oscalc – opening shock calculator version 1.01 … · 1 oscalc – opening shock calculator...

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OSCALC OSCALC –– Opening Shock CalculatorOpening Shock CalculatorVersion 1.01Version 1.01

User’s manual User’s manual

Gary Peek & Jean PotvinGary Peek & Jean PotvinParks College Parachute Research GroupParks College Parachute Research Group

Saint Louis University, St. Louis MOSaint Louis University, St. Louis MOContact: Contact: [email protected]@industrologic.com 800800--435435--19751975

[email protected]@slu.edu 314314--977977--84248424

Manual revised 07-17-06

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ContentsContents

AcknowledgmentAcknowledgmentWarning Warning -- DisclaimerDisclaimer1.1. What is OSCALC?What is OSCALC?2. Basic input data2. Basic input data3. How to run OSCALC?3. How to run OSCALC?4. More information on inflation time4. More information on inflation time5. Some tricks to estimate the fall speed at line stretch5. Some tricks to estimate the fall speed at line stretch6. Examples6. Examples7. OSCALC 7. OSCALC error/warningerror/warning messagesmessages8. Concluding remarks8. Concluding remarks

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AcknowledgmentAcknowledgmentOSCALC was developped under US ArmyOSCALC was developped under US Army--Natick contract W9124RNatick contract W9124R--0606--PP--1068. The authors would like to thank Dr. Dean F. Wolf for allo1068. The authors would like to thank Dr. Dean F. Wolf for allowing the wing the display of his two display of his two CCkk--RRmm graphs in this program. They would like tographs in this program. They would like tothank also thethank also the Natick Soldier Center (U.S. Army RDECOM), Natick Soldier Center (U.S. Army RDECOM), Airdrop/Aerial Delivery Directorate (Airdrop Technology Team) foAirdrop/Aerial Delivery Directorate (Airdrop Technology Team) for their r their continued support of this project.continued support of this project.

Version TrackerVersion TrackerThis manual covers the use of both OSCALC V1.0 and V1.01. VersioThis manual covers the use of both OSCALC V1.0 and V1.01. Version 1.01n 1.01is the same as version of V1.0, except for slightly modified inpis the same as version of V1.0, except for slightly modified input box titles.ut box titles.

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Warning Warning -- DisclaimerDisclaimerOSCALC provides the means to estimate the value of the maximumOSCALC provides the means to estimate the value of the maximumdrag generated during parachute inflation, based on inputs providrag generated during parachute inflation, based on inputs provided by ded by the user. The authors and their governmental funding agency cannthe user. The authors and their governmental funding agency cannototmake any claim on the accuracy of the results.make any claim on the accuracy of the results.

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1. What is OSCALC?1. What is OSCALC?

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1. 1. OOpening pening SShock hock CALCCALCulatorulator†† –– What is it?What is it?•• It is a simple program that estimates the maximum (drag) forceIt is a simple program that estimates the maximum (drag) force

FFmaxmax generated during parachute inflationgenerated during parachute inflation•• Uses inputs that are “straightforward” to obtain Uses inputs that are “straightforward” to obtain •• Calculation applies to Calculation applies to anyany parachute design and reefing type:parachute design and reefing type:

-- lowlow-- and highand high--porosity hemisphericals (unreefed, reefed, disporosity hemisphericals (unreefed, reefed, dis--reefingreefing))-- parafoils (unreefed, lineparafoils (unreefed, line--reefed, sliderreefed, slider--reefedreefed))-- in fact, in fact, anything that can be used as a parachuteanything that can be used as a parachute

•• Is it based on an equation commonly used in parachute engineeriIs it based on an equation commonly used in parachute engineering:ng:

ksdDstretch CSCVF ⎟⎠⎞⎜

⎝⎛⎟⎠⎞⎜

⎝⎛= 2

21

max ρ

From graph in pop-under/over window

From the inputs of the problem

OSCALC computesthis number

________________________________

††Pronounced as Pronounced as ““OO””--””SS”” –– ““CALCCALC””

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OSCALC OSCALC –– other features; restrictionsother features; restrictions

FeaturesFeatures

•• Run on the Microsoft Windows operating systemRun on the Microsoft Windows operating system•• Inputs can be made using any unit systemInputs can be made using any unit system•• Instant processing speedInstant processing speed

RestrictionsRestrictions

•• Restricted to parachutes attached to unpowered payloads (no motRestricted to parachutes attached to unpowered payloads (no motors ors ––gravity is OK); there is no guarantee that OSCALC will producegravity is OK); there is no guarantee that OSCALC will produce, for , for example, an accurate calculation of the maximum force sustaineexample, an accurate calculation of the maximum force sustained byd bya parachute deploying while being connected to an ejection seaa parachute deploying while being connected to an ejection seattpropelled by a rocketpropelled by a rocket

•• OSCALC is not a true predictor of opening shock since it requirOSCALC is not a true predictor of opening shock since it requires the es the use of use of ttfillfill ((nnfillfill), which is an actual inflation performance variable; but), which is an actual inflation performance variable; butthere is a lot of there is a lot of nnfillfill --data in the public domain already; otherwisedata in the public domain already; otherwisemeasuring measuring ttfillfill from video is a straightforward taskfrom video is a straightforward task

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What applications is it most useful for?What applications is it most useful for?

•• FFmaxmax--estimation at the DZ, right after a test: OSCALC provides estimation at the DZ, right after a test: OSCALC provides the means for calculating the means for calculating FFmaxmax, based solely on the basic canopy, based solely on the basic canopydimensions & drag properties, payload weight, deployment conddimensions & drag properties, payload weight, deployment conditionsitionsand video of the inflation process (for inflation time info).and video of the inflation process (for inflation time info). The tool The tool should be very useful during those tests where the payload isshould be very useful during those tests where the payload is not not equipped with load cells or accelerometers.equipped with load cells or accelerometers.

•• Provides a good guess for Provides a good guess for FFmaxmax, even for new parachute and reefing , even for new parachute and reefing designs, including designs that have not yet been documented designs, including designs that have not yet been documented in the in the public domain (see Section 6.6 for suggestions)public domain (see Section 6.6 for suggestions)

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What applications is it most useful for? What applications is it most useful for? –– cont’dcont’d

•• “Sanity”“Sanity”--check for developers of computer simulations of thecheck for developers of computer simulations of theinflation processinflation process

•• Calculation of Calculation of FFmaxmax sustained during inflation scenarios that are sustained during inflation scenarios that are not covered by computer simulations of inflation such as PIMSnot covered by computer simulations of inflation such as PIMS, , FSI/CFD, Sandia model, etc.; for example: malfunctions, misFSI/CFD, Sandia model, etc.; for example: malfunctions, mis--stagedstagedopenings, etc. Again, all one needs here is video to get the openings, etc. Again, all one needs here is video to get the inflationinflationtime informationtime information

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What is the unit system of OSCALC?What is the unit system of OSCALC?

•• No physical constants are being used explicitly No physical constants are being used explicitly –– the only dimensional the only dimensional equation isequation is

•• Most variables are used in nonMost variables are used in non--dimensional form (ratios)dimensional form (ratios)

Input values can be entered in any units, Input values can be entered in any units, as long as they areas long as they arebalanced and consistent.balanced and consistent. We recommend using either:We recommend using either:

••American StandardAmerican Standard Units, based on Units, based on feetfeet, , secondsseconds, , slugs and poundsslugs and pounds

oror

•• Metric Units, based on Metric Units, based on meters, seconds, kilograms and Newtonsmeters, seconds, kilograms and Newtons

The examples of Section 6 show how to enter OSCALC inputs using The examples of Section 6 show how to enter OSCALC inputs using American Standard Units.American Standard Units.


⎝⎛⎟⎠⎞⎜

⎝⎛= 2

21

max ρ

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2. Basic input data2. Basic input data

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2. Basic input data2. Basic input data

•• VVstretchstretch = parachute= parachute--payload fall rate at line stretch; or at the payload fall rate at line stretch; or at the moment of “first air” for canopymoment of “first air” for canopy--first deployments; or whenever thefirst deployments; or whenever thecanopy is stretched and its mouth opened (or wing inlets opencanopy is stretched and its mouth opened (or wing inlets opened)ed)

•• ρρ = Atmopsheric density at deployment altitude= Atmopsheric density at deployment altitude

•• (SC(SCDD))sdsd = Drag area of the fully opened canopy during steady = Drag area of the fully opened canopy during steady descent. descent.

