What is the physical foundation of Force Fields?

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

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

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); ...

• Thank you the complete answer. I am investigating how realistic blender deals with the mechanical laws. The description you give is clear and good to use. An example of how I approached the wind force can be downloaded via the following link.dropbox.com/s/4pzekj2ymgf4rc8/Wind.blend?dl=0 Dec 13 '18 at 10:57