International Journal of Crashworthiness

Construction of a method for designing, and manufacturing a parachute for an

unmanned aircraft
--Manuscript Draft--

Manuscript Number: IJCR.2432

Full Title: Construction of a method for designing, and manufacturing a parachute for an
unmanned aircraft

Article Type: Research Paper

Keywords: Unmanned aircraft; parachute; design; method; manufacture

Abstract: This research is oriented to the creation of a list of design criteria, gathering relevant,
and necessary characteristics for the production of a recovery element. A method of
designing and manufacturing a parachute for an unmanned aircraft with a payload of 5
kg is presented, where the availability of equipment, tools, materials, and labor
available to the national market is taken into account.

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method for designing and manufacturing a parachute for an

Construction of a method for designing, and manufacturing a parachute

for an unmanned aircraft
Juan Sebastián González Alfonso a, Luis Carlos Roldán Torres a, Xiomara Pamela Rozo Cruz a, Fabio Alejandro Merchán
Rincón a, Yeison Manuel Montoya Lemus a

a
Engineering Faculty, San Buenaventura University, Bogota, Colombia

Corresponding author:
Fabio Alejandro Merchán Rincón
fmerchan@usbbog.edu.co
ORCID: 0000-0002-3401-3913

ABSTRACT

This research is oriented to the creation of a list of design criteria, gathering relevant, and necessary characteristics for
the production of a recovery element. A method of designing and manufacturing a parachute for an unmanned aircraft
with a payload of 5 kg is presented, where the availability of equipment, tools, materials, and labor available to the
national market is taken into account.

KEY WORDS

Unmanned aircraft, parachute, design, method, manufacture

1. Introduction

The use of unmanned aircraft in the aeronautical industry in Colombia has had great relevance, providing practical
applications in work areas such as photography, geographic observation, and atmospheric analysis, among others, leading
to the implementation of recovery elements to prevent the non-occurrence of damaging events in the vehicle structure,
and effects on the payload. The fact that there is still no study that meets all the specifications for the design, manufacture,
and certification of parachutes in the country directly affects the projection of future developments.

2. Theoretical framework

2.1 Parachute Concept

It is a device that slows down the vertical descent of a body, being a recovery, and deceleration element that falls through
the atmosphere or the speed of a body such as people, aircraft, and more [1].

2.2 Parachute Configuration

The parachute configuration consists of an assembly element based on the analogy that “a chain is only as strong as its
weakest link”. Each component, from the container to the canopy, must carry its share of the maximum load that is applied
during parachute opening [2].

Commented [MOU1]: Mejor una imagen con

explicaciones en inglés

Commented [CA2R1]: Buscar las traducciones

Fig 1 Parachute main parts [3]

2.3 Parachute on Unmanned Aircraft

Parachutes are implemented in unmanned aircraft in order to reduce the speed of descent. Proper parachute size
selection should be considered, based on the size of the aircraft, plus the space available on the aircraft, the impact of
weight, and other protection implementation methods [4].

Fig 2 UAV Parachute Typical Adaptation

2.4 Parachute Materials Implemented
At the beginning of the history of skydiving, materials such as canvas, and silk were used for manufacturing, currently, the
commonly used materials are nylon, kevlar, and terylene. While canvas was the first material used, other materials, such
as nylon, and Kevlar, have offered greater benefits, such as increased wind resistance, resistance to damage or tears, and
more reliable flexibility camp [6].

2.5 Diameter Projected

This concept refers to the diameter of the canopy when it is inflated, it is calculated from the projected area, this value
varies depending on the type of parachute, the porosity of the canopy, length of suspension cords, speed, and the design
of the canopy camp [7].

2.6 Nominal Diameter

The nominal diameter of the parachute can be calculated from the total surface area of the canopy, thus including the
area of the stabilizer hole, and all other openings [7].

2.7 Construction Diameter

The construction diameter is the distance between the points where the maximum width of the opposing segments
crosses the radial seam. Therefore, the construction diameter is measured along the radial seam, and not along the center
line of the segment [8].

2.8 Drag Coefficient

The coefficient of drag is the value related to the total surface area of the canopy, it indicates the effectiveness with which
a parachute produces drag with a minimum of fabric area, thus minimizing weight, and volume [7].

2.9 Materials in Parachutes and its Properties

The beginnings of the history of skydiving were marked by the manufacture of these materials such as; canvas and silk.
Currently, the commonly implemented materials are nylon, Kevlar and polyester. While canvas was the first material used,
other materials such as nylon and Kevlar have been shown to have more reliable characteristics [6].

Nylon has a good picture of mechanical properties, high toughness, and wears resistance. It must be stabilized and heated
in ovens at temperatures close to melting for days, to eliminate the internal stresses that prevent cracks from appearing
when machining. In addition, nylon has the possibility of being modified with the additives [9].

As for Kevlar, it can provide very high static strength and medium stiffness, while having a very low density compared to
aluminum. These characteristics make Kevlar an excellent material for use in secondary structures without a high load
regime [10].

Another material used in parachutes is polyester, this material has high tenacity and tensile strength, its wet strength is
equal to its dry strength, and it has outstanding wrinkle recovery (resistance). This material has good thermoplastic
properties and is sensitive to hot and concentrated acids. [11].

