Lightweight Design Optimization of a Bow Riser in … Design Optimization of a Bow Riser in Olympic...

Bow Riser Design Optimization in Olympic Archery / 33

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Lightweight Design Optimizationof a Bow Riser in Olympic ArcheryApplying Evolutionary Computing

Jürgen Edelmann-Nusser, Mario Heller, Steffen Clement,Sandor Vajna, and André Jordan

Recurve bows that are used in competitions like the Olympic Games are high-technology products. Good risers are lightweight but retain a high stiffness. Theaim of this study was to design a riser with a stiffness comparable to that of thelightest riser currently used by the archers of the German National ArcheryTeam, but with a considerably reduced weight. We computed the loads that areapplied to a riser of a drawn recurve bow (the RADIAN model used by theGerman team) and created a 3-D solid CAD model of a riser with 24 variableparameters. We used evolutionary computing to optimize the 24 parameters ofthe model according to these criteria. We selected the most optimal riser out ofthe 1650 CAD models generated, manufactured it, and had it tested by threearchers of the German National Archery Team. The mass of our manufacturedriser is 871g, which is 243g or 22% less mass than the RADIAN riser.

Key Words: Archery, evolutionary computing, optimization, sports equipmentdesign

Key Points:

1. We optimized a CAD model of a riser of a recurve bow for mass and stiffness usingevolutionary computing.

2. The evolutionary computing process was applied to an initial CAD model whichwe developed using 24 variable parameters inspired by the design of the RADIANriser.

Dr. Jürgen Edelmann-Nusser studied Sports Science and Electrical Engineering iswith the Department of Sport Science at the Otto-von-Guericke-University Magdeburg. Hismain fields of research are sports equipment, computer science in sports, swimming andarchery. Mario Heller is with the Department of Sport Science at the Otto-von-Guericke-Universtity Magdeburg. Steffen Clement is scientific assistant of the chair of InformationTechnologies in Mechanical Engineering at the Otto-von-Guericke-University Magdeburg.His main fields of research are Autogenetic Design Theory and Integration of Calculation andDesign. Prof. Dr.-Ing. Sandor Vajna VDI, has 12 years of experience within industry onresearch & development, management, consulting, and international lecturing on integratedproduct development, design methodology, CAD/CAM, business & engineering processreengineering and engineering systems integration and is holder of the chair of InformationTechnologies in Mechanical Engineering at the Otto-von-Guericke-University Magdeburg.André Jordan is scientific assistant at the chair of Information Technologies in MechanicalEngineering. His main fields of research is Evolutionary Optimization in Product Development.

European Journal of Sport Science, vol. 4, issue 3©2005 by Human Kinetics Publishers and the European College of Sport Science

34 / Edelmann-Nusser, Heller, Clement, Vajna, and Jordan

3. We manufactured the most optimal riser generated, and had it tested by archersfrom the German National Archery Team, who approved it.

4. Our riser had a stiffness comparable to the RADIAN riser, and was lighter by nearly250 g.

Introduction

During the few thousand years that bows have been used, bows have changed fromsimple wooden sticks to high-technology products. Today there are many differentkinds of bows used for different purposes. In the Olympic competitions, the recurvebow is used. Figure 1 shows the major components of a recurve bow: its limbs, riserand stabilizers. In competition, some additional small components, such as a sight,are necessary.

Most risers are manufactured in two different sizes: 23 inch (58.4cm) and 25inch (63.5cm). In the 2000 Olympic Games, all archers on the German NationalTeam used one of the 25 inch risers manufactured by Hoyt (see Figure 2).

A good riser is typically lightweight but has a high degree of stiffness (4). Thecurrent trend in riser design has been to reduce weight. For the past twenty years,most risers have been made of aluminum alloys. The first risers were massivedesigns and therefore very heavy. Today, risers are made with lightweight designssuch as those shown in Figure 2.

We asked whether current riser designs, especially the design of the RADIANriser, really represent the best lightweight designs, or whether it would possible toconsiderably reduce the weight of a riser. Our inquiry was not solely inspired by the

Figure 1 — Components of a recurve bow. The limbs are flexible and store the energy.The riser is stiff and made of metal. The stabilizers damp the vibrations after the shot.The limbs are attached to the riser by snapping the limb butts into the limb pockets ofthe riser.


current trend to reduce riser weight. An empirical study shows that increasing themass of a bow by 200g results in a significant larger range of motion of the bowduring aiming, even after training (2). A larger range of motion during aimingcorrelates to a poorer score (2). Hence we can assume that a decrease in mass of thebow will influence the interaction between archer and bow in a way that mayproduce a better score. And this would be a plausible result: during an Olympiccompetition or a World Championship, an archer who achieves the finals must shootmore than 200 times in one day. A lighter weight would reduce archer fatigue.

