Introduction to Parachute Subsonic Aerodynamics

Introduction to Parachute Subsonic Aerodynamics
Giorgio Guglieri
Politecnico di Torino
Dipartimento di Ingegneria Aeronautica e Spaziale
Corso Duca degli Abruzzi 24
10129 Torino (Italy)
1

Parachutes
The material presented here will cover a short historical discussion, a look at structure, general
configuration and then aerodynamics in both steady state and transient phases. In the aerodynamics
sub-section some existing empirical models for drag, deceleration and filling time will be presented.
Introduction and Historical Perspective
Parachutes have been in use for a long time, as far back as two thousand years the Chinese used
them. Three centuries after Leonardo da Vinci made drawings of parachutes in the fifteenth century
they were being used in flight. However a major milestone in parachute development had to wait
until the 1930’s.
It was at the Flugtechnisches Institut der Technischen Hochschule Stuttgart (FIST) beginning in
1933 that more serious and thoughtful development of parachutes was begun. The purpose of the
research and development that they were undertaking was to find the most suitable method of
decelerating an aircraft in-flight and then landing safely. In order to achieve this the parachute
needed to have reliable and controllable inflation, high drag, low opening shock, stability, simple
design and construction and simple maintenance. To achieve the above characteristics it was found
that increasing the porosity of the canopy gave an increase in stability whilst giving a decrease in
drag. The result of this work was the FIST Ribbon Parachute, 1938.
Parachute technology has in the past taken the approach of development by evolution, also know as
trial and error. Which is to say that flight-testing was the primary method of iterating the design
process and gathering experience. This design philosophy worked very well and many good
parachutes have been born out of this process. However as the flight envelopes and cost of payloads
began to grow so did the costs associated with flight-testing. For this reason the time taken for
development had to be reduced significantly.
Reduction of development time, as caused by the disappearing availability of flight test time, meant
that a more analytical approach had to be adopted. In the case of parachute design this is not such a
simple thing because the fluid dynamics involve separated, unsteady flows that are coupled with the
structural dynamics of a flexible structure. The construction of approximate models was the only
option available. Indeed this still remains the only option available, however over many years of
dedicated research the knowledge of the phenomena involved in parachute aerodynamics has been
steadily improving.
2

Description of Parachutes
General Parachute Description and Components
The purpose of the parachute is to decelerate and provide stability to a payload in flight. The
aerodynamic and stability characteristics of the parachute system are governed by the geometry of
the parachute, as such careful consideration is paid to this in the design process. Storage should be
efficient in terms of volume and packed weight, as well as allowing a rapid and reliable
deployment. The effects of deployment and opening force are critical in the safe operation of the
parachute and the integrity of the payload. The opening characteristics also feature heavily in the
selection of geometry and other parameters in the design process.
Parachutes are in general symmetric about the system axis. This axis passes through the center of
the canopy and the confluence point of the suspension lines. The canopy is the cloth surface that
inflates in order to provide the desired lift, drag and stability. The suspension lines transmit the
retarding force from the canopy to the payload, either directly or through risers attached below the
confluence point of the suspension lines to the body. The point of convergence of all suspension
lines of a parachute is called the confluence point. The position extending below the major diameter
of the inflated canopy to the leading edge of the canopy is the skirt. The crown is the region of the
canopy above the major diameter of the inflated shape. The small circular opening at the center of
the crown is called the vent. The apex is the center of the canopy. A general circular parachute
layout is given below in Figure 1. Square parachutes, like the ones used widely in sporting
applications, will not be investigated since the parachutes used for aerospace applications are not of
this type.
Parachutes are formed from an even number of gores. The gore length is measured along the center
of the gore from the vent band to the skirt band. The simplest gore shape is triangular with a linear
variation of gore width between the vent band and the skirt band. Some parachutes use shaped gores
to optimize aerodynamic characteristics and / or minimize material stresses.
The parachute nominal area S0 is the actual three-dimensional canopy constructed surface area. For
most canopy designs, S0 is computed as the sum of the gore areas inclusive of vent area slots, and
their openings within the gore outline. Areas of surfaces such as ribs, flares, panels, or additional
fullness to the cloth are also included. Nominal diameter D0 is the diameter of a circle whose area
is S0 .
A second reference dimension of parachutes is the constructed diameter Dc . The constructed
diameter is the diameter of the parachute when projected on a planar surface. For the flat circular
parachute type these is the actual “as-built” diameter of the canopy. Therefore the nominal diameter
is the hypothetical effective diameter, and the constructed diameter concerns the actual dimension
of the parachute.
Aerodynamic forces change the shape of the canopy from its constructed configuration to a concave
scalloped contour when it fills to its inflated shape. To characterize the dimensions of the inflated
decelerator in constant-velocity flight requires projecting the area of the inflated canopy onto the
plane of the skirt reinforcement. This measured projected area is noted as SP . Projected diameter
DP is defined as the diameter of a circle with area equal to the measured projected area.
Two other parameters of the flat circular parachute is the vent opening diameter DV which is
directly proportional to the safe deployment of the parachute and the depth of inflated parachute hP
which characterizes the momentum of the air trapped into the concave shape.
3

