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Bow shape

In archery, the bow shape refers to the configuration of the bow's limbs when unstrung, which significantly influences the bow's performance characteristics, including energy storage, draw weight, arrow speed, and handling. Common shapes include straight bows with a linear profile for simplicity and ease of manufacture; recurve bows, where the tips curve away from the belly (the side facing the archer) to store more energy; and reflex bows, where the limbs bend toward the belly when unstrung, providing increased power but requiring more strength to draw.^[1] These shapes evolved historically to optimize power and portability, with traditional designs like recurves prominent in cultures such as ancient Egypt and the steppes, while modern variants include deflex and compound bows for enhanced efficiency and reduced shooter fatigue. The choice of shape depends on factors like intended use (target shooting, hunting, or historical reenactment), archer strength, and arrow dynamics, as detailed in subsequent sections.^[2]

Fundamentals of Design

Design factors

The design of a bow is fundamentally influenced by several key variables that dictate its shape and performance, including draw length, draw weight, arrow speed, stability, and energy efficiency. Draw length refers to the distance the bowstring is pulled back, which directly affects the amount of energy stored in the limbs, while draw weight measures the force required to achieve full draw, typically expressed in pounds and influencing the bow's power output. Arrow speed, often measured in feet per second, is optimized by balancing these factors to maximize propulsion without excessive vibration, and stability ensures consistent shot accuracy by minimizing torque during release. Energy efficiency, the ratio of kinetic energy delivered to the arrow versus the total elastic potential energy stored, can exceed 60% in well-designed bows, guiding shape selection to minimize energy loss through friction or hysteresis.^[3]^[4] At the core of bow physics lies the storage and release of elastic potential energy in the limbs, governed by principles such as Hooke's Law, where force is proportional to deformation (F = kx, with k as the spring constant). Limb geometry plays a critical role in shaping the force-draw curve, which plots draw force against displacement; the area under this curve quantifies the stored potential energy available for transfer to the arrow. Linear force-draw curves, common in simpler designs, provide consistent resistance throughout the draw, whereas progressive curves—achieved through tapered or layered limb structures—increase force more gradually at the start and steeply near full draw, enhancing efficiency by allowing archers to store more energy with less peak effort. This relationship between geometry and curve profile determines how effectively the bow converts human input into arrow kinetic energy upon release.^[3]^[4] Historically, bow shapes evolved from simple straight designs in ancient cultures to more curved forms to improve performance metrics like draw weight and energy storage. Around 3000 BCE, Egyptian archers used basic self-bows made from a single piece of wood, such as palm or acacia, which offered straightforward construction but limited power due to their linear force application. By the early New Kingdom, around 1600 BCE, Egyptians adopted composite bows, layering wood with horn and sinew to create inherent curvature when unstrung, enabling higher draw weights and greater elastic energy storage for warfare and hunting. In Mesopotamia, similar advancements occurred in the early second millennium BCE, with composite constructions adapting to regional needs for longer-range projectiles, marking a shift from uncurved to reflexed or recurved profiles for enhanced efficiency.^[5]^[6] Bow shapes also incorporate adaptations to environmental conditions, particularly in traditional versus modern contexts, to maintain performance amid variations in humidity, temperature, and material properties. Traditional wooden or composite bows, reliant on natural materials like yew or sinew, are prone to warping or reduced elasticity in high humidity, where moisture absorption can alter limb geometry and weaken string tension, necessitating designs with protective sealants or shorter, more resilient curves for humid climates. Temperature fluctuations affect wood's flexibility, causing expansion or contraction that impacts draw weight; ancient makers in arid regions like Mesopotamia favored heat-resistant horn overlays to preserve shape integrity. In contrast, modern bows employ synthetic materials such as fiberglass or carbon fiber, which exhibit greater resistance to these factors, allowing consistent limb geometry and force-draw characteristics across diverse conditions without frequent adjustments. For instance, recurve and reflex shapes in modern iterations leverage these materials to sustain higher energy storage in variable environments.^[7]^[8]

