How many force levels can be reliably told apart is limited by sensor precision and the stability of human force

What it is

A sensor can report finely while a hand cannot sit still; a hand can sit still while a sensor smears neighboring levels into noise. How many levels can be told apart reliably is jammed by both: the just noticeable difference for force and the actuator’s own tremor, plus sensor noise and quantization. The previous layer already said “few levels.” This one says how to measure the two ceilings and AND them.

Why it happens

Weber’s fraction makes two just-discriminable forces differ by about 7%–15% of current force (site and task vary). Actively sitting in a band adds isometric tremor, so useful bandwidth is narrower than passive discrimination. Sensor noise, nonlinearity, and temperature drift smear adjacent quantization steps: the person thinks they are in band 3, the system jumps among 2, 3, and 4. Reliable level count is the narrower of the two chains: draw the human stability band and the sensor’s separable band on one force axis; how many non-overlapping slots remain is the field count. ADC bit depth overestimates; so does a lab’s passive JND, because the field is an active hold.

Studying it

Measure passive discrimination (which of two forces is larger), active reproduction (return to the last band), and the sensor’s noise band at target temperature and mount.

Independent variables: site (thumb / index / palm), visual aid or not, sensor noise, a 1 s hold versus a tap. Dependent measures: ΔF/F at 75% correct, standard deviation of active reproduction, sensor RMS, non-overlapping slots when the three are stacked.

JND tasks should report a Weber fraction, not only “how many levels.” Drawing active-reproduction SD as slot width is more honest than treating the mean as a band center. Sensor bands from a temperature chamber and from different mount stresses belong on the same figure.

Where it stops holding

A mechanical second stage of travel no longer discriminates the second level by JND but by a travel event; level count can rise by one without violating the force Weber fraction. Continuous matching of a pen on paper (stroke width) is visually closed-loop, not discrete slots; JND still exists, but is not scored as “hit band n.” Children, gloves, and wet hands enlarge both human tremor and sensor noise, so slot count drops together. Hardware that claims “256 levels of pressure” often still has two or three separable slots in the field.

Applying it

• Cut slots from active-reproduction stability bands and sensor noise bands, not from advertised level counts.
• Leave tremor width between slots; do not put a boundary on the force where people most often sit.
• If temperature and mount move the sensor band, either calibrate boundaries with it or accept one fewer field level.
• Verify: no numeric prompt, 20 active hits per claimed band, plot the cloud of human landings with instantaneous sensor values. If a cloud crosses a boundary, merge those two bands. Report ΔF/F and field slot count, not ADC bits. One figure in gloves, one hot, one cold.

Related

• Same group: C10.12.1 A pressure sensor must separate a user’s resting-force baseline from an intentional extra push · C10.12.2 Holding a pressure level continuously fatigues the hand more than holding a position · C10.12.4 Without synced visual or haptic confirmation, people cannot tell which force level they have reached
• Adjacent: C10.04 Pressure Input · C5.01 Pressure Sensitivity
• Search: Weber fraction · force JND · level discriminability