1. Biomechanics of a Back Somersault
Franklin Jeng
BIOL438

2. What is a Back Somersault?
Also known as a Back Flip or Back Tuck
Common aerobatic stunt performed by gymnasts, divers, and dancers

3. What are the Benefits? Physical Emotional Body Strength
Flexible Upper Body
Coordination and Balance
Dexterity
Emotional
Determination
Resiliency
Courage
Self Confidence

4. What Muscles are Used? Primarily the Legs Quadriceps Gluteus Maximus
Hamstrings
Calves
Secondary Muscles include
Abdominals
Obliques
Lower Back
Biceps
Basically everything

5. Questions Which phase of the back somersault is highest in energy?
Which phase of the somersault do the muscles do the most work?
Does the rotational kinetic energy from the swing of the arms transfer into the rotational kinetic energy of the back somersault? If so, how much of it is transferred.
Does using a trampoline and taking away the factor of height decrease the rotational kinetic energy of the back somersault?

6. Which phase of the back somersault is highest in energy?
Question 1
Which phase of the back somersault is highest in energy?

7. Phases of a Back Somersault
Loading – Bend knees and swing arms back
Take off – Arms driven upward and knees straighten to jump
Tucking – Bring knees up to the chest to rotate
Landing – Complete the flip and land on the feet
Loading Phase – Gymnast bends his knees and swings his arms backward in preparation. The idea is to create the energy needed to jump up into the air and rotate over in the flip. By swinging his arms backward and bending his knees, the gymnast is loading up with potential energy.
Take Off Phase: Gymnast drives his arms upward and straightens his knees quickly as he jumps off the ground.
The Tuck: Gymnast needs to rotate over to land back on his feet. If the take off is good, this part should be easy. By taking off leaning slightly backward (angle of 75 to 80 degrees), you have already created the rotation you require and all you need to do is bring your knees to your chest, which increases rotational speed and easily completes the flip.

8. Standing Back Somersault

9. Center of Mass
(Ucke, 1993)

10. Marking the Center of Mass
Assumed Hip was the Center of Mass throughout the flip

11. Energy Graph
Loading
Take Off
Tucking
Landing

12. Loading Phase

13. Take Off Phase

14. Tucking Phase

15. Landing Phase

16. Change in Gravitational PE
Loading Phase: J – J
Take Off Phase: J – J
Tucking Phase: J – J
Landing Phase: J –
= Joules
= Joules
= Joules
= Joules

17. Max Vertical Kinetic Energy
Loading Phase:
Take Off Phase:
Tucking Phase:
Landing Phase:
Joules
Joules
Joules
Joules

18. Max Horizontal Kinetic Energy
Loading Phase:
Take Off Phase:
Tucking Phase:
Landing Phase:
28.58 Joules
47.79 Joules
Joules
62.55 Joules

19. Max Total Energy (PEgravity+KEhorizontal+KEvertical)
Loading Phase:
Take Off Phase:
Tucking Phase:
Landing Phase:
500.2 Joules
781.5 Joules
897.6 Joules
509.1 Joules

20. Rotational Kinetic Energy of Swing(Loading Phase)
KErotational = ½ Iω2
Moment of Inertia (I)
Assume arm is a rod rotating at 1 pt (shoulder)
Iarm = 1/3 (mupper arm + mforearm)Larm2
= 1/3 ( kg) (.6214 m)2
= kg*m2
Angular Velocity (ω)
ωaverage = Δθ/Δt
= ( rad – rad) / sec
= rad / sec
= rad/ sec
Body segment mass calculated using

21. Rotational Kinetic Energy of Swing(Loading Phase)
KErotational = ½ Iω2
= ½ ( kg*m2)(18.52 rad/ sec)2
= Joules
Two arms are at play during the rotational swing so this value is multiplied by 2
95.38 Joules

22. Rotational Kinetic Energy of the Swing (Take Off Phase)
Moment of Inertia (I)
Iarm = 1/3 (mupper arm + mforearm)Larm2
= 1/3 ( kg) (.6214 m)2
= kg*m2
Angular Velocity (ω)
ωaverage = Δθ/Δt
= ( rad – rad) / sec
= rad / sec
= rad / sec
Body segment mass calculated using

23. Rotational Kinetic Energy of the Swing (Take Off Phase)
KErotational = ½ Iω2
= ½ ( kg*m2)(33.57 rad / sec)2
= Joules
Two arms are at play during the rotational swing so this value is multiplied by 2
Joules

24. Rotational Kinetic Energy (Tucking Phase)
Moment of Inertia (I)
Assume Body is a Rod rotating around center
Ibody = 1/12 (mbody)Lankle to head2
= 1/12 (49.9 kg) ( m)2
= kg*m2
Angular Velocity (ω)
ωaverage = Δθ/Δt
= (1.389 rad rad) / .067 sec
= rad / .067 sec
= rad / sec

25. Rotational Kinetic Energy of the Tuck
KErotational = ½ Iω2
= ½ (5.628 kg*m2)(14.25rad/sec)2
Joules

26. Energy Comparison of the Four Phases
Gravitational
PE (J)
Vertical
KE (J)
Horizontal KE (J)
Rotational KE (J)
Total
Energy (J)
Initial
Phase
455.68
3.67
0.66
460.09
Loading Phase
462.26
12.64
25.33
95.38
595.61
Take Off Phase
492.59
288.48
0.45
313.48
Tucking Phase
542.42
244.32
110.79
571.81
Landing Phase
486.09
4.723
18.29
~ 0
509.10
Assume that Rotational KE is constant throughout each phase
Tucking Phase is highest in Energy

