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

CHAPTE
ANALYTICAL METHODS
Although parachutes and similar devices are found to be complex both structurally and functionally, signifi.
design analysis and the prediction
cant advantages have been made in the development of analytical tools for
their performance. The paraJfel development of large capacity, digital computers has made it possible to work
with mathematical models of sufficient completeness to produce results of acceptable accuracy in many instances.
1:5
Acqurscv of t10 percent Is
percent is a near-
considered good, representing current state-of-the-art, although
term goal. Higher confidence in the predictabilitv of limit loads, temperatures, and system motions through
analytical means would reduce the extent of high cast full scale test/ng.
Because most mathematical models of decelerawr systems embody empirical coefficients of different kinds
tWD of the major deterrents to the analytical approach are the shortage of dats of the kind and quality needed,
and the co$/ of obtaining such information. The most useful analytical methods are those capable of employing
existing test data of the kinds easy to measure with accuracy and that are abundant in the literature. Where
. adequate empirical data are at hand, suitable computer programs have been delleloped and utilzed,. the results of
which are generaJ/y more depondable than results of earlier leSl sophisticated methods.
If quick solutions to new
preliminary
design or performance problems are to be found, short empirical methods useful for
evaluation, as
well as advanced computerized methods are needed. Unfortunately; the complex behavior of flexible aerodynamic
structures during inflation and other dynamic loading conditions , cannot yet be analyzed with the same rigor
with wh;ch aircraft or spacecroft structures are treated. There is virtually no dependable intermediate approach
between the approximate empirical methods and the rigorous mathematical formulations dictated by theory. An
engineering understanding of the short methods require an appreciation of the theory and logic of rhe complex
methods.
The nature and complexitv of the physical phenomena surrounding decelerator operation is described distinct-
ly bV the authors of Reference
501 . Parachutes, drogues and similer decelerators function for periods of time that
range from stlconds to minutes. For example, the periods of operation of the Apollo drogue, pilot chute and
main parachutes for a normal entry were one minute, two seconds , and fivf! minutes respoctively. The manner in
which BElch of these components performs throughout its period of operation is of great interest, however, the
brief moments during the deployment and inflation of each canopy are the most critical.
It is during the inflatIon
process that critical design loads usually occur along with other phvsical phenomena Impinging on thl! ultimate
reliabilty of the system.
FUNDAMENTAL RELATIONSHIPS
The physical properties important to decelerator
operation have been related in a number of dimensionless
ratios drawn from classical aerodynamics, fluid
mechanics and strength of materials studies, plus 8
few peculiar to this particular
branch of aeromech-
anical engineering, e.g., air permeability, flexibility,
and viscoelasticity with amplified hysteresis. A convenient
way to present these fundamental relationships
is in terms of scaling laws and similarity criteria.
Scaling Laws
Always a ' difficult subject because of its complexity,
the derivation of suitable scaling laws for deployable
aerodynamic deceleration components and sys.
tens has been a cO:1tin'.Jing objective.
331
Scaling Ratios for thf! Design of Model Tests. Several
investigators have sought general scai:ng laws for
maintaining dynamic simil itude of the incompressible
parachute in Ilatlo'1 process. In general , to satisfy the
laws of dynamic similarity in a sCDbd test all forces in
the model equation of motion must be scaled to have
the same relative effect as the forces in the full-scale
equation of motion. This approach was advanced to
a wseful level by Barton 502 and further expanded by
Mickey 361 (Flexibility and elasticity ratios are added
herewith to complete the following list!
Quantity Ratio
Length fflrO rTlro
Time tf/tO= frlroJYz
Force F t/FO (p lIPO) (rtlrol
Mass m 11mO (p 1lpo) (i1/roP