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VOL. 11, NO. 12, JUNE 2016 ISSN 1819-6608
ARPN Journal of Engineering and Applied Sciences
©2006-2016 Asian Research Publishing Network (ARPN). All rights reserved.
www.arpnjournals.com
7443
DEVELOPMENT AND ANALYSIS OF ARROW FOR ARCHERY
Wong Fei Yong, Zulkifli Ahmad and Idris Mat Sahat
Human Engineering Group, Faculty of Mechanical Engineering, Universiti Malaysia Pahang, Pekan, Pahang, Malaysia
E-Mail: kifli@ump.edu.my
ABSTRACT
This project is about the development and analysis of arrow for archery. 3 types of arrow head been designed:
bullet shaped head, 3D shaped head and cone shaped head. The arrow performance measurement parameters were studied
such as the FOC values, static stiffness values and the drag forces. SolidWorks 2012 was used to designs the three types of
arrow head and the drag force is simulated by using SolidWork Flow Simulation. The material used for the arrow head
fabrication is stainless steel 304. The arrow shafts used are carbon shaft of 5.46mm outer diameter and 7mm fiberglass and
carbon fiber shaft. 3 different shaft properties are used to determine the effec t of static stiffness, arrow heads weight and
shaft diameter on the drag force generated at the arrow. The experimented result for Beman 570 -14 arrows are slightly
higher compared to simulation results obtained from Solid Works. The possible cause is the characteristic of the arrow
during flight where arrows starts to bend in C manner then straight again then bend again in reverse C manner and so on
when it been shot. These deformation causes energy losses to the surrounding due to air friction, natural damping effect
and shear friction. From the result obtained, it is shown that fiberglass shaft arrow has the highest drag force regardless o f
the arrow head types used compared to the other two types of shaft. Although Beman 570-14 shaft has smaller frontal area
compared to a 7mm outer diameter carbon fiber shaft, the drag force obtained from the experiment shows that both bullet
shaped head and 3D shaped head for carbon fiber shaft has lower drag force compared with the same arrow head shape.
Keywords: archery, arrow head, drag force, static stiffness.
INTRODUCTION
Archery has been used for centuries to hunt and
combat. In the modern day, archery main uses are for sport
and hunting. From the mid of 19 century, the attempt to
turn archery as modern sport has been done and now it is
even an official Olympic games. Since then, the factors
that help to promote better shooting accuracy has been
investigated scientifically. Archery equipment
performance is divided into: 1) the performance of the
bow launching the arrow; 2) the performance of the arrow
in flight; and 3) for bowhunters, the performance of the
arrow-broadhead combination on impact (Barton et al.,
2012).
In archery especially for sport, the performances
not only rely on the bow design and characteristics.
Instead, arrow design and parameter also play an
important rule and has a major effect on archery accuracy
and precision. There is only a few scientific studies are
known on the aerodynamic properties of an arrow,
although they have dominant effects on down-range
velocity and also on its drift in wind (Okawa, Komori,
Miyazaki, Taguchi, and Sugiura, 2013). Currently, most of
the current investigation is carried out to determine certain
current market arrow without designing the arrow and try
to improve it. The scope of previous investigation mostly
limits on the mechanics of arrow flight upon release, the
interaction between bow and arrow, and measurement of
arrow drag in a tunnel. Without the investigating the
velocity and trajectory of the arrow.
In archery, both bow and arrow play an important
roles in creating a stable, accurate and desired shooting
range. Arrows are made from stiff and low density
material such as wood, fibre glass, aluminium, carbon
fibre, and composite of carbon fibre and aluminium which
can be either rods or tubes shaft. A good arrows must be
able to bend at certain degree as the arrow will not be able
to shot if the shaft is too stiff (Leach, 2014). A higher
speed arrow able to remain their flight better. All the parts
of arrow play an important role in providing the arrow
speed as well as the flight stability. The main parameter
influencing the arrow behaviour during flight are: 1)
weight of arrow tip; 2) arrow spine and 3) fletching type
(Barton et al., 2011).
The common materials used for arrow head are
stainless steel, bronze, tungsten and aluminium. There are
two parameters of the arrow head that affect the arrow
flight: arrow head weight and type of arrow head. Arrow
head in market comes with various weights ranging
around 75gr to 125gr.