Another indication that a desirable riser should be lightweight comes from thereaction of competitive archers to a new product offered by Hoyt. Before the AXISmodel was manufactured, many archers of the German National Archery Team usedthe RADIAN. As promoted by the manufacturer, the AXIS riser is stiffer than theRADIAN. After some tests of the AXIS, most of the archers of the German Teamdeclined to change from the RADIAN because of the AXIS’ higher weight.

The goal of this study was to produce a 25 inch riser with a stiffness compa-rable to the RADIAN riser, the lightest riser in use by archers of the German Na-tional Archery Team, with a considerably reduced weight.

Figure 2 — Three 25’’ risers of the Hoyt company (USA) with a lightweight design (sideview and front view). From left to right: the models RADIAN, AVALON, and AXIS.The lightest riser is the RADIAN with a mass of 1114g. The masses of the AVALON andAXIS are 1154g and 1374g, respectively. Other risers made by this company are theMATRIX (1245g) and the AEROTECH (1302g).


Methods

The methods used consist of the following four parts:

1. An analysis of the loads that are applied to the riser of a drawn bow.2. A static structural analysis of the riser RADIAN using the loads of point 1.3. Design of a parametric CAD model of the riser4. Optimization of the parameters of the CAD model using evolutionary

computing.

The analysis of the loads

During aiming, when a bow is drawn, it can be assumed that there is a static balanceof forces. Figures 3, 4 and 5 show the external and internal forces in play. Theconstraints for the static balance of forces of a drawn bow are shown in equations (1),(2), and (3):

with:

(1)

(2)

(3)

(4)(5)

Figure 3 — Drawing of a drawn bow with the external forces FA (draw weight) and F

H(force of the hand that holds the bow) that are applied to it and the internal forces F

S(string forces). L

A: draw length; L

W: length of the limbs of the drawn bow; L

M: length of

the riser.


The objective here is to compute the forces FAs

, FBs

and FBp

as functions of thedraw weight F

A and of the geometric and trigonometric variables of Figures 3 and 4.

This results in the equations (6), (7) and (8):

Limb and limb pockets are standardized so that limbs and risers of differentmanufacturers can be interchanged. Limbs are available in three different sizes:short, medium and long. The combination of these different limb sizes with 23 inch(58.4 cm) or 25 inch (63.5 cm) risers results in bow lengths that are within a range of62 inches (157.5cm) up to 70 inches (177.8 cm) (see 5). The value of the variable a inFigure 4 is 75mm for all limbs. We used a bow with a 25 inch riser and long limbs toget the values of the other geometric and trigonometric variables in order to computethe forces F

As, F

Bs and F

Bp according to the equations (6), (7), and (8). The bow was

drawn with 71cm, 76 cm and 81cm draw lengths, and the values of the geometric andtrigonometric variables were measured. Long limbs were used to get a larger value

Figure 4 — Drawing of the internal forces of a limb of a drawn bow. The mounting of thelimb at the limb pockets is modeled as a floating bearing (bearing A) and a thrustbearing (bearing B). The names of the angles and the force F

S (string force) correspond

to Figure 3.

(6)

(7)

(8)


of LW

that results in larger values of the forces FBS

and FAS

in the equations (7) and (8).A 71cm draw length was used to approximate a 28’’(71.1cm) draw length, which isthe shortest draw length used for bows that have a 70 inch bow length, according toHoyt’s manual (see 5). Table 1 shows the forces F

As, F

Bs and F

Bp as well as the

geometric and trigonometric values for the three different draw lengths at a drawweight of 200 newtons (200N).

This 200N represents a relatively high value for the archers of the GermanTeam. The Hoyt manual (5) specifies a draw weight of 152N if a 25’’ riser with longlimbs is used. We used 200N to delineate a safety range for the subsequent structuralanalyses. Because the shortest draw length L

A of 71cm results in the greatest values

of all three forces FAs

, FBs

and FBp

(see Table 1), this 71 cm draw length is also used forsafety purposes.

