Introduction
This web page deals with the topic of parachutes and their use as a
recovery device for amateur rockets. In this page, I am presenting some
information relating to basic background aerodynamics, design and testing
of parachutes, as well as providing the details to how to fabricate your
own parachute for rocket recovery. Made from commonly available materials,
this parachute is both strong and efficient. Strong in the sense that it
's designed to withstand high speed deployment, and efficient in that it
provides for a high drag force for a given size and weight.
Basic Parachute Aerodynamics
The descent rate of any body (such as a rocket) equipped with a
parachute is dependant upon the drag force that the parachute develops, to
counteract the gravitational force resulting from the payload's mass.The
drag force is dependant upon 1) the dynamic pressure created by moving air
striking the parachute canopy (and which keeps the parachute inflated); 2)
the diameter of the parachute, which determines the area over which the
dynamic pressure acts; and 3) the drag coefficient, Cd, of the parachute.
Dynamic pressure is a function of velocity and air density, which in turn
is dependant upon altitude and temperature. The vertical descent rate
provided by a parachute in a stable descent is given by:
where Wt = total weight of body and parachute (lb.), S = canopy
reference (surface) area (ft2), and r
= air density (slug/ft3). The drag coefficient of any
parachute is dependant upon a number of factors. These include:
- the surface area ("reference" area) of the canopy, upon which the Cd
is based
- gliding characteristics
- air flow pattern around the canopy
- shape of the canopy
- the permeability of the fabric ("tightness" of weave)
- descent velocity
- length of shroud lines
These factors and others which influence parachute drag is covered in
detail in a book such as Parachute Recovery Systems Design
Manual (T.W.Knacke). However, I'll briefly discuss these
factors here, as they are of interest to anyone wishing to utilize a
parachute as a recovery device.
- The drag coefficient of any body is usually obtained by testing (for
instance, in a wind tunnel, or by drop tests) and is determined by
measuring the drag force at a certain velocity (or rather, dynamic
pressure). The equation employed is
Fd = p A
Cd, or, to determine Cd from the measured drag
force, Cd = Fd / (p A), where Fd is the
drag force, A is the cross-sectional area of the body, and p is the
dynamic pressure acting upon the body. For a simple shaped body such as
a nosecone, the cross-sectional reference area is
straightforward to determine, being simply p
R2, with R=radius of the nosecone. However, for a parachute,
this is not the case. The reference area used to calculate the drag
coefficient of a parachute is the canopy surface area. This
choice of reference area, although convenient, is less meaningful, and
makes the Cd a somewhat flawed measure of the effectiveness of a
parachute.
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The gliding nature of a parachute is another reason
that using Cd as a measure of the effectiveness of a parachute can
be misleading (Fig. 1). When a parachute descends, it may have
both a downward component of velocity as well as a
horizontal component (in other words, rather than
descending straight down, it will descend at an angle). Air
flowing around the parachute at a certain velocity (V) generates
both lift and drag forces -- the drag (D) acting opposite to its
line of motion, and the lift (L)acting perpendicular to this,
tending to reduce the descent rate, Therefore, the drag
coefficient measured from free fall "drop" tests may indicate a
significantly higher Cd (than, say, that measured in a wind
tunnel), as a result of this gliding phenomenon.
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- The flow of air around and over the canopy of a parachute may
produce an oscillating (spiralling), or coning, pattern to the
state of motion of the descending parachute, as flow separation and
suction forces alternate in direction. Therefore, a parachute may be
considered to be capable of descending in either a gliding mode, or an
oscillating mode, or a combination of both. Gliding tends to prevail at
lower descent rates, and oscillating at intermediate rates of descent.
The resulting Cd can vary significantly, depending on the mode of
descent, as indicated by the following data for a typical full sized
parachute:
Descent velocity |
Descent mode |
Cd |
23 fps |
restrained |
1.26 |
20 fps |
oscillating |
1.60 |
16 fps |
gliding |
2.40 |
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- The shape of a canopy, whether it be hemispherical, semi-ellipsoidal
(flattened hemisphere) or parasheet, does not have a
significant effect upon the drag coefficient. Rather, the significant
difference in these shapes relates to the "aerodynamic efficiency", that
is, the drag coefficient based upon developed canopy area. A
semi-ellipsoidal canopy may employ significantly less fabric than either
the hemispherical or parasheet type. This is an important consideration
for rockets, where mass and volume must be minimized.