-- For For hemispherical canopieshemispherical canopies ((SCSCDD))sdsd = C= CD0D0 SS00 = C= CD0D0 ((ππ DD0022/4)/4)

with with SS00 being to total canopy area, including ventsbeing to total canopy area, including vents’’ area [1]area [1]-- For For parafoilsparafoils (SC(SCDD))sdsd = = CCD0D0 SS00 ~ 1.0~ 1.0 xx wing chordwing chord xx wing spanwing span-- For a cluster of hemispherical canopies For a cluster of hemispherical canopies -- see example 6.5 in see example 6.5 in

Section 6Section 6 belowbelow

•• CCkk = Opening shock factor = Opening shock factor -- What are the values of What are the values of CCkk??


⎝⎛⎟⎠⎞⎜

⎝⎛= 2

21

max ρ

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Basic references about the Opening Shock FactorBasic references about the Opening Shock Factor CCkk

[1] T. W. Knacke, “Parachute Recovery Systems Design Manual”; Para Publishing (Santa Barbara, CA 1992).

[2] Ewing, E. G., Bixby, H. W. and Knacke, T. W.; “Recovery Systems Design guide”; pp. 254 – 257; report AFFL-TR-78-151. Submitted to: Air Force Flight Dynamics Laboratory, AF Wright Aeronautical Laboratories, Wright-Patterson Air Forced Base, December 1978. Unpublished.

[3] Wolf, D., “Opening Shock”, AIAA-99-1702, 15th CEAS/AIAA Aerodynamic Decelerator Systems Technology Conference, Toulouse, France, 8-11 June 1999.

[4] Potvin, J.; “On Opening Shock Factor - Mass Ratio Universality”; To appear in Journal of Aircraft (2006) Copies of manuscript available on request.

[5] Potvin, J., and Peek, G.; “Parachute Inflation I – General Phenomenoloy”; lecturedelivered at the 2006 H.G. Heinrich Parachute Systems Short Course; May 15 – 19, 2006;copies available on request.

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What are the values of What are the values of CCkk??

•• Originally defined asOriginally defined as

•• Over the years the values of Over the years the values of CCkk for different parachute systemsfor different parachute systemshave been collected by many authors have been collected by many authors –– see references [1 see references [1 –– 3]3]

•• It was found that this It was found that this CCkk data show distinct trends when plotteddata show distinct trends when plottedagainst the against the mass ratio mass ratio RRmm

Here Here mm = total mass of the payload= total mass of the payload--parachute systemparachute system

sdSCV

F

DstretchkC

⎟⎠⎞

⎜⎝⎛⎟⎠⎞⎜

⎝⎛

=2

21

max

ρ

( )( )m

SCR sdD

m

2/3ρ=

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Opening Shock Factor Opening Shock Factor –– Unreefed or permanently reefedUnreefed or permanently reefedhemispherical canopies (lowhemispherical canopies (low-- and highand high--porosity)porosity)(compiled by Wolf [3])

Drogues and pilot chutes;Drogues and pilot chutes;All chutes deployed in wind tunnelsAll chutes deployed in wind tunnels

Personnel and cargo airdropPersonnel and cargo airdropparachute applications @ low altitudesparachute applications @ low altitudes

CCkk at at RRm m = 0= 0is called is called CCXXin Knacke [1]in Knacke [1]

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Opening Shock Factor Opening Shock Factor –– disdis--reefing hemispherical canopies reefing hemispherical canopies (low(low-- and highand high--porosity)porosity)(compiled by Wolf[3])

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More CMore Ckk datadata

(Figure extracted from the USAF parachutedesign guide – reference [2])

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Some important questions about Some important questions about CCkk

1) Why is the value of 1) Why is the value of CCkk for the “unreefed/permanent reefing” for the “unreefed/permanent reefing” CCkk--vsvs--RRmmgraph different from that of the “disgraph different from that of the “dis--reefing” graph?reefing” graph?

2) These graphs were built out of the data collected on hemisphe2) These graphs were built out of the data collected on hemispherical rical parachutes; parachutes; what about the what about the CCkk data of parafoils, sliderdata of parafoils, slider--reefed parachutes reefed parachutes and other parachute and reefing types?and other parachute and reefing types?Would those data fit in the same two graphs??Would those data fit in the same two graphs??

AnswersAnswers

1)1) Filling timeFilling time (or “inflation” time) is the key(or “inflation” time) is the key--conceptconcept

2) Yes, these two graphs can accommodate the 2) Yes, these two graphs can accommodate the CCkk--data of data of anyany parachute parachute and reefing/disand reefing/dis--reefing typereefing type

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Back to college physics Back to college physics --MomentumMomentum--Impulse Theorem (details in reference [4]) Impulse Theorem (details in reference [4])

(integral version of F = ma)

∫ ∫+==−

f

i

f

i

dttWdttFimpulsemVmV Dif )(cos)( θ

( ) [ ] ∫+⋅−=−f

i

ifFif dttWItCSCVmVmV fillksdDi )(cos)(2

21 θρ

∫ −=

f

iif

D

ttF

dttFI if

F )(

)(

max

IIFFifif =Drag integral =Drag integral –– “area under the curve”“area under the curve”

Fmax

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Solve the momentumSolve the momentum--impulse equation to get impulse equation to get CCkk

Γ=gen

fillm

k

nRC 2

ifF

ifigen

fillI

SC

ttVn

sdD2/1)(

)( −≡

verticaltVg

VV

horizontalVV

V

dttgVV

fillii

f

i

f

i

f

i

if

+−=

−=

+−−

≡Γ∫

1

1

)(cos)( θMass ratioMass ratio

““Generalized” filling timeGeneralized” filling time

ifFfill

gen

fillI

SCDnn

sdD2/1)(

0=

GeneralResult!Reflectsdirectly F = ma;See ref. [4]

Standard filling time~ 0.4 – 0.5 @ high-Rm -&- 0.2 – 0.4 @ low-Rm

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stretchtfill

fillV

D

tn

0

=

•• The MomentumThe Momentum--Impulse Theorem confirms the importance of the mass Impulse Theorem confirms the importance of the mass ratio ratio RRmm in determining the value of in determining the value of CCkk

•• The Theorem also makes clear that the The Theorem also makes clear that the inflation time (or inflation time (or ““fillingfilling”” time)time) is is another crutial ingredientanother crutial ingredient

•• OSCALC uses three different concepts of filling time:OSCALC uses three different concepts of filling time:

-- Actual inflation time: Actual inflation time: ttfillfill (has dimensions of time)(has dimensions of time)-- Standard nonStandard non--dimensional filling time dimensional filling time nnfill fill (has no dimensions)(has no dimensions)-- Generalized nonGeneralized non--dimensional filling time dimensional filling time nnfillfill

gengen (has no dimensions)(has no dimensions)

Both Both ttfillfill and and DD00 are defined on next slide are defined on next slide →→

ifFfill

gen

fillI

SCDnn

sdD2/1)(

0=

Γ=gen

fillm

k

nRC 2

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Filling time, or inflation time Filling time, or inflation time ttfill fill -- DEFINITIONDEFINITION

•• At highAt high--RRmm: : ttfill fill = (dimensional) time interval elapsed between line stretch = (dimensional) time interval elapsed between line stretch and the moment when the canopy reaches its designed steadyand the moment when the canopy reaches its designed steady--state state diameter for the first time (as the parachute oftendiameter for the first time (as the parachute often--times overtimes over--inflates)inflates)

•• At lowAt low--RRmm: : ttfill fill = (dimensional) time interval elapsed between line= (dimensional) time interval elapsed between line--stretch stretch and the moment when the canopy reaches its maximum extensionand the moment when the canopy reaches its maximum extension

•• DD00 = “nominal” canopy diameter (= “nominal” canopy diameter (hemisphericalshemisphericals) = ) = (4S(4S00//ππ))1/21/2

with with SS00 = total canopy surface area, inlcuding the area of the vents= total canopy surface area, inlcuding the area of the ventsand all other openings [1]and all other openings [1]

•• DD00 = diameter of circle of same area as wing = diameter of circle of same area as wing span span x chordchord ((parafoilsparafoils))

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•• There is a lot of data on the nonThere is a lot of data on the non--dimensional filling time dimensional filling time nnfillfill ––for details see Section 4 below for details see Section 4 below

•• Note that Note that ttfillfill can be obtained from the analysis of the video of thecan be obtained from the analysis of the video of theinflation process; inflation process; nnfillfill is then calculated, using this value of is then calculated, using this value of ttfill fill , , as well as well as the value of as the value of DD00 and an estimate of and an estimate of VVstretchstretch

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How is inflation time used in the How is inflation time used in the CCkk--RRmm graphs?graphs?