Higher arrow weight result in higher Front of
Center (FOC) which allow better flight but the flight range
was sacrificed. Modern arrows also come with wide range
of arrow head type. The aerodynamic properties of the
arrow head influence the drag force on the arrow. The drag
coefficient of bullet point and bluff bodied is significantly
larger than streamlined point (Mukaiyama, Suzuki,
Miyazaki, and Sawada, 2011).
Arrow shaft also play an important role in giving
a stable arrow flight. The common shaft materials are
carbon, aluminium, fiberglass and wood (Barton et al.,
2011). The characteristics of an arrow shaft that affect the
flight behaviour is the weight and stiffness. Both
parameters greatly depend on the shaft design and the
material of shaft. Carbon shaft provide a stiff and lighter
shaft compare to aluminium which enable a lighter and
more aerodynamic shaft construction. Currently,
composite of carbon and aluminium is the optimum design
for an arrow shaft. A correct arrow spine help to ensure
the arrow neither bend too much creating a whippy arrow
or too little creating a stiff arrow (Elliot, 2002).The arrow
VOL. 11, NO. 12, JUNE 2016 ISSN 1819-6608
ARPN Journal of Engineering and Applied Sciences
©2006-2016 Asian Research Publishing Network (ARPN). All rights reserved.
www.arpnjournals.com
7444
spine was evaluated through static arrow spine and
dynamic arrow spine. Static spine is the measurement of
shaft deflection by supporting the arrow at two point
separated for 28 inches apart and suspend a weight of 1.94
lb at the middle. Static arrow spine is determined by the
shaft geometry and material elasticity. The geometry of
the shaft such as the cross section shape, the diameter and
material bonding has a great contribution in static arrow
spine. According to the archery rule, the shaft diameter
needs to be less than 9.3mm.
A projectile’s flight is at the most stable state
when the projectile’s mass is positioned at the Front of
Center (FOC). FOC is the position where the balance
between stability and range situated. The range of FOC
recommended for varies archery are: 11% to 16% for
FITA (Olympic style), 6% to 12% for 3-D archery, 10% to
15% for field archery and 10% to 15% for hunting (Ashby,
2005). Arrow will wobble when the FOC is near to its
center (Archery, 2008). The standard FOC calculation was
based on Archery Manufacturer Organization (AMO)
standard formula was expressed as in Equation. (1)
FOC = [(arrow balance point/ total arrow length)-.50] x 100 (1)
Arrow will turn round and fly backward if the
center of drag is in front of the center of mass (Leach,
2104). Larger mass at the arrow tip caused the shaft to
deform more (inertia effect) which is the same as
decreasing shaft stiffness (Lieu, Kim, and Kim).
Arrow performance is crucial for target archery.
The main parameter that determine an arrow performance
is the arrow flight pattern, arrow velocity and arrow
trajectory. In real flight situation, few methods such as in-
flight ballistic measurement system, high speed video
recording, ballistic chronographs and acoustic Doppler
shift are used to measure arrow performance. In general,
arrow performance can be evaluated by measuring the
arrow drag as instable arrow flight will increase the arrow
drag (Barton et al., 2012).
However, a cheaper way to determine an arrow
drag is the use of high speed video camera to record the
arrow during free flight. According to Miyazaki et al.
(2013) in their experiment, two high speed camera was
placed 45m apart and velocity decay rate is used to
determine the drag coefficient. The arrangement used by
Miyazaki et al. (2013) in their experiment set up is as
shown in Figure-1.
Figure-1. Experiment set up.
METHODOLOGY
Concept generation of arrow head will be divided
into three categories: bullet-shaped point, 3D-shaped point
and cone-shaped point. The results are obtained by using
Solidwork Flow Simulation 2012. The computational
domain used to analyse the arrow drag force is 3D
simulation. The arrowheads were designed according to
the dimension of Beman 570-14 carbon arrow shaft outer
and inner diameter of 5.46mm and 3.76mm respectively
and 7mm outer diameter with 5mm inner diameter shaft.
The arrowhead weight is designed to be 5.10 gram for
Beman shaft and 8.1 gram for 7mm shaft. The dimension
of the computational domain is shown in Table 1 and the
domain is as illustrated in Figure-2. There are several
parameter been set during the flow analysis. Table-1
shows the parameter been set before running the flow
analysis.
Table-1. Parameter used for flow analysis.
Velocity (m/s)
60
Gravitational acceleration
(m/s2)
9.81
Fluid type
Air
Computational domain
(m)
1.5 (L) X 0.14 (W) X 0.22
(H)
Figure-2. Computational domain used to analyse
arrow drag force.