Figure 1
There are a number of different kinds of parachutes that have been designed for various
applications. The different applications parachutes are typically used for are pilot, drogue,
deceleration, descent, extraction, supersonic drogue and stabilization. A list of parachute type, drag
coefficient and application is given below in Table 1.
4

Figure 2
Parachute Type CD General Application
Flat Circular Ribbon 0.45 – 0.50 Pilot, Drogue, Deceleration, Descent
Conical Ribbon 0.50 – 0.55 Pilot, Drogue, Deceleration, Descent
Lifting Conical Ribbon 0.55 – 0.65 Lifting Stores (L/D~0.7)
Hemisflo Ribbon 0.30 – 0.46 Supersonic Drogue
Ringslot 0.56 – 0.65 Extraction, Deceleration, Descent
Ringslot / Solid Canopy 0.85 – 0.95 Deceleration, Descent
Ringsail 0.75 – 0.90 Descent
Disk-Gap-Band 0.52 – 0.58 Supersonic Drogue, Descent
Guide Surface (Ribbed) 0.28 – 0.42 Stabilization, Pilot, Drogue, Descent
Guide Surface (Ribless) 0.30 – 0.34 Pilot, Drogue, Descent
Rotafoil 0.85 – 0.99 Drogue
Vortex Ring 1.50 – 1.80 Descent
Table 1
5

Conical Ribbon Parachutes
The Conical Ribbon parachute will be dealt with in more detail, the reason being that it is this type
of parachute being widely used for aerospace applications. The conical ribbon parachute makes use
of a shaped gore to produce the conical canopy when inflated. The conical ribbon parachute has an
advantage over the flat circular ribbon parachute because it has ≅10% higher drag without a
decrease in stability. So for this reason the conical ribbon parachute is far more widely used in high
performance applications.
As the demands placed on parachutes have risen the need for higher strength to weight ratios has
led to number of modifications to this kind of parachute. One of these modifications is to use a
continuous ribbon. Instead of ribbons being separate entities for each gore that are then sewn
together at the junction between each gore, there is one ribbon that goes the entire way around the
parachute. This method reduces the number of joints and as such makes the parachute stronger for
an equal mass. Another improvement that has been made is to align the verticals perpendicular to
the continuous ribbon thus changing them from verticals to mini-radials. This serves to lessen any
stress concentrations that occur from the verticals not being aligned at 90° to the ribbons. This is
known as “all radial construction”.
To optimise the usage of material in the parachute, areas of high stress concentration are identified.
The breaking strength of the ribbons in these areas are significantly higher than in others. Typically
the ribbons close to the apex and leading edge are of the highest breaking strength, with the
remainder of ribbons of lower strength. Also the width of the ribbons may be different throughout
the parachute, this is to tailor the amount of load that will be taken at a particular point or for an
aerodynamic purpose.
Discussion of Parachute Aerodynamics
The dynamics of parachutes are complex and difficult to model accurately. During both the
inflation process and the terminal descent stage, the dynamics of a parachute are governed by a
coupling between the structural dynamics of the parachute system and the surrounding fluid flow.
Both these dynamic systems must be addressed as a coupled system in order to gain a proper
representation of the dynamic system as a whole.
When the parachute is in a steady state the air flowing around the parachute will separate at some
location on the canopy. The shedding of the vortices from the canopy can affect the canopy stability
and cause a periodic motion of both parachute and payload. The wake from a porous parachute
consists of air that flowed around the canopy and air that flowed through the canopy. Generally the
payload - in the speed range of parachute usage - sheds a very turbulent wake. Part of the flow that
is entering the parachute is therefore of a disturbed nature and should be considered regarding the
aerodynamic performance of the parachute. For many high-performance parachutes, this change in
oncoming airflow can be quite significant during the time required for the parachute to inflate. The
implication of a rapid deceleration is that second order effects are likely to be present.
To summarize, calculation of parachute deployment, inflation, and deceleration requires a solution
to the full Navier-Stokes equations for a turbulent, separated airflow around and through blunt
bodies. The parachute is also a flexible body having dynamic behavior coupled with the behavior of
the flow which passes through and around it.
6