•• One chooses the “right” graph according to the value of theOne chooses the “right” graph according to the value of thegeneralized filling time generalized filling time nnfillfill

gengen -- see next two slides see next two slides ( the “colored” ( the “colored” data points were collected by GP and JPdata points were collected by GP and JP††††). More details can be found ). More details can be found in reference [4].in reference [4].

→→ If If nnfillfillgengen ≥≥ 44, the user chooses the graph formely associated with , the user chooses the graph formely associated with unun--reefedreefed

and reefedand reefed in Wolfin Wolf’’s compilations compilation

→→ If If 1 1 ≤≤ nnfillfillgengen < < 44, the user chooses the graph formely associated with, the user chooses the graph formely associated with

disdis--reefingreefing in Wolfin Wolf’’s compilations compilation

______________††††Note: The Note: The ““halfhalf--scale Cscale C--9 9 -- unreefedunreefed”” data shown on the smalldata shown on the small--nnfillfill graph characterized a graph characterized a

parachute system with unusually large riser separation, whichparachute system with unusually large riser separation, which yielded unusually shorter yielded unusually shorter filling timesfilling times

25

Full-scale TCD(Deep cone)

Original graph from: D. Wolf - paper AIAA-99-1702; “colored” data points collected by GP and JP

Unreefed C-9

Reefed C-9 (24%)

T-10C

MC1-1C

Half-scale C-9;Reefed at 16%

Aeroconical/steerable – GQ Security CrossbowAeroconical/steerable – National Phantom

Long NonLong Non--Dimensional Filling TimeDimensional Filling Timenfill

gen ≥ 4

26Parafoil - ParaFlite Strato Cloud – no sliderParafoil - Precision Aero Falcon 175 – no sliderHalf-scale C-9 - unreefed

Aeroconical/steerable – GQ Security CrossbowAeroconical/steerable – Pioneer K22

Aeroconical/steerable – National Phantom

Short NonShort Non--Dimensional Filling TimeDimensional Filling Time


Long NonLong Non--Dimensional Filling TimeDimensional Filling Time1 ≤ nfill

gen < 4

27

•• NOTE: OSCALC uses the following approximation for calculatingNOTE: OSCALC uses the following approximation for calculatingthe value of the value of IIFF

ifif

-- If If RRmm > 0.10 then > 0.10 then IIFFif if = 0.5= 0.5

-- If If RRmm < 0.01 then< 0.01 then IIFFif if = 0.2= 0.2

-- If 0.01 If 0.01 ≤≤ RRmm ≤≤ 0.10 then 0.10 then IIFFif if = (0.5 + 0.2)/2= (0.5 + 0.2)/2

•• NOTE: The integral NOTE: The integral ΓΓ is one of the factors that generates the scatteris one of the factors that generates the scatterin the two graphs; OSCALC does not computes in the two graphs; OSCALC does not computes ΓΓ but accounts forbut accounts forit through the it through the CCkk--lower and upper bounds that must be enteredlower and upper bounds that must be entered

ifFfill

acftgen

fillI

SC

Dnn

sdD2/1)(

0, =Γ=gen

fillm

k

nRC 2

28

To recapTo recap

•• The value of The value of nnfillfill determine which one of the two determine which one of the two CCkk vs. vs. RRmmgraphs to use graphs to use

•• From the chosen graph, the value of From the chosen graph, the value of CCkk, of its lower bound, of its lower boundand of its upper bound are obtained by spotting the and of its upper bound are obtained by spotting the RRmm––valuevalueof the system under consideration of the system under consideration -- see next slide for examplesee next slide for example

•• FFmaxmax is finally calculated from this is finally calculated from this CCkk data and from the other data and from the other basic inputs basic inputs (SC(SCDD))sdsd , , ρρ and and VVstretchstretch;; its upper and lower boundsits upper and lower boundsare estimated as well, using the upper and lower bounds of are estimated as well, using the upper and lower bounds of CCkk

•• Note: Section 7 explains what to do when Note: Section 7 explains what to do when nnfillfillgengen < 1< 1


⎝⎛⎟⎠⎞⎜

⎝⎛= 2

21

max ρ

29

Full-scale TCD(Deep cone)


Unreefed C-9

Reefed C-9 (24%)

T-10C

MC1-1C

Half-scale C-9;Reefed at 16%

Aeroconical/steerable – GQ Security CrossbowAeroconical/steerable – National Phantom

Long NonLong Non--Dimensional Filling TimeDimensional Filling Timenfill

gen ≥ 4

Lower boundLower bound

Upper boundUpper bound

RRmm --value of systemvalue of system

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3. How to run OSCALC? 3. How to run OSCALC?

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3. How to run OSCALC? The logic flow is as follows:3. How to run OSCALC? The logic flow is as follows:Parts 1 & 2 Parts 1 & 2 –– Input & intermediate calculationInput & intermediate calculation

OSCALC computes the values of OSCALC computes the values of RRmm and and nnfillfillgengen

-- User enters the values of User enters the values of ρρ, , VVstretchstretch and and mm

-- User enters User enters CCD0D0 and and SS00-- OSCALC computes OSCALC computes (SC(SCDD))sdsd

-- User enters engineering data that yields a calculation User enters engineering data that yields a calculation of of CCD0D0 , namely: , namely: SS00 , weight, weight, , atmospheric density atmospheric density andandmeasured steadymeasured steady--descent speed descent speed

-- OSCALC computes OSCALC computes (SC(SCDD))sdsd

--oror--

-- User enters User enters nnfillfill --oror----User enters User enters ttfillfill-- OSCALC computes OSCALC computes nnfillfill

Parts 3, 4 & 5Parts 3, 4 & 5

32

Parts 3, 4 & 5. Choice of the proper Parts 3, 4 & 5. Choice of the proper CCkk –– RRmm graph;graph;input of input of CCkk; final calculation; final calculation

-- User chooses either the highUser chooses either the high-- or lowor low--nnfillfillgengen graph of graph of CCkk vs. vs. RRmm, based on the , based on the

computed value of computed value of nnfillfillgengen

-- From the graph the user picks the From the graph the user picks the ““averageaverage”” value of value of CCkk , as well as its upper , as well as its upper and lower boundsand lower bounds

-- User enters those three values of User enters those three values of CCkk into OSCALCinto OSCALC

OSCALC computes OSCALC computes FFmaxmax and its upperand its upper-- and lowerand lower--boundsbounds

Parts 1 & 2Parts 1 & 2

33

How to run OSCALC?How to run OSCALC?††

•• Copy the file named Copy the file named OSCALC.exe OSCALC.exe in a directory of your choice;in a directory of your choice;OSCALC does not require any input files, nor does it generateOSCALC does not require any input files, nor does it generateany ouput filesany ouput files

•• Run Run OSCALC.exeOSCALC.exe

•• The main window appears with one graph tucked underThe main window appears with one graph tucked under–– see figure 3.1 belowsee figure 3.1 below

______________†† These instructions apply both to V1.0 and V1.01These instructions apply both to V1.0 and V1.01

34

Figure 3.1 “Default” calculation and windows displayed at Figure 3.1 “Default” calculation and windows displayed at the beginning an OSCALC session the beginning an OSCALC session

35

How to run OSCALC?How to run OSCALC? Cont’dCont’d

•• This window is the “Default” window; the graph shows how theThis window is the “Default” window; the graph shows how thevalues of values of CCkk were picked, given the mass ratio and inflation timewere picked, given the mass ratio and inflation timethat resulted from the default input values. The Default casethat resulted from the default input values. The Default case isisdiscussed further in Section 6 (example 6.1)discussed further in Section 6 (example 6.1)

•• Click on the graph to see it completely; click on the programClick on the graph to see it completely; click on the programwindow to return to the programwindow to return to the program

•• The correspondence between the input/output shown on the The correspondence between the input/output shown on the main window and the variables discussed in this manual main window and the variables discussed in this manual is shown in is shown in figures 3.2, 3.3 figures 3.2, 3.3 and and 3.43.4 belowbelow

•• Note about the Default graphNote about the Default graph –– the graph will be replaced by the the graph will be replaced by the same graph, but without comments, whenever the “Short Inflatiosame graph, but without comments, whenever the “Short InflationnTime” radioTime” radio--button is clicked. Exit OSCALC and start a new button is clicked. Exit OSCALC and start a new session if there is a need to look at the original Default grasession if there is a need to look at the original Default graph ph againagain

36

Figure 3.2 Basic input and output of OSCALC. The colorFigure 3.2 Basic input and output of OSCALC. The colorcoding for this figure is as follows: coding for this figure is as follows: CalculatedCalculated versus versus inputinput..