2.10 Design and manufacturing methods

Regarding the design of parachutes, the Mexican Space Agency exposes the design of a parachute based on
calculations of free fall, drag force and drag coefficient where it is evident that this coefficient depends directly on the
area of the canopy surface, characteristics of glide, flow patterns around the canopy, canopy shape, fabric permeability,
and rate of descent [12]. The method exposes a logical development order but does not take into account the mass of
the payload, nor specific geometric calculations of the canopy, by not taking into account these parameters the result of
the parachute design cannot offer the stability that the load useful requires and therefore the damage with the impact
on the ground can significantly affect the object.

According to How Products Are Made [13], the design of a parachute starts from the choice of the shape of the bell,
whether it is circular, it should not flat. It should have a vent hole at the apex for a fraction of the air to flow through the
inflated canopy. Specifies that it must have continuous suspension lines that run the full span of the canopy and extend
to the harness at each end, unlike other methods that use suspension line segments that are attached only to the outside
edge of the canopy.

2.11 Parachute Certification normative for UAV (ASTM F3322-18)

The ASTM F3322-18 normative [9] meets the parachute design requirements specifically for unmanned aircraft such
as drones, rockets, and gliders, among others, this standard was able to confirm and validate the equations found in other
sources such as the Parachute Recovery Systems Design Manual [7]. Equations such as rate of descent velocity, kinetic
energy, nominal canopy diameter, nominal area, drag coefficient, and density at sea level, were used to calculate the
geometry and physical parameters of the parachute. In the same way, characteristics of the materials that make up the
parachute were taken into account, such as the bell, suspension lines, central lines, etc., as well as the examination by
lighting method that allows the manufacturer to ensure a good finish of the manufacturing process. additionally, key
points were taken for the experimental tests of a parachute, but they were not completely carried out since this regulation
addresses tests of the prototype ejection system, involving electronic, and automatized components non-adaptable.

3. Design Method & Fabrication

3.1 Parachute Design

At the beginning of the consultation and research process, a series of characteristics and parameters were taken into
account that met the objective of the project. In the first instance, the mass of the payload of 5 kg was taken into
consideration because the unmanned aircraft that exceed this value are the ones that present the greatest damage due
to impact with the ground, since the heavier the payload, the higher the descent speed will be and consequently the
impact kinetic energy will also increase. The objective of the design and manufacturing method reduce energy
consumption with the incorporation of the parachute as a deceleration and recovery element. It should be noted that the
parachute in question can be used in unmanned aircraft, be it rockets, drones, aerodynes, etc. Taking this into account, a
design selection method was developed that is evidenced below.

Parachute prototype selection: To start the parachute prototype selection process, 5 steps must be taken into account as
stated in the document Engineering Design Process [15] which are; Define the problem, gather pertinent information,
generate multiple solutions, Analyze and select a solution, test and apply the solution.

The first design step is to define the problem, in this case, the parachute prototype to be designed to have the following
characteristics:

 Supporting 5 kg payload.
 The geometry of the hood must be circular or conical.
 The application of the parachute prototype must be for unmanned aircraft or for aircraft deceleration.
 The speed of descent of the parachute must allow the landing of the payload not to cause damage to the structure
due to impact on the ground.
 The parachute diameter projected must be greater than 1.65m. If the diameter is less than the reference, the
conditions of speed and drag coefficient are penalized. The parachute drag coefficient range is between 0.75 and 1.
According to The Parachute Recovery Systems Design Manual [7] is the recommended range for deceleration and
recovery elements in the aeronautical sector.

The second step consists of gathering information on the main characteristics of parachute configurations. , also the
application, advantages, geometric parameters and operating regime of these.

The third step must consider all the information previously recorded to classify those parachute configurations that meet
the criteria established in the previous steps. It is important to mention that those parachute configurations that have a
supersonic regime, that do not comply with the drag coefficient range and that do not have any geometric value, will be
discarded. Therefore, they are not taken into account for the next step.

According to the sections described above, the types of parachutes that meet the criteria are:

 Tricone.
 Full Extended Skirt 10%.
 Full Flat Extended.

The fourth step consists of analyzing and selecting the parachute prototype from the 3 alternatives that meet the design
criteria. Finally, within the parachute prototype selection process, a decision matrix is developed to select the most viable
alternative according to the factors stipulated in the first step. The criteria are arranged in order of importance and the
score is assigned as follows:

 Excellent: 9-10
 Good: 7-8
 Acceptable: 5-6
 Bad: 3-4
 Insufficient: 0-2

TABLE I
DECISION MATRIX
OWN ELABORATION
PARACHUTE CONFIGURATION
Full
Criteria Tricone Extended Full Flat Extended
Skirt 10%
0,8 – 0,88 0,78 – 0,87 0,75 – 0,9
Drag
Coefficient score: 9 score: 9 score: 10
Conical.
Conical Difficult Conical
Geometry fabrication
Bell
score: 10 score: 8 score: 10

2,55 m 2,55 m 2,55 m

Diameter
projected score: 10 score: 10 score: 10

These parachutes
were developed as Descent This configuration is effective and reliable
primary descent parachute for for airdrops and drone recovery
Application parachutes for air light loads. applications.
recovery systems.
score: 10 score: 8 score: 10
Total 39 35 40

Considering the postulated options and evaluating the characteristics exposed in the development of the document
and in the decision matrix, it is evident that the configuration of the Full Flat Extended type parachute obtained a higher
score since it has a drag coefficient range closer to that required, in addition, effective and reliable background for airdrops
and unmanned aircraft recovery applications, as indicated by the Parachute Recovery Systems Design [7].