- Permeability, which quantifies the speed of air flowing through
the canopy material, is dependant upon the porosity of the fabric.
The porosity is largely determined by the tightness of the fabric weave.
The drag coefficient is not greatly influenced by the
permeability, however, as long as the porosity is not excessive. Any
fabric that has a reasonably tight weave would therefore be suitable,
from this perspective.
- The Cd of a parachute is dependant upon its (descent) velocity to a
weak extent. At higher velocities, the Cd deceases. This may be a result
of increased porosity of the fabric due to increased tension loading in
the canopy. This may also be due to the influence of Reynolds number, as
the flow of air through the fabric pores is a function of such. As well,
at higher velocities, the tension in the shroud lines increases,
affecting the shape, and therefore effective area of the canopy.
- The inflated diameter (and therefore area) and shape of the canopy
are both influenced by the length of the shroud lines (L) in relation to
the canopy diameter (D). As the length of the lines are increased, the
Cd increases. This effect is more pronounced, not surprisingly, when the
lines are particularly short (i.e. L/D < 0.5), but becomes less
significant when L/D > 1.
Parachute Design
The design that is presented here is of a true parachute,
having a "shaped" canopy, as opposed to what is referred to as a
parasheet. A parasheet has a canopy that is flat when not
inflated, and may be cut from a single piece of fabric. When a parasheet
inflates, the canopy material is "gathered" by the shroud lines, forming
an approximately hemispherical shape. A parachute with a shaped
canopy is more efficient than a parasheet, since less fabric is
required to produce the inflated shape.
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For the design that is presented here, the canopy shape is that
of a semi-ellipsoid, which is basically a flattened
hemisphere and so the cross-sectional shape is semi-elliptical (Fig.
2). I originally planned to design a true hemispherical shaped
canopy, but further investigation revealed that a semi-elliptical
shape would provide essentially the same drag as that of a
hemispherical shape. Significantly less fabric material is required
to produce a semi-ellipsoidal shape, resulting in the advantage of
reduced weight and reduced stowed volume. The aspect ratio was
chosen as b/a = 0.707, which my structural analysis indicated would
provide the most favourable stress distribution in the
canopy. |
This particular parachute is comprised of 12 gores, or panels,
individually cut from the fabric material, and sewn together to form the
canopy. The shape of the gores was calculated such that the assembled
canopy would form a semi-ellipsoidal shell with the height to radius ratio
being 0.707. For strength and to prevent unravelling, the panels must be
hemmed along each side. Therefore a two centimetre allowance is required
over the basic panel dimensions along both sides, and base. In order
to cut out the fabric panels, a paper pattern is first made. This is done
by plotting the full-scale shape of the curve on paper, using x & y
coordinates, as given below. As a prototype, I constructed a one-metre
diameter parachute. The coordinates, and figure showing what the paper
pattern should look like are presented below. As well, a table to allow
calculations of the coordinates for any size parachute is also
given.
Click for larger image Left --
Fig. 3: Pattern for 1 metre diameter parachute Right -- Fig. 4: General
table to determine pattern for any size parachute
Full size printable gore patterns are now available for 60, 80,
100 & 150 cm. diameter parachutes. Also, gore pattern for a
paper model of a 22 cm. chute. GIF and CAD formats. GOREGIFS.ZIP GORECADS.ZIP
This parachute design is intended to be structurally rugged and capable
of withstanding high speed deployment. The safe deployment speed for any
particular parachute adhering to this design is dependant upon a number of
factors. This includes materials used in the construction, the most
significant being the canopy fabric. Also, the diameter of the parachute.
The structural loading due to drag is less for smaller parachutes, since
drag force is proportional to area. The maximum safe deployment velocity
for the one metre diameter prototype parachute that I constructed is
estimated to be 250 km/hr (155 mph), based on analysis and detail
structural tests.
