u/WizardofPhysics888

Forget juggling separate “weight minus buoyancy” forces. There’s a much smoother approach that’s mathematically identical to the classic added-mass equations but way more intuitive.

Start with one clean bounded density contrast:

χ = (ρₒ − ρₘ) / (ρₒ + ρₘ)

Then the initial acceleration right after release (before drag takes over) is simply:

a = g (ρₒ − ρₘ) / (ρₒ + C ρₘ)

where C is the familiar added-mass coefficient set by shape (0.5 for a sphere, 1.0 for a cylinder moving perpendicular to its axis).

Quick real-world example (object twice as dense as water, ρₒ = 2 ρₘ):

Sphere (C = 0.5): a ≈ 3.92 m/s²

Cylinder ⊥ axis (C = 1): a ≈ 3.27 m/s²

At the exact same density ratio, the sphere accelerates noticeably faster — geometry controls how much fluid it has to drag along with it.

Why this feels better

It collapses everything to one density-drive term plus a single geometry knob (C). The math stays exactly the same as classical added-mass theory, but it’s automatically bounded (|a| never exceeds g), symmetric, and perfect for quick calculations or teaching. Shape effects pop out immediately, making experiments (like the easy r=2 test) much more intuitive.

Please let me know your thoughts?

Has anyone here seen a genuinely high-resolution study of the earliest-time acceleration regime for objects moving vertically through fluids before substantial drag closure develops?

I’m interested in controlled comparisons using:

* identical density ratios,

* identical masses,

* but different geometries (sphere vs cylinder vs hemispherical-ended capsule),

* and ideally different surrounding media adjusted to equivalent densities.

The reason I ask is that most literature and demonstrations focus heavily on terminal behaviour, while the initial acceleration window seems comparatively underexplored experimentally despite being potentially important for separating:

* density contrast effects,

* added-mass coupling,

* geometry-dependent participation,

* and later drag evolution.

Would appreciate pointers to papers, datasets, or experimental groups working on this type of problem please.

Thankyou.

Repeat the torsion-balance test, but compare:

horizontal vs vertical detector orientation

metal spheres vs lightweight plastic cylinders with hemispherical ends

The idea is to see whether the signal stays stable when geometry, damping, airflow interaction, and torsion pathway are changed.

Just asking whether the classic result has been properly stress-tested from a mechanical/instrumentation angle.

Has anyone seen orientation-controlled Cavendish tests like this?