In order to support the selection, the following analysis is carried out, which exposes other factors to which the
parachute may be exposed once the design and manufacturing process is completed.
 TABLE II
FACTOR ANALYSIS – FULL FLAT EXTENDED PARACHUTE
OWN ELABORATION

FULL FLAT EXTENDED

Design calculations are supported by
the Parachute Recovery Systems
Functional Will the parachute
Design Manual [7], there it is possible
Analysis work properly?
to corroborate the veracity of the
procedure and results.

Does the design Yes, the type of parachute is conical

Design satisfy the purpose or or circular, which satisfies what was
application? stated in the first selection step.

Can the type of

parachute be Yes, Colombia has the machines and
Manufacture
manufactured in tools.
Colombia?

Will the type of

No, the launch protocol must be taken
Security and parachute not cause
into account so that no incident or
responsibility damage or injury to
accident occurs.
people or objects?

In the degree work entitled

Is there a cost analysis
"Construction of a Method of Design
if you want to
Economic and Manufacturing of a Parachute for
replicate the design
and market an Unmanned Aircraft" is the study of
and manufacture of
analysis costs of the design and manufacture of
the type of parachute
the parachute so that it can be
in Colombia?
replicated.

The regulation ASTM F3322-18 [14],

Regulations Are the regulations for
are taken into account? Are the
and parachute tests taken
restrictions of the Colombian Civil
compliance into account?
Aeronautics taken into account?.

3.2. materials and characteristics Selection

In this material selection phase, criteria must be considered in which it will be possible to rule out alternatives
because they do not meet the required properties and characteristics. There are specific methods to determine and
choose materials, these are the traditional method, graphic method and method with the help of databases. The
traditional method applies knowledge obtained in practice and makes comparisons with systems or components that
work under the same concept, in this way the material already used is selected and from which it is not necessary to carry
out previous studies [16].

The graphic method uses graphic tools called material maps, specifically this method is developed in design
conceptualization stages. If this method uses the Ashby map, this map consists of certain specific steps to properly carry
out the process. In this methodology, physical properties of the material, environmental conditions, cost and development
are handled, which generates greater assertiveness in the results obtained. [16].
 Fig 3 Material drawing Ashby [17].

Finally, there is the method with the help of databases, in these databases there is a compilation of investigations in
material tests which deal with specific properties and in general the main properties that the material must have for a
specific purpose [16].

In this article, the selection of materials will be carried out by implementing the traditional methodology, since it seeks to
give continuity to the materials that have been used in the manufacture of parachutes and in this way the supply of raw
materials or materials is already assured. The materials that will be exposed next must satisfy these three questions:

 To what is the material needed?

 What materials have you used or do you use?
 Is the material accessible and affordable in Colombia?

Establishing the level of relevance of each property of the material to be evaluated is vital at this point. These properties
are analyzed against each other taking into account the questions raised above. In this way, the material that has the best
relationship between its properties and the established need will be selected.

3.3 Parachute Sizing Calculations Real Scale Full Flat Extended

When starting the design calculations, and sizing of a parachute, it is important to have certain default
characteristics such as; type of configuration, materials of construction, application, and payload mass. Starting with the
calculations, we start by giving a value to the projected diameter Dp of the parachute, depending on the application
objective. In this case, one of 2.52 m is proposed, this diameter satisfies the range of impact kinetic energy of an
unmanned aircraft, which is from 0 to 34 J, according to Fruity Chutes. [4].

In the first instance, the nominal area of the parachute is obtained from the equations according to nel Parachute Recovery
Systems Design Manual [7].

𝐷𝑝
𝐷𝑜 =
0,70
Equation 1. Nominal Diameter
 2,52 𝑚
𝐷𝑜 =
0,70
𝐷𝑜 = 3,6 𝑚

𝐷𝑐 = 𝐷𝑜 (0,81)
Equation 2. Construction Diameter
𝐷𝑐 = 3,6𝑚(0,81)
𝐷𝑐 = 2,916 𝑚

𝜋 2
𝑆𝑜 = 𝐷
4 𝑐
Equation 3. Nominal Area
𝜋
𝑆𝑜 = (2,916 𝑚)2
4
𝑆𝑜 = 6,6782 𝑚2

Subsequently, the calculation of the descent speed of the parachute at sea level is performed.

