High Altitude Free Fall:High Altitude Free Fall:Theoretical Analysis of Theoretical Analysis of

Physical Hazards Impacting Physical Hazards Impacting Human SubjectsHuman Subjects

V. Rygalov, Ph.D., J. Jurist, Ph.D., V. Rygalov, Ph.D., J. Jurist, Ph.D., Space Studies Students Space Studies Students

(S. Ford, T. Perks, J. Greene)(S. Ford, T. Perks, J. Greene)UND Space StudiesUND Space Studies

Agenda Agenda Historic OutlineHistoric OutlineChallenges of ‘stratospheric sky-diving’Challenges of ‘stratospheric sky-diving’Free Fall equationFree Fall equation– Non-uniform atmospheresNon-uniform atmospheres– Solution Solution

Approximations & EstimatesApproximations & Estimates– Altitudes of maximum decelerationAltitudes of maximum deceleration– Maximum G-ForcesMaximum G-Forces– Altitudes of trans-sonic transitionsAltitudes of trans-sonic transitions– Parachuting from stratosphereParachuting from stratosphere

Conclusions Conclusions Future research directions Future research directions

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

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Historic OutlineHistoric Outline

Excelsior III, August 16, 1960Excelsior III, August 16, 1960– Joe Kittinger, Capt. USAFJoe Kittinger, Capt. USAF– 31,333 m (102,800 ft )31,333 m (102,800 ft )– 4 min 36 sec free fall (stabilizing chute)4 min 36 sec free fall (stabilizing chute)

988 km/h (614 mph), 9/10 speed of sound988 km/h (614 mph), 9/10 speed of sound

– 5,330 m (17,500 ft), main parachute open5,330 m (17,500 ft), main parachute open 13 min 45 sec, total parachuting time13 min 45 sec, total parachuting time

– Extremes: −94 °F (−70 °C )Extremes: −94 °F (−70 °C )

HALO/HAHOHALO/HAHO– 27,000 feet (8,200 m) 27,000 feet (8,200 m)

Felix BaumgartnerFelix Baumgartner October 14, 2012: jumped from 39km, reached 1.25 Mach October 14, 2012: jumped from 39km, reached 1.25 Mach (843.6 mph)(843.6 mph)

Notables: Notables: He started to flat spin right He started to flat spin right before the transonic transition, before the transonic transition, approximately between 20–22 kmapproximately between 20–22 km

G-Forces felt during flat spin, G-Forces felt during flat spin, less than 2 Gz less than 2 Gz

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Challenges of Stratosphere Challenges of Stratosphere Primary Life SupportPrimary Life Support– Supplementary oxygenSupplementary oxygen

Altered pressure environmentsAltered pressure environments– Pressurized suit Pressurized suit

Supersonic impact (I – Forces)Supersonic impact (I – Forces)– No countermeasures available (?...)No countermeasures available (?...)

Excessive heat releaseExcessive heat release– Heat-shield… under developmentHeat-shield… under development

Drag-Forces & G-ForcesDrag-Forces & G-Forces– No countermeasures available (?...)No countermeasures available (?...)

AssumptionsAssumptions

Speed of sound as 343.2 m/s (isothermal conditions)Speed of sound as 343.2 m/s (isothermal conditions)

Heights characterized for standard atmosphere (Laplace’s Heights characterized for standard atmosphere (Laplace’s isothermal atmosphere: P = Pisothermal atmosphere: P = Poo*e*e-z/l-z/l))

Neglected initial orbital velocity a spacecraft or space station Neglected initial orbital velocity a spacecraft or space station might possess prior to a jumpmight possess prior to a jump– Free fall is assumed with 0 m/sec initial velocity from 100 Km Free fall is assumed with 0 m/sec initial velocity from 100 Km

(Karman Line) (Karman Line)

Neglected engineering and technology of space suit Neglected engineering and technology of space suit constructionconstruction

Capsules or other equipment proposed for vehicle escape are Capsules or other equipment proposed for vehicle escape are not considered at this time not considered at this time – Individual rescue is considered as more controllable scenarioIndividual rescue is considered as more controllable scenario

