High Altitude Free Fall: Theoretical Analysis of Physical Hazards Impacting Human Subjects

1. High Altitude Free Fall:Theoretical Analysis of Physical Hazards Impacting Human Subjects V. Rygalov, Ph.D., J. Jurist, Ph.D., Space Studies Students (S. Ford, T. Perks, J. Greene) UND Space Studies

2. Agenda • Historic Outline • Challenges of ‘stratospheric sky-diving’ • Free Fall equation • Non-uniform atmospheres • Solution • Approximations & Estimates • Altitudes of maximum deceleration • Maximum G-Forces • Altitudes of trans-sonic transitions • Parachuting from stratosphere • Conclusions • Future research directions

3. Rescue From Space Scenarios • I. Approach based on safety of transportation vehicle • - complete reliance on vehicle safety - reduced capabilities for individual control on ascend/descend - example: traditional space transportation systems (space shuttleor capsule) • II. Approach based on individual rescue scenario • - reliance on individual safety gears and parachuting profile - more control on individual status (preliminary trainings required) - example: MOOSE rescue system which includes scenario of individual free fall/parachuting from stratosphere

4. Historic Outline • Excelsior III, August 16, 1960 • Joe Kittinger, Capt. USAF • 31,333 m (102,800 ft ) • 4 min 36 sec free fall (stabilizing chute) • 988 km/h (614 mph), 9/10 speed of sound • 5,330 m (17,500 ft), main parachute open • 13 min 45 sec, total parachuting time • Extremes: −94 °F (−70 °C ) • HALO/HAHO •  27,000 feet (8,200 m)

5. Felix Baumgartner October 14, 2012: jumped from 39km, reached 1.25 Mach (843.6 mph) • Notables: He started to flat spin right before the transonic transition, approximately between 20–22 km • G-Forces felt during flat spin, less than 2 Gz

6. Challenges of Stratosphere • Primary Life Support • Supplementary oxygen • Altered pressure environments • Pressurized suit • Supersonic impact (I – Forces) • No countermeasures available (?...) • Excessive heat release • Heat-shield… under development • Drag-Forces & G-Forces • No countermeasures available (?...)

7. Assumptions • Speed of sound as 343.2 m/s (isothermal conditions) • Heights characterized for standard atmosphere (Laplace’s isothermal atmosphere: P = Po*e-z/l) • Neglected initial orbital velocity a spacecraft or space station might possess prior to a jump • Free fall is assumed with 0 m/sec initial velocity from 100 Km (Karman Line) • Neglected engineering and technology of space suit construction • Capsules or other equipment proposed for vehicle escape are not considered at this time • Individual rescue is considered as more controllable scenario(preliminary training is critical)

8. Math Model

9. Analytical Solution

10. Free Fall Velocity Profiles Critical transitions

11. Theoretical Summary • Speed of sound depends mostly on atmospheric temperature (not pressure), from previous research • Speed of sound in free fall within Earth atmosphere could be achieved starting from altitudes ~ 38-39 Km (F. Baumgartner) • Maximum velocity in free fall increases non-linearly with initial fall altitude increase • Speed of sound transitions in free fall happens twice during mission:- first transition at higher altitudes (sub-sonic to super-sonic), practically in vacuum, does not provide safety issues- second transition from super-sonic to sub-sonic altitudes happen within dense atmospheric layers, this transition could provide safety concerns- velocity profile at transition is getting steeper with initial fall altitudes- altitude of second transition is approaching to certain limit with initial free fall altitude increase

12. Altitude of Speed of Sound Barrier Transition (formula)

13. Transonic Transition Altitudes Altitude of trans-sonictransition is approachingto ~17.7 Km for free fallfrom altitudes higherthan Karman Line

14. Drag in Laplace’s Atmosphere • Free Fall equation • Mass*Acceleration = Weight – Drag Force • dt = dz/V

15. Drag ~ G - Forces • Drag Forces • Drag in Laplace’s isothermal atmosphere • U = (V/Vt)2 • Const a = 2g/Vt2

16. Decelerations…

17. Analytical Approximations • Altitudes of maximum decelerations ? • Maximum G-Forces ?

18. Max Deceleration Altitudes

19. Max G-Forces

20. Effects of Parachuting

21. Conclusions • Transition from subsonic to supersonic velocities practically occurs in a vacuum when free falling from 100 Km (this transit does not present safety concerns) • Transition from supersonic to subsonic happens significantly lower but theoretically tolerable • It is going to occur at altitudes approximately 18 – 22 Km, in a rarified • Earth’s atmosphere environment • Atmospheric pressure shock waves do not have to present a big concern from a free fall originating from 100 Km and higher • Parachuting has further to mitigate shock waves impact • Analysis & development for free fall/parachuting profiles is required

22. Conclusions (G – Forces) • Stratospheric parachuting is tolerable for human subjects in terms of G-Forces • Altitudes up to 100 Km • Parachuting mitigates G-Forces impact • Scenario of parachute deployment requires independent research • Research & Development are required • Excessive heat reduction (???) • Attitude control • ???

23. Future Directions • Theoretical analysis • Excessive heat release • Which altitudes of free fall are critical? • Degree of criticality? • Potential countermeasures? • Supersonic impact • Which altitudes are critical? • Criticality? • Countermeasures? • Experimentation ???

24. Acknowledgements • UND JDOSAS Space Studies • ND EPSCoR • ICES 41 • Selection Committee • Reviewers • ICES507-A Organizers

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