From the above description it is obvious a full time dependent solution of this system is far from
being feasible. To make a mathematical model that is feasible simplifications must be made. As
long as the model can be validated satisfactorily by experiment, simplification is not seen to be a
problem.
Steady State Parachute Drag
The aerodynamic drag produced by the parachute decelerates the payload and accelerates the air in
the vicinity of the parachute. The primary source of parachute drag is the pressure differential
across the canopy. The parachute drag, D, is related to parachute drag area, CDSP the air density ρ,
and the velocity V.
1 2
D = ρV
C D S P
Equation 1
2
The drag area CDSP of a parachute depends on its type, inflated shape, size, Reynolds number,
Mach number, Froude number, material elasticity, and porosity. Depending on the relative size and
positions of the parachute and its payload, the payload wake may also affect the parachute drag.
Due to the absence theoretical methods drag coefficients are generally determined experimentally,
either from captive tests (wind-tunnels) or from free-flight tests (aircraft drop, balloon drop).
Conical Ribbon Parachute Drag Coefficient
In an effort to understand the steady state flow characteristics of parachutes it is now useful to look
at how the drag coefficient is related to various parachute parameters.
Parachute Shape
Figure 3
7

Figure 3 shows the change in drag coefficient for changing diameter ratio (inflated diameter divided
by constructed diameter). The trend that can be seen in this graph is as expected. Diameter ratio is a
non-dimensional measure of how elongated the parachute is when inflated. Increasing diameter
ratio is associated with a decrease in elongation. As elongation decreases it would be expected that
the flow would separate at a point closer to the leading edge and as such produce a larger area of
high pressure differential across the parachute.
Porosity and Suspension Line Length
Figure 4
Figure 4 shows both the effects of porosity and suspension line length ratio on drag coefficient.
Again both these parameters behave with a trend that is expected. Increasing porosity corresponds
to a decrease in drag coefficient. This is due to the porosity decreasing the pressure differential
across the parachute. The effect of decreasing the suspension line length causes the line angle to
increase an as a result the inward radial component of the line load becomes larger. When this
happens the diameter that the parachute can open to is restricted thus causing a decrease in drag
coefficient.
8

Figure 5
Figure 5 shows the above described effect of suspension line length more clearly over a larger range
of suspension line length ratio.
Reefing
Figure 6
9

The term reefing is used when the diameter of the parachute is restricted, this has the effect of
limiting the drag area of the parachute. The purpose of reefing is to limit the opening-shock load on
the parachute. The reefing line may be severed at a latter point to then allow the parachute to fully
open and provide greater drag. Reefing may be carried out in more than one stage to control the
deceleration more closely. A typical payload deceleration is shown below in Figure 6, note should
be taken of the effect of reefing. Reefing is usually performed by a band passing though the skirt
ribbon. The reefing lines are usually released by a pyrotechnic. Reefing also has positive effects on
stability, below in Table 2 the effect of reefing on drag coefficient and static stability can be seen.
Where Dr is the reefed diameter and Dc is the constructed diameter.
Clustering
Dr/Dc CD (for α=0) (dCm/dα) α=0
1.000 0.533 -0.0012
0.466 0.365 -0.0014
0.366 0.280 -0.0052
0.282 0.205 -0.0109
0.172 0.115 -0.0063
Table 2
There are various advantages and disadvantages associated with clustering. Clustered parachutes
open more quickly than a single parachute of the same size, they allow a degree of redundancy, the
same type of parachute may be used for varying payload weights. Clustering of parachutes does
reduce the drag coefficient of canopies. The amount by which the drag coefficient is affected is
related to riser length and the number of canopies. Below (Figure 7) the effect of the number of
canopies, for a given riser length, on cluster efficiency factor is shown. As the number of canopies
increases the efficiency of the cluster decreases.
Figure 7
10

