### Arrows

Arrow Selection Charts

Arrow Speed & Sight Mark Calculators

Apostolos: speed & sight mark calculator

Bertil Olsson: arrow speed calculator

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Documents

Development And Analysis Of Arrow For Archery

Wong Fei Yong et al, September 2015

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 effect of static stiffness, arrow heads weight and shaft diameter on the drag force generated at the arrow.

Rick McKinney, Carbon Tech

As many more companies are attempting to build arrow shafts it gets more and more confusing as to what makes a good arrow. Since most companies do not actually build their own arrows and others who may build arrows are not archers of any length of time, it becomes more and more critical to explain the mechanics of an arrow and why it is important to choose arrows that are truly the quality you should expect.

Amy Oliver

The winter season is always and a good time to test new things, so I decided to test Eli Vanes against Spin Wings. I started shooting them indoors in Sutherland Hall at Lilleshall as it was blooming cold outside and the Spin Wings where shooting better scores then the Eli Vanes. I tested them both in 720 rounds and also group tested them.

Hayri Ertan et al

Exploratory spatial data analysis is a statistical method to make observations from a sample of points upon an underlying continuous spatial distribution (Haining et al., 2000 & Jhonson, 2001). So, the purpose of the current study is to define hit distribution patterns on recurve archery target by using exploratory spatial data analysis methods among archers at different performance levels.

Inter-Rater Reliability and Criterion Validity of Scatter Diagrams as an Input Method for Marksmanship Analysis: Computerised Notational Analysis for Archery

Callaway, A.J. and Broomfield, S.A,  International Journal of Performance Analysis in Sport 112(2), 291-310 2012

This paper outlines the validity and reliability of using a computerised scatter diagram as an input method for the analysis  of marksmanship in target sports with Archery used as an example sport. Software was created to represent a standard FITA 122cm target face.

M. Andy Pedersen et al, Journal of the Southeastern Association of Fish and Wildlife Agencies 1:163-166

Bowhunting is often considered as an option for the harvest management of white-tailed deer (Odocoileus virginianus) in suburbs, parks, and similar restrictive environments. Higher deer recovery rates by bowhunters would promote better utilization of the resource and could lessen some of the objections to bowhunting. Bowhunters have a variety of equipment choices, yet little is known of the impact of these choices on bowhunter efficacy. The objective of this study was to evaluate the deer recovery metrics of bowhunters who used compound bows or crossbows with either fixed blade broadheads (having no moving parts) or mechanical broadheads (having moving parts). Our retrospective study relied on the daily reports of bowhunters who participated in a managed hunting program at the Naval Support Facility Indian Head, at Indian Head, Maryland.

Carbon Express Arrow Selection Chart

John Magera

George Tekmitchov, Bow International

Senior recurve engineer George Tekmitchov explains the  relationships between arrow spine and weight, and how to decipher your arrows’ weight codes

I.E. Kolayis et al, Procedia - Social and Behavioral Sciences 152 ( 2014 ) 451-456

Aim of this study is to assess the distribution of targeted arrows between the zones of the target and quantity of the errors. A totalof 18 athletes, seven females (age: 16.66±3.44; training age: 5.88±2.92) and 11 males (age: 22.33±12.95; training age: 4.11±2.80) were included in the study. Performances of the athletes were recorded with a digital camera, data were evaluated after being transferred to digital media. The differences in the number of arrows hitting the target and their distance from the center were assessed according to the zones, using the one-sided ANOVA test and the chi-square test. The number of arrows hitting the yellow zone have a statistically significant difference in their distribution percentage between the zones (p<0.05). Distribution of the total number of arrows between zones was statistically significantly different (p<0.05). The percentages of the arrows hitting the upper zone and the lower zone within the yellow ring were statistically significantly different.

