"lfk f; \"A Lt. - Airborne Systems

Iy in Figs. 7. 14b and c. Inflating ca'lOPV geometry is
defined in Fi ure 7. 14d. Motion of the body along
the fl ight path is desc;' ibed b,t this relationship
sb m/) sin e - leos CDA P$b 2
Rate of change of flight path angle
(mb JB sb (mb )gcos f) 7-
CO:lservation of momentum for the mass concentrated
at the parachute skirt (by equation 7- 14b)
and
"" F cos1/ Ftcostp
+ m s (s
+maR rl.
B S
sg sin f)
e sin 1/ -F/sin(/- FRL
+ m s (r rs!-maRS
Similarly, for the inflated canopy mess point
+ma c F cosif-CoScPs c 2
maRe
"" -
+ m g sin
For the added air mass terms
maRs
maRc
sc
.=
=:
()
sc S
e sin VI maRc re 7-
+ CR (25 sin!/J (CDS
if) ps/ /2
scP4u/13
BRsprrr/ h u eos
p1rr/ (4 /3 sin 1J cos '. J
The parecllute mass is distributed 3S sh:;wn in Figure
14e. It is assumed that halfthe suspensi on Ii ne mass
is concentrated in tne skirt and the other half attached
to the body. For reefed parachutes an over-inflation
angle llt/) was defined 8S shown in Fi;Jure 7. 14f/.
Finite- Element Elastic Models
Keck 516 and Sundberg 529 have developed finiteelement
models of the inflating parachute consisting
of a series aT point masses connected by massless elas.
tic members representing body, suspension lines and
canopy In Sundberg s ax i-symmetrical parachute
model, the elastic members have non-linear Joadelongation
characteristics, mass poins in the canopy
lie on the radials, and the towing body is treated as a
fini:e point mass with d-ag. Also, the cnange in
canopy porosity with material stretch is accounted
for. The motion of an individual suspension line is
confined to a plane containing the common centerline
of canopy and body. Aerodynamic forces are
applied to both Suspension lines and canopy, enabling
investigation of canopy interactions with transverse
Y'laves and tension waves ' n the suspension lines.
Basically, the dynamics of the system is analyzed
by solving Newton s second law (expressed in the vee-
350
tor form 3S mOl) or overy mass point Typically,
50- 100 mass points are used to model the suspension
lines, and 25- 50 the canopy. The accele atjon vector
of an indi'/idual mess point is written
aj (miUx (Fi J' - -14 )/2 + Ti+Jr
+ T ;J/mi
where is an aerodynamic force component tangent
to the structure (surfece) and is a tension force Tri
being the rad,al component of the 1"000 tension.
A sample of the data required for modeling parachute
deployment and inflation is fven in Reference
529, The process begins with canopy and wspension
lines eccordion folded in the deployment bag. The
model 'ng incl udes line deploymert and canopy
stretchout, inflation and disreefing. Solutions obtained
with the model , show the tension wave motion
which occurs during deploymcnt and early inflation.
Keck' s model516 includes point masses along the
gore center- line as well as radials. Like Sundberg
model , it consists of a network of point mass nodes
connected by massless elastic members. Assumption
of polysvmrnetry of parachute struc ure and the
forces acting on it permits the inflatiun analvsis to
deal with the moti::m of only one gore. Tre four differential
equation of motion of each node arc programmed
for solution by digital computer. Inputs to
Number of nodes
\Iass of each node
Unstretched lengths of interconnecting members
Breaking strengths of interconnecting members
initial positions and velocities of nodes
The original model had eleven radial nodes and nine
centerline nodes , requiring the c;om'.uter to solve
eighty differential equations sin'ultaneously. Because
the computer run-time proved prohibitive, the number
of nodes was reduced to seven and five respectively.
Initial results using the simplified model consisted
of a detailed description of canopy shape during Inflation
, showing the proper growth pattern, including
bulging of the gore be:ween radials, and the terminal
over. inflation process, A comparison of experimental
and predicted force-time data yielded shorter filling
times and higher peak leads than measured , indicating
the need for some further refinement of the mathematical
model.
Theoretical Approach
psyne 517 takes a fresh look at parachute opening
dynamics wi;:h the e,bjective of developing a simplified
model of parachute inflation from first principles
without any appeal to experimental measurements.
Confining his sil1pjifying aS$ulTptions to parameters
-y.