In days of yore the sword represented the pinnacle of personal weaponry. The development of the sword began in the bronze age with the extension of daggers. However, bronze is brittle, so bronze swords were mainly limited to stabbing. The cutting sword which has become the symbol of knights from all cultures had to wait for the development of good steel. From there we had an arms race between protective armor and the cutting sword, which in Europe was won by armor and let to a return of stabbing weapons, such as rapiers. Even so, the cutting sword underwent significant evolutionary development over a thousand or so years and a couple of physicists wanted to take a look at how these empirically discovered changes relate to what Newton's laws would tell us is the optimum design.
Before we can understand the development of the sword we need to understand what a sword is intended to do. Basically, when you hit someone with a sword, the intension from a physics perspective is to transfer all the energy in the sword and sword arm into the body of your opponent. Thus a sword designer is aiming for a maximum of stored energy, which means mass and speed. The sword user is aiming for a minimum of vibration and impact shock (that would be energy transferred in the wrong direction). Thus sword designers discovered that every striking instrument had a center of percussion, which was the point of impact where impact shock was minimized. For example take a hammer and hit a steel bar on the head of the hammer, you will only feel some vibrations and no shock. Now strike the same bar with the same force with the shaft of the hammer — the shock is… well… shocking. They also quickly discovered that they had to trade off weight and strength to make the swords lighter but also that redistributing the sword weight was an effective way of increasing stored energy while making the sword easier to handle.
The paper focuses on how some of the characteristic features of swords optimize sword handling. For instance, most swords from about 500 BCE onwards have a groove in the middle of the blade. This groove removes about 20 percent of the sword mass, however the resulting reduction in strength is only about 8 percent. Over time it was discovered that if this mass is not thrown away but is placed on the pommel of the sword (a small ball at the end of the grip), then the reaction force felt by the person striking out is reduced by between 5 and 10 percent. It also changes the moment of inertia of the sword (the moment of inertia is a measure of how hard it is to change rate and direction of a rotating body), since more of the mass is now located near the center of rotation so it is easier to control the sword by rolling the wrist, giving the handler more striking options.
It is pretty cool to see how over the centuries sword makers and fighters had developed a pretty comprehensive understanding of moments of inertia and Newton's third law. In fact according to physics education statistics their intuitive understanding outstrips that of formally educated first year university students. Just goes to show how the threat of imminent death can focus the mind.