Jihe Zhou et al, 23 International Symposium on Biomechanics in Sports (2005)

Athletes' technical skill must be matched with appropriate equipment if an archer ,is to be successful. A lot of key skills of archery are determined by the features of aerodynamics of a flying arrow. Therefore, the performance of bow and arrow and the understanding of them have a direct impact on archery skill and competition Iresult. Water and wind tunnel testing of arrows to establish their hydrodynamic characteristics are needed if performance is to be optimized.

Lt.-Cdr. W.F. Paterson, Journal of the Society of Archer Antiquaries, volume 21, 1978.

In that rare book, Arab Archery, translated and edited by N.A. Faris and R.P. Elmer (Princeton University Press, 1945), by an unknown author c. 1500, there is a chapter devoted to unusual forms of shooting. Pages 138-9 concern 'the returning arrow' which 'suddenly returns to the point whence it was shot, and may even hit the archer himself'. It gives details of construction and adds that, 'if it should fail to return to the place where you were standing when you shot it, know that you were not exact in its construction'. The author adds that 'the purpose of such an arrow is to deceive an enemy who happens to be at your side, and to shoot him while he is unaware'.

I. Zaniewski, Shock and Vibration 16 (2009) 307-317

Vibration processes in the compound and open kinematical chain with an external link, as a model of an archery bow and arrow system, are evaluated. A mechanical and mathematical model of bend oscillations of the system during accelerate motion of the external link is proposed. Correlation between longitudinal acceleration and natural frequencies is obtained. There are recommendations regarding determination of virtual forms to study arrow vibrations and buckling. The models and methods have been adapted for realization into the engineering method using well-known mathematical software packages.

Forward of Centre (FOC)

Joe Tapley

Dr. Ed Ashby

Bertil Olssen, Archery Focus Jan/Feb 2012

It turns out that using the distance to a sight’s  aperture from the archer’s eye and the distance between the 20 m and 60 m sight marks, arrow speed can be calculated quite accurately. This will come in handy for those of you who do not have access to a chronograph.

Elivanes

Product brochure 2013

Controlling Dynamic Arrow Spine

Larry Wise, Arrow Trade Magazine July 2006

Saggitarius Blackboard

Extracts of discussions relating to fletchings (mainly spin wings)

Fat or Thin

Andrew Smith (Perris Archery)

Some of the Pros and cons of using fat arrows indoors for line cutting purposes.

Easton Weight Codes - Sorting out the Mystery

George Tekmitchov

Guide to Easton arrow shaft weight codes

Aerodynamic Properties of an Archery Arrow

Takeshi Miyazaki et Al

Two support-interference-free measurements of aerodynamic forcesexerted on an archery arrow (A/C/E; Easton) are described. The .rst measurement is conducted in a wind tunnel with JAXA's 60 cm Magnetic Suspension and Balance System (MSBS), in which an arrow is suspended and balanced by magnetic force against gravity. The maximum wind velocity is 45m=sec, which is less than a typical velocity of an arrow (about 60m=sec) shot by an archer. The boundary layer of the arrow remains laminar in the measured Re number range (4:0 . 103 < Re < 1:5 . 104), and the drag coefficient is about 1:5 for Re > 1:0 . 104. The second measurement is performed by a free  flight experiment. Using two high-speed video cameras, we record the trajectory of an archery arrow and analyze its velocity decay rate, from which the drag coefficient is determined. In order to investigate Re number dependence of thedrag coefficient in a wider range (9:0 . 103 < Re < 2:4 . 104), we have developed an arrow-shooting system using compressed air as a power source, which launches the A/C/E arrow at an arbitrary velocity up to 75m=sec. We attach two points (piles) of different type (streamlined and bullet) to the arrow-nose.