Transient Aerodynamics
Transient aerodynamics refers to the period when time dependant events are taking place. In short
this refers to the period when the parachute is inflating.
Snatch Loads
The snatch load is defined as the force imposed on the suspended load by the decelerator to
accelerate the mass of the decelerator from its velocity at line extension to the velocity of the
payload. It should be noted that snatch loads are imposed before inflation, an example of a
measured snatch load can be seen in Figure 6.
Snatch loads have the potential, when excessively large, to damage parachute components and
mechanisms. Damage is usually caused as a result of the inertial loads that are generated by such a
shock. Controlling the snatch load can be achieved in a number of ways. One way is to pack the
parachute bag in such a way as to deploy the lines before the canopy, this means that the canopy is
not able the increase the differential in velocity between the parachute and payload. A second way
of reducing snatch loads is to decrease the mass of the parachute, this serves to minimise the
amount of mass that must be accelerated. Also reducing the uninflated area or the area of the drogue
or pilot parachute will reduce the snatch load. However changing these parameters could have
unwanted effects on the inflation and deployment of the parachute and as such should be treated
with care.
Canopy Inflation
Upon being pulled free from the deployment bag the parachute will begin to inflate. Air flows in
through the opening at the skirt and becomes trapped inside the canopy. The trapped air will rise in
pressure as more air enters the canopy. When the pressure rises above the air pressure outside the
canopy the canopy will begin to expand. The rate and extent of expansion is dependant on a number
of things. Expansion rate is restricted by the aerodynamic forces acting on the outside of canopy.
The aerodynamic forces are determined by the instantaneous shape of the canopy. Also effecting
the rate of expansion is the porosity of the canopy and the size of the vent. It can be intuitively seen
that the porosity and vent size have a strong influence on the internal pressure since they dictate
how much air is allowed to pass through the canopy. The extent of inflation is dictated by the
diameter of the skirt band ribbon and or the length of reefing lines.
The amount of porosity should not be so excessive so as to not allow full inflation. If this is the case
an oscillatory motion called “squidding” can occur, where the canopy inflates and deflates in a
periodic motion.
Below in Figure 8 a typical inflation sequence can be seen.
11

1.1 Parachute stability
Figure 8
Most of the drag generated by a parachute is created by the pressure differential between the
upstream (concave) and downstream (convex) sides of the canopy. The magnitude of the drag ( and
therefore the performance of the parachute) is largely determined by the magnitude and distribution
of pressure differential across the canopy. The canopy pressure distribution also determines the
stability of the canopy, and it must be known in order to predict stresses throughout the canopy
material during the inflation process.
The stability of the parachute may affect the motion of payload and the trajectory of the
payload/parachute system.
The stability of the parachute depends on its canopy configuration, its location behind its payload,
and the interaction of the payload wake with the parachute. Parachute aerodynamics considers two
classes of stability. The parachute is considered to be statically stable if it returns to its equilibrium
position when it is displaced from its equilibrium position. The parachute is considered to be
dynamically stable if its aerodynamic moments and forces damp out unsteady motion. A third type
of parachute “stability” involves the constancy of the canopy’s inflated shape rather than the motion
of the parachute with respect to its payload. Although this is not stability in the classical sense, the
stability of the inflated shape of the canopy is important for achieving adequate deceleration.
Static stability
A parachute is statically stable at angles-of-attack where the pitching-moment coefficient
C m decreases with increasing angle-of-attack i.e. Cmα αeq
( ) < 0 .
12

