Note: this section is going to take me a while so be patient please while I work on it.

Lift Me Up, Drag Me Down: The Aerodynamic Duo

Introduction

Juno: New Origins seems to use a surprisingly simple, but tricky to understand, method for calculating the collective drag (and lift) forces on a craft while in atmosphere. In this section we will discuss the basics of these forces, understand the part and craft parameters that contribute to them, and demonstrate how to calculate the forces and acceleration caused by them using Vizzy. For the purposes of simplicity and foreshadowing, hereafter we will refer to both drag and lift forces as just ‘drag’.

Note: this section is not intended to evaluate the lift dynamics associated with wing parts or propellers, only the resulting drag forces on static bodies such as rockets.

What is Drag?

Drag is the resistance force that pushes against an object moving through a fluid (like air or water), slowing it down. In real life, drag force is exclusively opposite (and parallel) to the direction of velocity, as shown in the image below.

However, there is also a lifting force that acts perpendicular to the direction of velocity, as shown in this image:

When added together, these drag and lift forces create a new resulting force that has a direction and magnitude equal to the vector sum of the individual forces (in three-dimensional space).

Calculating Drag Force

The drag force formula is:

Fd = 1/2 * p * v^2 * Cd * A

• Fd = Drag force (Newtons)
• Cd = Drag coefficient (unit-less, depends on shape and surface roughness)
• p = Fluid density (kg/m³)
• v = Object’s velocity relative to the fluid (m/s)
• A = Cross-sectional area facing the flow (m²)

How Drag Works in Juno: New Origins

Note: consider everything in this sub-section to be theory, and not absolute fact. It is based on my experiments and assumptions, and I am open to being corrected.

In order to understand how drag works in Juno, we need to build up from a simplified model. First, let’s start with a one-dimensional view of a craft falling to ground. In this example, the drag force acts exactly opposite to the velocity direction. It is easy to see that there will only be drag force acting against the bottom face, because there is no air pushing against the other faces. In this case let’s assume that the velocity is equal to 1m/s, air density is 1kg/m3, area is 1m2, and the drag coefficient is 1 and so the drag force is 1N. This will become important in the next example.

Now, imagine we add a second dimension and rotate the craft 30° clockwise, so that the bottom face experiences 2x the relative velocity compared with the right face. Because drag force is proportional to velocity squared, the drag force acting against the bottom face will actually be 4x the drag force on the right face.

The resulting drag force will now be in a different direction than the velocity. In reality the portion of drag force acting directly against velocity is truly drag, and the force acting perpendicular to velocity is lift. However, Juno treats both as drag when reporting.

Of course, we can now extend this to a 3-dimensional space and rotate along any of the craft axes (roll, pitch, yaw). At any given time, drag will be acting upon at most 3 different faces, and the other faces will be ‘shielded’ from the force. As long as we know the areas of each face, coefficients of drag, air density, velocity vector, and craft pointing vectors, we can build up a model of drag forces that can be validated.

Breaking It Down

In order to build up a fully functional drag model in Juno, we need to work through each of the critical parameters in the drag equation.

Air density

Luckily, there is a Vizzy block for this very thing!

Alternatively, we can calculate the air density for any planet at any height using these handy functions:

Area

This one can be a bit tricky to determine. For any part, we can use the tinker panel to examine the area and drag properties for the part.

For the part we’re examining (a cube command disc), the drag and area properties are the same. This is not usually the case, because curved and angled surfaces will introduce lower drag forces. It is helpful to think of the area properties as the ‘bounding box’ for the part, and the drag properties to directly determine the area that will directly contribute to drag equations.

The image below can help figure out which of the 6 drag/area properties apply to which faces:

1 = Front, 2 = Back, 3 = Top, 4 = Bottom, 5 = Right, 6 = Left

Coefficient of Drag

This one is interesting, as the coefficient of drag seems to be universal and exactly the same for every part. I have experimented with many different parts (nose cones, fuel tanks, engines, struts, capsules, motors, pistons, etc) and the value always returns approximately 0.875. From here on, we will consider this value to be a constant.

Velocity

This is the most straightforward parameter in principle, but in practice can be tricky. In order to determine the velocity acting against each face on the craft, we have to use dot product vector operations and knowledge of the craft axes unit vectors:

Examples & Applications

Work in progress