Arm design is an issue that comes up a lot. This page has information about several popular designs and tips for building them.
Arm Mass
Arm mass is very important. It is easy to make an arm strong enough, what is hard it getting the arm light. In the case of a arm, light does not refer to its mass, but its moment of inertia. The moment of inertia (
) is a measurement of how hard it is to turn something (ignoring friction). It is calculated by taking the sum of all the parts of the arm times their mass times the distance from the center of rotation squared.
Where (
) is the point's mass, and (
) is the radius.
What this means is that removing a pound from the arm 10 feet from the axle is 100 times better than removing a pound one foot from the axle. This combined with the fact that then bending load on the arm during the throw (but not necessarily during cocking) decreases the further you get from the axle means that all arms should be tapered to minimize weight. There are cases where this does not apply completely such as when cocking by pulling the arm tip down, the load on the arm can greater that it would ever be during operation, and not tapered as it would be during operation. An extreme case of this is the king Arthur design which is why alternate cocking methods were designed for it. Also mass near the axle can have a larger effect than suggested by the moment of inertia of the axle moves, as is the case with floating axle designs, or designs on wheels.
Torsion Arms
Torsion arms have to main differences from other arms. First they are subjected to large compression loads from the bundle, and second they often strike a hard stop.
Arm Base
The base of a torsion arm must withstand the compression loads applied, and the immense bending force right on the edge of the bundle. Failing to do this is one of the most common causes of torsion arms breaking. The compression from the bundle weakens the point arm to bending, and it just breaks off at the bundle. When trying to avoid this effect remember that mass at the point of rotation slows the arm down very little, so adding heavy reinforcements does not hurt performance significantly. Adding steel bars to the top and bottom of the arm is a common and effective approach. They should extend all the way from the end of the arm, through the bundle, and a significant distance up the arm.
Arm Stop
In the case where a torsion arm will strike a hard stop it needs to be protected. Padding the stop, often with leather, can help, but wrapping the arm with string/rope also helps.
Trebuchet Arms
Axle Holes
Around the axle hole is not only the point of highest bending load, but, but also a huge point load. Hanger axles also impose a huge point load on both the hangers and the arm. For the arm to survive these loads, around the axles should be the strongest part of the arm. The most common approach to handling this bending load is the Simple Tapered Sandwich, see below. While the bending reinforcements do help handle the point loads, several other things can be done to help. Because the biggest problem from these point loads is splitting wooden arms, adding reinforcements that will not split is usually a good choice. These reinforcements go on the side of the arm and the axle goes through them. Attaching some wood with the grain going in a different direction, or attaching metal plates are common methods. Especially in the case of hanger axles where the axle hole is near the end of the arm, adding these reinforcements can be important, but with of without reinforcements, leaving a significant length of material between the axle hole and the end of the arm is crucial.
All Arms
Firing Pins
Sling Attachments
Structural Designs
The following design elements can be combined or used individually.
Simple Tapered Sandwich
The tapered sandwich arm is made from a bunch of thin boards laminated together. One end of all the boards usually line up at the high stress end of the arm (The short arm for trebuchets, and the bundle end for torsion). The boards in the middle are full length and the ones on the sides are shorter, often extending just past the axle on trebuchets. The other board lengths are in between to produce a tapered arm. The boards do not have to be the same thickness or width. This design can be taken to the extreme to produce a wide arm to reduce the unsupported axle span.
Bridged
Bridged arms are arms where then tension load is removed from the main member and transfered to strictly tension members such as steel cables. The cables car heald away from the arm by rods protruding from the arm, usually one near the axle and occasionally more further down the long arm. Sometimes arm are bridged on just the top/from which only helps during cocking and acceleration. These arms have been known do break on deceleration after release, which is why many arms are also bridged (but usually to a lesser extent) on the bottom.
Aluminum Extension
Many arms recently have been extended with aluminum bars or tubes.
Open Web
Open web beams work on a similar system to bridging except the outer members can often accept compression loads, so rigid bars are used instead of cables, and more bracing is usually included between them and the rest of the arm.
Structural Steel or Aluminum Beam
Some arms are made out of a single metal beam such as an Aluminum tube or a steel I-beam. These arms can be hard to taper.
Composite
Various composite materials can be very strong and light and therefor great for arms. Composites arms often consist of the composite shell over a light core to hold the shell material where it is most effective. A great example of composite arms can be found at Siege-Engine.com's Mista Ballista Arms page.
Core Material
The core material is often a light foam. Is some cases the core can just be hollow.
Fiberglass
Carbon-Fiber
Metal
Steel sheet metal on wood for example.
Draw Down Point
Placement
Load
Attachment to Arm
Attachment to Draw Down Line or Trigger
Material
Pictures
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