The static structural analysis of the riser RADIAN

Based on a three-dimensional scan of a 25 inch RADIAN riser, a 3-D solid CAD(Computer Aided Design) model was created, using Pro/ENGINEER 2001 soft-ware. Materials testing, such as bending tests, atom emission spectroscopy, andscanning electron microscopy, was performed upon a 25 inch RADIAN riser toobtain information about its Young’s modulus, yield point, the composition of itsaluminum alloy, and the production process of the aluminum alloy. Table 2 andTable 3 show the results of this materials testing.

The static structural analysis was done using Geometric Element Analysis(GEA), a process similar to Finite Elements Modeling (FEM), by using Pro/MECHANICA software. A value of 72 GPa was assumed for the Young’s modulus,the median of the range shown in Table 3. As loads were applied to the riser, theforces F

As, F

Bs, F

Bp and F

H=F

A (see Figure 5) at a draw length of 710mm were

calculated according to Table 1.

Figure 5 — Forces that result in loads of the riser of a drawn bow (compare Figures 3and 4).


A dynamic structural analysis was not performed, because a study by Gros (3)demonstrates that the stress induced in the bow by releasing the shot exceeds thestress caused by drawing the bow by only about 5%—and that this 5% excess existsfor less than 10 milliseconds.

Figures 6 and 7 show the results of the three-dimensional static structuralanalysis.

The maximum value of the stresses is 135N/mm_, the maximum value of thedisplacements is 1.85mm, and the mass of the riser is 1048g. This differs from theactual mass of the RADIAN (1114g) because the Radian riser includes three steelbushings used to connect the stabilizers to the riser. These steel bushings were notincluded in our model.

The design of a parametric CAD model of a riser

We then designed a 24-parameter CAD model based upon the CAD model obtainedfrom the RADIAN riser. Figure 8 shows our CAD model and 12 of the 24 parametersused

Table 1 Three Different Draw Lengths LA of a Bow with a 25’’ Riser and

Long Limbs, the Forces FAs

, FBs

and FBp

and the Trigonometric and GeometricVariables According to the Figures 3, 4 and 5 at a Draw Weight F

A of 200N

LA

a c LW

FA

FAs

FBs

FBp

[mm] a b d [mm] [mm] [mm] [N] [N] [N] [N]

710 22.5° 22.5° 34° 1583 1729 216760 25° 24° 36° 75 86 545 200 1503 1646 189810 27° 26° 39° 1462 1604 169

Table 2 Alloying Additions of a Riser RADIAN (mean values of five analysesusing atom emission spectroscopy); the composition corresponds to theMaterial AlMg1SiCu (see Aluminium-Zentrale, 1995)

Addition Si Fe Cu Mn Mg Zn Ni Cr Pb

% 0.713 0.3814 0.2958 0.0749 0.921 0.1251 0.0046 0.3086 <0.01

Addition Sn Ti B Cd Na Sr Zr Al

% <0.001 0.0246 0.0013 0.0015 0.0035 <0.0005 0.0048 97.14


Table 3 Mechanical characteristics of the riser RADIAN

Material production density yield point Rp0,2

Young’s modulusprocess [g/cm3] [N/mm2] [kN/mm2]

Precipitation hardening 2.77 < 400 69-75of AlMg1SiCu

Figure 6 — The CAD model shows the stresses that result from the forces FAs

, FBs

, FBp

and FH=F

A at a draw length of 710mm (compare Table 1 and Figure 5). The colors

encode the values of the stresses in N/mm_ according to the scale top right. The maxi-mum value of the stresses is 135N/mm_.

Figure 7 — The CAD model shows the displacements that result from the forces FAs

, FBs

,F

Bp and F

H=F


encode the values of the displacements in mm according to the scale top right. Themaximum value of the displacements is 1.85mm. The displacements were computedrelatively to the point of the load incidence of the force F

H in Figure 5.


We chose to use an aluminum alloy used in aircraft industries as the materialfor the optimization of the riser. This alloy, AS 28, is similar to AlMgSi1. Table 4shows the alloy additions of AS 28. The density of AS 28 is 2.71g/cm_, its yieldpoint is 403N/mm_ and its Young’s modulus is 72GPa.

Optimization of the parameters of the CAD modelusing evolutionary computing.

In evolutionary computing, populations of artificial individuals are created (com-pare 6, 7, 8). Each artificial individual is represented by a chromosome. The artifi-cial individuals reproduce like biological individuals, creating new artificial indi-viduals. To perform an optimization, the artificial individuals are evaluated (compare9), and the fitness of each is calculated with respect to the optimization parameters.Artificial individuals which are more fit are more likely to reproduce. Operationssuch as crossover, mutation and recombination can be performed on the artificialindividuals.