Aerodynamic properties of an arrow: Influence of point shape on the boundary layer transition

K Mukaiyamaa et al, Procedia Engineering Volume 13, 2011, Pages 265-270

Using two high-speed video cameras, we recorded the trajectory of an arrow (archery and crossbow) and analyzed its velocity decay rate, from which we determined the drag coefficient. In order to investigate Re number dependence of the drag coefficient, we developed a new arrow-shooting system using compressed air as a power source, which enabled us to launch an arrow at an arbitrary velocity (up to 60m/sec). We attached three points of different type (streamlined, bullet and bluff bodied) to the arrow-nose. The boundary layer is laminar for the streamlined point and turbulent for other points, in the measured Re-range (0.78 × 106 < Re < 1.65 × 106). These results are consistent with those from support-free wind tunnel measurements using JAXA's 60 cm Magnetic Suspension and Balance System (MSBS), confirming that the point-shape has a crucial effect on the laminar-turbulent transition of the boundary layer.

Free flight and Wind Tunnel Measurements of the Drag Exerted on an Archery Arrow

K. Okawa et al,  6th Asia Pacific Congress on Sports Technology 2013

We describe two support-interference-free measurements of aerodynamic forces exerted on an archery arrow. The first measurement is performed in a wind tunnel with JAXA’s 60 cm Magnetic Suspension and Balance System, whereas the second measurement is carried out by a free flight experiment. In the latter measurement, the trajectory and rotation of the arrow is recorded by two high-speed video cameras and the arrow’s down range velocity decay rate is analyzed to determine the drag coefficient..... We attach two points (piles) of different type (streamlined and bullet) to the arrow-head and two kinds of vanes (SPIN-WING-VANE and GAS PRO) to the arrow-tail. The boundary layer remains laminar for any combination of point and vane, if Re is less than 1.0 x 10E4. It becomes turbulent for Re larger than  1.0 x 10E4 and the drag coefficient increases to about 2.6, when the bullet point and SPIN-WING-VANE are attached. In the same Re range, two values of drag coefficient are found for the combination of streamlined point and SPIN-WING-VANE. The lower value (about 1.6) corresponds to a laminar boundary layer and the larger value (about 2.6) to a turbulent boundary layer. In contrast, for GAS PRO vanes, the boundary layer remains laminar at any Re considered, irrespective of the point-shape. These findings confirm that both the point- and vane-shapes have a crucial influence on the laminar to turbulent transition of the boundary layer.

Air Flow around the point of an Arrow

J.L. Park et al, Journal of Sports Engineering and Technology 2013 227:64

The aerodynamic drag of an arrow is of importance in relation to the arrow’s drift in wind and to its down-range velocity. A significant contributor to that drag is the viscous drag from the arrow shaft, and consequently the nature of air flow over the arrow point and the location of the transition from laminar to turbulent flow are of interest. In this paper the flow was investigated using a scale model in a water channel for two arrow point profiles and for circumferential gaps at the rear of the arrow point. The normal ‘bullet point’ was found to have laminar flow along the front of the shaft and transition at a Reynolds number of approximately 450,000, and that circumferential gaps did not affect the flow. The frequently used ‘short bulge point’ was found to have flow separation at the rear taper of the point and turbulent flow for the full length of the shaft, which would be expected to result in greater drag than for the bullet point or for a bulge point with less aggressive rear taper.

Measurement and Calibration System of Arrow’s Impact Point using High Speed Object Detecting Sensor

Yeongsang Jeong et al,  INTELLI 2013 : The Second International Conference on Intelligent Systems and Applications

Currently, the method used to analyze the manufactured arrow’s performance is to use the accumulated impact points of arrow. The impact point of arrow is appeared by shooting the arrow repeatedly with same force to a target paper using a shooting device. The method has some weak points, such as low accuracy, it needs long time to do the experiments because the arrow is shoot in several times, and difficult to digitize between impact points......In this paper, line lasers are placed upper side and left side of a squareshaped frame, and photodiode sensors are installed at the opposite side of line lasers. When fired arrow goes through the square shaped frame, the voltage acquisition device measures the voltage level difference of photodiodes. Impact points of arrow are shown using the data derived by voltage acquisition device. A neural network calibration method is implemented using impact points which are printed out precisely by manufactured grid plate.

