Recovery Systems: Parachutes 101
Material taken from: Parachutes for
Planetary Entry Systems
Juan R. Cruz
Exploration Systems Engineering Branch
NASA Langley Research Center
Also, Images from:
Knacke, T. W.: Parachute Recovery Systems Design
Manual, Para Publishing, Santa Barbara, CA, 1992.
and
Ewing, E. G., Bixby, H.W., and Knacke, T.W.: Recovery
System Design Guide, AFFDL-TR-78-151, 1978.
MAE 5930, Rocket Systems Design 1
Basic Terminology
MAE 5930, Rocket Systems Design 2
Basic Terminology (2)
For
our
purposed
conical
and
ellip/cal
parachutes
are
same
thing”
MAE 5930, Rocket Systems Design 3
Basic Terminology (3)
Fdrag
Fdrag = q ! C D ! S0
1
q= # !V$ 2 "incompressible dynamic pressure"
2
"
C D = "drag coefficient " V!
C D ! S0 = "drag area"
MAE 5930, Rocket Systems Design 4
Basic Terminology (4)
In general, under parachute, 2-DOF equations of motion are ….
(ignore centrifugal & Coriolis forces)
V! " V 2 r + V# 2
!
"Vr % $
(
" Fdrag ) ( )
+ Fdrag vehicle %
( sin ) * g '
parachute
$ ' $ m '
=
(F )
drag parachute
$ ' $
$#V!! '& $
*
F ( )
drag parachute + (
F )
drag vehicle
( cos )
'
'
$# '&
+(F )
m
drag vehicle
Vehicle decelerates very rapidly
in horizontal direction
MAE 5930, Rocket Systems Design 5
Basic Terminology (4)
“Terminal Velocity” .. Equilibrium velocity where
parachute + vehicle are no longer accelerating
"V!r % " 0 % " ) * 90" %
$ ' $ ' $ '
$ '( $ '( $ F ( ) (
+ Fdrag ) = m + g'
$#V!! '& $# 0 '& # drag parachute vehicle &
1
! "Vterminal 2 " #$( C D " S0 ) parachute + ( C D " S0 )vehicle %& = m " g
2
2!m!g $
Vterminal = # ( C D ! S0 ) parachute + ( C D ! S0 )vehicle &
" % '
MAE 5930, Rocket Systems Design 6
Basic Terminology (5)
“Impact Energy” .Kinetic Energy of “hard object” striking ground
1
K.E.impact = m ⋅V 2 terminal
2 ground
Typically mass of soft items like canopy
Are not accounted for in impact energy
MAE 5930, Rocket Systems Design 7
Parachute Types
We’ll
be
using
solid
parachutes
MAE 5930, Rocket Systems Design 8
Parachute Shapes
• Hemispherical parachute:
- Deployed canopy takes on the shape of a hemisphere.
- Three dimensional hemispherical shape divided into a number of
2-D panels, called gores
• Angle subtended on the
left hand side of the pattern
is 60 degrees
• When all six gores are
joined they complete the
360 degree circle.
MAE 5930, Rocket Systems Design 9
Parachute Shapes (2)
• Conical Parachute
- 2-D Canopy shape in form of a triangle
MAE 5930, Rocket Systems Design 10
Parachute Shapes (3)
• Conical Parachute Gore Shape
- 2-D Canopy shape in form of a triangle
• Higher drag coefficient than hemispherical parachutes, but also less stability
MAE 5930, Rocket Systems Design 11
Parachute Shapes (4)
• Elliptical parachute:
- Parachute where vertical axis is smaller than horizontal axis
- A parachute with an elliptical canopy has essentially the same CD
as a hemispherical parachute, but with less surface material
“h”
“r”
Canopy profile for different height / radius ratios
MAE 5930, Rocket Systems Design 12
Parachute Shapes (5)
Comparison of gore shapes for different height : radius ratios
MAE 5930, Rocket Systems Design 13
Parachute Types (2)
MAE 5930, Rocket Systems Design 14
Parachute Types (3)
MAE 5930, Rocket Systems Design 15
Example Calculation: Drogue Chute
Terminal Velocity
hapogee = hagl + hlaunch =
site
(1609.23 + 240 )meters !! 1850 meters
!apogee = 1.0218 kg
m3
3.9860044 " 10 5 km 3
µ
g= 2 = sec 2
= 9.815
r ( 6371 + 1.85 ) km2
2
m
sec 2
Maximum mass at apogee : mapogee = mlaunch ! m fuel = (14.188 ! 1.76 ) = 12.428 kg
mapogee " g = 12.428 " 9.815 = 121.975 Nt
MAE 5930, Rocket Systems Design 16
Example Calculation: Drogue Chute
Terminal Velocity (2)
• Descent rate under drogue, 50-100 ft/sec
• Go with minimum value ~ 15.24 m/sec (50 ft/sec)
“Vehicle Drag Area” ..
