The Physical Demands of Numbers Juggling (Jack Boyce)

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B.Phases of Learning, or "Why Do I Drop?"
1.The Release-Limited Phase
2.The Strength-Limited Phase
3.The Timing-Limited Phase
4.The Reach-Limited Phase
5.The Form-Limited Phase
6.The Collision-Limited Phase
7.The Endurance-Limited Phase
C.Quantifying the Demands of Numbers Juggling
1.The Pattern
2.Throws and Throwing Errors
3.Aside Regarding
4.Avoiding Collisions and Maintaining Good Form
5.A Model Juggler, Simula
6.Results of the Calculation
7.Assumptions and Limitations of the Model
D.Training Summary
help us refine our practice techniques at various point
s along the learning curve, particularly those of us

-- a
1.The first objects thrown are usually the most pr
ecariously-positioned in the hands, and are also the
least familiar. If you are practici
2.The first throws are made with al
fact, on the first throw an arm has to work
roblem there is that
Height (m)
Allowed Height
Error (cm)
5 1.0 13
6 1.5 15
7 1.6 13
8 2.2 16
9 2.2 14
10 3.5 19
11 3.5 18
12 5.0 23
r -- throw to the correct points in space. If it is
The Reach-Limited Phase
ful wa
Height (m)
5 1.0 4.4
6 1.5 2.9
7 1.6 2.7
8 2.2 2.0
9 2.2 2.0
10 3.5 1.2
11 3.5 1.2
12 5.0 0.87
2.Visualize a hoop in space at th
However, it is important to realize th
makes collisions more
computer animation one ca
wing point moves away from the center, closer to
the catching point.
1.My results regarding collisi
2.Above I showed a table indicating the throwing accu
at you don't need to see the first ball clearly to spot
l, although the conclusions
. Refer to the followin
is the height of the pattern,
, which is the fraction of time that each
relatively easy to achieve, as they are just the pos
variation in the catching position is always much gr
directions, respectively.
some average value in a bell-curve way, with some t
of the "bell" (statistically, they are
urement schemes could be devised in that case.
= E = e
average of the
average of the
average of the
(delta H)
(delta X)
(delta Y)
for the balls in their path (his
Height (m)
5 1.0 4.5
6 1.5 1.0
performance: average run
) throws (the former is sometimes called a
ne correspond to throwing errors so large that the
Jack Kalvan
1.At the rightmost (highest
2.As the juggler improves and
ler is throwin
collision-prone, you can to some extent avoid thes
ler. Assum
30 cm, from where it should); we
must keep in mind that the curves above are cert
It would be an interesting line of research to de
velop a more realistic juggling model than we've done
them consistently
pattern, while maintaining
"drop test" to listen for rhythm
h-limited then most
call it "numbers"?), try to ignore the objects in the air. Don't throw
to avoid collisions, but rather focus on maintaini
ed by the fact that everything seems to be going
As an example from my own juggling, I have been sp
ntly so I can catch the balls. I
visualize the two peaking points in space and try to ignor
physical movement and one
stages, as dictated by the various
th toward progress. I would be interested to see how others might
nd identify that certain things about juggling are
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