RRmmnnfillfill

gengen FFmaxmax

Upper FUpper Fmaxmax

Lower FLower Fmaxmax

CCkkUpper CUpper CkkLower CLower Ckk

ρρmmVVstretchstretch

CCD0D0SS00

??SeeSeeFig. 3.3Fig. 3.3belowbelow

nnfillfillttfill fill ????SeeSeeFig 3.4Fig 3.4belowbelow

37

•• Again, note that the user can either: Again, note that the user can either:

-- enter the values of enter the values of CCD0D0 and and SS00 and have OSCALC compute theand have OSCALC compute thevalue of value of (SC(SCDD))sdsd = C= CD0D0 SS00 (in the case of parafoils, enter (in the case of parafoils, enter CCD0D0 = 1= 1 & & SS00 = chord * span= chord * span))

-- enter proprietary engineering data related to the steady descenenter proprietary engineering data related to the steady descent t of the canopy in order for OSCALC to compute of the canopy in order for OSCALC to compute CCD0D0 andand(SC(SCDD))sdsd = C= CD0D0 SS00 (note: (note: WWsdsd and and ρρsdsd can becan be different fromdifferent fromthe values of the values of m(g) m(g) and and ρρ used for the calculation of used for the calculation of FFmaxmax).).NoteNote: this alternative applies only to hemispherical parachutes.: this alternative applies only to hemispherical parachutes.

Just click the relevant radioJust click the relevant radio--buttonbutton(only one button can be clicked (only one button can be clicked during the same run)during the same run)

20

0

2

sdsd

sdD VS

WCρ

=

Figure 3.3 Drag area optionsFigure 3.3 Drag area options

WWsdsdρρsdsdVVsdsdSS00

38

•• Note also that the user can either:Note also that the user can either:

-- enter the values of enter the values of nnfillfillor…or…

-- enter the dimensional inflation time enter the dimensional inflation time ttfillfill (as measured on video);(as measured on video);OSCALC will then compute OSCALC will then compute nnfillfill

Just click the relevant radioJust click the relevant radio--button (only one button can be clicked button (only one button can be clicked during the same run)during the same run)

nnfillfill

ttfillfill

π/4 00

0

SD

VD

tn stretcht

fill

fill

=

=

Figure 3.4 Inflation time optionsFigure 3.4 Inflation time options

39

•• After entering the input data in After entering the input data in “1. Initial inputs”“1. Initial inputs”, click the , click the “Calculate Initial”“Calculate Initial” buttonbutton

•• After looking at the values of After looking at the values of RRmm and and nnfillfillgengen in in “2. Intermediate “2. Intermediate

results”results”, click the relevant graph in , click the relevant graph in “3. Graph choice” “3. Graph choice” in order toin order tofind find CCkk and its bounds; enter these values in and its bounds; enter these values in “4. Final inputs”“4. Final inputs”. Then. Thenclick the click the “Calculate Final”“Calculate Final” button and look at the calculated force button and look at the calculated force in in “5. Final results”“5. Final results”

Figure 3.5 Parts 3, 4 and 5 of anFigure 3.5 Parts 3, 4 and 5 of anOSCALC runOSCALC run

40

•• Note: the button Note: the button “Print”“Print” sends to the printer an image of the sends to the printer an image of the worksheet (but not of the graph)worksheet (but not of the graph)

•• Note: the button Note: the button “Help”“Help” generates a window that shows copyright generates a window that shows copyright information, a list of suggested units, an acknowledgement andinformation, a list of suggested units, an acknowledgement andlimited information on the programlimited information on the program

Figure 3.6 The “Print” and Figure 3.6 The “Print” and “Help”buttons “Help”buttons

41

4. More information on filling time4. More information on filling time

42

•• The following references contain experimental data on theThe following references contain experimental data on theinflation time of several types of parachutes.inflation time of several types of parachutes.

•• References [1] and [2] previously mentioned also containReferences [1] and [2] previously mentioned also containinflation time data inflation time data

43

4. References on inflation time 4. References on inflation time

[[6] Lee, C. K., “Modeling of Parachute Opening: an Experimental Investigation”, Journal of Aircraft, 26, 444 – 451, 1989.[7] Cruz, J. R., Kandis, M. and Witkowski, A.; “Opening Loads Analyses for Various Disk-Gap-Band Parachutes”; paper AIAA 2003-2131. 17thAIAA Aerodynamic Decelerator Systems Technology Conference and Seminar, Monterey, CA, May 19 -22, 2003.[8] Johari, H., and Desabrais, K. J.; “Stiffness Scaling for Solid-Cloth Parachutes”; Journal of Aircraft, 40, pp. 631 – 637, 2003.[9] Berndt R. J. and DeWeese J. H., “A Filling Time Prediction Approach for Solid Cloth Type Parachute Canopies”, 2nd AIAA Aerodynamic Decelerator Systems Technology Conference, Houston, TX, September 7-9, 1966, pp. 17-32.[10] Wolf, D.; “A Simplified Dynamic Model of Parachute Inflation”; Journal of Aircraft, 11, No. 1, pp. 28 - 33, 1974.

44

4. References on inflation time (cont’d)4. References on inflation time (cont’d)

[11] Lingard, J. S.; "A Semi-empirical Theory to Predict the Load-time History of an Inflating Parachute"; AIAA-84-0814, 8th AIAA Aerodynamic Decelerator and Balloon Technology Conference, 1984,Hyannis, MA, April 2-4, 1984. [12] Lee, C. K.; “Experimental Investigation of Full-Scale and Model Parachute Opening”; paper AIAA 84-0820; 8th AIAA Aerodynamic Decelerator and Balloon Technology Conference, 1984, Hyannis, MA, April 2-4, 1984.[13] Lee, C. K., Lanza, J. and Buckley, J.; “Experimental Investigation of Clustered Parachute Inflation”; paper AIAA 97-1478. 14thAIAA Aerodynamic Decelerator Systems Technology Conference and Seminar, San Francisco, CA, May 19 -22, 1997.[14] Lingard, S. J.; Ram-Air Parachute Design; AIAA Aerodynamic Decelerator Systems Technology Seminar; May, 1995; 63 pp. Unpublished.

45

4. References on inflation time (cont’d)4. References on inflation time (cont’d)

[15] Barnard, G. A.; “The Effect of Extreme Altitude of Parachute Filling Distance”; AIAA-93-1207; 12th AIAA Aerodynamic Decelerator Systems Technology Conference and Seminar (RAeS/AIAA) London, England, May 10-13, 1993.[16] Heinrich, H.G.; “The Opening Time of Parachutes Under Infinite Mass Conditions”; AIAA-68-12; 3rd AIAA Aerodynamic Decelerator Systems Technology Conference, El Centro, CA, September 23-25, 1968.[17] Heinrich, H.G.; “The Opening Time of Parachutes Under Infinite Mass Conditions”; Journal of Aircraft; 6, No.3, pp. 268 – 272; 1969.[18] J. Potvin and G. E. Peek; “Inflation and Steady-Descent Characteristics of Truncated Cone Decelerators”; AIAA paper 2005-1620; 18th AIAA Aerodynamic Decelerator Systems Conference and Seminar, Munich, Germany, May 23-26, 2005.