2 𝑊𝑇
𝑉𝑒𝑜 = √
𝑆𝑜 𝐶𝐷𝑂 𝜌𝑂

Equation 4. Descent Velocity at the sea level

2 (49,01𝑁)
𝑉𝑒𝑜 = √
𝑘𝑔
(6,6782𝑚2 ) (0,9) (1,2 )
𝑚3

𝑉𝑒𝑜 = 3,6879 𝑚/𝑠

Once the calculation of the descent speed has been carried out, it is possible to verify if the value of the kinetic energy of
the impact is within the range initially established. Following the certification standards of the parachutes produced by
the Fruity Chutes company [4] under the ASTM F3322-18, normative establishes that a category 3 unmanned aircraft
(having a mass of no less than 4 kg, and no more than 25 kg), which falls in free fall, and deploys its recovery system, must
not exceed approximately 34 J, of kinetic energy at the moment of impact with the surface.

1
𝐸𝐶 = 𝑚𝑉 2
2
Equation 5. Kinetic Energy
1
𝐸𝐶 = (5 𝑘𝑔)(3,6879 𝑚/𝑠)2
2
𝐸𝐶 = 34,00 𝐽

Given the consistency of the results obtained, it is possible to proceed to calculate the dimensions, and remaining design
parameters of the parachute, these equations are according to the Parachute Recovery Systems Design Manual [7].

𝑆𝑣 = 0,01𝑆𝑜
Equation 6. Stabilizer Hole Area
𝑆𝑣 = 0,01( 6,67828 𝑚2 )
𝑆𝑣 = 0,0667 𝑚2
 𝑆𝑣 ∗ 4
𝐷𝑣 = √
𝜋
Equation 7. Stabilizer Hole Diameter

(0,0667 𝑚2 )(4)
𝐷𝑣 = √
𝜋
𝐷𝑣 = 0,2916 𝑚

𝐷𝑣
𝑅𝑣 =
2
Equation 8. Stabilizer Hole Radius
0,2916 𝑚
𝑅𝑣 =
2
𝑅𝑣 = 0,1458 𝑚

Each suspension line of a Full Flat Extended type parachute is equivalent to 0.75 of the nominal diameter of the canopy.

𝐿𝑠 = 0,75 𝐷𝑜
Equation 9. Length suspension line.
𝐿𝑠 = 0,75 (3,6𝑚)
𝐿𝑠 = 2,7 𝑚

Fig 4 Parachute Suspension Lines

The parachute has 18 segments, in addition to 18 suspension lines, and a central suspension line, since in the design of a
parachute it must be taken into account that, for each end of the segment, a line will be attached.
 Fig 5 Parachute Central Line
𝑆𝑜
𝑆𝑔 =
𝑁𝐺
Equation 10. Gore Area
6,6782 𝑚2
𝑆𝑔 =
18
𝑆𝑔 = 0,3710 𝑚2

The bell cone angle μ selected was 25° (0.4363212 radians), because the optimum angle range for this type of parachute
is between 25°, and 30°.

360 𝑑𝑒𝑔
𝛾=
𝑁𝐺
Equation 11. The base angle of the segment
360 𝑑𝑒𝑔
𝛾=
18
𝛾 = 20 𝑑𝑒𝑔

180
𝛽 = sin−1 [𝑐𝑜𝑠 𝜇 [𝑠𝑖𝑛 ]]
𝑁𝐺

Equation 12. The base angle of the segment

180
𝛽 = sin−1 [𝑐𝑜𝑠 (25𝑑𝑒𝑔) [𝑠𝑖𝑛 ]]
18
𝛽 = 9,05477 𝑑𝑒𝑔

(0,214 𝑆𝑜 )
ℎ1 = √
𝛽
𝑁𝐺 tan
2

Equation 13. Segment height

 (0,214)(6,6782 𝑚2 )
ℎ1 = √
9,05477 𝑑𝑒𝑔
18 tan
2

ℎ1 = 1,0013 𝑚

ℎ2 = 0,676ℎ1
Equation 14. Skirt height of the segment
ℎ2 = 0,676 (1,0013 𝑚)
ℎ2 = 0,676 𝑚

ℎ𝑝 = ℎ1 + ℎ2
Equation 15. total segment height
ℎ𝑝 = 1,0013 𝑚 + 0,676 𝑚
ℎ𝑝 = 1,677 𝑚

𝛽
𝑒𝑠 = 2ℎ1 3,2 𝑡𝑎𝑛 ( )
2
Equation 16. Distance of the skirt in the segment
9,05477 𝑑𝑒𝑔
𝑒𝑠 = 2(1,0013 𝑚) 3,2𝑡𝑎𝑛 ( )
2
𝑒𝑠 = 0,5074 𝑚

𝑒1 = 0,127𝑒𝑠
Equation 17. Smaller distance of the segment
𝑒1 = 0,127(0,5074 𝑚)
𝑒1 = 0,064 𝑚

180°
∝1 = 90° −
𝑁𝐺
Equation 18. Angle 1
180°
∝1 = 90° − = 80°
18

B. Manufacture of parachutes Full Flat Extended Real Scale

Ripstop nylon fabric is spread out on the table of the textile laser cutting machine, then the Solid Edge file containing the
measurements of the segments (triangular cut) is exported to the Corel Draw software of the machine so that the process
of cutting begins. cut following the pattern assigned by the program. 18 segment cuts are made, 9 with the red fabric,
and 9 with the white fabric, for this case. It is worth mentioning that the measurements of the segment (Fig. 5) have 3 cm
rims since these will be used for the joints that are made later.
 Fig 6 laser machine segment cutting

At the end of the process of cutting the segments, they are joined, they are placed one next to the other so that they
adapt to the shape of the completely circular bell. This step is done using a double-needle sewing machine (90/14 stainless
steel needle), where two parallel rows are sewn, maintaining a constant separation between them, and implementing the
"point to point" sewing type, in order to provide the joint with sufficient strength and to assemble the edges of the
segments more accurately.

