The drag coefficient
In the world of parachutes, where adventurers soar through the skies and expensive payloads fall back to earth, there lies an intriguing physics concept: drag. Drag or air resistance is the force that works directly opposite of the velocity vector. The more drag an object generates, the higher the drag coefficient. This coefficient holds the key to how parachutes interact with air during their descent.
In simple terms, the drag coefficient is a number that reveals the amount of air resistance an object experiences while moving through a fluid—in our case, the fluid is air. This coefficient depends on several factors, including the object's shape.
A quick thought experiment: two parachutes with the same material, shape, and design. The only difference is their size—parachute A has a larger canopy area compared to Parachute B. As parachute A, with its larger surface area, makes its descent, it encounters more air molecules compared to the smaller parachute B. This increased interaction with the surrounding air results in a higher drag coefficient for parachute A. In simple terms, parachute A experiences more air resistance, allowing it to slow down more. This makes sense, the same parachute type but larger creates more drag.
Now imagine two parachutes of the same size but a different shape and form. Say a cross parachute versus a Ringsail. Which parachute would slow down most? This time it is harder to say as we need to know the efficiency of the parachutes, in other words, we need to know the drag coefficients of the parachutes.
To understand this more, let's dive into the equations governing the problem. To determine the terminal velocity, we need to equal the gravity (m*g) to the drag force of the parachute.
Drag Force (F) = 0.5 * ρ * V^2 * A * Cd
In this formula:
- ρ represents the density of the fluid, which is air in this case.
- V signifies the velocity of the parachute relative to the fluid (how fast it's falling).
- A is the reference area—a standardized value used for comparison (typically the frontal area of the parachute).
- Cd represents the drag coefficient—the elusive number we've been exploring.
With this formula, we can clearly observe how a parachute's area (A) directly influences the drag force. As the parachute's size increases, so does the reference area, consequently leading to a higher drag force and a higher drag coefficient (Cd).
Influence on the drag coefficient
The drag coefficient is influenced by many factors, several are named below, but there are many more.
- Shape: Parachutes come in various shapes—square, rectangular, circular, and more. Each shape interacts uniquely with the air, influencing the drag coefficient. Generally, round parachutes tend to have lower drag coefficients than their square counterparts.
- Material: The type of fabric used in parachute construction also affects the drag coefficient. Lighter, smoother fabrics generally yield lower drag coefficients, whereas heavier or rougher materials may lead to higher drag coefficients.
- Porosity: The porosity of the parachute material refers to its ability to allow air to pass through it. More porous materials create additional aerodynamic drag, contributing to a higher drag coefficient.
Which area to use
As you can see in the equation the drag coefficient is dependent on the area. the big question is which area. Generally, the area used is the A0 or the area of the inlet of the parachute. This area is dependent on the D0. Alternatively one can use the total area of the material used or the area of the entire canopy. As the drag coefficient is a number used in engineering it does not matter which area is chosen as long as it is clear what the reference area is. To mitigate this one can use the CdA or drag area. This number is not dimensionless and thus there is no reference area.
