Biomechanics of Jump-rope
Yoonsun (Sunny) Jang
Professor Rome
BIOL 438
Spring 2012
What is Jump-rope?
• Very efficient cardiovascular workout and
muscle toning
• Good calorie burner
• Excellent footwork, coordination, agility, and
balance
• Great stamina, endurance, and strength
required
• Total body workout without leaving home
• Low price & Portable
History of Jump-rope
• 1600 B.C Egyptians and Aborigines of
Australia
• The first Jump-rope: bamboo and vines
found in jungles
• The first evidence: medieval paintings
• 1940s, 1950s: game of choice for city or
town children
• 1970s: increased interest for physical
fitness
Different Types of Jump-rope
1. Basic/Easy Jump
2. Alternate Foot Jump (speed step)
3. Criss-Cross
4. Long Jump
5. Double Under
6. Double Dutch
• Video
• http://www.youtube.com/watch?v=QiGKtLYX90video Video
7. Combination Jumps
Research Questions
1. The relationship between Potential Energy,
and Kinetic Energy during doing jump-rope
2. Comparison of Normal jump-rope and
High jump-rope
3. Clinical use of jump-rope
Definitions
• Center of Mass: middle of my hips
(m: 51kg)
• Upper points: when COM is at the highest
• Lower points: when COM is at the lowest
• One cycle of jump-rope: one full turn of jumprope
2 Phases of Jump-Rope
①
②
① Taking off to Highest Point
② Highest Point to Landing
*Highest point
 Highest potential energy,
 Lowest kinetic energy with almost 0 Velocity
(Logger Pro)
Case 1) Normal Jump-rope:
Front View
Case 1) Normal Jump-rope:
Side View
Muscles Involved in Jump-rope
1.
Primary:
Anterior and Posterior
Deltoids, Biceps, Calf
Forearms, Hips, Triceps,
Hamstrings,
Quadriceps, Gluteus
Maximus,
2.
Supporting:
Pectorals,
Upper and Lower
Abdominals
3.
No Auxiliary
Muscles Continued…
Case 1) Displacement VS Time
Case 1) Velocity VS Time
Calculations
• My Body Mass =51kg
• Potential Energy: U=mgh=51kg*(9.81m/s^2)* “height”
* Minimum: 377.2J
* Maximum: 517.8J
• Kinetic Energy:
KE=(1/2)mv^2=0.5*51kg*(“velocity”^2)
* Minimum: 0 J
* Maximum:
1) Take off- ①170.9J ② 96.17J ③ 123.1J
2) Land- ①168.3J ② 267.0J ③ 118.6J
Summary
Height (m)
Potential Velocity (m/s)
Energy (J)
Kinetic Energy (J)
0.754m
377.2J
0 m/s
0J
Maximum 1.035m
517.8J
①st Cycle)
Take off: 2.589 m/s
Land: -2.569 m/s
①st Cycle)
Take off: 170.9J
Land: 168.3J
②nd Cycle)
Take off: 1.942 m/s
Land: -3.236 m/s
②nd Cycle)
Take off: 96.17J
Land: 267.0J
③rd Cycle)
Take off: 2.197 m/s
Land: -2.157 m/s
③rd Cycle)
Take off: 123.1J
Land: 118.6J
Minimum
Case 2) High Jump-rope:
Front View
Case 2) High Jump-rope
Case 2) High Jump-rope:
Side View
Case 2) High Jump-rope
Case 1) Normal Jump-rope
Additional Background
Information
• Howard Stone,
a professor of mechanical
and aerospace engineering
at Princeton university
found out interesting fact
about aerodynamics of a
moving jump rope. He
devised a mathematical
model that captures the
rope’s bending action.
Then, he discovered that
the middle of the rope,
which moves faster than
the ends, bent away from
the direction of motion.
