What is the physical foundation of Force Fields?

Question

I would like to know the physical foundation of the force fields in blender.

For instance: what are "Wind", "force strength", "flow"?

Answer 1

The "practical" definition of these parameters is here:

Force Fields in the manual

I don't think there is much documentation about their workings under the hood.

Anyway, each Force type implements one particular type of force in Newton physics.

Forces, the $\mathbf{F}$ in the second law of motion $\mathbf{F}=m\cdot\mathbf{a}$, are the entities that cause an acceleration $\mathbf{a}$ on a object of mass $m$. Different kind of forces can be described as a function that depends on several features of the object being acted on, or of the space in which the force acts:

$$\mathbf{F} = \mathbf{F}(\mathbf{r}, \mathbf{u}, m, q; \mathbf{r_0}, \eta, \ldots)$$

($\mathbf{r}, \mathbf{u}$ = position and velocity vectors of the test object, $m, q$ = mass and charge of the test object, $\mathbf{r_0}$ = position of the effector object, $\eta$ = viscosity of the medium, ...).

Each force can or cannot depend on each of these variables, and it may depend on them in different ways.

• Wind is an acceleration field with a total translational symmetry, if the falloff is 0 and there is no min/max distance, or a 2D translational symmetry otherwise. It doesn't depend on anything except its own force parameters and, if falloff is enabled, on $\mathbf{r_0}$

• Force and Charge are (typically spherically symmetric) central force fields (they are aligned along the $\mathbf{r}-\mathbf{r_0}$ direction), the latter depending on $q$

• Harmonic is a Hookean field. Same variables as Force, but a different equation.

• Drag is a force depending on the object's velocity $\mathbf{u}$ according to Stoke's or Rayleigh's law

and so on.

Within each type of force, there are options that control the overall strength (Force Strength, a parameter that basically appears the $\mathbf{F}$ functions above as a multiplying factor); allow to tweak the dependence of the strength on the distance from the emitter (Falloff, ...); convert part of the dependence on $\mathbf{r}$ to dependence on $\mathbf{u}$ (Flow); ...