A two-body computerized mathematical model is used to calculate planar dynamics of the LADT #3 and supersonic BLDT parachute inflations. Results indicate that the calculated loads and motions of the LADT #3 inflation are not affected appreciably by variation in the suspension-line damping coefficient. However, variation of the coefficient results in significant changes in the calculated loads and strain rates of the supersonic BLDT inflation

Poole, Lamont R.

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EFFECTS OF SUSPENSION-LINE DAMPING ON LADT #3
AND SUPERSONIC BLDT PARACHUTE INFLKFION DYNAMICS
By Lamont R. Poole
SUMMARY
A two-body computerized mathematical model is used to calculate planar
dynamics of the LADT #3 and supersonic BLDT parachute inflations. Results
indicate that the calculated loads and motions of the LADT #3 inflation are
not affected appreciably by variation in the suspension-line damping coefficient.
However, variation of the coefficient results in significant changes in the
calculated loads and strain rates of the supersonic BLDT inflation.
INTRODUCTION
Two parameters which are important in the design of parachute systems and
tile preflight analysis of missions employing such systems are the maximum
drag force produced by the inflating canopy and the maximum force transmitted
to the towing vehicle. Estimates of these parameters are normally based on
previous flight experience or on approximate analytical solutions assuming a
constant dynamic pressure. The analysis presented in reference 1 showed that
suspension-line elasticity is a significant parameter in the prediction of
opening loads under the assumption of constant dynamic pressure and considering
the suspension system as an undamped linear massless spring.
A computer program (ref. 2) has been developed for numerical integration
of the planar equations of motion of a general vehicle and parachute canopy.
The equations are coupled by a two-component (bridle assembly and suspension
lines) massless-spring mathematical model of suspension-system elasticity which
1
allows for nonlinear restoring forces and nonlinear damping. It is the purpose
of this paper to present results obtained using this computer program which
shows the influence of suspension-line damping on both the loads and motions
of parachute inflation.
Specifically, this paper will apply the computer program to two inflations
of the Viking parachute system. One inflation will be similar to that of the
LADT #3 test extended to a probable time of full inflation; the other will be
a simulation of the BLDT supersonic inflation. As actual damping characteristics
of suspension-system material are presently not well defined, loads and motions
for each case will be calculated for a wide range of suspension-line damping
• coefficients to show the influence thereof•
' SYMBOLS
CDS canopy drag area, meters 2
Fv instantaneous suspension-_;ystem force at vehicle attachment
point, newtons
Fv,ma x maximum calculated suspension-system force at vehicle attachment
point for a particular damping coefficient, newtons
q dynamic pressure, newtons/meter 2
q_,bs freestream dynamic pressure at bag strip (the beginning of inflation)_
newtons/meters 2
Sp instantaneous canopy projected area, meters 2
Sp,fi canopy projected area at full inflation, meters 2
t time, sec
tf filling time, or time from bag strip to full inflation, sec
SYSTEM DESCRIPTION
A description of the LADT #3 decelerator system is given in reference 3.
It is assumed that the mass of the LADT parachute system consists of the
material mass plus enclosed and apparent air mass as described in that
reference. A description of the BLDT Viking decelerator system is given in
reference 4. For the BLDT system, it is considered that the mass of the added
air is negligible due to the high altitude of the supersonic flight test.
Suspension-line and bridle-leg material force elongation data, as obtained
by the Langley Research Center are presented in reference 3. For the purpose
of this analysis, the bridle-leg material is assumed to have zero damping and
each leg is considered to have four layers of material for computation of
force-elongation characteristics for the total bridle assembly.
' SIMULATION AND RESULTS
Program Input
For each of the inflations under study, vehicle and decelerator physical
properties are used as program inputs. Inflation is assumed to begin under
zero-load conditions at bag strip. Initial conditions at bag strip for each
inflation were chosen so as to closely approximate the actual (or expected)
flight conditions. For LADT #3, initial conditions are as follows: altitude,
13.4 kilometers; Mach number, 0.33; flight=path angle, -65.7 degrees. For the
BLDT supersonic cases, initial conditions are as follows: altitude, 45 kilometers;
Mach number, 2.16; flight-path angle, 16.0 degrees.
The opening time, or time from bag strip to full inflation, for LADT #3
has been selected, based on extension of the flight test data, as 0.7 seconds.
3
For the supersonic BLDT, a lower-bound opening time of 0.185 seconds has been
selected based on data from the Planetary Entry Parachute Program. By the same
methods, typical histories of drag area and projected area ratio have been
selected for each flight test. The histories are shown in figure 1 for LADT #3,
and in figure 2 for the supersonic BLDT. The drag area histories are chosen so
as to result in maximum canopy drag forces of about 150,000 newtons for LADT #3
and about i00,000 newtons for the supersonic BLDT.
To examine the influence of suspension-line damping on the dynamics of
each inflation, a series of cases are run for which all inputs except the
suspension-line damping coefficient are held constant.
Program Results
The results of this study are not intended to be precise duplications
(or predictions) of flight test data. The results are intended to show the