27. Question 2
Which phase of the back somersault do the muscles do the most work?

28. Total Energy (without KErotational) Take-Off Phase
Within the phase, adding KE rotational would not affect difference in Work needed to be done
Muscles does Joules positive work during Take-Off Phase
Did not take into account Elastic PE

29. Total Energy (without KErotational) Tucking Phase
Muscles only does Joules positive work during Tucking Phase
Tucking does not require as much work as the initial take off

30. Question 3
Does the rotational kinetic energy from the swing of the arms transfer into the rotational kinetic energy of the back somersault? If so, how much of it is transferred.

31. Standing Back Somersault (Trampoline)

32. Trampoline – Rotational KE (Arm Swing)
Moment of Inertia (I)
Iarm = 1/3 (mupper arm + mforearm)Larm2
= 1/3 ( kg) (.6214 m)2
= kg*m2
Angular Velocity (ω)
ωaverage = Δθ/Δt
= (1.041 rad – rad) / sec
= .444 rad / sec
= rad / sec

33. Trampoline – Rotational KE (Arm Swing)
KErotational = ½ Iω2
= ½ ( kg*m2)(13.33 rad / sec)2
= Joules
Two arms are at play during the rotational swing so this value is multiplied by 2
49.44 Joules

34. Trampoline – Rotational KE (Tucking Phase)
Moment of Inertia (I)
Ibody = 1/12 (mbody)Lankle to head2
= 1/12 (49.9 kg) (1.051 m)2
= kg*m2
Angular Velocity (ω)
ωaverage = Δθ/Δt
= (1.542 rad – rad) / .066 sec
= rad / .066 sec
= rad / sec

35. Trampoline – Rotational KE (Tucking Phase)
KErotational = ½ Iω2
= ½ (4.593 kg*m2)(16.61 rad/sec)2
Joules

36. Standing Back Somersault No Arms (Trampoline)

37. Trampoline No Arms– Rotational KE (Take Off Phase)
Moment of Inertia (I)
Iarm = 1/3 (mupper arm + mforearm)Larm2
= 1/3 ( kg) (.6214 m)2
= kg*m2
Angular Velocity (ω)
ωaverage = Δθ/Δt
= (1.231 rad – .981 rad) / sec
= rad / sec
= 7.49 rad / sec

38. Trampoline No Arms– Rotational KE (Take Off Phase)
KErotational = ½ Iω2
= ½ ( kg*m2)(7.49 rad / sec)2
= 7.80 Joules
Two arms are at play during the rotational swing so this value is multiplied by 2
15.60 Joules

39. Trampoline No Arms– Rotational KE (Tucking Phase)
Moment of Inertia (I)
Ibody = 1/12 (mbody)Lankle to head2
= 1/12 (49.9 kg) (1.449m)2
= kg*m2
Angular Velocity (ω)
ωaverage = Δθ/Δt
= (0.822 rad – rad) / .033 sec
= rad / sec
= 9.88 rad / sec

40. Trampoline No Arms– Rotational KE (Tucking Phase)
KErotational = ½ Iω2
= ½ (8.731 kg*m2)(9.88 rad / sec)2
Joules

41. Ratio of Rotational KEarm swing to Rotational KEtuck
Floor
155.29
313.48
.495:1
Trampoline
49.44
633.29
.078:1
(No Arms)
15.60
426.03
.037:1
Perhaps KE rotation of arm has a strong relationship to the change in PE
No correlation seen between the two

42. Question 4
Does using a trampoline and taking away the factor of height decrease the rotational kinetic energy of the back somersault?

43. Comparing Rotational KE on the Floor vs Trampoline
KEarm swing
KEtuck
Floor
155.29
313.48
Trampoline
49.44
633.29
(No Arms)
15.60
426.03
Trampoline tends to increase Rotational KEtuck

44. Conclusions Tucking Phase of the back somersault is highest in energy
Muscles do the most work during the Take Off Phase
Most likely to be smaller if we took Elastic PE into consideration
The work required to tuck is less than the work required to take off.
The Rotational Kinetic Energy of the arm swing into a back somersault does not determine determine the Rotational Kinetic Energy of the body during the tucking phase
A trampoline tends to increase the Rotational Kinetic Energy of the tuck even though it eliminates the factor of height

45. Future Direction
How does Elastic Potential Energy come in play during a back somersault?
How does a Round-Off contribute to the overall energy of a back somersault?
How does size and weight contribute to the Rotational KE of a back somersault?
Compare a back somersault to a front somersault:
Which uses more energy?
Which is easier to complete?
How do different landing techniques affect likelihood for injury?

46. References
Body Segment Data. Retrieved from Rush, Morgan. “What are the Benefits of Doing a Back Flip.” Retrieved from Shaw, Lynne. “Muscles that Gymnasts Use.” Retrieved from Ucke, Christian. “Back Somersaults with Jumping Toy Animals.” Physik in der Schule 31 (1993), pg