46

•• The following tables summarize some of the data found in theseThe following tables summarize some of the data found in thesereferences. Please go to the references to get the details onreferences. Please go to the references to get the details on the the parachute construction dimensions, payload characteristics anparachute construction dimensions, payload characteristics and d drop conditionsdrop conditions

47

LowLow-- and high porosity hemisphericalsand high porosity hemisphericals -- see Knacke [1]see Knacke [1]

48

Note about the previous Table Note about the previous Table ––Why the differences in Why the differences in nnfill fill between reefed between reefed opening, disreef opening and unreefed opening? opening, disreef opening and unreefed opening?

Relative to unreefed opening….Relative to unreefed opening….

•• reefed opening involves a canopy mouth which over time reefed opening involves a canopy mouth which over time does not open as widely does not open as widely –– nnfillfill should be larger (longer inflation time);should be larger (longer inflation time);However! However! nnfillfill can be can be shortershorter as well, with parachutes reefed by veryas well, with parachutes reefed by veryshort reefing lines: small reefing ratios result in inflated cshort reefing lines: small reefing ratios result in inflated canopy volumes anopy volumes that are that are smaller smaller than the inflated volumes of the unreefed configurations.than the inflated volumes of the unreefed configurations.

•• disreefed opening needs a smaller amount of air to fill thedisreefed opening needs a smaller amount of air to fill thecanopy from its initial state (i.e. inflated but “reefed”) to canopy from its initial state (i.e. inflated but “reefed”) to it final stateit final state(i.e. fully opened) (i.e. fully opened) –– nnfillfill should be smaller (shorter inflation time)should be smaller (shorter inflation time)

49

Deep coneDeep cone

See reference [18];calculation

based on D0

6 - 10No reefing18lbs; 700ft MSL;110ft/sec

Deep ConeCone height = 16.00ftCone base = 10.66ftD0 = 32.72ft (hypothenuse of half cone)

ReferencesnfillReefingTotal weight, deploy altitude,

Vinit

Size

50

ParafoilsParafoils

10 -19(Typical drop-to-drop variations)

Slider(sail/free)

200lbs; 4000ft MSL;160 - 170ft/sec

ParafoilPD Sabre150(skydiving/elliptical)1990’s design9 cells – 150ft2

factory configuration

16 – 20(Typical drop-to-drop variations)

Slider(sail/free)

200lbs; 4000ft MSL;160 - 170ft/sec

ParafoilPD Stiletto150(skydiving/elliptical)1990’s design9 cells – 150ft2


2.8None160lbs; 700ft MSL;105ft/sec

ParafoilParaflite Strato Cloudchord = 10.08ftspan = 19.16

ReferencesnfillReefingTotal weight,

deploy altitude, Vinit

Size

Note: with sliderNote: with slider--reefed systems, reefed systems, nnfillfill will depend on the actual dimensions ofwill depend on the actual dimensions ofcanopy rigging anglecanopy rigging angle; ; brake settingbrake setting; ; inlet, canopy and slider design and dimensionsinlet, canopy and slider design and dimensions

51

ParafoilsParafoils

Reference [14]3.5No reefingNo dataParafoil

No data; 1980's designfor personnel applications

Reference [14]14Slider

(sail/free)No dataParafoil

No data; 1980's design for personnel applications

12 -19(Typical drop-

to-drop variations)

Slider(both sail/free

and pilot-chute-controlled)

274-360lbs; 10,000ft MSL;270-310ft/sec

ParafoilParaflite MT-1X(skydiving/rectangular)1980’s design7 cells – 370ft2


ReferencesnfillReefingTotal weight, deploy altitude,

Vinit

Size

Note: on sliderNote: on slider--reefed systems, suspension linereefed systems, suspension line--abrasion can significantlyabrasion can significantlyincrease the value of increase the value of nnfillfill, to values well, to values well--exceeding exceeding nnfillfill = 20= 20

52

RemarksRemarks

•• These tables show that These tables show that nnfillfill depends on canopy design and reefingdepends on canopy design and reefing

•• BUTBUT nnfillfill also depends on how wide the canopy mouth is opened at the also depends on how wide the canopy mouth is opened at the beginning of the inflation process (time of line stretch in mabeginning of the inflation process (time of line stretch in many cases)ny cases)

-- wide mouth = lots of air gulpedwide mouth = lots of air gulped--in fast in fast →→ fast inflation fast inflation –– low value of low value of nnfillfill

-- narrow mouth = air entering at a slower rate → slow inflation narrow mouth = air entering at a slower rate → slow inflation –– large value of large value of nnfillfill

•• The actual amount of opened mouth area is often and stronglyThe actual amount of opened mouth area is often and stronglydetermined by the way the parachute gets out of its containerdetermined by the way the parachute gets out of its container bag and alignsbag and alignsinto the wind into the wind –– nnfillfill depends on what happened during depends on what happened during deployment!deployment!

•• Expect to see dropExpect to see drop--toto--drop variations of drop variations of nnfill fill –– next slidenext slide

53

DropDrop--toto--dropdropvariations variations during test drops,during test drops,from nfrom nfillfill ~ 5 to ~ 5 to nnfill fill ~ 7~ 7

(Figure by Desabrais &Johari [8])

54

More remarksMore remarks

•• nnfillfill depends on how wide the canopy mouth is opened at the depends on how wide the canopy mouth is opened at the beginning of the inflation process beginning of the inflation process ––oftentimes a random processoftentimes a random processdue to the canopy being in a limp state (i.e. nondue to the canopy being in a limp state (i.e. non--tension bearing) tension bearing) as it is exposed to the windas it is exposed to the wind

•• Sometimes such mouth state is determined by designSometimes such mouth state is determined by design(payload width, reefing, etc.). Check out the following formul(payload width, reefing, etc.). Check out the following formula, whicha, whichfollows from this definition of the filling time:follows from this definition of the filling time:

Fill time ~ Needed air to fill canopy volume / (air speed Fill time ~ Needed air to fill canopy volume / (air speed x x mouth opened area)mouth opened area)

…which together with the definition of …which together with the definition of nnfillfill implies:implies:

0DSn

netmouthinit

tofillfill

∨=

55

•• Note: In most cases the “toNote: In most cases the “to--fill” volume fill” volume VVtofill tofill is impossible to calculate a is impossible to calculate a priori because of porosity (no one can track accurately the aipriori because of porosity (no one can track accurately the air that goes inr that goes inand then later leaves)and then later leaves)

•• The formula is more useful in studies whereThe formula is more useful in studies where the scaling properties of the scaling properties of VVtofill tofill are known, eventhough its precise value is not; see examples on are known, eventhough its precise value is not; see examples on nextnextthe slidethe slide

0DSn

netmouthinit

tofillfill

∨=

56

•• Here how the mouth state is determined by designHere how the mouth state is determined by design

Example 1Example 1: comparison of the filling time between a full: comparison of the filling time between a full--scale andscale anda halfa half--scale canopy, hooked to the scale canopy, hooked to the samesame (i.e. “unscaled”)(i.e. “unscaled”)payload container payload container

Example 2Example 2: comparison of the filling time of a: comparison of the filling time of a given given lowlow--porosity porosity canopy canopy involved in:involved in:

→→ unreefed inflationunreefed inflationversusversus

→→ disdis--reef inflation, from a reef inflation, from a very smallvery small reefing ratio ( ~20%)reefing ratio ( ~20%)

0DSn

netmouthinit

tofillfill

∨=

nfillhalf scale ~ (1/4) nfill

full scale

29.0~29~20D

S

n

n unreefmouthinit

unreeffill

disreeffill

−

57

Filling time and deployment strategyFilling time and deployment strategy

•• nnfillfill will vary depending on whether the parachute is deployed will vary depending on whether the parachute is deployed in in a crossa cross--windwind or or facing the windfacing the wind. Typically . Typically nnfillfill will be larger, will be larger, and withand withmore dropmore drop--toto--drop variationsdrop variations, with the former approach than with the , with the former approach than with the latter. See next slide.latter. See next slide.