Fig 7 Segment Unions

Each segment and seam is carefully inspected using a lighting fixture (flashlight), in order to make sure that the seams are
precisely placed, and sewn correctly so that there are no subsequent flaws in the fabric, and seams. If any fabric defects,
sewn folds, or wrong stitch direction are found, the bell is rejected, and the procedure must be restarted.

Fig 8 Edge stitching of segments

Note: If greater firmness and safety in the parachute are desired, a seam reinforcement is made exactly the same as in
the previous step, parallel to the one that had been made for the joining process, this allows strengthening the fastening
between the segments of the parachute bell.
 Fig 9 United segments

Having assembled all the segments, the stabilizing hole is made, which is a circle with a diameter of 29.16 cm that is
located in the center of the bell, for this, the circle with the aforementioned diameter is demarcated on the fabric, using
a mould or compass, and proceed to cut with soldering iron as evidenced in Fig. 10.

Fig 10 Stabilizer Hole Cut

With this step, the union of the components of the canopy of the parachute is finalized.

Fig 11 finished bell

Next, the unions of the 18 main suspension lines are made, which have a length of 2.7 meters, and their material is Kevlar,
in Fig. 11 it is possible to show the marking of the exact measurement of the rope.

Fig 12 Mark suspension lines

At the end of the measurement, and cutting of the suspension lines, points are located on each of the lower edges of the
segments of the parachute skirt, as shown in Fig. 13. When delimiting these points, the holes are made with a hot 0.4
mm diameter awl so that it passes through the fabric, at the end of this step, the suspension lines are inserted into each
of the holes, and a safety knot is made so that they do not come loose. If it is evident that the knot can be easily undone,
it is recommended to make 1 or 2 more knots.

Fig 13 Suspension lines fastening

After the assembly of the suspension lines, the process of joining the central suspension lines begins, which requires the
use of a sewing machine with a 90/14 stainless steel needle, and implementation of the type of seam " zig-zag” reinforced,
since this provides greater support, and firmness, this factor is very important because it is at these assembly points
where high tensions, and high risks of tearing occur.

The seam is made with a length of 6 centimeters, and a width of 4 mm each, these are located in the upper section of the
segments, where the stabilizing hole of the bell is located. At the end of the seam, the green nylon fasteners are adapted
to hold each of the strings, as shown in Fig. 14.

Fig 14 Central Suspension Line Adapters

Once the process of joining all the lines to the hood is finished, the next step is carried out, which is to make the coupling
at the end of the length of the suspension lines. At this point, the suspension lines are joined by attaching to a 1 cm wide,
30 cm long, red nylon rope, and reinforcing this coupling with a zig-zag seam.

Fig 15 Line coupling union

At the other end of the fastening of the nylon rope, a fastening shackle is adapted by folding the tape (rope)
joining, and reinforcing it by means of a zig-zag seam.
 Fig 16 Straight seam reinforcement

This procedure is carried out in order to couple the parachute's 5 kg payload through this mechanism, as shown in Fig.
17.

Fig 17 Shackle bra

In this way, the manufacturing process of the Full Flat Extended parachute in its real scale is concluded and prepared for
its start-up, and launch tests as evidenced in Fig. 18.

Fig 18 Parachute drop with payload

3.4 Verification of the Design, and Manufacturing Method

3.4.1 parachute free fall calculations:

The built parachute does not have an ejection system so the initial speed is Vo=0 because it starts from rest. When the
parachute is released fully extended it is assumed that the fall is free, and that weight and drag are the only forces acting
on the parachute [10] when the parachute is fully extended, and fully conforms to its inflated profile, the speed is greatly
reduced until a constant limiting speed Vl is achieved and is described when an object falling under the influence of gravity
or under some other constant driving force, is subjected to a drag force that increases with speed, it will reach a maximum
speed where the thrust and drag forces are equal [11].

Starting with the development of the calculations, the limit speed is expressed as follows.

mg
Vl = √
k
Equation 21. The speed limit of a parachute

In order to solve the above equation, it is first necessary to find the value of the proportionality constant k.

ρ A CD
k=
2
Equation 22. proportionality constant
kg
(1,2 ) (6,678284 m2 )(0,9)
m3
k=
2
k = 3,606

Where ρ is the density, in this case at sea level since all the calculations are being carried out under these conditions. A is
the parachute nominal area, and CD is the parachute drag coefficient. Having the value of the proportionality constant it
is possible to solve equation 21.

m
(5kg) (9,81 )
Vl = √ s2
3,606
m
Vl = 3,688
s

The limit speed of the parachute with a payload of 5 kg corresponds to 3.6881 m/s, now it is necessary to know at what
moment of the free fall this speed is reached. For this, the free fall equations are solved for the y-axis, which is the axis
corresponding to the launch.

