Drag
The equation for drag force on an object is:
F_d = 0.5 * rho * v^2 * A * c_d
Where rho
is the density of the fluid, v
is the velocity of the object relative to the fluid,
A
is the area of the object, and c_d
is the drag coefficient. In this equation v^2
represents
a vector with the magnitude of v
squared, and the same direction as v
.
Implementing drag
Since there are no changes to the actual integration equations, we can reuse the engine's builtin integration. We'll just need to add the drag force to each body.
// These are declared with `const` instead of `let`
// so that they can't be changed later
const RHO = 1.0;
const DRAG_COEFFICIENT = 5 * 0.1**9;
let update = ids, bodies {
for body in ids {
let v = body.get_vel();
let v_mag = v.length;
let v_hat = v / v_mag;
let r = body.get_radius();
let A = ???;
let F_d = ???;
body.add_force(F_d);
}
};
This code works for moving objects, but it has a problem. If the object is stationary,
v_mag
will be zero, so we'll be dividing by zero and crash the script. Additionally,
it will keep applying a force even when the simulation is paused, so the object will
shoot off the screen when you unpause it.
To fix the first problem, we'll add a check to see if the velocity is very low, and if so, skip the body. Additionally, we'll add a check to see if the simulation is paused, and if so, skip the whole function.
Finalize the script by filling in the ellipses with your drag code from before:
// These are declared with `const` instead of `let`
// so that they can't be changed later
const RHO = 1.0;
const DRAG_COEFFICIENT = 5 * 0.1**9;
let update = ids, bodies {
for body in ids {
if (is_paused()) {
return;
}
let v = body.get_vel();
let v_mag = v.length;
if (v_mag < 1.0) {
body.set_vel(vec(0.0, 0.0));
continue; // skip this body
}
let v_hat = v / v_mag;
let r = body.get_radius();
let A = ...;
let F_d = ...;
body.add_force(F_d);
}
};
Exercises

Using the
add_body()
function before the update function, create two bodies with the same starting velocity, but one with half the radius of the other. Make sure the radii are more than 250.0, and the masses are 1.0, or else the drag force will not be noticeable. Run the simulation. Approximately how far did the larger body travel in relation to the smaller one? 
Add this line to the start of your loop after the if statement to simulate fixed gravity:
body.add_force(vec(0.0, 1.0) * body.get_mass())
. Additionally, useadd_body()
beforeupdate
to create an object with radius 50.0 and mass 10.0. Run the script. The body should accelerate downwards from gravity, and then reach a fixed velocity due to drag. What is the terminal velocity of this object? It might be helpful to follow the body through its inspect panel.