•• In crossIn cross--wind deployments the canopy mouth is kept shut for a whilewind deployments the canopy mouth is kept shut for a whilelonger during the early stages of inflationlonger during the early stages of inflation

CrossCross--wind wind

Facing the windFacing the wind

58

DropDrop--toto--dropdropvariations variations during test drops,during test drops,from nfrom nfillfill ~ 5 to ~ 5 to nnfill fill ~ 7 ~ 7 –– “facing the wind”“facing the wind”deploymentsdeployments


CC--9 deployments:9 deployments:Data by GP and JP;Data by GP and JP;“cross“cross--wind”wind”

59

Other dependencesOther dependences

•• Dependence on mass ratio Dependence on mass ratio –– example [11]example [11]

68.50501.0 += mfill Rn USAF CUSAF C--9 (low9 (low--porosity flatporosity flat--circular)circular)

Yes, that makes sense:Yes, that makes sense: nnfillfill should be smaller if the parachuteshould be smaller if the parachute--payload moves at payload moves at constant speed, compared to the same system undergoing a decelerconstant speed, compared to the same system undergoing a deceleration ation ––in other words the air inin other words the air in--flux is larger with the former than with the latter.flux is larger with the former than with the latter.In the small In the small RRmm-- regime the dependence may not be as dramatic. regime the dependence may not be as dramatic.

•• Dependence on relative stiffness:Dependence on relative stiffness:important issue when working withimportant issue when working withsmall & subsmall & sub--scale modelsscale models

064.0

022064.0

)1(3.13.1

−

−⎥⎥

⎦

⎤

⎢⎢

⎣

⎡

−==

DV

En

stretchfill

δ

νρς

Tunnel data by Heinrich and alsoBy Johari and Desabrais [8]

60

5. Some tricks to estimate the fall 5. Some tricks to estimate the fall speed at line stretchspeed at line stretch

61

5. Some tricks to estimate the fall speed at line stretch5. Some tricks to estimate the fall speed at line stretch

•• VVstretchstretch = parachute= parachute--payload fall rate @ the beginning of inflationpayload fall rate @ the beginning of inflation•• Most often Most often ≠≠ VVaircraftaircraft•• Depends on deployment strategy:Depends on deployment strategy:

-- After long, stabilized freefallAfter long, stabilized freefall

-- Deployment by static line and for a mostly preDeployment by static line and for a mostly pre--inflation inflation horizontal trajectoryhorizontal trajectory

( ) drogueDdrogue

stretchCS

WVρ

2≈

acftstretch VtX

V −∆∆

= 21-dim; const-acceleration kinematics:∆X = acft-payload distance∆t = deployment duration

62

-- Deployment static line and for a mostlyDeployment static line and for a mostly--vertical vertical prepre--inflation trajectoryinflation trajectory

( ) ( )

( )

( ) ⎟⎟⎠

⎞⎜⎜⎝

⎛++

⋅

+=

susplinesstaticlineverticalstretch

acfthorizstretch

verticalstretchhorizstretchstretch

LDLgV

VFUDGEV

VVV

22~

)(~

0_

_

2_

2_

Adjust “FUDGE” to match mean flight angleseen on video – payloaddrag is slowing-downhorizontal motion of payload over time

Vertical acceleration dominated by gravityVertical acceleration dominated by gravity

63

6. Examples6. Examples

64

6. Examples6. Examples

6.1 Unreefed low6.1 Unreefed low--porosity hemispherical canopy (“Default” case)porosity hemispherical canopy (“Default” case)

6.2 Permanently reefed high6.2 Permanently reefed high--porosity hemispherical canopy, porosity hemispherical canopy, deployed at high altitude and at low mass ratiodeployed at high altitude and at low mass ratio

6.3 Un6.3 Un--reefed parafoil vs. disreefed parafoil vs. dis--reefing parafoilreefing parafoil

6.4 Dis6.4 Dis--reefing hemispherical canopyreefing hemispherical canopy

6.5 Parachute cluster (unreefed)6.5 Parachute cluster (unreefed)

6.6 What to do with a new design that is not documented in the6.6 What to do with a new design that is not documented in theWorld’s database on inflation time and opening shock factoWorld’s database on inflation time and opening shock factorr

65

6.1 Unreefed low6.1 Unreefed low--porosity hemispherical canopy porosity hemispherical canopy (“Default” case)(“Default” case)

This example would be typical of the USAF CThis example would be typical of the USAF C--9 canopy 9 canopy -- aa“flat circular” canopy made of low permeability fabric. This can“flat circular” canopy made of low permeability fabric. This canopyopyhas no drive slots has no drive slots –– just a small vent at the apex.just a small vent at the apex.

ρρ = 0.002 sl/ft= 0.002 sl/ft33 –– deployment at 5000ft MSL deployment at 5000ft MSL mm = 6.21 sl (corresponding to 200 lbs on Earth)= 6.21 sl (corresponding to 200 lbs on Earth)VVstretchstretch = 120 ft/sec = 120 ft/sec CCD0D0 = 0.75= 0.75 from reference [1] from reference [1] -- see figure 6.1see figure 6.1SS00 = 616 ft= 616 ft22 –– calculated from calculated from SS00 = = ππ (28ft)(28ft)22/4/4

nnfillfill = 6 = 6 –– See figure 6.2See figure 6.2

OSCALC gives: OSCALC gives: RRmm = 3.19 and = 3.19 and nnfillfillgengen = 3.91= 3.91

User should choose the User should choose the ““Short Inflation TimeShort Inflation Time”” graphgraphUser would pick User would pick CCkk = 0.25 with ~ 0.4 and ~ 0.1 as bounds= 0.25 with ~ 0.4 and ~ 0.1 as boundsSee figures 3.1 and 6.3See figures 3.1 and 6.3

The result is The result is FFmax max == 1663.2 lbs with 2661.1 lbs and 665.3 lbs as bounds1663.2 lbs with 2661.1 lbs and 665.3 lbs as bounds

66

Figure 6.1.Figure 6.1. Where to get steadyWhere to get steady--state drag coefficient data? state drag coefficient data? Go to Knacke [1] Tables 5Go to Knacke [1] Tables 5--1 1 –– 55--4.4.

Figure below is from Table 5Figure below is from Table 5--11

67

DropDrop--toto--dropdropvariations variations during test drops,during test drops,from nfrom nfillfill ~ 5 to ~ 5 to nnfill fill ~ 7 ~ 7 ––“facing the wind”“facing the wind”deploymentsdeployments


Figure 6.2 Choosing the nonFigure 6.2 Choosing the non--dimensional inflation time for a dimensional inflation time for a CC--9 type canopy (low9 type canopy (low--porosity hemispherical canopy)porosity hemispherical canopy)

xx

68

Figure 6.3 Chosen graph and Figure 6.3 Chosen graph and CCkk--values for the “Default” casevalues for the “Default” case

69

6.2 Permanently reefed high6.2 Permanently reefed high--porosity hemispherical canopy,porosity hemispherical canopy,deployed at high altitude and at low mass ratiodeployed at high altitude and at low mass ratio

This example would be typical of 28ftThis example would be typical of 28ft--diameter ribbondiameter ribbon--type canopy, type canopy, reefed at 20%reefed at 20%

ρρ = 0.001 sl/ft= 0.001 sl/ft33 –– deployment at 27,000ft MSLdeployment at 27,000ft MSLmm = 62.1 sl (corresponding to 2000 lbs on Earth)= 62.1 sl (corresponding to 2000 lbs on Earth)VVstretchstretch = 300 ft/sec (typical if launched from cargo acft flying @ ~130= 300 ft/sec (typical if launched from cargo acft flying @ ~130KTSI)KTSI)CCD0D0

unreefed unreefed = 0.38 = 0.38 –– unreefed unreefed -- from reference [1] from reference [1] -- see figure 6.4see figure 6.4SS00 = 616 ft= 616 ft22 –– calculated from calculated from SS00 = = ππ (28ft)(28ft)22/4/4(SC(SCDD))sdsd = = εε (SC(SCDD))sdsd||unreefedunreefed = 0.27 = 0.27 x x 0.38 0.38 x 616ftx 616ft22 = 63.2ft= 63.2ft2 2 -- see figure 6.5 see figure 6.5

nnfillfill = 10 = 10 –– See figure 6.6See figure 6.6


User should choose the User should choose the ““Long Inflation TimeLong Inflation Time”” graphgraphUser would pick User would pick CCkk = 1.25 with ~ 1.50 and ~ 1.00 as bounds= 1.25 with ~ 1.50 and ~ 1.00 as bounds

The result is The result is FFmax max == 3465 lbs with 4158 lbs and 2772 lbs as bounds3465 lbs with 4158 lbs and 2772 lbs as bounds

70

Figure 6.4.Figure 6.4. Knacke [1] Tables 5Knacke [1] Tables 5--1 1 –– 55--4.4.