It should be noted that the formal mathematical definition of static stability contradicts the common
vocabulary used by parachute research. The flat circular parachutes (solid canopy) meet the formal
mathematical stability criteria for equilibrium at large angles-of-attack. They exhibit limit cycles or
pendulum motions with an amplitude of 25 degrees from the flow direction. Hence, these
parachutes are sometimes considered to be “unstable”. In the case of solid flat circular parachutes,
the airflow separates from the leading edge of the hemisphere in alternating vortices. This
alternating flow separation causes large differences in the skirt’s pressure differential on opposite
sides of the canopy, which in turn produce large destabilizing normal forces and large amplitudes of
oscillation. Now, for parachute of this type with geometric porosity, part of the air flows through
the canopy and pushes vortices in the near wake farther downstream behind the canopy. Since more
air passes through the canopy, less air flows around the canopy skirt; hence, the vortices shed at the
skirt are weaker for porous-canopy parachutes than for solid-canopy parachutes. Separation can
occur at each slot in the canopy, rather than only at the skirt. As a result, the air flow separates more
uniformly around the canopy, thereby minimizing the destabilizing alternate flow separation of the
vortex trail. This is the aerodynamic design principle for the stable ribbon and slotted parachute
canopies.
From past systematic analysis, it can also be observed that the static stability increases with
increasing riser length. An example is when the forebody is small relative to the parachute diameter,
the destabilizing effect of the wake on the parachute’s static stability is negligible. Problems can be
avoided when small parachutes are used as drogues or payload stabilizers by placing the parachute
far behind the payload. If this is not possible, the strong body wake interaction with a smalldiameter
parachute (at both subsonic and supersonic deployment conditions) requires very careful
design trade-off on type of parachute, suspension line length, permanent reefing, porosity, and gore
shaping. Using a porous canopy and placing it as far behind the payload as practical (10 body
diameters aft of the base is desirable) are perhaps the most effective design strategies for
minimizing wake effects on static stability.
Dynamic stability
A system is dynamically stable when the parachute’s aerodynamic forces and moments decrease the
amplitude of each succeeding oscillation towards zero or to a small steady-state amplitude. In
general, achieving acceptable dynamic stability has not been a major problem in high-performance
parachute design. This conclusion is largely due to the fact hat high-performance parachutes usually
have high porosity, which gives them excellent static and dynamic stability.
Inflation instabilities
Inflation instabilities can cause a parachute to lose drag and to develop motions that may fatigue
canopy materials and result in the failure of the parachute (Figure 9). These instabilities are not
related to the slope of the pitching moment curve. They are caused by the periodic coupling
between the canopy shape and the unsteady airflow in and around the canopy. At low speeds,
(subsonic interval of 0.7 Mach) inflation instabilities are often called “squidding” and are usually
observed in parachutes whose porosity is so high that inflation becomes marginal. In order to
understand those instabilities, it is useful to begin from the very first inflation stages of the
parachute.
The inflation stages of a circular parachute are easy to visualize. After unfurling out of the bag, the
parachute first adopts a rather elongated shape, not dissimilar to that of a vertical tube opened at its
lower end. Because of the system's rapid descent, air rushes in through the tube's opening and
accumulates at the apex of the canopy to create a high pressure air “bubble”. Steady inflow
continues to build up internal pressure, thus allowing the bubble's volume to expand horizontally as
13

well as vertically. However, there is more expansion along the vertical than the horizontal. This
process goes on until the bubble is large enough to occupy the entire design volume of the
parachute.
The shape of the expanding air bubble being trapped inside the canopy is dictated by the balance of
aerodynamic forces that act in opposite directions along the boundary defined by the parachute's
fabric. The bubble's expansion rate first depends on the pressure differential between the outside
and inside of the parachute. Like for any blunt objects (generic payload) moving through air, wake
turbulence generated on the downwind side of the parachute causes the external pressure to be
lower than the internal pressure near the apex.
The faster the parachute, the larger the pressure differential, the faster the inflow into the parachute
and, consequently, the faster the bubble expansion. On the other hand, rapid expansion generates a
large external pressure which squeezes the bubble on its upwind side, thus slowing down the
expansion. Again, this squeezing effect increases with the parachute's descent speed.
The balance between these factors (i.e. rapid inflow, low external pressures near the apex and
squeezing force at the lower end) is achieved by the bubble adopting the “optimal” shape and leads
to faster expansion along the vertical than the horizontal. Because the parachute/payload system
decelerates during inflation, this balance of pressure inside and outside the parachute is
continuously readjusted as the inflow becomes slower.
Figure 9
On the other hand we need not to decelerate very fast, by means, to pay extra attention on the
opening forces (aerodynamic forces) acting on our inflated canopy. The opening forces in some
designs may be so large to cause the destruction of the parachute itself and total damage of its
payload. Typically, if a parachute inflates too quickly, little or no deceleration has occurred: the
parachute and its load still travel at very large speeds by the time the parachute has opened, thus
generating a very large amount of drag and consequently a large force on the parachute structures.
14

Reefing devices are used to limit - for a given time - the rate of canopy expansion during the early
phase of inflation. With some circular parachutes for example, a line routed around the skirt limits
the inflow and permits early deceleration, until a pyrotechnic device cuts the latter at a preset time
or altitude.
Canopy porosity also plays an important role in establishing the inflation rate. When the total
porosity is excessive, the radial forces generated by the pressure inside the canopy may not exceed
the inward component of the load in the suspension lines. This results in an oscillatory motion of
the canopy, which stops the inflation process. Permanent reefing of the ribbon canopy can eliminate
the subsonic oscillations.
It can be concluded that permanent reefing, extended skirts, improved porosity, and gore shaping
improve subsonic parachute drag, enhance stability, and reduce the maximum opening-shock loads
of ribbon parachutes.
15

