Recurve vs Longbow: Stored Energy & Arrow Velocity

[manitoba]

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,

 

[mgb_phys]

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"

 

[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.

 

[Danger]

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.

 

[LURCH]

Just a little more clarification; is a "recurve" bow a compound bow, or a rams-horn bow?

 

[zoobyshoe]

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.

http://www.springerlink.com/content/u84x876863520065/

 

[Naty1]

In general I have understood post # 2 to be accurate: english longbows did not have the "punch" of saracen bows. Apparently the smaller design of the saracens was untilized to facilite shooting from horses while the english and Europeans utilized foot bowman. As I have read historical related texts, it appears different woods and fabrication techniques were also apparent between the two designs...layered wood (I think) for the recurve vs single wood (can't remember the two of three most popular english woods) for the longbows. And the Saracens used a rather unique glue..resin based I believe...to glue different woods toegther in layers.

From the above posts it appears that both materials and design of the two types leads to greater deformation energy storage in the saracen version...

 

[jambaugh]

I think something has been missed (except for the external references)... you can in principle design long vs. recurved bows with the same tension.

But look at the geometry as the arrow is pushed forward. The angle of the string at the back of the arrow will affect how much of the tension pushes forward vs. purely in opposition to the other half of the string. Since the recurve bow curls the string around the curved ends (like a pulley) it maintains more forward component of the tension for a longer distance in the draw.

Take this one step further and you have the modern compound bow which uses a more efficient pulley system to give you much longer draw at a given tension and bow width.

The ultimate bow would be say a crossbow with two pulleys attached at the stock so that the string is pulled straight back parallel to the arrow and all the tension is used to push the arrow forward.

 

[mgb_phys]

Historically the main reason for longbow vs recurve bows is the weather.
When it's raining wooden longbows work, compound bows made from sinew and bone don't - if you are fighting in northern Europe longbows will still work.

There are also political/economic reasons if most of your army is made up of peasants that supply their own weapons vs a full time standing army supplied with horses.

 

[markkrebs]

I don't think this has been answered though jambaugh is close.
Speed comes from energy, the integral of force x draw stroke.
Given a max holding weight, you'd like to have that be constant (or heck, unsustainably large before you reach your anchor (see "compound" (note some people confused compound with composite, earlier))) So you'd wish that as you relax your draw (imagine the arrow being shot) the weight didn't drop. On a recurve this is achieved by stealing lever arm as the draw length decreases. The curve shortens the lever arm through which you can bend the limbs. It's related to jambaugh's angle. There's one more effect, which is that the changing geometry alters which part of the limb can bend at each different displacement during the draw. That allows the possibility that the tips are softer, since they come into bending last. Overall,we want the bow to soften as the draw lengthens. That cancels the basic hooke's law of force proportional to a constant x distance, making the force vs draw curve more constant and less progressive. Once you get that, you set the value at full draw to the highest level you can hold with preload, and the lower slope of the force displacement curve thus means it's integral is larger, and that's your fastest shooting option. Limb weight matters too (the bow accelerates both the arrow and it's limbs) but as you said, assuming other things equal...