As both weight and stowed volume are important parameters, these have
been taken into account in the design of the parachute. For example,
hemming the panels and apex caps serves the dual purpose of preventing
unravelling of the fabric along the edges, and to provide structural
reinforcement. For the one metre prototype parachute, the weight is 170
grams (6 oz.), and has a stowed (cylindrical) volume 2.5 in x 4.5 in. (6.4
cm x 11.4 cm). By using lighter weight fabric, both may be reduced
further.
Parachute Construction
Click for Parts
List
To make the parachute, it is necessary to have (or borrow, as I did) a
sewing machine in order to stitch the whole thing together. The sewing
machine should preferably have the capability to make zig-zag stitches. Do
not be intimidated by the idea of using a sewing machine, it is not
particularly difficult, and improvement comes quickly as you gain
experience. Before making my prototype parachute, I'd never used a sewing
machine before. Just make sure and practice on scrap pieces
of fabric, first! Other than that, and the
parts listed, all that is required is some patience, attention to detail,
and a free weekend or two.
The following table shows the sewing machine settings that I found
works well. Undoubtedly, these settings vary with sewing machine model,
but hopefully this will act as a guide. The sewing machine that I used was
a Sears Kenmore Model YM-40-35R, a portable unit, approximately
twenty-five years old.
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Stitch width |
Stitch length |
Thread tension |
Hem stitching |
0 |
8 |
4 |
Seam binding |
3 |
12 |
9 |
Shroud lines |
4 |
12 |
10 |
- The first step in fabricating the parachute is to create the full
scale pattern for the panels by tracing out the shape on a sheet of
paper
- For increased visibility, the parachute is best made from panels of
alternating and contrasting colours, such as red and white. The fabric
that I purchased was all white. I cut simply cut it in half, then dyed
one half red. Nylon takes on dye very well, especially if it is done
using the "stovetop" method.
- Using the pattern, trace out the panel shapes onto the fabric, then
cut out the twelve panels.
- The next step is to hem the panels along both curved edges and along
bottom edge. The hem is to be made one centimetre in width, and is
formed by folding the edge over twice, as illustrated in Figure 5. It is
best to use straight pins to temporarily fasten the hem. Then baste
(hand stitch, using needle and thread) the hem using stitches with a
large pitch (approx. 2 cm.). This is the way that I did it. Hemming the
panels is quite time consuming, and is the most tedious step in the
entire process of making the parachute, but it is important to spend
the time to get it right. Or else, the panels will not fit together
well, and may end up as an unsightly mess.
After basting, machine
stitch the hem, using a straight stitch (I used a pitch setting of
8/inch). The hem stitch should be positioned as illustrated in Figure 5.
After sewing, the thread from the basting stitch is simply pulled out.
A finished panel is illustrated in Figure 6.
Figure 5 -- Hem
is made by folding the edge over twice
Figure 6 -- Top side view of completed
panel
- The next step is to join the panels together. Cut six
lengths of seam binding which are long enough to span the
entire arc length of the canopy, with a little extra length that may be
trimmed later. Note that this binding must be continuous from one bottom
edge of the canopy to the opposite bottom edge, a structural
necessity.
- Lay two panels (of contrasting colours) side by side, top
sides up. Starting at the base of the panels, line up the
edges, and apply strips of masking tape to (temporarily) hold the panels
together along adjacent edges. Continue until panels are joined entirely
along their edges. Flip the panels over, such that the underside
is facing up. Using an electric iron, position and then bond
the seam binding along the two edges of a panel to join them (this bond
is not meant to be structural, but simply to fasten the seam binding to
the panel so that it may be easily stitched). Then sew the binding to
the panels using a zig-zag stitch. This is illustrated in Figures 7a and
8.
Do not be too concerned with the apex (tip) of the panels, as this
can be trimmed later, and is covered by the cap pieces. However, the
length of seam binding between opposite gores should be as shown in
Figure 7b.
Figure 7a --
Detail of panel joint
Figure 7b --
Canopy gores at apex
Click for
full size image Figure 8 -- Photo
showing partially assembled parachute canopy
- Continue this process until all twelve panels have been joined
together to form the full canopy.