Added Mass Approximation
When a parachute passes through the air it drags some of the surrounding with it, this means that
this air must be accelerated from rest up to the speed of the parachute. The parachute will also
accelerate some of the air immediately in front and behind. The energy that is required to facilitate
this acceleration is taken from the kinetic energy of the payload parachute system.
These fluid inertia effects are taken into account in the equation of motion by the “Added Mass
Approximation”. The idea is that the mass in this equation has a component added to take into
account the extra mass m a associated with the accelerated air. This can be seen below in Equation
2, where the change in momentum of the payload/parachute system (mass m b) is equal to the sum
of the drag force and gravitational force component.
d
dt MV
1
[ ] = −
2 ρV2 CDSP + mbgsinθ Equation 2
M = m a + m b Equation 3
After combining Equations 2 and 3 and then rearranging the following expression for system
acceleration (or deceleration) can be used.
( mb + ma)
dV 1
= −
dt 2 ρV 2 CDSP − V dma
dt + mbgsinθ Equation 4
However for Equation 4 to be useful an expression or knowledge of ma(t) must be known. Shown
below is an expression for added mass, similar to that for apparent mass, that has been used widely:
ma = ka 4
3 ρπr3 Equation 5
The value of ka, a constant, can be found in various ways. From a purely analytical approach for
example, potential flow around simple geometric shapes can be used. For example Ibrahim used
potential flow solutions for flow around spherical cups (ka=1.068), whereas Klimas used potential
flow solutions for flow around a vortex sheet (ka=0.994). Klimas also calculated values of ka for
porous hemispherical ribbon parachutes. These calculations are useful to us because they offer a
usable method of estimating ka. Figure 10 shows the relationship between ka and porosity λ
(ka=1.068 for zero porosity) for hemispherical ribbon parachutes. Using this figure a value for ka at
any porosity can then be estimated.
16

Figure 10
Equation 4 and 5 can then be combined to give the following expression for acceleration.
− dV
dt =
1
2 ρV 2 CDS +8kaπr 2 ⎡⎡
1 dr
⎢⎢
⎣⎣
V dt
mb + ka 4
3 πρr3
− 2
ρV
⎤⎤
2
mbgsinθ
⎥⎥
⎦⎦
Equation 6
The significance of fluid inertial effects has been verified by flight tests over the years, one such
example being in 1944. The US Army Corps tested personnel parachutes at varying altitudes for the
same indicated airspeed. The result of this testing showed that opening times and loads increased
with altitude. The reason for this can be seen when it is considered that at increasing altitude the
true airspeed will increase for constant indicated airspeed, as such the inertial effects of the air are
greater.
After comparison with flight test data the added mass approximation tends to over estimate the
deceleration that will occur. From a structural design point of view this means that results obtained
from the added mass approximation can be viewed as conservative. This is of course assuming that
the loads in other phases of parachute operation (for example snatch) are not larger. So while the
concept of added mass is only an approximation, the effects of fluid inertia in transient parachute
aerodynamics are significant enough to be included in modeling. At present this method of
accounting for the inertial effects of air is the most practical tool available to be used in the transient
phase of parachute operation.
Filling Time
Due to the complexity involved with the filling process, filling time is not able to be calculated by a
purely analytical method. The alternative once again lies with an empirical approach that is
validated by flight test. Knackle worked on ideas presented by French and O’Hara to arrive at the
following empirical relation for filling time.
17

t f = 8D 0
V S 0.9
Where D0 is nominal diameter (ft) and VS is velocity at line stretch (ft/s).
Equation 7
It should be noted here that Equation 7 is dimensionally incorrect. This means that the actual
physics of the system are not properly represented. While Equation 7 has been shown to provide
reasonably good answers, care should always be taken in using such an equation so that it is not
being used outside the intended range of conditions.
References
Maydew, R.C., Peterson, C.W., “Design and Testing of High-Performance Parachutes”, AGARD-
AG-319, 1991
“Deployable Aerodynamic Deceleration Systems”, NASA-SP-8066, 1971
18

Flat circular ribbon parachute
19

Conical ribbon parachute
20

Slanted ribbon lifting parachute
21

Hemisflo parachute
22

Ringslot parachute
23

Ringsail parachute
24

Disk-gap-band parachute
25

Ribless guide surface parachute
26

Rotafoil parachute
27