t2
Yf = Yo − g
2
Equation 23. final free fall height

To solve equation 23, Yf is the distance when the canopy of the parachute is already adapted to the inflated profile, and
Yo is the distance when the parachute starts from rest. At this point, it should be taken into account that Yo is the reference
taken for a launch made from the terrace of the William of Ockham building, as evidenced in Fig. 18, and Yf is determined
according to the audiovisual records captured in the launch tests at the San Buenaventura university, and an estimate is
given that the parachute, when launched fully extended, and traveling 1 meter in height, adapts its fully inflated profile.

t2
18,13 m = 17,43 m − 9,81 m/s
2

Solving the time of the previous equation, we have that:

 2 (18,13m + 17,43m)
t=√ m
9,81 2
s
t = 2,69 s

When the parachute has traveled in free fall for 2.69 seconds, it reaches the constant speed limit.

Full-scale parachute launch tests:

The minimum height of the parachute launch is determined. The entire length of the parachute must be taken into
consideration, including the dimensions of the canopy, the suspension lines, the restraining line, and the payload, where
a total length of 4.29 m was obtained. The 1 meter must be added, according to the previous calculations, this is the
distance required to reach the constant speed limit of 3.688 m/s in an estimated time of 2.69 seconds.
In this way, the minimum launch height of the Full Flat Extended full-scale parachute corresponds to 4.29 m in order to
reach the required conditions and adapt the adequate stability behavior.
Fully extended with loads of 1.2, 3, 4, and 5 kg, as the loads established for this study, with a height of 17.13 meters
corresponds to the Guillermo de Ockham building located in front of the maintenance workshop of the University of San
Buenaventura. In this launch, the measurement of time is carried out by means of a stopwatch, to later determine the
speed of the free fall of the parachute.

Fig 19 Location of the parachute drop site

At the time of launch, the parachute is not launched retracted or folded, it is launched fully open, and extended so that
upon contact with the air it adapts its inflation profile, and begins its descent, which means that the initial speed of each
launch corresponds to Vo=0

Fig 20 Parachute release tests

 TABLE III
LAUNCH TEST. OWN ELABORATION

The average rate

Launch Mass descent ∆
of descent ( 𝒔 )
∆𝒕
(𝒎) time (𝒕)
I 1 kg 5,57 s 3,075 m/s
II 2 kg 5,42 s 3,1605 m/s
III 3 kg 5,36 S 3,1958 m/s
IV 4 kg 5,11 s 3,3522 m/s
V 5 kg 4,98 s 3,4397 m/s

Upon completion of the test, and grouping of the data in the table shown previously, it was possible to show a similarity
in the data obtained, since in the practical launch test the parachute with a payload of 5 kg had a speed of 3.4397 m/s.

3.4.2 wind tunnel tests:

To verify the design, and manufacture of the wind tunnel, a test is carried out in a wind tunnel with the model scaled to
10%, since the parachute prototype for these tests must not be less than 25 cm in diameter of the canopy. since it can
significantly affect the results due to the geometric proportion. The main objective of this test is to know the behaviour
of the parachute inflation profile, the oscillations that are generated at different speeds, and that the drag coefficients
coincide with the design characteristics proposed by the Parachute Recovery System Design Guide Manual [7].
Subsequently, a comparison of results is made, thus evidencing the similarity in both theoretical, and experimental data,
thus demonstrating the fidelity, and accuracy of the proposed design, and manufacturing method, this verification is
possible since the fabric of construction of the prototype is the same as the real parachute, they have exactly the same
properties.
Prior to the wind tunnel tests, it is necessary to find the Reynolds number in the conditions that occur on the day of the
test. Parachutes operate in a turbulent flow regime due to airflow separation at the leading edge of the parachute canopy,
the Reynolds number for these bodies does not significantly change the drag coefficient of parachutes compared to
various airfoils.

𝑚
v 𝑙 𝐹𝑙𝑜𝑤 𝑠𝑝𝑒𝑒𝑑 [ 𝑠 ] . 𝐶ℎ𝑎𝑟𝑎𝑐𝑡𝑒𝑟𝑖𝑠𝑡𝑖𝑐 𝑙𝑒𝑛𝑔𝑡ℎ [𝑚]
𝑅𝑒 = =
𝑣 𝑚2
𝐾𝑖𝑛𝑒𝑚𝑎𝑡𝑖𝑐 𝑣𝑖𝑠𝑐𝑜𝑠𝑖𝑡𝑦 [ ]
𝑠
Equation 24. Reynolds number for a parachute

Equation 24 describes the Reynolds number for a parachute, and the parameter corresponding to the characteristic length
refers to the nominal diameter of the parachute since this dimension is the main one in terms of calculations, and design
of a recovery element.