In our case, the artificial individuals evaluated were computer models ofrisers. Each model riser was represented by its “chromosome” consisting of our 24individual parameters. The program used all three techniques of recombination,mutation, and crossover in causing the model risers to reproduce. New model risers

Figure 8 — Four side views of the parametric CAD model. 12 parameters of the 24parameters are drawn in exemplarily. The Figure was created using randomized valuesof the 24 parameters. A pattern consists of two triangular elements; i. e. there are fourpatterns above and three patterns below the grip.


were thus created. The fitness of each new model riser was defined according to itsfitness value. To get the fitness value for each model riser, the stresses and thedisplacements were computed according to Figures 6 and 7. On the basis of thesestresses and displacements, the fitness f

i of each model riser was calculated using

equation (9).

with:a, b, c, d ... weighting factorsfi

fitness (quality) of the riser im

imass of the riser i

max, imax, imaximal value of the displacements of the riser

s,istandard deviation of the stresses of the riser i

In this equation, the mass is the criterion for the desired lightweight quality,and the displacement is the criterion for the desired stiffness quality.

To calculate fi, we also used the standard deviation of the stresses to eliminate

risers with a too-large variance in the stresses. We did not use the maximal value ofthe stresses because the maximal value of the stresses could be assumed to be muchlower than the yield point of the material: maximal value of the stresses in Figure 6 is135N/mm_ ; the yield point in Table 3 and for AS 28 is about 400N/mm_. Therefore,we assumed that the maximal value of the stresses would not be a problem.

Figure 9 shows a schematic diagram of the evolutionary computing. Thealgorithm can be explained in the following eight steps:

Step 1: The algorithm starts with 31 individuals that are initialized with ran-domized values.

Step 2: The 31 individuals are evaluated on the basis of the analyses of stressesand displacements. The fitness value fi of each individual is calculated (see equationno. 9). The fittest individual is selected.

Table 4 Alloying Additions of AS 28

Addition Si Cu Mn Mg Zn Ti Zr

% 0.9 0.3 0.6 0.9 0.1 0.06 0.12

Addition Cr others Al

% 0.15 <0.15 96.8

(9)


Step 3: Using a roulette-wheel selection, 15 couples (parents) are linkedtogether to be used for reproduction. Roulette-wheel selection means that the prob-ability for each individual to be selected is proportional to its fitness value f

i (see 8).

In such a selection, it is possible for an individual to be selected more than once andto be coupled with itself.

Step 4: The 15 parents recombine with a probability of 80% according to themethod “uniform order based crossover” and create two children each. There is a20% probability that the parents’ traits will not recombine, and that the “children”produced are in fact clones of a parent.

Step 5: For each of the 30 children, there is a 5% probability that one random-ized parameter out of the 24 will mutate. In the case of a mutation, the actual value ofthat parameter is changed to a uniformly distributed value within the range of theparameter.

Step 6: For each of the 30 children, there is an 0.8% probability that all 24parameters will be reinitialized with randomized values.

Step 7: Once this is done we now have the next generation of 31 individualsconsisting of 30 children and the old best individual (generation i+1 in Figure 9).Each of these 31 individuals is evaluated on the basis of the analyses of its stressesand displacements according to Figures 6 and 7, and the fitness value f

i of each

individual is calculated (see equation no. 9). The new fittest individual is picked out.Step 8: go to step 3. Repeat for all successive iterations.

Figure 9 — Schematic diagram of the evolutionary computing. The algorithm startsdown right with 31 individuals that are initialized with randomized values. “pb” means“probability” More explanation to the Figure see in the accompanying text.


The algorithm stops after a pre-defined number of loops or generations. Wedid two runs of this algorithm using different weighting factors (see equation 9) anddifferent numbers of generations to stop the algorithm (see Table 5).

When finished, we short-listed the ten individuals identified as having thebest fitness values out of all of the generations of both runs, to be tested in making thefinal selection of the riser that would be manufactured and then tested by the archers.

In this final selection we added three criteria to the criterion fitness value fi:

• The maximal displacement should not be much larger than the maximal dis-placement of the riser RADIAN—i.e., it should be less than 2mm.

• The displacements of the upper and lower limb pocket should be approxi-mately the same—i.e., there should be some kind of symmetry in the displace-ments (see Figure 10).

• There should be a minimum of torsion in the riser, especially at the upper limbpocket (see Figure 10).