(preliminary training is critical)(preliminary training is critical)

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Math ModelMath Model

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Analytical SolutionAnalytical Solution

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Free Fall Velocity ProfilesFree Fall Velocity Profiles

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Critical transitions

Theoretical Summary Theoretical Summary Speed of sound depends mostly on atmospheric temperature (not Speed of sound depends mostly on atmospheric temperature (not pressure), pressure), from previous researchfrom previous research

Speed of sound in free fall within Earth atmosphere could be achieved Speed of sound in free fall within Earth atmosphere could be achieved starting from altitudes ~ 38-39 Km (F. Baumgartner)starting from altitudes ~ 38-39 Km (F. Baumgartner)

Maximum velocity in free fall increases non-linearly with initial fall Maximum velocity in free fall increases non-linearly with initial fall altitude increasealtitude increase

Speed of sound transitions in free fall happens twice during mission:Speed of sound transitions in free fall happens twice during mission:- first transition at higher altitudes (sub-sonic to super-sonic), - first transition at higher altitudes (sub-sonic to super-sonic), practically in vacuum, does not provide safety issuespractically in vacuum, does not provide safety issues- - second transition from super-sonic to sub-sonic altitudes second transition from super-sonic to sub-sonic altitudes happen within dense atmospheric layers, this transition could happen within dense atmospheric layers, this transition could provide safety concernsprovide safety concerns- - velocity profile at transition is getting steeper with initial fall velocity profile at transition is getting steeper with initial fall altitudesaltitudes- altitude of second transition is approaching to certain limit with initial - altitude of second transition is approaching to certain limit with initial free fall altitude increasefree fall altitude increase

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

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Transonic Transition Altitudes Transonic Transition Altitudes

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Altitude of trans-sonictransition is approachingto ~17.7 Km for free fallfrom altitudes higherthan Karman Line

Drag in Laplace’s AtmosphereDrag in Laplace’s Atmosphere

Free Fall equationFree Fall equation– Mass*Acceleration = Weight – Drag ForceMass*Acceleration = Weight – Drag Force–

– dt = dz/Vdt = dz/V–

Drag ~ G - ForcesDrag ~ G - Forces

Drag ForcesDrag Forces–

Drag in Laplace’s isothermal atmosphereDrag in Laplace’s isothermal atmosphere– U = (V/Vt)U = (V/Vt)22

– Const a = 2gConst a = 2g/Vt/Vt22

Decelerations…Decelerations…

Analytical ApproximationsAnalytical Approximations

Altitudes of maximum decelerations ?Altitudes of maximum decelerations ?

Maximum G-Forces ?Maximum G-Forces ?

Max Deceleration Altitudes Max Deceleration Altitudes

Max G-ForcesMax G-Forces

Effects of ParachutingEffects of Parachuting

ConclusionsConclusions

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Conclusions (G – Forces) Conclusions (G – Forces) Stratospheric parachuting is tolerable for Stratospheric parachuting is tolerable for human subjects in terms of G-Forceshuman subjects in terms of G-Forces– Altitudes up to 100 KmAltitudes up to 100 Km– Parachuting mitigates G-Forces impactParachuting mitigates G-Forces impact

Scenario of parachute deployment requires Scenario of parachute deployment requires independent researchindependent research

Research & Development are requiredResearch & Development are required– Excessive heat reduction (???)Excessive heat reduction (???)– Attitude controlAttitude control– ??????

Future Directions Future Directions

Theoretical analysisTheoretical analysis– Excessive heat releaseExcessive heat release

Which altitudes of free fall are critical?Which altitudes of free fall are critical?

Degree of criticality?Degree of criticality?

Potential countermeasures?Potential countermeasures?

– Supersonic impactSupersonic impact Which altitudes are critical?Which altitudes are critical?

Criticality?Criticality?

Countermeasures?Countermeasures?

Experimentation ???Experimentation ???

AcknowledgementsAcknowledgements

UND JDOSAS Space Studies UND JDOSAS Space Studies – ND EPSCoRND EPSCoR

ICES 41ICES 41– Selection CommitteeSelection Committee– ReviewersReviewers– ICES507-A Organizers

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