𝜇 𝑑𝑦𝑛𝑎𝑚𝑖𝑐 𝑣𝑖𝑠𝑐𝑜𝑠𝑖𝑡𝑦 [𝑘𝑔/(𝑚 𝑠)]

𝑣= =
𝜌 𝑘𝑔
𝑎𝑖𝑟 𝑑𝑒𝑛𝑠𝑖𝑡𝑦 [ 3 ]
𝑚
Equation 25. Kinematic viscosity

According to Parachute Recovery System Design Guide Manual [7], the kinematic viscosity at sea level corresponds to:

𝑓𝑡 2 0,092903 𝑚2
𝑣 = 0,0001576 =
𝑠 1 𝑓𝑡 2
 𝑚2
𝑣 = 1,46415 × 10−5
𝑠
Solving equation 24:

(3,6879 𝑚/𝑠)(2,52 𝑚)
𝑅𝑒 =
𝑚2
1,46415 × 10−5
𝑠
𝑅𝑒 = 634737,4244

Once the Reynolds number is found, the scaled parachute prototype is placed in the test section of the wind tunnel. In
this case, a fastening structure was made, securing the fastening line, and at the other end the parachute bell to carry out
the tests, to maintain a stable shape of the prototype, and to make possible greater precision in results, stability, and that
the location of the prototype is not altered without the direction of flow in the wind tunnel affecting.

Fig 21 Parachute in the wind tunnel

When locating the scaled parachute prototype, the steps indicated in the "Wind Tunnel Check List" are carried out so that
no unexpected event occurs. Once each of the steps has been completed, the test is started with an angle of attack α=0°.
In the tunnel software called "HM 170" the variables were chosen as follows: on the x-axis speed, and on the y-axis the
drag force. As the variable selected on the y-axis is drag force (D), the drag coefficients must be found from these results,
as follows:

1
𝐶𝐷 = 𝜌 𝑣2𝐷 𝐴
2
Equation 26. Drag coefficient.

Note: The value of A in equation 26 corresponds to the parachute's nominal area, which is 6,678 m².

TABLE IV
WIND TUNNEL TESTING RESULTS FROM α= 0
ATTACK ANGLE 0°
Flow rate 𝒗 drag force 𝑫 (N) drag coefficient 𝑪𝑫
(m/s)
1,2627 0,2148 0,262482853
2,8235 0,5078 0,620525106
3,3408 0,7227 0,883130158
3,7881 0,8008 0,978567359
3,993 0,9766 1,193392711
4,3741 1,1328 1,384267113
 4. ANALYSIS OF RESULTS

4.1 Parachute design, and manufacturing method:

The distinctive element of the design and manufacturing method created is based on the precision of cuts of the
parts that make up the parachute, in this method, it is evident that the cut of the stabilizing hole is made after the union
of the segments, unlike the methods known manufacturing. In other manufacturing processes, when the cutting pattern
of the segments is made by means of the textile laser cutting machine, they include all the fractions of the circumference
in each segment so that when the entire bell is assembled, the shape of the stabilizer hole is included. This difference
allows greater accuracy in the shape of the circumference that is located in the upper part of the canopy, which provides
an important stabilizing factor in the fall of the parachute together with its useful load.

Once the method of design, manufacture, and construction of the real prototype, and scaling to 10% of the conical
type Full Flat Extended parachute is completed, the final result is a functional prototype, with a uniform appearance in its
dimensions, precise cuts, exact seams, and applicable to aircraft. unmanned as a recovery, and deceleration element.

In the development of the method, it was possible to identify different ways to make the cuts to the components of
the parachute bell, these differ from the other thanks to their precision, as mentioned in several sections of the document,
the cut made with a laser cutting machine textile is the most precise, which means that if results with a high degree of
accuracy, and good finishes are required, there should be used this machine. On the other hand, the scalpel and soldering
iron have acceptable, and good precision, and accuracy, respectively.

4.2 parachute drop test:

The experimental data resulted in a speed of 3.4397 m/s while the value of the speed calculated theoretically gave
3.6888 m/s, this difference is due to the fact that there are variations in the speed of the wind, in the direction of the
wind. wind flow, launch technique, etc., which can influence the results, and give less precise figures compared to the
theoretical ones. It should be noted that the speed values in the practice tests are quite favorable if they are lower than
those found theoretically, since if there is a lower descent speed, the impact kinetic energy will decrease, which will
provide greater safety, and prevent damage to payload structure.

The results obtained at higher heights are even better since, as there is a greater launch height, the impact with the
ground will be less because the speed of descent will decrease.

4.3 wind tunnel test:

The results were quite consistent, and satisfactory since the calculated descent speed of the Full Flat Extended
parachute is 3.6879 m/s where, according to Table 2, drag coefficients between 0.75, and 0.90 are presented. In the wind
tunnel test at speeds between 2.8235 m/s, and 3.7881 m/s, drag coefficients between 0.62, and 0.97 are presented, the
differences between the coefficients may be due to the addition of the structure that holds the parachute in the test
section. Since there is a similarity in the values, it is possible to determine that the parachute scale prototype meets the
aerodynamic drag conditions. In this way, the veracity of the constructed method is verified.

drag coefficient vs. Velocity

1.5
1.384267113

1.193392711
drag coefficient

1 0.978567359
0.883130158

0.620525106
0.5
0.262482853

0
0 1 2 3 4 5
Velocity (m/s)
Fig 22 Coefficient of drag vs. Velocity
 According to the previous graph, it is possible to show the existence of a positive trend in the curve, since as the speed
increases, the drag coefficient of the studied prototype increases, in addition, it can be identified that a straight line is not
obtained since that in the moments in which the measurement was made, the values of the speeds varied, and it is
difficult to capture points with speeds at specific points. On the other hand, it was possible to determine that as the speed
of the flow increased in ranges that exceeded the reference speed (>3.68 m/s), the values of the drag coefficients were
not correct because the prototype within the test section began to oscillate abruptly, the suspension lines twisted, this
phenomenon occurred because the parachute is not designed to operate at those speed regimes.

