The Key Force 1TM
is able to directly measure the ability of the key to return
to its rest position, from some depressed position within the "pre let-off" region.
This new parameter is termed Key Return Time (KRT), and is a function of not
only true inertia in the key mechanism, but also of gravitational and frictional
effects. It is measured in simple milliseconds. Gravitational force on the ham-
mer head aids the return movement of the keystick, while the hammer head's
mass (i.e. inertia) impedes it. Regarding key leads in the front half of the key,
both gravity and
their own inertia (small though it is!) hinder this movement.
KRT is independent of any "aiding" forces from the repetition lever spring.
It's defined so that it is only affected by the static forces, along with inertia of
the mechanism. These static forces are due to friction, gravity, and any springs
or magnets that are in play during the pre-letoff region of the stroke. KRT is
parameter, as opposed to a component-level one such as
Front Weight or keystick mass. It's physically defined as the amount of time
it takes the front of the key mechanism to rise unimpeded from some initial
"depressed" position to some higher position. This initial position must be
in the pre-letoff region of the keystroke, thus removing all effects from the
repetition lever spring. Both the initial and final positions should be consist-
ent - from note to note - relative to a known reference point, like the at-rest
position of each key. The larger the value of Key Return Time, the worse "key
returnability" that key action exhibits. Stated another way, the more sluggish
that particular key action is.
A method for determining Key Return Time involves temporarily placing
the KF1's finger in a "key depressed" state, but at a known point relative to rest
position of the key. As mentioned, this point must be in the pre-letoff region
of the keystroke. The machine begins reading the forces at the finger. The
finger ascends very quickly, to a point at or just below the at-rest position of
the key, where it quickly comes to a stop. The startpoint of this quick upstroke
might be 5 or 6 mm below the at-rest position of the key, with the endpoint
at, say, 0.5 mm below the at-rest point. With the finger rising so fast, it will
separate from the key and reach its endpoint before the key does. When the
key finally catches up, it will collide with the stopped finger, with the acquired
forces revealing this collision event. The point where the force data shows the
rising key beginning to collide with the finger is called the Key Return Collision
Point. KRT is the elapsed time between "start" and this collision point.
The deceleration of the finger and associated load cell - at the top of the KRT
movement - inevitably leads to an "inertia hump". This hump is always very
repeatable, particularly with respect to time. It is therefore fairly easy for the
Key Force 1 system to filter it out, so it's not mistaken for the key colliding with
the stopped finger. In the run above, it begins and ends at 65 and 82 ms, respec-
tively. Things have been calibrated so that the start point of the KRT movement
is always at 41 ms. This is when the finger begins its extremely fast upstroke.
The force data from two related KRT routines are shown in the figure above.
The "as is" key action had a hammer mass of 8 or 10 grams. The only difference
in the second graph was that exactly 5 grams had been added to the hammerhead
mass. The Balance Force increased from 37 to 63.5 grams, indicating an Action
Ratio of about 5.3. More to the discussion here, the Key Return Time decreased
from 116 ms to 104 ms...about a 10% decrease. The friction increased by 3.9 grams
as well, when the 5 grams was added to the hammerhead. All three factors - BF,
Inertia at the Key, and Friction - played their part in this behavior change, as fully
dictated by the KRT equation shown up above.
We at Full-Measure Response were not content to merely devise the KRT
parameter. After all, a parameter that cannot be measured is not very useful.
We also developed a way - using the Key Force One - to measure it. Perhaps
more importantly, we derived an analytical equation for it! The resulting equa-
tion - elegantly connected to Inertia at the Key, Balance Force, and Friction -
helped establish that KRT is indeed a fundamental parameter of a key action.
In fact, its ability to be relatively easily measured allows us to use KRT - rather
than Inertia at the Key (IK) - as one of the measured inputs for our Dyna-StatTM
action balancing system. Of course, this would not be possible without the
connection between the two, evident in the equation. The equation for KRT is:
where "k" is a simple geometric parameter related to key and hammer dimen-
sions. Of course, BF and FF are the Balance Force and Frictional Force, respec-
tively. Since BF minus FF is equal to Up Force (UF), the denominator is also
equivalent to the square root of Up Force!