Stu Miller's Dynamic Spine Calculator

XLS format spine calculator. Leans towards traditional archery

Dynamic Spine and Building Heavy Arrows

Harry Marx

After various and long discussions and investigations with fellow archers, and some investigation on my part, I have come to realise how little we know about dynamic spine. In case you didn’t know, there are two types of spine: static and dynamic. Essentially, spine is about how stiff an arrow is or acts. Static spine is measured simply by how far 28 inches (71.12 centimetres) of the shaft bends if a lateral force of 1.94 pounds (880 grams) is applied. If the arrow bends 0.300 inches, its static spine (s-spine) is 300 (it’s a bit confusing the first time, but the stiffer an arrow is, the “bigger” the spine, but the smaller this number.) Dynamic spine (d-spine) is how the arrow bends when accelerated by the bow.

Uphill - Downhill Shooting

Perry Ratcliffe, 1999

To understand how to adjust for uphill/downhill shots you need to understand what you are adjusting for when setting your sight. We all know that as the range increases, you must lower your front sight to compensate for the Arrow Drop. However, you are not adjusting simply for Arrow Drop. You are also adjusting for Parallax Error.

Variable Spine / Variable Weight Arrow

[Following the barreled arrow (Easton) and the All-carbon arrow (Carbon Tech) the Carbon Express variable spine arrow represents the third significant technical advancement in arrow design of recent years.  Editor comment]

Understanding Arrow Penetration

J.L. Spinks

Modelling the vibrational behaviour of composite archery arrows

Marianne Rieckmann et al, Proc. Acoustics 2011

In the sport of archery, recent developments in materials technology have seen the introduction of carbon-fibre aluminium
composite arrows. Archery performance has been shown to be dependent on the vibrational behaviour of arrows
(including the natural frequencies and mode shapes). This paper investigates the vibration of composite archery
arrows through analytical and finite element modelling. Computer models used in this paper employ modal analysis
to identify the significant modes of vibration. Results from the numerical simulations are also compared to experimental
measurements using a Polytec scanning laser Doppler vibrometer (PSV-400). Experiments use both mechanically
and acoustically coupled vibration actuators to vibrate the composite arrow structure. Evaluation of the modal
behaviour shows good agreement between the theoretical models and the experiments.

The Mechanics of Arrow Flight upon release

DK Lieu, J. Kim,Jinho and Kim, Ki Chan Korea National Sport University,

Arrow Behaviour in Free Flight

J. L. Park

Arrowmatch Ballistic Flight Simulator

Arrowmatcher is a ballistic application, released under the GPL. It is for Windows, Mac OS and Linux:

This is a simple tool for mainly for crossbow archers. But it can also used for rifles or other bullets. It can calculate the trajectory of arrows and a little bit more. arrowmatcher2 can handle wind.

Eli Vanes

Eli-vanes product description

Recurve Vane Evaluation

Rick McKniney/Vittorio Frangilli (Forum Post)

Why Rockets have Fins

Wernher von Braun

Jim Hill's Spine Tester

Description of a make it yourself arrow spine tester.

Matching Arrow Weights

How close do arrows need to be matched by weight to achieve a required vertical height distribution by Kleanthes Koniaris

They spin HOW fast ??!!

George Tekmitchov

Streamlined Body Aerodynamics

Anon

Understanding and applying FOC

E. Ashby

Anon

Ihor Zanevsky,  16 International Symposium on Biomechanics in Sports (1998)

The archer's paradox is the fact that an arrow does not fly to its mark along the line represented by its axis. The explanation of the archer's paradox was found by means of high speed spark photography which P. E. Klopsteg undertook in order to secure direct evidence of what an arrow does as it leaves the bow [1]. The impulse normal to the axis of the arrow, caused by the release of the fingers from the string, as well as the column-like force of the string on the arrow during its acceleration, results in a significant bending of the arrow shaft as it transits the bow. ..... The objective of our study is to develop the mathematical methods of the archer's paradox.