Table 5 Weighting Factors and Numbers of Generations for the Two Runsof the Evolutionary Computing

b c d Numbers ofRun no. a [1/kg] [1/mm] [mm_/N] generations

1 50 70 4 0.4 202 50 50 4 0.4 35

Figure 10 — Displacements of the upper (on the left) and lower (on the right) limbpockets of the riser RADIAN. The colors encode the values of the displacements in mmaccording to the central scale. The maximal displacement at the upper limb pocket is1.42mm, at the lower limb pocket 1.85mm. On the left side we see that there is torsion atthe upper limb pocket.


The riser that we finally selected was manufactured with forged AS 28 using aCNC (computerized numerical control) milling machine. The first practice testswere conducted at the Olympic Training Center in Berlin by three athletes of theGerman National Archery Team. Two athletes shot nine times each; the third athleteshot 300 times.

Results

Figures 11 and 12 show the masses and maximal displacements of the risers thatwere created in the two runs of the evolutionary computing. We see clearly that themass of the RADIAN riser is very large compared to the masses of the risers createdby the evolutionary computing. We also see in Figure 12 that there even are riserswith less mass and less maximal displacement. As mass was given a lower weight-ing factor (see Table 5) in the second run, the selection pressure changed to individu-als with larger masses and smaller maximal displacements. This resulted in a shift ofthe scatter plots to the top and to the left if we compare Figure 11 with Figure 12. Thischange in the selection pressure also leads to different mean values of the massesand different mean values of the maximal displacements between the individuals ofthe first and of the second run. In the first run (see Figure 11) the mean value of themasses is 864g and the mean value of the maximal displacements is 2.74mm. In thesecond run (see Figure 12) these values are 880g and 2.63mm, respectively.

The riser that was selected for manufacture according to the fitness value fi and

the additional three criterions described above is marked with a blue rhomb inFigure 12. Figure 13 shows a computer model of this riser; Figure 14 shows itsdisplacements; Figure 15 shows the displacements of its upper and lower limbpockets (compare Figure 10); and Figure 16 shows the stresses.

Figure 11 — The black rhombs mark the mass and the maximal displacement of eachindividual of the first run with 20 generations. The red circle marks the mass (1048g)and the maximal displacement (1.85mm) of the riser RADIAN for comparison. Not allindividuals are included in the Figure for there were individuals with a maximal dis-placement of more than 5mm or a mass of more than 1050g.


Figure 12 — The black rhombs mark the mass and the maximal displacement of eachindividual of the second run with 35 generations. The red circle marks the mass (1048g)and the maximal displacement (1.85mm) of the riser RADIAN for comparison. Theblue rhomb marks the riser that was selected for manufacturing. Not all individuals areincluded in the Figure for there were individuals with a maximal displacement of morethan 5mm or a mass of more than 1050g.

Figure 13 — CAD model of the riser that was manufactured. Its mass is 869g, itsmaximal displacement is 1.94mm and the maximal value of its stresses is 160N/mm_.

Figure 17 shows a photo of the manufactured riser. Its total mass, includingthree HELICOIL threaded inserts for the connection of the stabilizers, is 871g. It is243g lighter than the RADIAN riser (1114g).

Figure 18 shows on the left side a complete bow with the new riser; on the rightwe see an archer of the German National Archery Team testing the riser.

In the shooting tests, the three archers were asked to tell us their subjectiveimpressions of shooting with the new riser:

All stated that the new riser suits them: It is not only stiff and light, but alsodamps the vibrations after the shot very well. The archer who shot 300 times alsotold us that the bow groups shots well. In this context, “to group well” means that, if


Figure 14 — The CAD model shows the displacements that result from the forces FAs

,F

Bs, F

Bp and F

H=F

A at a draw length of 710mm (compare Table 1 and Figure 5). The mass

of the model is 869g (riser RADIAN 1048g). The colors encode the values of the displace-ments in mm. The maximum value of the displacements is 1.94mm (riser RADIAN:1.85mm). The displacements were computed relatively to the point of the load incidenceof the force F

H in Figure 5.

Figure 15 — Displacements of the upper (on the left) and lower (on the right) limbpockets of the new riser. The colors encode the values of the displacements in mm. Wesee that the maximal displacements at the upper and lower limb pocket have almost thevalue of 1.94mm. On the left side we see the torsion at the upper limb pocket (compareFigure 10).


Figure 16 — The CAD model shows the stresses that result from the forces FAs

, FBs

, FBp

and FH=F


encode the values of the stresses in N/mm_. The maximum value of the stresses is 160N/mm_ at a yield point of 403N/mm_.

