What are Some Math Formulas for Recovery Parachute Design?
When designing a parachute system for rocket recovery, several formulas and concepts are employed. Here are some key formulas and considerations:
- Descent Rate: The descent rate of the rocket under the parachute can be estimated using the following equation:
V = sqrt((2 * m * g) / (ρ * A * Cd))
where V is the descent rate, m is the mass of the rocket, g is the acceleration due to gravity, ρ is the air density, A is the reference area (parachute canopy area), and Cd is the drag coefficient. - Parachute Sizing: The size or diameter of the parachute required to achieve a desired descent rate can be estimated using:
D = sqrt((8 * m * g) / (ρ * V^2 * Cd))
where D is the parachute diameter. - Parachute Shape Factor: The shape factor (SF) of the parachute canopy affects its drag coefficient and performance. It is given by:
SF = (Canopy Area) / (Canopy Perimeter)^2
A higher shape factor generally leads to a more efficient parachute. - Descent Time: The descent time can be estimated by dividing the descent altitude by the descent rate.
- Parachute Material: The choice of parachute material is important for durability and performance. Factors to consider include weight, strength, porosity, and fabric type.
- Reefing: For larger rockets or higher velocities, it may be necessary to incorporate a reefing system to limit the initial drag and prevent parachute shock loads. Reefing can be achieved by using multiple stages or mechanisms to reduce the effective parachute area initially and gradually increase it during descent.
The above formulas provide a starting point for parachute design, but they may need to be refined and adjusted based on specific requirements, desired performance, safety factors, and real-world testing.
Additionally, considerations such as wind conditions, altitude, and deployment mechanisms also influence parachute design and performance.
Custom Parachute Design
One Way Rocketry can help you design your perfect parachute based on your specifications. You will simply need to choose a diameter in inches, the total number of parachute gores (panels), and the desired seam size in fractional inches.
As output, we will send you a set of files in PDF format to help you print, cut, and assemble your gore panel into a cutting jig, which can be made from a va…