Shaping and tapering

The tillering process is a gradual, iterative method used to shape bow limbs for even flex and balance, typically employing a tiller stick—a notched wooden tool that holds the bowstring at a fixed brace height—to monitor limb curvature during drawing.^[9] To begin, the rough-shaped bow is strung with a heavy temporary string set at about 5 inches from the handle to the string, and the limbs are gently warmed by rubbing to improve pliability.^[9] The bow is then drawn partially (6-8 inches) and observed for uneven bending; the stiffer limb is marked on its belly side, and wood is carefully scraped away over a broad area using a sharp knife held perpendicular to the surface, avoiding localized cuts that could create weaknesses.^[9] This cycle of drawing, marking, scraping, and flexing the bow 10 or more times is repeated, progressing to fuller draws as balance improves, until both limbs curve symmetrically when viewed against the tiller stick or a flat reference surface like a tiled floor.^[9]^[10] Tapering profiles refine the limb's cross-section and width to distribute bending stress progressively from the thicker handle area to narrower tips, enhancing energy storage and reducing fracture risk. Common variations include linear taper, where limb width decreases at a constant rate for straightforward stress progression; parabolic taper, which curves the width reduction more gradually to mimic natural flex patterns; and elliptical cross-sections, which provide a rounded profile that equalizes stress along the limb length while allowing slight "whip-end" action at the tips for smoother release.^[11] These profiles are achieved by planing or rasping the limb sides during initial rough shaping, with the handle remaining widest (often 1.5-2 inches) and tips narrowing to 0.5 inches or less, ensuring the limb bends as a continuous arc rather than hinging at weak points.^[11] Material-specific shaping adapts techniques to the wood's properties, such as density and grain response to heat. For wooden bows like those from yew or osage orange, steam treatment softens the fibers for bending: yew staves are boiled for 30-45 minutes or steamed similarly before clamping into forms to correct twists or set reflex at the handle, leveraging the wood's elasticity for durable curves.^[12] Osage orange, being denser, responds better to dry heat from a gun or flame with oil lubrication, applied for 5-10 minutes per section to straighten limbs or add reflex without moisture, as steam can cause cracking; clamps hold the shape during cooling.^[13] Horn composite bows involve preparing horn (e.g., gemsbok) by splitting, filing the exterior smooth, and shaving the interior to 3/16-inch thickness, then boiling and clamping between flat plates to flatten before gluing to a straight-grained wood core like maple with epoxy, followed by sinew backing for tension.^[14] Fiberglass laminates are shaped using wooden forms cut to the desired profile (e.g., via bandsaw and sanding), with layers pressed and heated in a box at 200-250°F to cure epoxy, allowing tapered widths without further bending post-lamination.^[15] Common defects during shaping include hinges—thin, abrupt bends from over-removal of wood in one spot—set (permanent limb deformation after release), twists (lateral warping), and weak spots (uneven grain causing localized stress). Hinges are corrected by marking the area and scraping wood from both sides until the flex smooths, always addressing them early to avoid fractures.^[10] Set and twists in wood bows are remedied by reheating the affected limb (steam for yew, dry heat for osage) and clamping straight or twisted oppositely until cooled, preventing permanent warp.^[12]^[13] Weak spots, often from knots or cross-grain, require reinforcing with sinew wraps or discarding the stave section, monitored via repeated tillering checks to ensure uniform strength.^[10]

Traditional Bow Shapes

Straight bows

Straight bows represent the most rudimentary form of bow design, characterized by limbs that remain parallel or slightly converging in the unstrung state, creating a distinctive D-shaped profile when strung and braced. This geometry arises from the straight alignment of the limbs, which bend uniformly under tension without inherent curvatures, allowing the string to connect directly to the nocks.^[16]^[17] Historically, straight bows dominated early archery practices due to their simplicity. The English longbow exemplifies this type, typically measuring 6 to 7 feet (1.8 to 2.1 meters) in length with draw weights between 100 and 180 pounds (45 to 82 kilograms), enabling effective use in medieval warfare for long-range volleys capable of penetrating armor.^[16]^[18] Native American self-bows, another key example, were crafted by tribes such as the Osage using resilient woods like hickory or osage orange, serving primarily for hunting and intertribal conflict with lengths often around 5 to 6 feet to suit mounted or pedestrian use.^[19]^[20] In terms of performance, straight bows produce a linear force-draw curve, where drawing force increases proportionally with draw length, resulting in lower stored energy compared to curved variants that leverage nonlinear mechanics for greater efficiency—typically 100 to 250 joules for historical war longbows like the English longbow. This linearity contributes to straightforward handling but limits arrow velocities to around 150-180 feet per second, though the design excels in durability under repeated stress and requires less maintenance. For instance, unlike recurves, straight bows do not accelerate arrow speed through tip leverage, prioritizing reliability over peak power.^[21] Construction of straight bows emphasizes accessibility, utilizing a single full-length wood stave—often yew, ash, or hickory—without additional backing materials to reinforce the limbs. The process involves minimal tapering from the handle to the tips, as the straight geometry distributes stress uniformly across the limb cross-section, reducing the risk of localized failure and simplifying tillering to achieve balanced flex.^[22]^[23] This approach allowed ancient bowyers to produce functional weapons using basic tools, with the stave's natural growth rings oriented to optimize compression on the belly and tension on the back.^[21]

Recurve bows

A recurve bow features limbs that curve away from the belly (the side facing the archer) toward the tips when the bow is unstrung, with the central portion of the limbs typically straight or slightly reflexed to facilitate bracing.^[24] This geometry includes sharply recurving siyahs, or rigid tips, which act as levers to store additional elastic energy during the draw by increasing the effective limb length and preload in the braced position.^[24] The siyahs remain relatively stiff, contributing to a nonlinear force-draw curve where the force rises more gradually after the string bridges are cleared, enhancing overall energy efficiency compared to simpler designs.^[24] The recurve shape originated in ancient Asian composite bows, constructed from layered horn, wood, and sinew, with evidence of such designs dating back to around 1000 BCE in Central Asia.^[25] These early recurves evolved into the compact Mongol horse bows by the 13th century CE, prized for their power and portability in mounted warfare, often featuring pronounced siyahs for rapid shooting from horseback.^[25] In modern target archery, the recurve bow gained prominence after the 1930s through standardized rules established by the International Archery Federation (now World Archery), becoming the primary form for competitive shooting due to its balance of speed and control.^[26] It was formally adopted for Olympic archery in 1972, where it remains the standard for events requiring precision at distances up to 70 meters.^[26] Recurve bows offer performance advantages through their design, producing a nonlinear force-draw curve that stores more potential energy per unit mass than straight-limbed bows, leading to higher initial arrow velocities—for instance, up to 6-10% greater muzzle speeds in modeled comparisons depending on draw length and materials.^[27] This efficiency arises from the siyahs' leverage, which allows for greater deformation energy in the limbs while minimizing mass, resulting in smoother energy transfer and reduced vibration upon release, often described as lower hand shock for the archer.^[24] Such characteristics make recurves particularly effective in traditional hunting and Olympic target disciplines, where arrow speed directly impacts accuracy and flat trajectory.^[26] Variants of recurve bows include working recurves, where the curved tips actively bend during the draw to contribute to energy storage, and static recurves, where the siyahs remain rigid and the curve is confined to the non-working portion for preload without flexing the tips.^[24] Takedown designs, featuring a central riser with detachable limbs, enhance modularity by allowing archers to adjust draw weight or length through interchangeable components, a feature standardized in competitive archery for maintenance and customization.^[28] These variants build briefly on tapering techniques in the limbs to reinforce stress distribution, ensuring durability under high loads.^[24]

Reflex bows

A reflex bow features limbs that curve away from the string side—toward the archer's back—when unstrung, with the entire limb belly bending in this direction to create a pronounced preload.^[29] When strung, this geometry straightens the limbs into a distinctive C-shape, enhancing the bow's compact profile and initial tension.^[30] Historically, reflex bows were prevalent in Scythian designs dating to around 500 BCE, where composite construction using horn, wood, and sinew allowed for short, powerful limbs ideal for mounted warfare.^[30] Turkish bows, evolving from similar steppe traditions by the Ottoman era, incorporated reflex curvature with rigid siyah tips to optimize performance in horseback archery, enabling rapid shots from galloping horses due to their reduced length of about 50-60 inches when strung.^[30] Mechanically, the reflex design imparts a higher initial draw force, often described as "stack," which builds preload energy for superior transfer to the arrow, resulting in greater velocity compared to straight bows of similar size.^[30] This preload relates to broader design factors by storing potential energy early in the draw cycle, though it can increase archer fatigue during prolonged use.^[31] Typical draw weights for such bows range from 40 to 60 pounds, balancing power with controllability. In modern contexts, reflex bows are frequently integrated with recurve tips in hybrid longbow designs, prized in field archery for their blend of speed, compactness, and smooth release on uneven terrain.^[32]

Modern and Variant Shapes

Deflex bows

Deflex bows feature limbs that curve toward the belly (the side facing the target) when unstrung, creating a geometry where the limbs bend forward relative to the handle area in a relaxed state. This design results in a more open limb profile when the bow is strung, with the grip positioned ahead of the line connecting the limb attachment points, promoting a higher brace height.^[33]^[34] The deflex configuration gained popularity in 20th-century target archery, particularly through American designs in the 1940s and 1950s, such as those pioneered by Earl Hoyt with his introduction of deflex-reflex bows in 1951, including models like the Pro Medalist in the mid-1960s. These innovations aimed to mitigate archer's paradox—the flexing of the arrow around the riser during release—and enhance shooting accuracy by increasing stability and reducing torque on the bow.^[35]^[33] In terms of performance, deflex bows exhibit a smoother force-draw curve with reduced initial stack, making them easier to draw and more forgiving, which suits beginners and precision-oriented target shooting. They store less energy compared to reflex designs—typically resulting in lower arrow speeds—but offer greater stability and accuracy due to the higher brace height and minimized hand shock.^[33]^[34] Deflex geometry is commonly integrated into modern takedown bow risers, where adjustable limb pockets allow for interchangeable limbs and customization of draw weight, facilitating versatility in target archery setups.^[34]

Decurve bows

Decurve bows exhibit a mild curvature in their limbs that bends towards the archer when unstrung, resulting in the tips pointing outward relative to the string when the bow is strung—a configuration opposite to that of recurve bows. This geometry creates a uniform sweep along the limbs, often seen in self-bows, which minimizes stress on the string angle and allows the bow to be carried strung with reduced risk of deformation.^[36]^[37] The advantages of decurve bows include enhanced arrow clearance due to the outward tip orientation, which positions the string farther from the arrow's path, and greater stability during instinctive shooting without sights, promoting a smoother draw cycle. Typical draw weights for these bows range from 30 to 50 pounds, balancing power for hunting with ease of use for shorter draws. In modern contexts, decurve designs find a niche in traditional recreational archery and hunting bows, where their gentle profiles contribute to minimal vibration and hand shock upon release.^[37]^[38]

Compound bows

Compound bows represent a significant evolution in bow design, incorporating mechanical systems to enhance performance and usability. These bows feature limbs that are typically parallel or slightly angled relative to the riser, connected at the tips to eccentric cams or wheels that control the draw cycle. The cams, often oval-shaped rather than round, allow the bowstring to travel a longer path during the initial draw while shortening the effective string length at full draw, resulting in a let-off of 60-80%, where the holding weight drops dramatically to enable prolonged aiming without fatigue.^[39]^[40] The compound bow was invented by Holless Wilbur Allen, who filed for a patent on June 23, 1966, with the design granted as U.S. Patent 3,486,495 in 1969. Allen's innovation introduced the pulley-cam system to archery, allowing higher peak draw weights with reduced holding effort, and by the 1980s, compound bows had become widespread in the U.S. market. Evolution since then has included diverse cam configurations: single-cam systems for simpler tuning and reduced nock travel issues; twin-cam (dual) systems for balanced power; hybrid cams combining elements of both for smoother draws; and binary cams, where cables interconnect the cams for synchronized rotation and minimal timing adjustments.^[41]^[42]^[43] Performance advantages stem from the mechanical efficiency, with modern compounds achieving 80-90% energy transfer from the archer's input to the arrow's kinetic energy, far surpassing traditional bows. Draw length and weight are adjustable via modular cams and limb bolts, typically ranging from 50-70 pounds peak draw weight for hunting applications, enabling customization for user strength and intended use. These bows often incorporate deflexed risers—curving away from the archer—for enhanced stability and reduced torque during the shot. Limb profiles are optimized, frequently parallel to minimize rotational forces and vibration, promoting accuracy and consistency.^[44]^[45]^[40]

References

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bow, n.¹ meanings, etymology and more | Oxford English Dictionary
A thing bent or fashioned so as to form part of the circumference of a circle or other curve; a bend, a bent line. Not actually exemplified in Old English, but ...
[3]
Area of bow shape - Calculator Site
Calculates the area of the bow, the length of the arc, and the length of the chord from the specified radius and central angle. · Area of bow shape.
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Circular Segment -- from Wolfram MathWorld
A circular segment is a portion of a disk with an arc as its upper boundary and a chord as its lower boundary, forming a central angle less than pi radians.Missing: bow | Show results with:bow
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Oct 8, 2025 · Bay windows consist of three windows and are more angular, while bow windows have four or more windows creating a subtle curve.
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Jan 21, 2019 · The Cylindrical Bows can have minimal Wave Making Resistance if designed with proper attention to the bluntness of form and stem edge at ...
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Ship shape: the design that shook the world
Mar 27, 2017 · The bulb lowers resistance by partially canceling out the bow waves that push against a traditional hull as it plows through the water.
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Aug 22, 2022 · The second group, the 'horse bow', is the bow shape that was originally utilised on horseback. These bows are shorter, are very flexible, ...Missing: definition - | Show results with:definition -
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Jun 23, 2023 · The term "bow echo" is based on how bands of rain showers or thunderstorms "bow out" when the storm's strong winds reach the surface and spread horizontally.
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ELASTIC POTENTIAL ENERGY. Elastic potential energy is energy stored as a result of the deformation of an elastic object, such as the stretching of a spring ...Missing: factors | Show results with:factors
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The first composite bow was produced by the Egyptians, made from wood, tipped with animal horn and held together with animal sinew and glue. Unstrung, it ...
[13]
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Oct 16, 2025 · Prevailing theories suggest that the composite bow originated in the fourth millennium BCE and developed independently in multiple regions.
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[17]
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Aug 4, 2020 · Remove wood from either side of the hinge until it is removed. The later in the tillering process, the more dangerous hinges become. I often ...
[18]
Cast - The Archery Library
I prefer the ellipse which is shown solid as it gives a slight whipendedness and a tapering limb. The extreme of whipendedness that is obtainable with an ...
[19]
[PDF] FLAT BOW
Yew, Osage, locust, or hickory require from 30 to 45 minutes of actual steaming. If rope is used, wrap it around the whole plank. Allow the bow to remain on ...
[20]
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Apr 3, 2018 · With seasoned osage I think your original method with dry heat and oil is best but some prefer steaming and boiling with thicker wood.Steam Bending guide & tips, OsageSteam bending Osage ?More results from www.primitivearcher.com
[21]
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[22]
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[24]
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[25]
None
### Summary of English Longbow Information
[26]
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Jan 26, 2023 · The traditional process is to immediately coat the ends of the stave with varnish or glue. This will prevent it from drying too quickly — ...
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Nov 6, 2015 · In this paper we discuss physics laws that relate to the mechanics of bow and arrow, to the shooting process and to the flight of the arrow. In ...
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1: Draw force curve for a simple bow MEASURING DRAW FORCE CURVE The first simple experimental investigation is to measure the draw force curve. The obvious ...
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Usually a 'Self' or 'Backed' bow, the longbow is effectively a s traight (or slightly curved) length of wood with string on each end. Fiberglass, steel and ...
[31]
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Jul 1, 1988 · Examples of such reinforced bows are preserved in muséum coUections, and descriptions of them are found in historic and ethnographie accounts.
[32]
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Because of the stiff ears or a recurve of the working parts of the limbs, much energy is stored in the static-recurve bow. In a recurved bow, the amount of ...
[33]
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[34]
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The recurve bow has been used at the Olympic Games since archery became a permanent fixture on the programme in 1972. It is also used at the Paralympic Games ...
[35]
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[36]
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The bow shall be of a simple design, either take-apart (with wooden or metal riser) or of one-piece construction. The bow is braced for use by a single ...
[37]
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Reflex bow is bow that has curved or curled limbs away from the archer when it is not strung. This gives them same or greater velocity as much larger bows.<|control11|><|separator|>
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None
Below is a merged summary of the information on deflex bows extracted from the provided segments of the document at https://www.1066.co.nz/Mosaic%20DVD/library/Bows%20and%20Arrows.pdf. To retain all details in a dense and organized format, I will use a table in CSV format for key attributes (Geometry, Development History, Performance Characteristics, and 20th-Century/Target Archery Designs), followed by a consolidated list of useful URLs. This approach ensures all information is preserved and easily accessible.
[42]
None
### Summary of Deflex Bows from Merlin Bows Technical Advice Sheet
[43]
Hoyt - Vintage Archery
Hoyt was among the first to use deflex-reflex bow design. He then began designing bows with a semi-pistol grip, and in 1956 the full pistol grip. He later ...
[44]
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[45]
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[47]
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[48]
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[51]
Inductee - Hollis Wilbur Allen - Archery Hall of Fame and Museum
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[52]
Holless Wilbur Allen - Linda Hall Library
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[53]
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Oct 14, 2022 · Having had his invention patented, H W Allen tried to convince established manufacturers to mass-produce his bow, but without success. His ...
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How Compound Bows Work
Apr 11, 2017 · Jeff Ozanne, a bow designer for Mathews Archery, tells us his bows are 87 to 89 percent efficient at transferring the archer's input energy to ...
[55]
Cam systems explained - Bow International
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