Water-tunnel study of transition flow around circular cylinders

Almosnino, D.; Mcalister, K. W

Zilliac, Gregory G.

Daryl Hrdlicka

Spin Wing Vanes

Rick McKinney

Measuring the flight of an arrow using the Acoustic Doppler Shift

Mark French

Measuring the velocity of an arrow in flight is a task of interest to archers, but can be difficult without specialized equipment. We show how accurate velocity measurements can be made by recording the sound made by the arrow as it travels over one or more microphones. Useful recordings can be made with a data acquisition system or with the sound
recorder built into most PC operating systems. Estimates of the drag coefficient of different arrows can be made using several microphones to record each shot.

Buckling & Vibrational Analysis of s Simply Supported Column With a Piecewise Constant Cross Section

Mark S. Lake

Spine,Straightness and Weight Information

Rick Mckinney

Reliability and Validity Testing of an Archery Chronometer

H. Ertan et al

ArrowPattern Analysis

Colin Ledsome

On the mechanics of the Arrow: Archers Paradox

Bob Kooi

Finite fringe analysis of two dimensional and axially-symmetric flows

A.F.P. HOUWING et al

Optimisingthe Javelin Throw in the Presence of Prevailing Winds

Les Hatton

The measurement of arrow velocities in the students’ laboratory

C. Tuijn, B.W. Kooi

Kuo-Bin Lin  et al, Machine Learning and Cybernetics, 2009 International Conference on  (Volume:6 )

An emulated archery machine is designed for eliminating the human motion effect, so the performance analysis related to the various setting of archery individual equipment can be easily conducted and very its effect on the archery performance. The associated specifications of the emulated archery machine considered to be suitable for archery sport are also illustrated in details. The functions of arrow speed and pull forces sensors are also described. Four dissimilar types of vanes have been tested to compare their stability of the arrow speed. Four distinct positions for attaching the vane have also been tried to check their influence on the arrow speed. The effects of various numbers of strings on the arrow speed have also been observed by two different settings. The popularity of the spin-wing vane can be verified by the experimental results such as the fast average arrow speed and high stability associated with this particular vane.

Aerospace Analysis for a Non-Aerospace Archery Application

Eric T. Martin et al, 51st AIAA Aerospace Sciences Meeting January 2013

Describes the application of arospace technics applied to arrow fletching design.

Hydrodynamical Analysis on the Arrow

Ji He Zhou et al, Applied Mechanics and Materials (Volumes 644 - 650) September 2014 pp527-530

The water tunnel and wind tunnel test carried on the arrow aims to have a better understanding of the hydrodynamics performance of arrows and to improve the technical knowledge of the archery movement Through the experimental research, we can draw conclusions as follows: within the range of angle of attack ( -6°---6°), the arrow can keep the state of attached flow: The state of flow of the arrow with spiral plastic pinna is better than that of arrow with straight one; Within the experimental angle of attack, the lift coefficient Cy will become larger with the pitching moment coefficient Mz getting smaller with the increase of the angle of attack.

Experimental Hydro- and Aerodynamics Research on Arrow

Helen Zhang e al, Advanced Materials Research (Volume 1022) pp113-117

This study aims to investigate the hydro- and aerodynamic characteristics of arrows as understood within the field of archery and to contribute to theoretical knowledge, upon which archery techniques are based. The water tunnel and wind tunnel are used to test different arrows consisting of four famous brands.The results showed that when the angles of attack from -6°to 6°, the arrow remained in the state of attached flow. Arrows that had spiral plastic fletches demonstrated better states of flow than arrows with straight fletches.

