and actual numbers will vary with performer.
This is intended as a first draft for more in
depth analysis in a suitable sports science
department. The next slide presents data
measured using motionview 7.2 showing body angles
on last contact Vs amount of rotation generated.
There is clearly good correlation for the
performers used.
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Rotation vector
From the leg body angle a leg to vertical angle
can be inferred And this can be used to calculate
the amount of energy converted from bounce
height into kinetic rotational energy (Whether
this is valid to do so is up for comment) The
body has to bend forward in this front somersault
example to keep the Center of mass d above the
Base of support Back somersault rotation seems to
use a straighter body position to gain the same
amount of rotation. (Noisy) Poor timed
somersaults caused by pushing on the landing
phase rather than in the take-off phase require
a greater angle of body bend (hip displacement)
as they are getting less energy from the
trampoline
b
d
q
a
Force
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To exemplify the theory that rotational energy
can be calculated from the vector of Leg angle
and total potential energy of the performer
(assuming no extra leg forces in operation) the
first thing to do was calculate the total energy
gained. This has been done using a 60kg model
body and is plotted below for different 10 bounce
times
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Assuming a straight shape for a 60kg body of
1.75m the amount of energy required per degree of
rotation can be calculated. The graph below has
this re-plotted in terms of the height energy
converted for different degrees of rotation
assuming bounce time of 16 seconds for 10 bounces.
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This graph is the least evidence based as I
didnt have good enough images. So it is
essentially a theoretical graph on a load of
assumptions about how vertical force from the
trampoline is split by different angles of the
leg. However, the next slide Shows good agreement
between this and the theoretical energy used for
rotation Calculated from angular velocity and
mass in straight shape.
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Comparison of the two methods for calculation of
energy of rotation suggests that leg angle is a
good predictor of the total rotation initiated
and is likely to be the main factor determining
the degree of rotation.
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Calculation of absolute energy required for
rotation in a straight shape allows us to then
calculate energy used for phased tuck and pike
somersaults. (with some assumptions of Moments
of inertia and body size and weight) These have
been plotted below vs 10 bounce time
The preceding graphs all assume no extra leg
push. So I wanted to check that It is possible
for a gymnast to put in enough extra energy to
compensate for height loss.
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In order to do this the graph above was
calculated for standing jump for a 60kg person.
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Adult vertical jump norms
Clearly the range of vertical jump for most
gymnasts is clearly able to produce sufficient
PE to account for the degrees of height otherwise
lost in somersault rotation
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Arm setting
Finally I wanted to examine the affect of arm set
position for front somersault take off positions.
The method used was to balance in different front
rotation positions relating to different
somersaults, then lift arms up while maintaining
balance and measure the resulting body angle
changes. This was done for both front and back
rotation positions with the front
somersault results presented here.
What is the advantage of arm setting?
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c
b
b
c
d
115 Degrees
107
d
107
107 Degrees
157 degrees
160 degrees
a
a
To maintain body COM above feet the body has to
move 8 degrees while maintaining same leg
position (degree of rotation initiation) for 107
deg starting position. Arms up therefore results
in a more upright body position for the same
rotation. This example uses the body angle used
for triple straight front somersaults 107
and front drop 157 degrees. The chart on the
next slide shows actual measured differences for
an 80kg male.
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Actual measured adjustment to maintain balance on
raising arms
As expected this is broadly following a sin wave
trigonometric function, the actual magnitude of
which will be determined by the ratio of arm and
torso mass and length. A vertical arm position
clearly has more effect the more rotation is
initiated. The effect on body position for back
somersault rotation was approximately half as
much.
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Conclusions for somersaulting
1. Simple application of vectors based on body
angles and leg position can be used to describe
trampoline somersaults 2. Conservation of energy
suggests that extra leg push is therefore
necessary to maintain height. Bouncing at 100
max height will therefore result in height
loss. 3. A significant amount of energy is used
in straight shapes and bounce time above 14
seconds appear to be a reasonable minimum for
teaching more than 360 deg in this shape. 4. Arm
position has a large effect on body angle while
maintaining the same degree of likely
somersault. 5. Degree of somersault is likely to
be set predominantly by the leg angle. 6. Body
angle to maintain the Centre of mass will adjust
but it will not change the height gained. 7. Arm
sets will therefore not change the amount of
somersault but will make the body position
easier to reach (more upright) for multiple
somersaults 8. Height gain through an arm swing
technique will give about 30 joules height gain
(5cm) This is approximately the same as 50 of a
tuck somersault. 9. Arm set should therefore have
as much bed contact as possible to incorporate
the energy from Arm swing. Vertical arms on
first contact will not add to height. 10. There
is good video based evidence that body to leg
angle correlates with degree of rotation.