basic differences between the inflation dynamics of LADT #3 and the BLDT
supersonic cases and the extent to which the dynamics are affected by suspension-
line damping. Therefore, the calculated data are presented in a normalized
manner.
Normalized calculated histories of vehicle and canopy dynamic pressure
for LADT #3, under the assumption of a 50 newton-second per line damping coef-
ficient, are presented in figure 3. The canopy dynamic pressure is less than
freestream dynamic pressure throughout most of the inflation process. Similar
results were obtained when the suspension-line damping coefficient was varied
from 0 to 200 newton-seconds per line. The fluctuation in canopy dynamic
pressure is due to the inclusion of added mass terms in the equations of motion.
4
Norm_)lized calculated histories of vehicle and canopy dynamic pressure
for the BLDT supersonic case are presented in figure 4, again assuming a
damping coefficient of 50 newton-seconds per line. Again, the canopy dynamic
pressure is less than both the initial and instantaneous freestream dynamic
pressure throughout the inflation range. Similar results were obtained when
the damping coefficient was varied.
In figure 5 are shown the ratios of the maximum vehicle load to maximum
canopy drag force for both LADT #3 and the BLDT supersonic case. These are
presented as functions of the assumed suspension-line damping coefficient.
For LADT #3, the load ratio is not significantly affected by the damping
coefficlent; it increases from a value of about 1.055 for a damping coefficient
of zero to a value of 1.067 for a damping coefficient of 200 newton-seconds per
line. However, for the BLDT supersonic case, the load ratio is strongly
affected by the damping coefficient. From a maximum of 1.142 for a damping
coefficient of zero, the load ratio decreases to 0.829 for a damping coefficient
of 200 newton-seconds per line.
Another parameter which exemplifies the differences in the two inflations
is the relationship between the rate at which the suspension lines are strained
during inflation and the force which the lines must carry at these rates. Curves
of normalized suspension-system force (force/maximum vehicle force) versus
strain rate for damping coefficients of 0 and 200 newton-seconds per line for
LADT #3 are presented in figure 6. It can be seen that maximum strain rates
are low (_70_/sec) and these rates occur at times when the lines are
experiencing only about 40 percent of the maximum load. It can also be seen
that the general characteristics of the curve are not strongly affected by the
damping coefficient.
5
Analogous curves for the BLDT supersonic case for damping coefficients of
O, 100, and 200 newton-seconds per line are presented in figure 7. In this
case, maximum strain rates are high (250-300%/sec). The maximum-load/maximum-
rate relationship is quite strongly affected by the damping coefficient. As
an example, for a damping coefficient of 200 newton-seconds per line, the
maximum rate and maximum load occur almost simultaneously.
CONCLUSIONS
A two-body computerized mathematical model of parachute inflation, which
includes nonlinear suspension-system elastic properties, has been used to
calculate the loads and motions for two inflations of the Viking parachute
system: an inflation similar to that of the LADT #3; and a simulation of the
supersonic BI,DT inflation. A series of cases was run for each inflation,
varying the suspension-line damping coefficient from 0 to 200 newton-seconds
per line in order to determine the effects thereof. Based on the results of
these calculations, the following conclusions are made:
I. The dynamic pressure history of neither the LADT #3 nor the supersonic
_ BLDT inflation was significantly affected by variations in the damping
coefficient.
!i
2. The ratio of the maximum vehicle load to the maximum canopy drag force,
in the case of LADT #3, is not significantly affected by variations in the
_i damping coefficient. The ratio varies from 1.055 for a damping coefficient
of zero to 1.067 for a damping coefficient of 200 newton-seconds per line.
3. For the BLDT supersonic inflation, the load ratio is quite strongly
affected by the damping coefficient. The ratio decreases from 1.142, for a
damping coefficient of zero ,to 0.829 for a damping coefficient of 200 newton-
seconds per line.
6
4. For LADT #3, maximum suspension-line strain rates are on the order of
70 percent per second, which occur at times when the lines are experiencing
about 40 percent of the maximum force for that particular case. The general
characteristics of the force/strain-rate curve are not significantly affected
by variation in the damping coefficient.
S. For the BLDT supersonic inflation, maximum suspension-line strain rates
vary from 250 to 300 percent per second. The force/strain-rate curve is
strongly affected by the damping coefficient. As an example, for a damping
coefficient of 200 newton-seconds per line, the maximum load and the maximum
strain rate occur almost simultaneously.
REFERENCES
i. Preisser, John S.; and Greene, George C.: Effect of Suspension=Line
Elasticity on Parachute Loads. J, Spacecraft Rockets, Vol. 7, no. I0,
Oct. 1970, pp. 1278=1280.
2. Poole, Lamont R.: Computer Program for Calculating Planar Inflation
Dynamics of Parachutes Having Nonlinear Suspension-System Elastic Properties.
Prospective NASA TM.
3. Talay, Theodore A.; and Poole, Lamont R.: The Effects of Parachute System
Mass and Suspension-Line Elastic Properties on the LADT #3 Viking Parachute
Inflation Loads. LWP_1021, December 1971.
4. Talay, Theodore A.; Pooie, Lamont R.; and Whitlock, Charles H.: The Effect
of Suspension-Line Length on Viking Parachute Inflation Loads. LWP-985,
September 1971.
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Effects Of Suspension-Line Damping On LADT #3 And Supersonic BLDT Parachute Inflation Dynamics

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