Figure-3, Figure-4 and Figure-5 show the result
from Solidworks Flow Simulation base on the parameter
been set as shown in Table-1 and Figure-2. Table-2 shows
the drag force value obtained.
Figure-3. Result for bullet shape head.
VOL. 11, NO. 12, JUNE 2016 ISSN 1819-6608
ARPN Journal of Engineering and Applied Sciences
©2006-2016 Asian Research Publishing Network (ARPN). All rights reserved.
www.arpnjournals.com
7445
Figure-4. Result for 3D shaped head.
Figure-5. Result for cone shaped head.
Table-2. Arrow head drag force.
Point
Averaged drag force (N)
3D shaped 3
0.1176
Bullet shaped 3
0.1139
Cone shaped 1
0.1088
The arrow head was fabricated from stainless
steel type 304 by using CNC lathe machine. Stainless steel
type 304 is used as it is the most flexible and widely used
stainless steel type which make it easily available. Three
types of arrow head was fabricated which is the 3D-
shaped, cone-shaped and bullet-shaped as shown in
Figure-6.
Figure-6. Fabricated arrow head.
A test rig as shown in Figure-7 was designed and
fabricated by using 3D printing. A mild steel solid rod
with the weight of 880gram was hanged at the middle of
the test rig as the load to determine the deflection of the
tested shaft. The deflection value of the shaft was
measured by using Vernier calliper. The deflection value
was tabulated as shown in Table-3.
Table-3. Static spine stiffness according to type of shaft.
Shaft
Beman 570-14
Fiberglass
Carbon fibre
Diameter
5.47
7
7
Spine stiffness, mm
16.58
18.94
6.08
16.54
19.5
6.08
16.6
19.2
5.34
Average, mm
16.57
19.21
5.83
Figure-7. Test rig for arrow shaft.
To analyse arrow drag force by using high speed
camera, there are two main parameters need to be know:
video recording frame rate used and the arrangement of
the cameras. In this experiment, the method used to
determine the arrow drag force is by determining the
velocity decay rate has been conducted by Miyazaki et al.
(2013). The video recording frame rate used will be 240
fps which is the maximum frame rate for Casio Exilim HS
EX-ZR500 digital camera. The bow used for the arrow
shooting is Hoyt Pro Comp Elite as shown in Figure-8.
Hoyt Pro Comp Elite is a compound type bow. Compound
bow is used for the shooting of arrows it has higher
launching efficiency thus minimizing the error during
shooting. This will able to provide a more accurate data.
VOL. 11, NO. 12, JUNE 2016 ISSN 1819-6608
ARPN Journal of Engineering and Applied Sciences
©2006-2016 Asian Research Publishing Network (ARPN). All rights reserved.
www.arpnjournals.com
7446
Figure-8. Hoyt Pro comp elite.
The determination of drag coefficient was by
using Equation. (2), the velocity decay rate need to be
determined by using Equation. (3) have been proposed by
Miyazaki et al. (2013).
RESULTS AND DISCUSSIONS
The properties and parameters for all the arrows
are tabulated in Table-4. All these parameters are
important for the result analysis.
Table-4. Parameter for each arrows according to shaft and head types.
Arrow
FOC, %
Spine stiffness, mm
5.46mm carbon shaft:
Original head
6.2883
16.57
Bullet shaped head
6.4417
16.57
3D shaped head
6.1350
16.57
Cone shaped head
6.1350
16.57
7mm fiberglass shaft:
Bullet shaped head
7.3620
19.21
3D shaped head
7.3620
19.21
Cone shaped head
7.3620
19.21
7mm carbon fiber shaft:
Bullet shaped head
9.0491
5.83
3D shaped head
9.0491
5.83
Cone shaped head
9.2025
5.83
From Table-4, 7mm carbon fiber shafts have the
lower spine stiffness showing that these shaft is stiffer
compared to 7mm fiberglass shaft and Beman 570-14
(5.46mm carbon shaft). In overall, all the arrows have a
constant FOC ranging from 6% to 10%. In order to
determine the drag force, the drag coefficient need to be
determined beforehand by using both Equation. (2) and
Equation. (3). The iron rule is that higher drag coefficient
value creates higher drag force on the arrow. This causes
higher velocity drop across the distances.
The velocity for the arrow and the angle of the
arrow velocity was determined by using Kinovea software.