71

Figure 6.5Figure 6.5

Using reference [1] toUsing reference [1] todetermine the dragdetermine the dragarea of a permanently area of a permanently reefed canopy. Note:reefed canopy. Note:using this curve for theusing this curve for theribbon chute of figuresribbon chute of figures6.4 (above) and 6.6 (below)6.4 (above) and 6.6 (below)may be an approximation,may be an approximation,since the two chutes may not since the two chutes may not be exactly the samebe exactly the same

72

Figure 6.6 Choosing the nonFigure 6.6 Choosing the non--dimensional filling time using reference [1].dimensional filling time using reference [1].

73


Part 1 Part 1 -- Consider the example of a 250ftConsider the example of a 250ft22 parafoil that is parafoil that is notnot equipped equipped with a slider; this parafoil has no reefing whatsoever. In this with a slider; this parafoil has no reefing whatsoever. In this exampleexamplethe values of the values of SS00 is computed from the product of is computed from the product of wing chordwing chord times times spanspan..

ρρ = 0.002 sl/ft= 0.002 sl/ft33 –– deployment at 5000ft MSL deployment at 5000ft MSL mm = 6.21 sl (corresponding to 200 lbs on Earth)= 6.21 sl (corresponding to 200 lbs on Earth)VVstretchstretch = 130 ft/sec = 130 ft/sec CCD0D0 = 1.0= 1.0 -- during inflation the parafoil during inflation the parafoil ““lookslooks”” like a flat platelike a flat plateSS00 = 250 ft= 250 ft22

nnfillfill = 2 = 2 –– no reefing no reefing -- see table, section 2see table, section 2


User should choose the User should choose the ““Short Inflation TimeShort Inflation Time”” graphgraphUser would pick User would pick CCkk = 0.6 with ~ 0.9 and ~ 0.3 as bounds= 0.6 with ~ 0.9 and ~ 0.3 as bounds


74


Part 2 Part 2 -- Consider the same 250ftConsider the same 250ft22 parafoil but equipped with a slider.parafoil but equipped with a slider.Assume the same payload and deployment conditions. Assume the same payload and deployment conditions. The only differenceThe only differenceis the nonis the non--dimensional filling time which is increased (sliders do that).dimensional filling time which is increased (sliders do that).

ρρ = 0.002 sl/ft= 0.002 sl/ft3 3 –– deployment at 5000ft MSL deployment at 5000ft MSL mm = 6.21 sl (corresponding to 200 lbs on Earth)= 6.21 sl (corresponding to 200 lbs on Earth)VVstretchstretch = 130 ft/sec = 130 ft/sec CCD0D0 = 1.0= 1.0 -- during inflation the parafoil during inflation the parafoil ““lookslooks”” like a flat platelike a flat plateSS00 = 250 ft= 250 ft22

nnfillfill = 14 = 14 –– See table, section 2 See table, section 2 –– old 1980old 1980’’s 7s 7--cell design cell design (they are(they arein the in the nnfillfill ~ 15 ~ 15 -- 25 range with the 199025 range with the 1990’’s and 2000s and 2000’’s designs)s designs)


User should choose the User should choose the ““Long Inflation TimeLong Inflation Time”” graphgraphUser would pick User would pick CCkk = 0.2 with ~ 0.3 and ~ 0.1 as bounds= 0.2 with ~ 0.3 and ~ 0.1 as bounds

The result is The result is FFmax max == 845 lbs with 1267 lbs and 422 lbs as bounds845 lbs with 1267 lbs and 422 lbs as boundsQUITE A REDUCTION OF OPENING SHOCK!QUITE A REDUCTION OF OPENING SHOCK!

75

6.4 Dis6.4 Dis--reefing hemispherical canopyreefing hemispherical canopyConsider a 20%Consider a 20%--reefed USAF Creefed USAF C--9 canopy, which has been falling9 canopy, which has been fallingsteadily in its reefed configuration, until reefing line cutter steadily in its reefed configuration, until reefing line cutter activationactivationat 5000ft MSLat 5000ft MSL

ρρ = 0.002 sl/ft= 0.002 sl/ft33 –– cutter activation at 5000ft MSL cutter activation at 5000ft MSL mm = 6.21 sl (corresponding to 200 lbs on Earth)= 6.21 sl (corresponding to 200 lbs on Earth)VVstretch stretch = V= Vfallfall = 40.3 ft/sec = 40.3 ft/sec -- using reefing drag area data of figure 6.7using reefing drag area data of figure 6.7to compute the fall rate prior to disto compute the fall rate prior to dis--reefing inflationreefing inflationCCD0D0 = 0.75= 0.75 unreefed value (from reference [1]) unreefed value (from reference [1]) -- see figure 6.1see figure 6.1SS00 = 616 ft= 616 ft22 –– calculated from calculated from SS00 = = ππ (28ft)(28ft)22/4/4

nnfillfill = 0.3 = 0.3 x x 6 = 1.8 6 = 1.8 –– See figure 6.8See figure 6.8




76


Using reference [1] toUsing reference [1] todetermine the dragdetermine the dragarea of a permanently area of a permanently reefed canopy. reefed canopy.

77

Figure 6.8 Choosing the nonFigure 6.8 Choosing the non--dimensional filling time.dimensional filling time.

29.0~29~20D

S

n

n unreefmouthinit

unreeffill

disreeffill

−

What to do?What to do?

Used simple estimateUsed simple estimatediscussed in section 4discussed in section 4(limited to very low (limited to very low reefing ratios and lowreefing ratios and low--porosity canopies)porosity canopies)

??

78

6.5 Parachute cluster (unreefed)6.5 Parachute cluster (unreefed)Consider a cluster of four 100ft flat circular canopies.Consider a cluster of four 100ft flat circular canopies.

ρρ = 0.002 sl/ft= 0.002 sl/ft33 –– deployment at 5000ft MSL deployment at 5000ft MSL mm = 622 sl (corresponding to 20,000 lbs on Earth)= 622 sl (corresponding to 20,000 lbs on Earth)VVstretch stretch = 200= 200 ft/secft/secCCD0D0

single chutesingle chute= 0.75= 0.75 unreefed value (reference [1]) unreefed value (reference [1]) -- see figure 6.1see figure 6.1SS00 = 4 = 4 xx ((ππ (100ft)(100ft)22/4) = 31,400ft/4) = 31,400ft22

We need the drag coefficient of the cluster We need the drag coefficient of the cluster -- use figure 6.9:use figure 6.9:(SC(SCD0D0))sdsd = (0.83 = (0.83 CCD0D0

single single ) ) SS00 = 0.83 = 0.83 xx 0.75 0.75 xx 31,400ft31,400ft22 = 19,547ft= 19,547ft22

So So CCD0D044--clustercluster = 0.83 = 0.83 CCD0D0

singlesingle= 0.62 = 0.62 to be entered in OSCALC, together with to be entered in OSCALC, together with SS00

nnfillfillsinglesingle = 6= 6 –– see figure 6.2see figure 6.2

nnfillfill44--clustercluster= 0.5 = 0.5 x x 6 = 3 6 = 3 –– See figure 6.10See figure 6.10



The result is The result is FFmax max == 77,872lbs with 155,744lbs and 38,936lbs as bounds77,872lbs with 155,744lbs and 38,936lbs as bounds

79


Net drag coefficient Net drag coefficient of a parachute clusterof a parachute cluster(w/r to the drag coefficient(w/r to the drag coefficientof the member parachuteof the member parachutemaking up the clustermaking up the cluster

80

chutechutefill

clusterclusterfillfillstretch DnDntV −−−− == 1

014

04

Since the Since the inflation time of the clusterinflation time of the cluster ~ ~ inflation time of each parachute of the clusterinflation time of each parachute of the cluster

then:then:

411

40

1014 chute

fillcluster

chutechute

fillcluster

fill nnnS

S −

−

−−− ==

Figure 6.10 Assumptions used to compute Figure 6.10 Assumptions used to compute the nonthe non--dimensional inflation time of a cluster.dimensional inflation time of a cluster.