Case 2) Displacement VS Time
Case 2) Velocity VS Time
Summary
Height (m) Potential Velocity (m/s)
Energy (J)
Kinetic Energy (J)
Minimum
0.798m
399.2J
0J
Maximum
1.120m
560.3J
0 m/s
①st Cycle)
Take off: 2.594 m/s
Land: -3.891 m/s
①st Cycle)
Take off: 171.6J
Land: 386.1J
②nd Cycle)
Take off: 3.472m/s
Land: -4.569m/s
②nd Cycle)
Take off: 307.4J
Land: 532.3J
③rd Cycle)
Take off: 3.871m/s
Land: -3.631m/s
③rd Cycle)
Take off: 382.1J
Land: 336.2J
Comparison Between 2 Cases
Displacement VS Time
Case 1) Normal Jump-rope
Case 2) High Jump-rope
Comparison Between 2 Cases
Velocity VS Time
Case 1) Normal Jump-rope
Case 2) High Jump-rope
Height
(m)
Potential Velocity (m/s)
Energy (J)
Kinetic Energy (J)
Case 1) Min
0.754m
377.2J
0 m/s
0J
Case 1) Max
1.035m
517.8J
①T:
L:
②T:
L:
③T:
L:
①T:
L:
②T:
L:
③T:
L:
Range
0.281m
140.6J
①0.020 ②1.29 ③0.040 ①2.60 ②171 ③4.50
Case 2) Min
0.798m
399.2J
0 m/s
0J
Case 2) Max
1.120m
560.3J
①T:
L:
②T:
L:
③T:
L:
①T:
L:
②T:
L:
③T:
L:
Range
0.322m
161.1J
①1.30 ②0.240 ③1.30
2.589 m/s
-2.569 m/s
1.942 m/s
-3.236 m/s
2.197 m/s
-2.157 m/s
2.594 m/s
-3.891 m/s
3.472m/s
-4.569m/s
3.871m/s
-3.631m/s
170.9J
168.3J
96.17J
267.0J
123.1J
118.6J
171.6J
386.1J
307.4J
532.3J
382.1J
336.2J
①215 ②225 ③45.9
Conclusion
1. At the highest point, Potential Energy is
Maximum while Kinetic Energy is minimum (0). Also,
Kinetic Energy is maximum when taking off and landing.
(KE for both are similar)
* Total Energy > Potential Energy +
Kinetic Energy (due to Elastic Energy)
2. Wider range of Height, PE, Velocity, and KE
difference for 2nd High Jump-rope case; more
influenced by other variables;
high jump does not necessarily mean fast jump
3. The converse relationship between the position
of the middle of the rope and the position of
COM
Clinical Significance
JUMPING IS KINDER ON
YOUR JOINTS THAN RUNNING
• Cardiovascular Endurance
(Arrhythmia; Jump Rope for Heart)
& Muscular Endurance
• Run: each foot absorbs up to 5
• Spatial Awareness, Reading Skills,
times body weight from the force
Memory, and Mental Alertness
of impact as they hit the ground.
(hemispheres of the brain)
(heel)
• Improves Dynamic Balance and
 injury to your feet, ankles, hips,
Coordination, Reflexes, Bone
and knees if you overdo it.
density
Jump roping: the impact is
(balls of the feet
absorbed by both feet (balls of
make neural muscular adjustments
feet), letting calf muscles help
to imbalances created from
control the impact.
continuous jumping )
• American College of Sports
Medicine: to improve heart
health, people should skip rope at
least 3~5 times a week for 12 to
20 minutes.
• 10 minutes non-stop Jump-roping
= 1 mile run =18 holes of golf
= 2 sets of tennis singles
=720 yards of swimming
Limits
1. Huge difference sometimes in different cycles:
* My left-to-right motion in X-direction (horizontal W)
* Only 3 cycles used for calculating KE
* Many environmental variables exist
(wind, broken tripod)
2. Calculation of stored elastic energy was in fact
impossible.
Qualitatively, it is stored when you bend your knees
and land down and decreases when you take off
from the ground
3. Energy by friction might be lost
Future Study Questions
1. Measuring the value of stored elastic
energy
2. Comparison in impact between running
and jump-rope
3. Making other variables constant
(ex: wind-experimenting inside with a lot of
light)
4. Designing objects moving through the air
by engineers
5. Angular momentum of Jump-rope
For those who are interested in
• USA Jump Rope (USAJR): hundreds of
teams and jumpers all over the country
• Athletes of all ages, but mostly graduate
school to high school-aged people
• Compete against each other every June
Reference
* Content:
•Campus Note Book, FYI: Findings. March 7. Princeton Alumni Weekly, 2012. 21. Print.
(http://paw.princeton.edu/issues/2012/03/07/pages/0811/index.xml)
•Rudd, Johnny. "Exercise Jump Rope." . United States Patent, 19061990. Web. 18 Apr
2012.
<http://www.google.com/patents?hl=ko&lr=&vid=USPAT4934691&id=_f8gAAAAEBAJ
&oi=fnd&dq=jump-rope muscle&printsec=abstract>
•Jump Rope Institute: http://www.jumpropeinstitute.com/benefits.htm
•Jump Rope for Heart: http://www.aahperd.org/jump/aboutjump/
•Muscles Involved in Jump-rope: http://www.youtube.com/watch?v=ioA1wfq7vcg
•Logger Pro 3.8.3
* Images:
•http://www.livestrong.com/article/25493-muscles-used-jump-rope/
•http://www.wikihow.com/Jump-Rope
•http://www.foothillforce.com/images/photos/classMay2010.jpg
•http://www.jumpropeinstitute.com/kids.htm
•http://www.divavillage.com/article/id/43668/section_name/Food+%26+Fitness/title/Ju
mp+Rope+for+Fitness/pg/1
•http://www.stretchingworld.com/anterior_deltiod_stretches.html