Refining Crossbow Deployment Techniques of Suction Cup Attached Tags for Cetacean Field Studies

Woodward, Becky L et al,  Marine Technology Society Journal, Volume 36, Number 2, Summer 2002 , pp. 50-57(8)

Remote deployment of non-invasive suction cup attached tags on free ranging cetaceans continues to be problematic for researchers. In an effort to increase the chances of success, the factors affecting the velocity, range, and drop of crossbow deployed tags were examined. The exit velocity of a tag is primarily governed by the tag's weight and can be predicted for a particular bow. Higher exit velocities correspond to a smaller drop for a given range. Compound crossbows are able to achieve higher exit velocities and hence longer ranges for a given tag weight than simple re-curve bows of the same draw weight. Varying the position of the tag's center of mass has a greater effect on the drop of the tag than arrow length, shaft material, diameter or wall thickness...

Arrow behaviour in the vertical plane during and immediately following the power stroke of a recurve bow

James Park,  Journal of Sports Engineering and Technology September 17 2013

Arrow behaviour in the vertical plane as it leaves a recurve archery bow is mainly determined by the path taken by the bow’s nocking point during the power stroke. That path is generally not a straight line as a consequence of the arrow not being placed at the geometric centre of the bow. The arrow behaviour is important to the archer in trying to launch the arrow with minimal angle of attack and minimal angular velocity.

Lateral deflection of archery arrows

I. Zanevskyy,  Sports Engineering 4(1) Feb 2001

A whole mechanical and mathematical model of an arrow–bow motion system, which accounts for arrow deflection in the lateral plane, has been created. The arrow is modelled as a shaft within the framework of the technical theory of vibration of beams with particles at the ends. The model takes into consideration the mechanical properties of a string, bow limbs and a grip as an oscillator of concentrated elastic and inertial elements connected with the feathered end of the arrow. Experimental methods for measuring arrow stiffness in sport archery practice are discussed with reference to the dynamic stability of the internal ballistics.

Arrow Behaviour in Free Flight

J. L. Park, J. Sports Engineering & Technology Dec 2011

As an arrow exits a bow, it may have a non-zero angle of attack in both the vertical and the horizontal planes. It might also have a non-zero angular rotation about its centre of mass and will probably be flexing longitudinally. In this paper, the arrow behaviour in free flight in the horizontal plane and without wind has been analysed. A finite difference method was used to solve the equations of motion. This was compared with the measured behaviour for arrows shot from a compound archery bow.

The Impact of Material Selection on arrow design and optimal selection for competition

James L. Park, Journal of Sports Engineering and Technology May 2, 2013

Modern arrow shafts are usually tubular and are constructed using high-strength materials, with most competition arrows now using carbon fibre composites. The need to mount the arrow components (and in particular the arrow point) internally and the need to retain sufficient wall strength to avoid crushing combine to set design limits on the arrow’s mass–diameter relationship for a given arrow shaft material. This article considers those design limits and the consequent selection of the optimal arrow shafts to use for the various types of major archery competitions, depending upon the major score-detracting factors. It is shown that for a given arrow shaft material, a simple set of rules can be used for the selection.

Aerodynamic Properties of an Archery Arrow

Takeshi Myazaki et al, Sports Engineering 15(3) Sept 2012

Two support-interference-free measurements of aerodynamic forces exerted on an archery arrow (A/C/E; Easton Technical Products) are described. The first measurement is conducted in a wind tunnel with JAXA’s 60 cm Magnetic Suspension and Balance System, in which an arrow is suspended and balanced by magnetic force against gravity. The maximum wind velocity is 45 m/s, which is less than a typical velocity of an arrow (about 60 m/s) shot by an archer. The boundary layer of the arrow remains laminar in the measured Re number range (4.0 × 103 < Re < 1.5 × 104), and the drag coefficient is about 1.5 for Re > 1.0 × 104. The second measurement is performed by a free flight experiment. Using two high-speed video cameras, we record the trajectory of an archery arrow and analyze its velocity decay rate, from which the drag coefficient is determined. In order to investigate Re number dependence of the drag coefficient in a wider range (9.0 × 103 < Re < 2.4 × 104), we have developed an arrow-shooting system using compressed air as a power source, which launches the A/C/E arrow at an arbitrary velocity up to 75 m/s. We attach two points (piles) of different type (streamlined and bullet) to the arrow-nose. The boundary layer is laminar for both points for Re less than about 1.2 × 104. It becomes turbulent for Re larger than 1.2 × 104 and the drag coefficient increases to about 2.6, when the bullet point is attached. In the same Re range, two values of drag coefficient are found for the streamlined point, of which the lower value is about 1.6 (laminar boundary layer) and the larger value is about 2.6 (turbulent boundary layer), confirming that the point-shape has a crucial influence on the laminar to turbulent transition of the boundary layer.