Rocket is broken into two pieces
(CD ! S0 )vehicle " 2 ! #$(CD )rocket ! ( Aref )rocket %& = ( 2 ! 0.35 ! 0.01589 ) " 0.0111m 2
“Double up” nominal rocket drag area
MAE 5930, Rocket Systems Design 17
Example Calculation: Drogue Chute
Terminal Velocity (3)
• Parachute Drag Coefficient
• Elliptical Parachute .. Take median value
(CD )chute ! 0.76 ± 0.115
MAE 5930, Rocket Systems Design 18
Example Calculation: Drogue Chute
Terminal Velocity (4)
• Calculate required chute area:
2!m!g $
Vterminal = # ( C D ! S0 ) parachute + ( C D ! S0 )vehicle &
" % '
m!g
# ( C D ! S0 )vehicle
1
" !Vterminal 2
( ( S0 ) parachute = 2 =
(CD ) parachute
121.965 4 ! ( S0 ) parachute
& 0.0111 D0 = =
"
$ 1 1.0218 ! 22.86 2%
"2 #
% 4! 1.33783 &
0.5 39.37
1.3378 m2 = 4.28 ft
# $
" 12
0.76
MAE 5930, Rocket Systems Design 19
Example Calculation: Drogue Chute
Terminal Velocity (5)
Drag Chute Areas Versus Terminal Velocity
MAE 5930, Rocket Systems Design 20
Example Calculation: Drogue Chute
Terminal Velocity (6)
Drag Chute Diameter Versus Terminal Velocity
MAE 5930, Rocket Systems Design 21
Example Calculation: Drogue Chute
Terminal Velocity (7)
MAE 5930, Rocket Systems Design 22
Parachute Opening Loads
Largest Tensile Load on Vehicle … often the Ultimate
Design Load Driver
Design
Tool
Verifica/on
Tool
(Direct
Simula/on)
MAE 5930, Rocket Systems Design 23
Parachute Opening Loads (2)
MAE 5930, Rocket Systems Design 24
Parachute Opening Loads (3)
D0 n = canopy fill constant
t inf = n ! k "
V1 k = decceleration exponent
MAE 5930, Rocket Systems Design 25
Parachute Opening Loads (4)
MAE 5930, Rocket Systems Design 26
Parachute Opening Loads (5)
Infinite-‐Mass
Infla/on
MAE 5930, Rocket Systems Design 27
Parachute Opening Loads (6)
Finite-‐Mass
Infla/on
MAE 5930, Rocket Systems Design 28
Pflanz’s Method
• Pflanz' (1942):
-introduced analytical functions for the drag area
• Simple, frst-order, design book type method
-Requires least knowledge of the system compared to other methods
-Assumes no gravity acceleration – limits application to shallow fight
path angles at parachute deployment
- Neglects entry vehicle drag
- Yields only peak opening load
- Allows for finite mass approximation
• Doherr (2003) extended method to account for gravity and
arbitrary fight path angles
MAE 5930, Rocket Systems Design 29
Pflanz’s Method (2)
Fmax = q1 ! ( C D ! S0 ) ! C x ! X1
2!m
Aballistic =
(CD ! S0 ) ! "1 !V1 ! tinfl
(finite
mass
infla/on
approxima/on)
MAE 5930, Rocket Systems Design 30
Pflanz’s Method (3)
• Assume “opening load “velocity at
• Drogue Chute Opening Loads 4 seconds past apogee, ~45 m/sec
• Dynamic Pressure ~ 1.1 kPa
• Cx ~ 1.7
MAE 5930, Rocket Systems Design 31
Pflanz’s Method (4)
Subsonic Inflation time …
D0 n = canopy fill constant
t inf = n! k
"
Vopen k = decceleration exponent
n#4
elliptical parachute "
k # 0.85
0.5
4 $" 1.3378 %#
4
t inf = !
0.85
= 0.2053 sec
45
2!m 2! 12.428
Aballistic = =
( 0.76 ! 1.3378 ) 1.0218 ! 45.0 ! 0.2053 =
2.590
(CD ! S0 ) ! "1 !V1 ! tinfl
MAE 5930, Rocket Systems Design 32
Pflanz’s Method (5)
2!m
Aballistic = =
2.590
(CD ! S0 ) ! "1 !V1 ! tinfl
X1 ! 0.72
Fmax = q1 ! ( C D ! S0 ) ! C x ! X1 =
3
1.1 !10 ( 0.76 " 1.3378 ) 1.7 " 0.72
= 1368.9 Nt (307.7 lbf)
MAE 5930, Rocket Systems Design 33
Pflanz’s Method (6)
(2)
MAE 5930, Rocket Systems Design 34
Inflation Curve Method
n
# t ! t si &
FP = q(t !tsi ) " ( C D " S0 ) " C x " %
$ t inf ! t si ('
Ignores
parachute
mass
(conserva?ve)
Direct
Simula/on
Verifica/on
Tool
Allowing
for
parachute
mass
MAE 5930, Rocket Systems Design 35
Inflation Curve Method (2)
Infla?on
Data
from
Doherr
(CD ! S0 )t
(CD ! S0 )steady
" t ! t si %
$# t ! t '&
inf si
36
MAE 5930, Rocket Systems Design
Questions??
MAE 5930, Rocket Systems Design 37
