Reefed Parachute & Tether Shock Loads
One canopy instead of three, and the analysis and testing needed to show the recovery hardware survives the loads of opening.
01 / CONTEXT
What a responsible engineer owns
MASA is Michigan's student rocketry team, building large liquid-fueled rockets. On the recovery subteam I'm the responsible engineer for parachutes and tethers. That means I own the design, the analysis, and the verification evidence that those parts will survive flight, and I present it for flight certification.
Two problems sit on my plate. The current recovery system uses three separate parachutes, and every extra parachute adds another deployment event, another set of hardware, and another way to fail. And every load path, from the canopy through the shroud lines and bridle to the rocket, needs evidence that it won't break when the parachute snaps open.
02 / CONCEPT
One canopy that opens twice
A skirt-reefed parachute has a line threaded around its skirt that holds the canopy partly closed. Reefed to a small diameter, the main parachute can come out at apogee and act as the drogue for most of the descent, falling fast enough to limit drift. Near the ground, a line cutter severs the reefing line and the canopy opens fully for a soft landing.
That turns three parachutes into one. The tradeoff is that the second opening happens at speed with a big canopy, so the disreef shock becomes the load case that sizes everything downstream.
03 / ANALYSIS
Predicting the opening shock
I built the opening-shock model in MATLAB from the methods in Knacke's Parachute Recovery Systems Design Manual, starting from a teammate's single-stage main parachute script and extending it to a two-stage reefed opening. Each opening uses Knacke's fill-time relation, which scales with canopy diameter and the speed at line stretch, and steps the equations of motion for the rocket under the growing drag area.
fill time t_f = n · D / v^0.85 drag area (C_D·S)(t) grows from η·S_reefed to S_full over t_f motion m · dv/dt = m·g − ½ ρ v² (C_D·S)(t) reefed hold integrate until altitude = disreef altitude, then cut
To keep it fast, the solver uses a 0.1 ms step during the two opening transients, where the load spikes, and a 10 ms step for the long reefed descent between them. The disreef is triggered by altitude rather than a timer, the way a dual-deploy altimeter would fire it.
- Rocket mass383 lbm
- Apogee / deployment10,000 ft
- Canopy, full open24 ft, CD 2.2
- Reefed diameter7 ft
- Disreef altitude1,000 ft
- Bridle rating5,000 lb
- Shroud lines24 × 250 lb
- Ejection velocity20 ft/s
This is a first look, not a certified number. A few inputs are still placeholders, including the fill constant and opening-force coefficient (taken from flat-circular canopy values until toroidal values are confirmed) and the apogee and disreef altitudes. The model is set up so those can be swapped in as the design firms up.
04 / VERIFICATION
A tether test to 4,000 lbf
Analysis alone doesn't certify hardware, so I'm leading a shock-load verification test on the parachute and tether. The tricky part is predicting what the heavy drop will do before running it, so the test can be set up safely and the result has something to be checked against.
The plan uses two drops. A light drop with a known mass and drop height calibrates the tether's stiffness. Setting the potential energy lost equal to the spring energy at maximum stretch gives the stiffness directly. That stiffness then predicts the heavy drop: how far the tether stretches, whether the load reaches the ground, and when.
calibrate k = 2·m_L·g·(h + y_L) / y_L² heavy drop v₀ = √(2·g·H) max stretch y_max = [m_H·g + √((m_H·g)² + 2·k·m_H·g·H)] / k ground check L + y_max ≥ H_ground ? motion y(t) = δ(1 − cos ωt) + (v₀/ω)·sin ωt, ω = √(k/m_H)
The script checks whether the stretched tether reaches the ground. If it does, it solves the motion equation for the time and speed at impact and the time spent on the ground versus in the air, which sets up the test fixture and the safety zone. The MATLAB model of the full parachute and tether system then predicts the response to verify structural integrity to 4,000 lbf for flight certification.
05 / SIMULATION
A 6-DOF flight simulator
Recovery loads depend on the state the rocket is in when the parachute comes out, so the team needs a full flight simulation. I'm building a six-degree-of-freedom simulator in C++ on NASA's Trick simulation framework and the JEOD orbital-dynamics package, running on Linux.
Most of the work so far is architecture: how Trick schedules jobs, how the integration loop advances the state, and how physics models (thrust, aerodynamics, mass properties, gravity) plug in. The goal is a structure that handles more than one rocket configuration, so a new vehicle is a new set of models rather than a new simulator.
- Job schedulingSeparating what runs every integration step from what runs at a slower rate or only on events like burnout and deployment.
- Integration loopAdvancing translational and rotational state together with a consistent time step across models.
- Physics modelsThrust, aerodynamics, changing mass properties, and gravity as interchangeable modules.
- ConfigurationsVehicle-specific data kept out of the core so multiple rockets share one simulator.