For every types of arrow, 6 values were taken from the
video analysis in order to minimize the error in result
obtained. The velocity and the angle was tabulated
according to the type of arrow shaft namely Beman 570-
14, 7mm fiberglass and 7mm carbon fiber.
Beman 570-14
Beman 570-14 is a carbon shaft with 5.46mm
outer diameter. 4 type of heads were tested and analysed in
order to compare the designed arrow head drag force with
the original arrow head which comes together with the
shaft. Excluding the arrow head geometry, all the other
parameters of the arrows were remained unchanged. The
drag coefficient and drag force for all the 4 arrows were
tabulated in Table-5.
VOL. 11, NO. 12, JUNE 2016 ISSN 1819-6608
ARPN Journal of Engineering and Applied Sciences
©2006-2016 Asian Research Publishing Network (ARPN). All rights reserved.
www.arpnjournals.com
7447
Table-5. Drag coefficient and drag force for Beman 570-14 arrows.
Head
Drag coefficient, CD
Drag force, N
Bullet
0.9055
0.0942
0.8865
0.0990
1.2811
0.1071
4.5647
0.3484
2.7252
0.2355
1.9394
0.1484
Cone
2.3237
0.1507
1.7887
0.1361
2.0258
0.1413
2.3770
0.1573
1.7613
0.1454
1.5789
0.1263
3D
1.9484
0.1696
2.0336
0.1391
1.5584
0.1047
1.9234
0.1401
1.6358
0.1232
2.1125
0.1361
Original head
2.5293
0.1719
2.0185
0.1443
1.1478
0.0831
5.3230
0.3496
4.4038
0.3030
2.8852
0.2026
The drag coefficients and drag forces obtained is
averaged and tabulated in Table-6. The result which has
huge different such as the original head result in Table-5
with the value of 5.3230 and 4.4038 drag coefficient is
neglected when calculating for the average value as it is
too large compared to other value which is around 1.1 to
2.9. It is believed that these result deviates from other
result too much due to error in analysis and the state of
oscillation of the arrow during flight which create
inaccurate result been read by the video analysis software.
Table-6. Averaged drag coefficient and drag force.
Head
Average drag coefficient, CD
Average drag force, N
Bullet
1.5475
0.1339
Cone
1.9759
0.1429
3D
1.8687
0.1355
Original Head
2.1452
0.2422
Table-6 shows that bullet head has the least drag
force compared to other arrow heads with 0.1083N less
drag force compared to original arrow head. The result
shows that both 3D shaped and bullet shaped head has a
high potential to replace the original head for long range
shooting.
7mm fiberglass shaft arrow
7mm outer diameter fiberglass shaft was attached
with 3 types of arrow heads namely bullet shaped head,
cone shaped head and 3D shaped head. The drag
coefficient and drag force for all the 3 arrows were
VOL. 11, NO. 12, JUNE 2016 ISSN 1819-6608
ARPN Journal of Engineering and Applied Sciences
©2006-2016 Asian Research Publishing Network (ARPN). All rights reserved.
www.arpnjournals.com
7448
tabulated in Table-7. Table-8 shows the averaged value for
both drag coefficient and drag force.
Table-7. Drag coefficient and drag force for 7mm
fiberglass shaft.
Head
Drag coefficient, CD
Drag force, N
Bullet
2.4225
0.3065
1.8732
0.2560
1.7339
0.1551
1.5816
0.1377
2.6838
0.2152
2.9445
0.2322
Cone
2.0451
0.2405
3.8843
0.3329
3.0735
0.3294
2.9369
0.3052
3.0426
0.2672
6.0291
0.5392
3D
2.5930
0.3814
2.4083
0.2977
1.2752
0.1282
1.8692
0.1926
2.3221
0.2025
2.3951
0.2041
Table-8. Averaged drag coefficient and drag force for
7mm fiberglass shaft.
Head
Average drag
coefficient, CD
Average drag
force, N
Bullet
2.2066
0.2171
Cone
2.9965
0.2950
3D
2.1438
0.2344
7mm carbon fiber shaft arrow
7mm outer diameter carbon fiber shaft was
attached with 3 types of arrow heads namely bullet shaped
head, cone shaped head and 3D shaped head. The drag
coefficient and drag force for all the 3 arrows were
tabulated in Table-9. Table-10 shows the averaged value
for both drag coefficient and drag force.
