The Biomechanics of
a Shaposhnikova:
The Impact of a Kconstant
Laura DiPaolo
April 19,2012
Bio438
Springs and Gymnastics
Uneven Bars
•Yeager
•Ginger
•Tkachev
•Shaposhnikova
Muscles Involved in a
Shaposhnikova
My Research Questions:
 How much potential energy is stored in the high
bar during a major release?
 Ex. A Shaposhnikova
 How much energy is lost in a Shaposhnikova?
 Considerations
 How does this impact performance?
 Adjustments
 Testing the Bar
The Shaposhnikova
(shaposh)
Marking Movement: COM
 Center of Mass: the point of balance
 Formula For a two mass system:
 X (cm) = (m1X1 + m2X2) / (m1 + m2)
 Study by Dr. Glen Elert: “The Center of Mass of a
Human” puts the average person’s center of
mass at a location slightly below the belly button.
Ratio:
Center of Mass to Height
http://hypertextbook.com/facts/2006/centerofmass.shtml
Following my movement:
•The Average is about a 0.55 ratio
• 0.55 of my height comes to the place just above my hip (marked
with athletic tape)
Position vs. Time of COM
Potential Energy
 Gravitational Potential Energy:
 PE= mgh
 Spring Potential Energy:
 Hook’s Law
 F= - KX
 PE= ½ KX2
Change in Gravitational
Potential Energy:
 Point1:
 Point 2:
 PE= mgh
 PE= mgh
 PE= (54.4310 kg) (9.8m/s2) (1.92m)
 PE= (54.4310 kg) (9.8m/s2) (2.07m)
 PE= 1024.17 Kg *m2/S2
 PE= 1104.19 Kg *m2/S2
 PE=1.02417 KJ
 PE=1.10419 KJ
Change in PE= 80.02 J
What does this mean?
 This is the change in potential energy as a result
of 2 factors:
 Added elastic potential energy from the bar
 Lost energy in muscles, heat, the bar moving
the wrong way (Ex. Trampoline)
 Back to the research Questions:
 How much potential energy is stored in the high bar
during a major release?
 How much energy is lost in a Shaposhnikova?
Question 1 Part 1:
Finding the K constant
 Hooke’s Law
 F= -K*ΔX
 ma = -K*ΔX
 (54.4310 kg) (-9.8m/s2)= -K*ΔX
 533.424 kg*m/s = K*ΔX
SO, WHAT’S “ΔX”?
Question 1 Part 1:
Finding the K constant
 ΔX=
measured in
Logger Pro
Question 1 Part 1:
Finding the K constant
 Displacement (ΔX):
ΔX1= 0.087m
Question 1 Part 1:
Finding the K constant
 K Constant (Kg/s2):
 K= ma/ΔX
 K= (533.424 kg*m/s2) /0.087m
 K=6131 kg/s2
Question 1 Part 2:
Finding the Elastic Potential
Energy
PE= ½ KX2
ΔX=0.261m
Question 1 Conclusion:
 PE= ½ KX2
 PE=1/2 * (6131.3 kg/s2) * (0.261)2m
 PE=208.8 kg*m2/s2
PE= 208.8 J of energy stored in the
bar– this is the increase I should
have seen in potential energy if I
didn’t lose any energy.
2004 Olympian Tasha schwikert
Question 2: How much
Energy is Lost?
Question 2: Conclusion
 I gained 80.02J, but lost energy
 Considerations:
 Heat
 K-constant calculation: difficulty
associated with clicking accuracy.
 Pulling back on the bar: reaction of the
bar. (Ex. Trampoline)
 Center of mass
Another Look…
1. Pulling back on
bar during the
catch
2. COM
Center of Mass
•
•
•
Cannot be avoided because must pass the low bar
My center of mass is not actually at my hip as I clear the low bar. The center
of mass is returns to my hip in the back-swing.
This breaking of my body position makes me lose “swing”– actually a
technique to slow yourself down in other bar skills
• “Killing the swing”
• Energy is dispersed  arms, shoulders, abdominal muscles
Question 3: Impact on
Performance
 I gained 80.02 J energy from the bar!
 Why is this helpful?