High-speed video analysis of arrow behaviour during the power stroke of a recurve archery bow

James L Park, et al, J. Sports Engineering & Technology June 1 2012

The manner in which an archer holds and releases the string of a recurve bow causes the arrow to flex during the bow’s power stroke and on its way from the bow to the target. While an experienced observer can subjectively evaluate an arrow’s pitch and yaw visually after it has left the bow, the arrow’s behaviour during the bow’s power stroke happens too quickly for visual observation. High-speed video is consequently a much more effective tool. Similarly, high-speed video is an effective tool for studying an archer’s technique during the bow’s power stroke.

Mathematical models of the arrow’s behaviour in the horizontal plane during the bow’s power stroke have, to date, relied upon comparison of the arrow’s flexural shape with photographs. However, an implicit assumption of that process is that the archer’s technique is perfect. This paper provides an analysis of event times and the magnitudes of several key components of the arrow flex during the bow’s power stroke for sixteen world-class archers. Aside from being a powerful analysis tool in its own right, that data can also be used to evaluate mathematical models of arrow behaviour. It is concluded that archer technique variations could be a significant source of error where a single archer is used as a comparison for the mathematics, even if that single archer is amongst the world’s best.

# Wind tunnel test of Japanese arrows with the JAXA 60-cm magnetic suspension and balance system

Hideo Sawada et al,   Experiments in Fluids DOI: 10.1007/s00348-012-1300-x

In order to understand the aerodynamic properties of Japanese arrows, several types of shafts without fletching and various types of Japanese arrows were examined in a low-speed wind tunnel equipped with the JAXA 60-cm magnetic suspension and balance system. The main component of drag acting on the shaft is viscous drag from the boundary layer. This viscous drag can be evaluated analytically. A simple new method to estimate the effects of fletching on the lift of the arrow was proposed in which we found that lift is proportional to the angle of attack of the arrow but not to the rotation speed or angle. Time history results for the lift on rotating arrows in the magnetic suspension and balance system indicate that this method effectively estimates the lift on an actual rotating arrow in flight. The lift and pitching moment were mainly generated by fletching, and the drag from the fletching was similar in magnitude to that of the arrow shaft. For Japanese bamboo arrows tested with a field point, the drag, lift, and pitching moment coefficients were evaluated to be in the ranges of 3.5–3.7, 0.4–0.8, and −0.15 to −0.25, respectively, at Reynolds numbers of an arrow in flight.

# Modelling the three-dimensional vibration of composite archery arrows under free–free boundary conditions

Marianne Rieckmann et al, J. Sports Engineering & Technology April 3 2012

Archery performance has been shown to be dependent on the resonance frequencies and operational deflection shape of the arrows. This vibrational behaviour is influenced by the design and material of the arrow and the presence of damage in the arrow structure. In recent years arrow design has progressed to use lightweight and stiff composite materials. This paper investigates the vibration of composite archery arrows through a finite difference model based on Euler–Bernoulli theory, and a three-dimensional finite element modal analysis. Results from the numerical simulations are compared to experimental measurements using a Polytec scanning laser Doppler vibrometer (PSV-400).

