Measuring Force in Piano Technique

A force may be measured by the work it does, which in turn is shown in the time and distance through which an object is moved. Assuming that

1. inertia,
2. atmospheric and joint resistances,
3. and gravity

are constants. A force of 1 will move the arm through 1 inch in 1 second, then a force of 6 will move the arm through 6 inches in 1 second. At the end of the first second the arm has a velocity of 6 inches per second. If, immediately, the force ceases to act, the arm will continue at this rate (ignoring the factors of inertia and resistance mentioned).
At the end of 5 seconds, therefore, the arm will have covered a distance of 30 inches.
Now suppose that a force of 1 acts during the first second.
This will move the arm through 1 inch (5 inches less than the distance before).
Then a force of 3.5 will move it 3.5 inches during the 2nd second, giving a total displacement of 4.5 inches in two seconds.
At a similar rate of increase of force, the arm will move

1. 6 inches during the third second (or a total of 10.5 inches) ;
2. 8.5 in the fourth;
3. 11.0 in the fifth.

Totaling these distances gives a displacement equal to the other, 30 inches. These relationships may be diagrammatically illustrated as in Fig. 32.
The straight line shows the arm-displacements when the maximum velocity is attained at the beginning and maintained throughout the stroke. The upper, curved line shows the displacements with a slow beginning and increase of velocity during the movement. The dark points show the positions of the moving body at each second.

Finally, the shaded portion may serve to indicate the excess energy required in giving to the arm its necessary final velocity after a slow beginning. The figure is purely diagrammatic. Records of actual movements are given later.
Thus, by using a maximum at the beginning of the movement, a force of six suffices.
By beginning slowly and adding force throughout the movement, a final maximum force of eleven is needed, almost double the other. Various rates of increase are possible, but regardless of the actual rate, any increase during the movement represents excess energy. Which, as we have seen is characteristic of in-coordinated, not coordinated movements.

But it does not follow that this advantage applies to slow movements. The slower the movement the greater is the effect of the constant factors, previously ignored:

1. atmospheric and joint resistances,
2. gravity, and
3. inertia.

Take the action of gravity, for instance in a horizontal movement. Assume its numerical value to be 2. Its direction of pull in a horizontal movement, will be at right angles to the line of arm-movement , and will tend to pull the arm down. If the movement lasts two seconds, gravity will exert a total force-effect of 2 x 2 or 4, the product of the numerical value of the force and the time through which it acts. If the movement lasts 10 seconds, gravity will exert a total force of 10 x 2 or 20, which is five times as great as before.
Again, assume the joint-resistance through the 30 inches of movement to be 60, the mass of the arm 10, and its acceleration 6.

The alternative would be a jerky movement, in which the arm would move in spurts, resting between them. Such a movement is so obviously at a mechanical and physiological disadvantage that we can at once exclude it from consideration. In recording slow movements, therefore, we may expect to find a less intense but more prolonged muscular contraction than in rapid movements. As the speed of movement increases, the initial muscular contraction should become more and more noticeable.