 Need to be within 10° of horizontal
 The more energy from the bar, the less energy must be
transferred to the swing from the body by “tapping”
 How it impacts performance?
 Adjustments: NO universal K constant
 High K constant  less bar movement  “tighter bar” 
more internal work needed by athlete
 Lower K constant  more bar movement  “loose bar”
 athlete must remain “tight” and perform less internal
work
 Testing the bar
Literature
 “The amount of energy stored in the bar is proportional
to the deflection of the bar. Not all the energy stored in
the bar will be returned and so the gymnast needs to
input some extra energy from his muscles to
compensate for this loss. A 'springy' bar is beneficial in a
number if ways” (Kerwin 2005) *study published in 2003
 “Gymnasts have a tendency to pike in the front of the
swing to get their feet above the bars. This ends up
killing the swing” (“Drills and Skills”)
 Varying the tension in the stabilizing cables of the high
bar did not affect the stiffness of the bar (Kerwin 2003).
 Horizontal movement
Future Studies
 Varying the K-constant: Performing the
skill on different equipment
 different age, AAI vs. Speith
 Comparing the energy loss with my
shaposh and someone who is short
enough to maintain a straight body
position
 Closer look at energy loss here
 Measure differences in energy loss and
angle of the “rounded” or “piked”
position
 Compare men and women’s high
bars
Jordyn Weiber
#1 Prospect for 2012 Olympic Games
References
 "Center of Mass." Web. 2 Apr. 2012. <http://hyperphysics.phyastr.gsu.edu/hbase/cm.html>.
 "Center of Mass." Web. 2 Apr. 2012. http://hyperphysics.phyastr.gsu.edu/hbase/cm.html.
 Elastic Potential Energy." Web. 2 Apr. 2012. <http://hyperphysics.phyastr.gsu.edu/hbase/pespr.html>.
 Kerwin, D. G., and M. J. Hiley. "Estimation of Reaction Forces in High Bar Swinging."
Sports Engineering 6.1 (2003): 21-30. Loughborough University. Springer / © ISEA. Web.
25 Mar. 2012. <https://dspace.lboro.ac.uk/dspace-jspui/handle/2134/6528>.
 Kerwin, David. "Swinging in Gymnastics." Swinging in Gymnastics. Gymnastics Info.com,
2005. Web. 14 Apr. 2012.
<http://www.coachesinfo.com/index.php?option=com_content&view=article&id=101
99:gymnastics-isbs-swinging&catid=183:mens-high-bar&Itemid=290>.
 "Mass of a Human Head." Hypertextbook.com. Ed. Glenn Elert. Web. 2 Apr. 2012.
http://hypertextbook.com/facts/2006/DmitriyGekhman.shtml.
 "Parallel Bars Drills and Skills." Gymnastics Page. Web. 14 Apr. 2012.
<http://www.drillsandskills.com/skills/pbar/>.
References
Images:
 http://aura.nswebhost.com/~ballet/images/Spring-Floors.jpg
 http://www.american-gymnast.com/shop/Assets/ProductImages/aai_T10_Vault_Spring_Board.jpg
 http://www.gymn.ca/gymnasticgreats/images/wag/shaposh.jpg
 http://www.unitedathletic.com/images/UAI%20CLUB%20BARS%20WITH%20MATS.jpg
 http://hyperphysics.phy-astr.gsu.edu/hbase/pespr.html
 http://content.clickbooq.com/86/photos/6bc6a5a809.jpg
 http://johngeddert.com/wp-content/uploads/2010/11/Uneven-Bars.jpg
http://laist.com/attachments/la_adam1/tashaschwikert.jpg
 http://gymnasticscoaching.files.wordpress.com/2009/06/gymnast-chalking.jpg
 http://3.bp.blogspot.com/_1rmyHrVm294/TKNVClTL04I/AAAAAAAAACI/ehsyWdL6Zy4/s160
0/trampoline.gif
 https://usagym.org/pages/home/publications/technique/2008/10/cover_lg.jpg
 http://www.medicalook.com/systems_images/Muscles_of_the_Abdominal_Wall.jpg
 http://www.getbodysmart.com/ap/muscularsystem/armmuscles/menu/image.gif