Ceilidh fiddle playing and Newton's Laws of Motion

Now let us look at the position that a solo violinist or a Ceilidh Band fiddle player will stand in. (Not all fiddle players or ceilidh and barn dance bands will stand  but by the end of this section you should appreciate the difference in sound that the standing position produces, and why this is a desirable position if you are going to have a barn dance band with real drive and excitement. )

So, stand up straight with your feet a couple of feet apart. Bend your knees slightly so they are not locked rigidly.  Now hold up your arm and wag it violently from left to right once more. You should find two things in this standing position, firstly that you are able to waggle your arm much more quickly than before, and secondly that your upper body is much more stable. Why is this? It's all to do with Newton. Before Newton invented the laws of motion presume it was much easier to play a violin!

Newton's Laws of Motion: 

The second law states that the rate of change of momentum of a moving body is proportional to the force acting to produce the change.

The third law states that if one body exerts a force on another, there is an equal and opposite force (or reaction) exerted by the second body on the first.

(The first law of motion states that a body continues in a state of rest or uniform motion in a straight line unless it is acted on by an external force, But it is not relevant to violin playing, although it is probably relevant to me as a violinist in that I continue in a state of rest for as long as I can, but that is to do with me getting out of bed in the morning!)

 So, interpreting this in terms of playing a violin, we start with the second law of motion. The rate of change of momentum, which is proportional to the force acting on it to produce that change is about accelerating and decelerating your right arm, your bowing arm. How do you change direction of your arm, bring it to a standstill and then accelerating it up to speed in the opposite direction? It is by your muscles are applying a force to your arm. This force can be considerable, on occasions taking all your muscle power to do this. It is like weightlifting all the time.

Many people don't appreciate how heavy an arm is. Have you ever picked up a severed arm? Unless you are in the ambulance service or in the Army Medical Corps, I would think that it is unlikely that you have. I have picked up a severed arm , though it wasn't one that had previously been attached to a live person. It was an arm of a crash test dummy, the kind you sometimes see in television adverts showing how safe a particular model of car is. Crash Test Dummies are built to be identical in every way possible to a live human body, including the weight of all the parts. A human arm is extremely heavy. If you think that about 60% of the human body is water, and the remainder is stuff that is slightly heavier or slightly lighter than water, then you can think of the volume of an arm being filled with water. Depending how big you are and how muscly, you can think of your arm as being made up of three or four large Coca-Cola bottles. Pick up a large Coca-Cola bottle. They are heavy aren't they. This is the weight of your arm, the weight that you are trying to waggle backwards and forwards without throwing your body all over the place.

 But most people would say, my arm doesn't weigh anything like this! It certainly doesn't feel like that sort of weight when it's on your body when you're picking up a cup of tea. The reason for this is that your brain controls your muscles to balance your arm, but does not feed that weight back to your conscious mind. All your brain feeds back to you is the additional weight your arm might be supporting. So when you pick up your mug of tea, you consciously feel the weight of that mug of tea, but your brain doesn't give you any indication that you are also holding up 3 or 4 Coke bottles weight of arm. The brain is very clever, very clever indeed.

Getting back to Newtown, who knew nothing about Coca Cola bottles or as far as I know, violin playing; he had worked out that to accelerate a violinist's arm, or any other mass in the universe for that matter, requires an external Force. In the case of a violinist arm, this force is provided by their muscles. Not just their arm muscles though, but muscles in their hand, arm, shoulder, back, and legs in order to to stabilize the whole torso so that the person doesn't fall over. You probably will have seen video on television of walking robots and experimenters giving them a little push, and the whole thing falling over. Stability in a walking robot is a very difficult thing to achieve,  as it requires fast muscular actions in an appropriate direction, which has to be calculated from accelerometers within the robot and force sensors in the feet and other parts of the body. This requires fast servo motors and a large amount of computing power. I recall seeing a video of a single legged robot which bounced up and down rather like a person on a pogo stick, but could adjust the angle and speed of that Pogo Stick very rapidly. Its way of balancing was to bounce up and down moving the Pogo Stick to keep it stable. It was very impressive to see it being pushed by the researcher, falling back slightly and then moving it's single leg as it bounces up and down to stabilise herself. I think it was an American military project, I'm not too sure.

Anyway, back from walking robots to violinists. As the muscles work very hard to produce the forces to accelerate and decelerate the arm,  an equal and opposite force is generated as described in Newton's Third Law of Motion. So what does this mean? It means that if you fling your right arm to your right hand side, your body will tend to be thrown to the left. As you accelerate your right arm towards your left side, the rest of your body will be wobbles to the right. In other words your body wobbles in antiphase to the movement of your arm.

Why does your body only move a small amount compared with a large movements of your arm? This is described by Newton's equation, Force = mass x acceleration  and by equation Distance = ½ Acceleration x time squared.

If you like maths, you can plug in the mass of your arm and the mass of your body. Your arm might be 3 or 4 for Coke bottles ( large sized bottle) worth of weight,  but your torso and head is probably 20 or 30 full size Coke bottles worth of mass. If you don't like playing with numbers, this simply means that your body is much heavier than your arm,  so when your arm waggles a along way your body only wobbles a bit.

But it is not just stability in terms of wobbling that is at issue here, it is stability in terms of the accuracy and speed that can be achieved in the movement of your arm. This is getting a bit technical, but to understand this more you can consider the difference between a centurion tank and its gun and a musician playing in a string quartet. Even better a comparison is a String Quartet player and the gun on a first world war battleship. There would seem to be no relationship between the two in any way, but there is in terms of closed loop servo control systems. What are closed loop servo control system? It is precisely what allows your brain to, nd your arm or any other part of your body to move in a controlled and meaningful way.

Closed loop feedback control theory in its modern form originated from the work of a biologist looking at how animals, including humans, achieve muscular control. This was soon put to work in the military field during the First World War. If a person can control their arm to pick up a cup of tea, the same scientific method can be used to point your gun accurately at an enemy ship  when your ship is rolling from side to side, or two track an enemy aircraft with a sight that a soldier can move, and get a heavy searchlight to follow that motion. So guns on ships became driven by closed  loop servo control systems. Similarly, guns on the more modern tanks are aimed and controlled buy closed loop servo control systems, so that the gun can remain pointing accurately at the target while the tank is travelling over rough terrain.

 A violinist by comparison is  moving their arm in what has to be an accurate motion, whilst balanced on a torso and legs that are moving and swaying from side to side. But it is much more difficult for the human being to do this than to achieve it in the military situations that I described above. What is the difference? The difference is the proportion of weight of the object you're moving compared with the base that the object is attached to.

 On a military tank the gun is heavy, but the tank body itself is very much heavier. On a first world war battleship the difference in relative weight is even more extreme. The gunbarrel may weigh several tons, but the base it is mounted or, the whole of the ship and all its superstructure is many thousands of times heavier. In comparison, the torso of a violinist is only ten or twenty times heavier than the arm that is being move backwards and forwards at great speed, even if the violinist is very fat.