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I am looking into detailed HDD principles of operation and I cannot get my head around this. Slider of the read/write head maintains about 5nm gap between itself and the platter surface using air bearing (basically flying on the cushion of air). I presume this force pushes the slider away from the platter. But in that case, what is the position of the slider when the drive is not spinning (head is parked)? And how it transitions from parked to "flying" above platter without contacting that platter?

The actuator arm is quite thin and I find it hard to believe, there is a 5nm clearance (and manufacturing precision) when heads are moving from parked outside the platter to the platter. I could imagine a situation, where there is a larger gap by default and the slider is "pressed" towards the platter once it is above it and spinning. But of cource the actuator is not spring loaded 😁. It would help though if the air bearing principle was able to keep the slider in constant distance not only by pushing away, but also by "pulling in".

So where is the bug in my presumptions? Is there really a 5nm gap that is maintained in all drive states? Is the air bearing not only pushing slider away?

Related to this, when watching people unstucking the heads, they move the head across stationary platter (sometimes rotating the platter a bit simultaneously). Are the sliders in contact with the platter in that case or not?

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But in that case, what is the position of the slider when the drive is not spinning (head is parked)?

The typical modern HDD will always (try to) reposition the R/W head assembly on shutdown or power loss to a safe area of the platter(s) called the landing zone.
This is typically located between the innermost cylinder and the spindle/hub, and is an area not used for data storage. This scheme is known as Contact Start/Stop.

Another scheme used in HDDs is load/unload ramps at the outer edge of the platters that can keep the R/W heads from touching the surfaces.

Disk drives with removable platters have head assemblies that can retract/lift the R/W heads away from the platter surfaces, and move heads and arms away from the platters and off to the side.

And how it transitions from parked to "flying" above platter without contacting that platter?

On initial spin-up, the R/W heads are either (a) in contact with the platter surfaces, but in the designated landing zone, or (b) parked on the ramps. Only after the drive verifies that the spindle-motor/platters have achieved the required rotational speed is the R/W head assembly commanded to perform a recalibrate seek to cylinder zero.

As long as the platters maintain some minimal rotational speed, the air bearing should be sufficient (under normal conditions, i.e. no shock or vibrations) to avoid a head landing/crash on the platter surface.

But of cource the actuator is not spring loaded ...

Your assumption is incorrect.
The R/W heads typically have torsion or leaf springs on their arms so that the "normal" (i.e. parked) position is light pressure on the platter surface.
The spring tension can be adjusted to achieve the proper flying height of the R/W heads.

So where is the bug in my presumptions?

Seems like you have more than just one misconception.

Is there really a 5nm gap that is maintained in all drive states?

No, the flying height can only be maintained while the platters are spinning.

Is the air bearing not only pushing slider away?

(The negation in the question is superfluous. Don't try to assert your assumption while asking a question.)
The air bearing gives each R/W head lift (away from the platter surface) to counteract the opposing spring which pushes the heads towards the platter surface.

Related to this, when watching people unstucking the heads, they move the head across stationary platter (sometimes rotating the platter a bit simultaneously). Are the sliders in contact with the platter in that case or not?

The R/W heads would be in contact with the platter surfaces, but such minor contact should be inconsequential. The larger risk is contamination.


Addendum

A WD white paper on Contact Start/Stop versus load/unload ramps (PDF, 957KiB): Ramp Load/Unload Technology in Hard Disk Drives.

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    In ye olden days, parking the heads was not necessarily automatic. There were utilities to specifically park the heads before shutdown to avoid problems. Aug 29, 2021 at 16:12
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    Note that apart from air bearing acting as a cushion preventing the head from touching the surface there can also be a suction force created if the head is too far away from the surface depending on the shape of the head. The combination allows the head to be aerodynamically designed to maintain a specific height. Iomega used to have a patent that used this suction force to have the surface sucked up to the head which they marketed as Bernoulli hard disks where the platter was made up of floppy disk material and later as Zip disks when they made the platter removable
    – slebetman
    Aug 30, 2021 at 7:22
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    What happens in the phase of spinning up when the heads are in the landing zone? Are they sliding on the platter surface? Does that result in head wear?
    – jiwopene
    Aug 30, 2021 at 10:50
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    The linked paper says they are sliding on the surface and it results in head wear.
    – jiwopene
    Aug 30, 2021 at 11:03

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