Minimizing the Wind Drift of an Arrow

J.L. Park

Journal of Sports Engineering and Technology, September 30 2011

The selection and performance of different arrows in a wind can be a significant differentiator between competitors in outdoor archery competitions. Lateral displacement due to wind (wind drift) has two components: the first due to the arrow aligning itself with the resultant airflow, and the second due to the lateral component of the arrow’s aerodynamic drag. In this paper those components are calculated and compared with the measured wind drift in a large wind tunnel and with the standard deviation of the group size of different arrows shot outdoors in a wind. The wind drift of arrows can be compared by considering their diameter and mass. This is used to select the optimum arrow for outdoor target archery, together with optimization of the various arrow components to minimize the wind drift of a particular arrow.

The Aerodynamic drag and axial rotation of an arrow

J.L. Park

Journal of Sports Engineering and Technology, August 13 2011

The down-range behaviour of arrows has a strong influence on an archer’s ability to obtain good scores. A major input to that performance is the arrow’s aerodynamic drag. A wide variety of arrow types are available, and within each type there are a number of sizes and combinations of the various component parts of the arrow. Consequently the drag can be expected to vary significantly from arrow to arrow. In addition, the arrow’s fletching is usually set at an angle to the shaft’s longitudinal axis, causing the arrow to spin in order to minimize inaccuracies due to, for example, arrow straightness variation, and this will also affect the down-range behaviour. This paper provides a means of calculating the arrow’s drag and axial spin, and uses that to compare predicted down-range velocity with that measured for three quite different, but representative arrows.

K. Mukaiyam

Procedia Engineering, Volume 13, 2011 Pages 265-270

Using two high-speed video cameras, we recorded the trajectory of an arrow (archery and crossbow) and analyzed its velocity decay rate, from which we determined the drag coefficient. In order to investigate Re number dependence of the drag coefficient, we developed a new arrow-shooting system using compressed air as a power source, which enabled us to launch an arrow at an arbitrary velocity (up to 60m/sec). We attached three points of different type (streamlined, bullet and bluff bodied) to the arrow-nose. The boundary layer is laminar for the streamlined point and turbulent for other points, in the measured Re-range (0.78 × 106 < Re < 1.65 × 106). These results are consistent with those from support-free wind tunnel measurements using JAXA's 60 cm Magnetic Suspension and Balance System (MSBS), confirming that the point-shape has a crucial effect on the laminar-turbulent transition of the boundary layer.

Eli Vanes compared with Spin Wings

Interesting photographic comparison between the two vane types.

Carbon Arrow University

General review about arrows for the Compound Bow and Bow Hunting

Excel based arrow selection utility biased towards traditional archery.

This is a short video that attempts to explain why arrow application charts are so complicated. The first three minutes or so present a model of a shaft to help visualize the independent factors that drive each section of the chart.

Arrow Speed Calculator

This program can calculate your arrow speed, given two previously known sight marks. The only thing you need to know is the distance from your eye to the sight pin. This is usually something around draw length + sight extension but it's best if you measure it accurately. It can also compute your other sight marks for FITA and other distances.

Using KE=M * v2 / 450,240

Measuring the flight of an arrow using the Acoustic Doppler Shift

Measuring the velocity of an arrow in flight is a task of interest to archers, but can be difficult without specialized equipment. We show how accurate velocity measurements can be made by recording the sound made by the arrow as it travels over one or more microphones

Experimental archery: projectile velocities and comparison of bow performances

Experimental study with replica bows and projectiles of a variety of types indicates the superiority of archery over the throwing of spears, and makes it possible to indicate a hierarchy of increasing efficiency in the main classes of bows.

Projectile paths corrected for recoil and air resistance

The angle of projection of a bullet is not the same as the angle of the bore of the firearm just before firing. This is because recoil alters the  direction of the barrel as the bullet moves along the barrel. Neither is the angle of projection of an arrow the same as the direction of the arrow just before it is projected.

Aiming trajectory analysis based on ARMAX model

In this paper, the linear time invariant auto-regressive moving average exogeneous (ARMAX) process is adopted to model the aiming trajectory. Both of the vertical and the horizontal deviations are studied instead of the radius or score only

Momentum, Kinetic Energy and Arrow Penetration

E. Ashby