5. CONCLUSIONS

One of the purposes of this project is to provide a starting point for the development of more parachute prototypes for
unmanned aircraft, such as the one built Full Flat Extended, since Colombia currently does not have a fully constituted
industry. It has already been shown that, if it is possible through the application of theoretical/practical, and economic
resources, to design, and manufacture a fully functional parachute at the University of San Buenaventura, Bogotá, this
leads to the beginning of many more advances, and later to be recognized by to be a pioneer entity in the manufacture
of recovery elements.

If greater stability, low parachute descent speeds, and imminent damage to the attached payload are required, it is
important to note that the larger the canopy diameter, the better these factors will be. It is possible that on many
occasions this is considered an "oversizing" and that is why it is necessary to keep in mind the reason for the configuration,
and the benefits that it brings thanks to the high resistance that they generate.

For the verification of the present method of design, and manufacture of a parachute for an unmanned aircraft of 5 kg,
validations were carried out through different tests, and thanks to the construction of the scaled parachute it was possible
to corroborate drag coefficients of the prototype, similar to those contained in the design manuals of these recovery
elements, giving truth to what was elaborated.

Thanks to the development of this degree project, it was possible to conclude that the construction of a parachute is a
simple manufacturing process since the infrastructure that must be counted on is easily accessible in Colombia, and the
procedures are not highly complex if not precise.

What is visualized is to continue expanding more, and more information, and continue with studies about these recovery
elements so that Colombia becomes a supplier of certified parachutes.
DISCLOSURE STATEMENT

The authors report there are no competing interests to declare.

6. REFERENCES

[1] R. Pallardy, «Britannica,» 2021. [Online]. Available: https://www.britannica.com/technology/parachute. [Last

access: 03/23/2021].
[2] «Integrated Publishing,» [Online]. Available: http://www.tpub.com/1ase2/3.htm. [Last access: 23 Marzo 2021].
[3] «StratoCat,» [Online]. Available: http://stratocat.com.ar/stratopedia/119.htm. [Last access: 23 Marzo 2021].
[4] «Fruity Chutes,» 2018. [Online]. Available: https://fruitychutes.com/uav_rpv_drone_recovery_parachutes.htm.
[5] «Manta Air,» 2020. [Online]. Available: https://manta-air.com/uav_safety_, and_recovery_systems/.
[6] «ES.411ANSWERS.COM,» [Online]. Available: https://es.411answers.com/a/que-materiales-se-utilizan-para-
hacer-paracaidas.html.
[7] T. W. Knacke, Parachute Recovery Systems Design Manual, California: Santa Bárbara, 1991.
[8] L. E. Castillo Vargas y N. A. Jiménez Chocontá, «Diseño, desarrollo y pruebas del sistema de recuperación para el
cohete sonda Libertador I,» Bogotá D.C, 2014.
[9] «Standard Specification for Small Unmanned Aircraft System (sUAS) Parachutes,» ASTM International, 2018.
[10] Á. Franco García, «Física con ordenador,» 2010. [Online]. Available:
http://www.sc.ehu.es/sbweb/fisica/dinamica/paracaidista/paracaidista.html#:~:text=Coeficiente%20de%20forma%20d
%20%3D0.8.
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astr.gsu.edu/hbasees/airfri2.html.
[12] «Fruity Chutes,» 2018. [En línea]. Available: https://fruitychutes.com/.

Figure captions

Fig 1 Parachute main parts [3]........................................................................................................................................ 2

Fig 2 UAV Parachute Typical Adaptation ........................................................................................................................2
Fig 3 Material drawing Ashby [17]. ................................................................................................................................7
Fig 4 Parachute Suspension Lines................................................................................................................................... 9
Fig 5 Parachute Central Line .........................................................................................................................................10
Fig 6 laser machine segment cutting ...........................................................................................................................12
Fig 7 Segment Unions....................................................................................................................................................12
Fig 8 Edge stitching of segments ..................................................................................................................................12
Fig 9 United segments ..................................................................................................................................................13
Fig 10 Stabilizer Hole Cut ..............................................................................................................................................13
Fig 11 finished bell.........................................................................................................................................................13
Fig 12 Mark suspension lines ........................................................................................................................................13
Fig 13 Suspension lines fastening .................................................................................................................................14
Fig 14 Central Suspension Line Adapters .....................................................................................................................14
Fig 15 Line coupling union ............................................................................................................................................14
Fig 16 Straight seam reinforcement .............................................................................................................................15
Fig 17 Shackle bra ..........................................................................................................................................................15
Fig 18 Parachute drop with payload ............................................................................................................................15
Fig 19 Location of the parachute drop site ..................................................................................................................17
Fig 20 Parachute release tests ......................................................................................................................................17
Fig 21 Parachute in the wind tunnel ............................................................................................................................19
Fig 22 Coefficient of drag vs. Velocity ..........................................................................................................................20