Table-9. Drag coefficient and drag force for 7mm carbon
fiber shaft.
Head
Drag coefficient, CD
Drag force, N
Bullet
0.6046
0.0901
0.7278
0.1050
0.9377
0.0865
0.6446
0.0616
1.6757
0.1763
0.9540
0.1012
Cone
1.1018
0.1180
0.8964
0.1065
2.6292
0.2737
4.0069
0.4053
2.2547
0.2338
1.5051
0.1560
3D
0.7519
0.1236
1.0950
0.1719
0.1991
0.0204
0.7060
0.0726
0.5569
0.0592
0.9110
0.0964
Table-10. Averaged drag coefficient and drag force for
7mm carbon fiber shaft.
Head
Average drag
coefficient, CD
Average drag
force, N
Bullet
2.1452
0.2422
Cone
1.5475
0.1339
3D
1.8687
0.1355
Figure-9 shows that experimented result is
slightly higher compared to simulation results. The
possible cause is the characteristic of the arrow during
flight. In real life, arrow will starts to bend in C manner
then straight again then bend again in reverse C manner
and so on when it been shot. These deformation causes
energy losses to the surrounding due to air friction, natural
damping effect and shear friction. Thus, it results in higher
drag forces compared to simulation results which are
under ideal condition.
VOL. 11, NO. 12, JUNE 2016 ISSN 1819-6608
ARPN Journal of Engineering and Applied Sciences
©2006-2016 Asian Research Publishing Network (ARPN). All rights reserved.
www.arpnjournals.com
7449
Figure-9. Comparison of simulation and experimented
drag force bar chart.
From the bar chart in Figure-10, it shows that
fiberglass shaft arrow has higher drag coefficient
regardless of the arrow head geometry used. On the other
hand, 5.46mm carbon shaft (Beman 570-14) arrow has the
second highest drag coefficient for every types of arrow
head used. Although carbon shaft has larger diameter of
7mm compared to Beman shaft, it has the lowest drag
coefficient for all of the arrow head types used. This is due
to the stiffness of the shaft compared to all the other two
types of shaft. As the formula used relate velocity decay
rate with the drag coefficient, thus, the higher the velocity
decay, the higher the drag coefficient value will be.
Figure-10. Averaged drag coefficient bar chart.
From the bar chart in Figure-11, it shows that
fiberglass shaft arrow has higher drag force regardless of
the arrow head geometry used. On the other hand, 5.46mm
carbon shaft (Beman 570-14) arrow has the lowest drag
force when cone shaped head is used. Although carbon
shaft has larger diameter of 7mm compared to Beman
shaft, it has the lowest drag force when bullet shaped head
and 3D shaped arrow head types used. This is due to the
stiffness of the shaft compared to all the other two types of
shaft.
Figure-11. Averaged drag force bar chart.
As the formula used relate velocity decay rate
with the drag coefficient, thus, the higher the velocity
decay, the higher the drag coefficient value will be.
CONCLUSIONS
From the result obtained, it is shown that
fiberglass shaft arrow has the highest drag force regardless
of the arrow head types used compared to the other two
types of shaft. The result shows that although Beman 570-
14 shaft has smaller frontal area compared to a 7mm outer
diameter carbon fiber shaft, the drag force obtained from
the experiment shows that both bullet shaped head and 3D
shaped head for carbon fiber shaft has lower drag force
compared with the same arrow head shape. From the
experiment for Beman 570-14 arrow, it shows that bullet
shaped head has the lowest drag force compared to other
head shape under same shaft which is in contrast with the
result obtained by simulation showing that the cone
shaped head has the lowest drag force.
The recommendations for this project are:
1. Use high speed camera with better resolution and
frame rate.
2. Conduct the experiment in indoor which allow a more
accurate set up.
3. Conduct in an environment which as bright as
possible.
4. Conduct the experiment with different arrow head
weight
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Barton, John, Včelák, Jan, Torres-Sanchez, Javier,
O’Flynn, Brendan, O’Mathuna, Cian and Donahoe, Robert
V. 2012. Arrow-mounted Ballistic System for Measuring
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head
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head
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7mm carbon fiber shaft
VOL. 11, NO. 12, JUNE 2016 ISSN 1819-6608
ARPN Journal of Engineering and Applied Sciences
©2006-2016 Asian Research Publishing Network (ARPN). All rights reserved.
www.arpnjournals.com
7450
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