It is assumed here that all the parachutes of the cluster inflatIt is assumed here that all the parachutes of the cluster inflate at thee at thesame time and with the same inflation time same time and with the same inflation time –– Warning Warning -- this is not this is not always true! See Knacke’s description of the “leadalways true! See Knacke’s description of the “lead--lag” phenomenonlag” phenomenon

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6.6 What to do with a new design that is not documented 6.6 What to do with a new design that is not documented in the World’s database on inflation time and opening in the World’s database on inflation time and opening shock factorshock factor

•• The momentumThe momentum--impulse theorem discussed in section 2 guarantees impulse theorem discussed in section 2 guarantees that the that the CCkk data of the new parachute data of the new parachute will will duplicate the trend shownduplicate the trend shownin the in the CCkk –– RRmm graphs, graphs, as long as its generalized filling time is such thatas long as its generalized filling time is such thatnnfillfill

gengen ≥≥ 11

•• Coming up with an educated guess of the filling/inflation time Coming up with an educated guess of the filling/inflation time may bemay bepossible possible –– for example by using the values of documented parachute for example by using the values of documented parachute systems that are similar; or by guessing filling times valuessystems that are similar; or by guessing filling times values that could that could single out worse case scenarios (i.e. the largest realistic vsingle out worse case scenarios (i.e. the largest realistic values of alues of FFmaxmax))

•• Better filling time information will be obtained after the vidBetter filling time information will be obtained after the video of the eo of the ““first flightfirst flight”” is analyzedis analyzed

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7. OSCALC error/warning messages7. OSCALC error/warning messages

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7. OSCALC 7. OSCALC error/warningerror/warning messagesmessages

So far there are only two builtSo far there are only two built--in warning/error messages:in warning/error messages:

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OSCALCOSCALC warningwarning messagemessage

Warning: clicking the “Calculate Final” button before clicking tWarning: clicking the “Calculate Final” button before clicking the he “Calculate Initial” button any time new input data is entered.“Calculate Initial” button any time new input data is entered.

To clear the warning message: click To clear the warning message: click ““OKOK””; then click ; then click ““Calculate InitialCalculate Initial””

In this example, the In this example, the mass was changed frommass was changed from“6.21” to “6”, followed“6.21” to “6”, followedby the clicking of the by the clicking of the “Calculate Final” button. “Calculate Final” button.

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OSCALCOSCALC error error messagemessage

Error: Considering a case where the generalized filling time is Error: Considering a case where the generalized filling time is less than unity.less than unity.

See next page See next page →→

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The case of veryThe case of very small filling timesmall filling time

•• This error message is triggered whenever This error message is triggered whenever nnfillfillgengen < 1< 1. . The problem is that The problem is that

neither graph apply to this case. If this value is not the reneither graph apply to this case. If this value is not the result of a typing sult of a typing error, the user may consider using the Momentumerror, the user may consider using the Momentum--Impulse Theorem in Impulse Theorem in tandem with OSCALC:tandem with OSCALC:

1) Run OSCALC for the same type of parachute and1) Run OSCALC for the same type of parachute andreefing, but with canopy diameters, atmospherreefing, but with canopy diameters, atmosphericicdensity and payload weight that is characteridensity and payload weight that is characterized by the same zed by the same RRmmand a larger nand a larger nfillfill ((≡≡ nnfillfill

altalt), thereby obtaining a ), thereby obtaining a CCk k = C= Ckkaltalt

(“alt” = “alternate”)(“alt” = “alternate”)

2) Use the formula below to estimate the 2) Use the formula below to estimate the CCkk of the actual systemof the actual system

actualfill

altfillalt

kactualk

n

nCC =

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8. Concluding remarks8. Concluding remarks

•• This is the OSCALCThis is the OSCALC--Version 1.0 familyVersion 1.0 family. Future versions will provide . Future versions will provide updated updated CCkk –– RRmm graphs that include data points of parachute drops carriedgraphs that include data points of parachute drops carriedout more recently. These updates should close the gaps on the out more recently. These updates should close the gaps on the plots. This newplots. This newdata could also help create a new graph for the case data could also help create a new graph for the case nnfillfill

gengen < 1< 1

•• Remember, the data scatter on the graphs is not due to lack of Remember, the data scatter on the graphs is not due to lack of knowledgeknowledgeor measurement errors but rather to: or measurement errors but rather to:

1) the integral 1) the integral ΓΓ changing with flight angle (at the same value of changing with flight angle (at the same value of RRmm); );

2) 2) nnfillfill being defined over a range of values (for each graph); and being defined over a range of values (for each graph); and

3) the drop3) the drop--toto--drop variations associated with both drop variations associated with both ΓΓ and and nnfillfill

More details on all this can be found in reference [4]More details on all this can be found in reference [4]

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•• OSCALC is not a true predictor of opening shock since it requireOSCALC is not a true predictor of opening shock since it requires the s the use of use of ttfillfill ((nnfillfill), which is an actual inflation performance variable), which is an actual inflation performance variable

•• OSCALC is not a design tool either, with regards to changing thOSCALC is not a design tool either, with regards to changing the dimensionse dimensionsof of subsub--componentscomponents. For example, changing slider. For example, changing slider--size on a parafoil willsize on a parafoil willbe reflected in a change in be reflected in a change in ttfillfill. But even if the designer knew how to . But even if the designer knew how to predict this change of predict this change of ttfillfill, OSCALC may still give the same , OSCALC may still give the same FFmaxmax if the new if the new ttfillfillinvolves the same involves the same CCkk--RRmm graph. One way out of this problem, especiallygraph. One way out of this problem, especiallyif if ttfillfill is known, is to use the equation is known, is to use the equation

shown on slide #20 and discussed in details in ref [4])shown on slide #20 and discussed in details in ref [4])

•• Note that OSCALC can be of some use to the designer if the overNote that OSCALC can be of some use to the designer if the overallallsize and porosity of the canopy, payload weight, deployment alsize and porosity of the canopy, payload weight, deployment altitudetitudeand/or preand/or pre--inflation fall speed are changedinflation fall speed are changed

Γ=gen

fillm

k

nRC 2

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•• Design Design is where the detailed simulations of the drag force evolution wois where the detailed simulations of the drag force evolution woulduldbe most desirable; i.e. models sought to provide both be most desirable; i.e. models sought to provide both FFmaxmax andand ttfillfill as as outputsoutputs, , depending on the actual design and constuction of the parachudepending on the actual design and constuction of the parachute, and onte, and onthe actual drop conditionsthe actual drop conditions

Will such models ever replace OSCALC? Will such models ever replace OSCALC?

•• Even with these detailed simulation tools being around, OSCALC Even with these detailed simulation tools being around, OSCALC willwillstill be useful, in particular for calculating still be useful, in particular for calculating FFmaxmax sustained during inflation sustained during inflation scenarios that are not covered by the detailed models, for exascenarios that are not covered by the detailed models, for example:mple:malfunctionsmalfunctions, , mismis--staged inflationstaged inflation or inflation sequences that beginor inflation sequences that beginwith with unusual canopy shapesunusual canopy shapes

Long live OSCALC!Long live OSCALC!

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Please send all questions to:Please send all questions to:

Gary Peek & Jean PotvinGary Peek & Jean PotvinParks College Parachute Research GroupParks College Parachute Research GroupC/O Dr. J. Potvin, Physics DepartmentC/O Dr. J. Potvin, Physics DepartmentSaint Louis UniversitySaint Louis University3450 Lindell blvd.3450 Lindell blvd.St. Louis, MO 63103St. Louis, MO 63103

Contact: Contact: [email protected]@industrologic.com [email protected]@slu.edu 314314--977977--84248424

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