- Cut out two circular pieces of fabric to form the topside and
underside apex caps. The finished diameter of these caps should be about
15% of the basic diameter of the parachute. Cut the caps to a diameter
2 cm. larger than this, to allow for the hem, which is
formed with a single fold. The hem is important to prevent unravelling
and to provide structural reinforcement to the parachute in the "hoop"
direction. Recall that the hem on the panels is important for these same
reasons, except with the panels, the hem (plus the seam binding)
provides reinforcement in the "longitudinal" direction.
- Hem the caps in a manner similar to that of the panels. Again, the
use of straight pins and hand basting greatly improves the final result.
Figure 9 illustrates the caps after basting, prior to machine stitching
the hems.
Sew the hems using a straight stitch.
Figure 9 -- Photo showing canopy apex caps with
basted hem, prior to machine stitching
- The next step is to attach the caps to the canopy. Making sure the
hem is on the inside of the joint, position the underside cap and baste
stitch into position. Flip the canopy over, and do the same for the
topside cap. Sew both caps in place using a zig-zag stitch with the
canopy sandwiched in between, as illustrated in Figure 10.
Figure 10 -- Apex cap / canopy joint
- With the canopy now completed, the final step is to attach the cords
which make up the shroud lines, which is done by sewing the ends to the
canopy. Cut six lengths of cord which comprise the
twelve shroud lines. The length of each of these six cords is given by
L = 2 .25 * ( D + S ) where D = basic diameter of
parachute, S = stitching length. The stitching length, which is the
length of cord sewn to the canopy, should be between 5% and 10% of the
basic parachute diameter. Less percentage length is required for smaller
parachutes, more for larger. For the 1 metre diameter parachute that I
constructed, I used 7%. The cut cord length was L = 2.25 * (100 + 7) =
240 cm.
- To protect the cords from abrasive damage at the tethering loop, and
to distribute the tension loading in the lines more uniformly, slip the
six cords through a length of heat-shrinkable tubing cut to
approximately 7% of the cord length. The diameter of the tubing should
be minimum, such that when shrunken, it firmly embraces the lines.
Do not heat-shrink the tubing at this stage,
however.
- Sew the ends of the cords to the underside of the
canopy, using a zig-zag stitch, with one end each at opposing panel
joint. The cord should be sewed offcentre at the joint, at the
centreline of the zig-zag stitch (see Figure 7a). Figure 11 illustrates
a properly sewn cord.
Click for
full size image Figure 11 -- Photo
showing cord attachment to parachute canopy
- The final step in completing the parachute is to form the tethering
loop. Position the piece of heat-shrink tubing such that all twelve
shroud lines are equal length as measured from the centre of the tubing.
Heat shrink this tubing in place.
To form the tether loop, a second,
larger sized, piece of heat-shrink tubing is slid over the shrunken
piece of tubing, as illustrated in Figure 12. Heat shrink this piece of
tubing in position.
Figure 12 --
Detail of tethering loop
This completes the parachute construction!
Click for full size image
Photos of the completed one metre diameter
"prototype" parachute
Click for full size image
A 3 metre semi-ellipsoidal parachute recently
fabricated by Phil Vukovich of New Zealand
Structural and Drag Testing
In order to design a parachute, it is necessary to know the strength
of the various components of which it is to be fabricated, for example,
the fabric, shroud lines, seam binding, as well as the strength of the
joints. A number of these tests were conducted and used together with
structural analysis to estimate the strength (safe deployment velocity)
of the prototype parachute. Included was a "proof loading" deployment
test conducted at half its safe design deployment speed. Also
conducted were tests to determine the drag force (and coefficient) of
the prototype parachute, at various velocities. This information is
important to estimate the descent velocity of a rocket equipped with
such a parachute.
Structural
and Drag Testing
For more information about parachutes as a recovery system,
check out:
- The Recovery of
Rockets (parach1.pdf) Jorgen
Franck (Danish Amateur Rocket Club)
This report discusses the use
of parachutes as a recovery method, and provides details on how to
determine parachute drag and descent rates. Available for download from the DARK
website
- How to build a rocket
recovery system using a
parachute Dr. Jean Potvin
Describes a clever means to estimate the safe descent rate for a
rocket.
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