Figure 17 — Photo of the manufactured riser. Its mass is 871g.

the archer thinks that an arrow should hit the target next to the hit of another shot, thearrow really will hit the target in that spot–that is, the archer perceives that thevariance in the hits results from the variability in his or her muscle control, and notfrom some mechanical slackness of the bow. Furthermore, the 300-shot archerasked to use our new riser in the next season’s competition.

Discussion

Figures 11 and 12 show that the RADIAN riser is in no way optimized for mass orstiffness. Evolutionary computing creates risers with less mass and less maximaldisplacement (see Figure 12). Thus we can assume that if we had increased theselection pressure in some manner to get less displacement, we would have seen a


Figure 18 — (a) Complete recurve bow. (b): Archer of the German National ArcheryTeam testing the riser.

a(a)

(b)


shift of the scatter plot in Figure 12 to the left and to the top. Quite a few risers couldhave been created with less mass and less maximal displacement than the RADIANriser.

In Figures 11 and 12 we also see that it is possible to design risers with a massof less than 800g, if we will accept maximal displacements up to 4mm. The problemis that we do not really know how reduced stiffness will influence archers’ shooting.Though the literature gives high stiffness as a criterion of a good riser, and trainersand archers also believe this to be true, there are no empirical studies supporting thisopinion. When we consider the degree of displacement of the flexible limbs whenthe archer draws the bow, which can be 700, 800 or 900 mm, it seems implausiblethat the one, two, or three millimeters of variance in the maximal displacement ofdifferent risers could really influence the shooting. A more plausible criterion couldbe torsion, especially torsion of the upper limb pocket. If the torsion is too great,when the shot is released, the arrow can be accelerated not only in its axial direction,but also in a direction orthogonal to its axis. As a result, the arrow does not flystraight on to the target but skids a little bit to the side. This would negatively affectboth the shot and the score.

Our selection of a riser with a maximal displacement of 1.94 mm was there-fore conservative, reflecting the current standards of the sport. Even so, our riser’smass is nearly 250g lower than the mass of the RADIAN.

In further empirical studies, it would be interesting to manufacture the riserderived from the evolutionary computing that had the smallest mass (779g) but amaximal displacement of 3.53 mm (see Figure 11), and to compare it against ourmanufactured riser.

Conclusion

We achieved our goal of designing a riser with a considerably reduced weight yet astiffness comparable to the RADIAN riser. The evolutionary computing createdmany risers and we selected the best one, according to our present criteria. But wecannot assume that our riser really is the absolutely best optimal riser, because ouroptimization was based on 24 parameters, which we defined according to consider-ations of plausibility and practicability; and which were inspired by the design andshape of the RADIAN riser. Equation no. 9, used to compute the fitness variable f

i, is

based upon similar considerations. Hence, an experiment using different param-eters, a differently-shaped riser, or a different equation to compute the fitness vari-able could lead to different and perhaps better results. Furthermore, we only investi-gated the use of aluminum alloys for manufacture. Other materials could also proveuseful.

For these reasons, we are currently conducting a further study with a com-pletely new design, including a differently-shaped riser, using magnesium alloys.We chose magnesium because its density is only 1.8g/cm_. The problem with usingmagnesuim alloys is that the Young’s modulus of these alloys is only about 40 kN/mm_. We therefore do not know whether we can reduce the mass to less than 870gand yet achieve a similar stiffness compared to our manufactured riser, made of AS28. Fig. 19 shows a preliminary CAD model of a riser made of magnesium. Thismodel is not yet optimized for mass and stiffness, but demonstrates its approximateshape.


Figure 19 – CAD model of an riser made of a magnesium alloy.

AcknowledgmentsThe authors gratefully acknowledge the supplies and the technical discussions offered

by Dr. Doris Regener from the Department of Materials and Materials Testing of the Otto-von-Guericke University Magdeburg. The authors also wish to thank the German FederalInstitute of Sports Science (Bundesinstitut für Sportwissenschaft, Bonn, Germany, projectno. VF 0408/15/40/2003) for their support in the manufacturing process.

References

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4. Haidn O, Weineck J. 2001. Bogenschießen: trainingswissenschaftliche GrundlagenBalingen: Spitta. 416 p.

5. Hoyt. 2003. Recurve Bow Owners Manual. http://www.hoytusa.com /technical/images/2003_Recurve_Manual.pdf. Accessed 2003 November 28.

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