1. Biomechanics of Jump-rope
Yoonsun (Sunny) Jang
Professor Rome
BIOL 438
Spring 2012

2. 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
* Also called skipping-rope in British
*Great Stamina, endurance, and strength required
(especially to jump fast without stopping; elementary school experience)
*Jumping rope burns up to 1,000 calories an hour and tones calves thighs, upper body, and even firms abdominals.
It can also help with agility, posture, balance, coordination.

3. 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
Exact origin unclear;
(some say it’s originated in China)

4. 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
Video
7. Combination Jumps
2. Alternate Foot Jump (speed step)
Doubles the number of skips per minute
4. Long Jump
(at least three people; elementary school reminiscence-while singing songs)
5. Double Under
(long jump with two jump-ropes triple-under quadruple, quintruples)

5. Research Questions 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
Elastic energy: impossible to measure
But it’s stored in your leg when you bend down the knee and consumed when you stretch out your knee

6. 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 jump-rope

7. 2 Phases of Jump-Rope 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) ① ②

8. Case 1) Normal Jump-rope: Front View

9. Case 1) Normal Jump-rope: Side View

10. 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 

11. Muscles Continued…

12. Case 1) Displacement VS Time

13. Case 1) Velocity VS Time

14. 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

15. Summary Height (m) Potential Energy (J) Velocity (m/s)
Kinetic Energy (J)
Minimum
0.754m
377.2J
0 m/s 0J
Maximum
1.035m
517.8J
①st Cycle)
Take off: m/s
Land: m/s
②nd Cycle)
Take off: m/s
Land: m/s
③rd Cycle)
Take off: m/s
Land: m/s
Take off: 170.9J
Land: 168.3J
Take off: 96.17J
Land: 267.0J
Take off: 123.1J
Land: 118.6J
Maximum velocity & Kinetic energy of take-off and land are supposed to be same

16. Case 2) High Jump-rope: Front View

17. Case 2) High Jump-rope: Side View
Case 1) Normal Jump-rope

18. 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.

19. Case 2) Displacement VS Time

20. Case 2) Velocity VS Time

21. Summary Height (m) Potential Energy (J) Velocity (m/s)
Kinetic Energy (J)
Minimum
0.798m
399.2J
0 m/s 0J
Maximum
1.120m
560.3J
①st Cycle)
Take off: m/s
Land: m/s
②nd Cycle)
Take off: 3.472m/s
Land: m/s
③rd Cycle)
Take off: 3.871m/s
Land: m/s
Take off: 171.6J
Land: 386.1J
Take off: 307.4J
Land: 532.3J
Take off: 382.1J
Land: 336.2J

22. Comparison Between 2 Cases Displacement VS Time
Case 1) Normal Jump-rope
Case 2) High Jump-rope

23. Comparison Between 2 Cases Velocity VS Time
Case 1) Normal Jump-rope
Case 2) High Jump-rope

24. Height (m)
Potential Energy (J)
Velocity (m/s)
Kinetic Energy (J)
Case 1) Min
0.754m
377.2J
0 m/s
0 J
Case 1) Max
1.035m
517.8J
①T: m/s
L: m/s
②T: m/s
L: m/s
③T: m/s
L: m/s
①T: 170.9J
L: 168.3J
②T: 96.17J
L: 267.0J
③T: 123.1J
L: 118.6J
Range
0.281m
140.6J
①0.020 ②1.29 ③0.040
①2.60 ②171 ③4.50
Case 2) Min
0.798m
399.2J
Case 2) Max
1.120m
560.3J
①T: m/s
L: m/s
②T: 3.472m/s
L: m/s
③T: 3.871m/s
L: m/s
①T: 171.6J
L: 386.1J
②T: 307.4J
L: 532.3J
③T: 382.1J
L: 336.2J
0.322m
161.1J
①1.30 ②0.240 ③1.30
①215 ②225 ③45.9

25. Conclusion 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

26. Clinical Significance
JUMPING IS KINDER ON
YOUR JOINTS THAN RUNNING
Run: each foot absorbs up to 5 times body weight from the force of impact as they hit the ground. (heel)
 injury to your feet, ankles, hips, and knees if you overdo it.
Jump roping: the impact is absorbed by both feet (balls of feet), letting calf muscles help control the impact.
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
Cardiovascular Endurance
(Arrhythmia; Jump Rope for Heart)
& Muscular Endurance
Spatial Awareness, Reading Skills, Memory, and Mental Alertness
(hemispheres of the brain)
Improves Dynamic Balance and Coordination, Reflexes, Bone density
(balls of the feet
make neural muscular adjustments
to imbalances created from
continuous jumping )
(Jump Rope for Heart)
national fundraising program;
These programs promote physical education and provide children with knowledge of heart disease and stroke while raising funds for cardiovascular disease research, stroke research, and health education
* there’s minimal impact on your joints.
This is because the bounce comes from the balls of your feet as opposed to your heel, as in running. This decreases the impact on your patella-femoral joint,

27. Limits 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

28. Future Study Questions
Measuring the value of stored elastic energy
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
3. Designing objects moving through the air by engineers
(also referring to the Princeton professor’s finding)

29. 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
(Starting from 2012, the USA Jump Rope Nationals is taking place at Long Beach, California (originally in Texas, though), so feel free to join the competition! Although it might be really hard if you have to do things like the complex double dutch video we just watched)

30. Reference
* Content:
Campus Note Book, FYI: Findings. March 7. Princeton Alumni Weekly, Print. (
Rudd, Johnny. "Exercise Jump Rope." . United States Patent, Web. 18 Apr < muscle&printsec=abstract>
Jump Rope Institute:
Jump Rope for Heart:
Muscles Involved in Jump-rope:
Logger Pro 3.8.3
* Images: