# recurve vs. longbow

by manitoba
Tags: longbow, recurve
 P: 4 Hello, I am writing to ask about the specifics behind the concept that recurve bows have an arrow velocity advantage over longbows , all else being equal: (bow, string, and draw length, and force applied to the string)Does the recurve bow have more stored energy just from the extra curve of the limbs, and how does this end up in releasing more energy upon release?. My question may need clarification as well. Thank you for your consideration,
 Sci Advisor HW Helper P: 8,961 Compound bows have a higher spring stiffness and so take more effort to pull a shorter distance, they also are preloaded so they still have tension when the string is straight. There are lots of web sites describing this or if it's in your library, JE Gordon's excellent "Structures: Or Why Things Don't Fall Down"
 P: 4 Hello, again, Thank you for your reply. I will try to clarify. Given two bows made of the same material and same dimensions (overall length, and thickness) under the same string tension at rest, with equal length from riser to knock at rest, under the same draw weight, shooting the same projectile, with the only difference being a recurve on one bow: will the recurve bow release the projectile with more velocity? I am looking for to see, if all else is equal, does the shape of the bow store and release more energy when released? I have found many sites where it states "a recurve bow has more stored energy and has a mechanical advantage over the traditional longbow" or to that effect. I am looking for a physics proof of this claim.
PF Gold
P: 8,963

## recurve vs. longbow

 Quote by mgb_phys they also are preloaded so they still have tension when the string is straight.
I don't know whether this is the reason for that design, or a good side-effect of it, but that preloading means that the arrow is under full acceleration when it leaves the string. In a standard bow, it starts to decelerate when the string reaches minimal tension.
 Sci Advisor P: 2,506 Just a little more clarification; is a "recurve" bow a compound bow, or a rams-horn bow?
P: 5,610
 Quote by manitoba Hello, again, Thank you for your reply. I will try to clarify. Given two bows made of the same material and same dimensions (overall length, and thickness) under the same string tension at rest, with equal length from riser to knock at rest, under the same draw weight, shooting the same projectile, with the only difference being a recurve on one bow: will the recurve bow release the projectile with more velocity? I am looking for to see, if all else is equal, does the shape of the bow store and release more energy when released? I have found many sites where it states "a recurve bow has more stored energy and has a mechanical advantage over the traditional longbow" or to that effect. I am looking for a physics proof of this claim.
This paper may be what you're looking for: "On the mechanics of the modern working-recurve bow"

 Abstract Characteristic for the bow are the slender elastic arms or limbs. The bow is braced by putting a string shorter than the bow between the tips of the limbs. Additional deformation energy is stored in the elastic limbs by drawing the bow into the fully drawn position. Part of this amount of energy is transformed into kinetic energy of a light arrow. In the 1930's the design of the bow became a subject of scientific research. Experiments were performed in which design parameters were changed more or less systematically. However, the mathematical models were rather simple. Because fast computers are now available the presented model in this paper can be much more advanced. The resulting set of partial differential equations with known initial values and moving boundaries is solved numberically using a finite-difference method. In this paper the design parameters associated with the developed model are charted accurately. Bows used in the past and nowadays on shooting meetings such as the Olympic Games are compared. It turns out that the application of better materials which can store more deformation energy per unit of mass and that this material is used to a larger extent, contribute most to the improvement of the bow. The parameters which fix the mechanical performance of the bow appear to be less important as is often claimed.