How to model flight of simple parachute in 2D?

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To model the flight of a simple parachute in 2D, one must consider the forces of lift, drag, and weight, which influence the parachute's position, velocity, and glide angle over time. A mathematical formula is sought to represent these dynamics, ideally capturing the transition from free fall to a steady-state glide characterized by a consistent speed and glide angle. The discussion suggests that the parachute's descent could resemble a diminishing sine wave as it stabilizes. Additionally, the impact of toggles or brakes on glide angle and speed introduces complexity, potentially creating a pendulum-like effect during descent. A clear formula that encapsulates these variables would greatly aid in simulating parachute behavior.
callagga
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How would one model flight of simple parachute in 2D?

For example a formula(s) that would effectively allow you to map the parachute's position/velocity/glideAngle over time. I'm imaging dropping the parachute (consider in 2D only to make easier) and then it will be affected by forces Lift/Drag/Weight, and as these play out the parachute would over a number of seconds angle down, pick up forward speed, and then settle down into some steady state glide with a given speed and glide angle. So perhaps it would arrive at steady state kind of like a sine wave of reducing size as it settles down perhaps(?)

So I was hoping for a formula that gives something like:

position(x,y)/speed/glideAngle = function(time)


(Bonus extra would be effect of toggles/brakes that can be applied at various levels that affect glide angle & speed, but this might be quite complicate as it causes a time based pendulum effect to the parachute too...)

canopy_diagram.jpg
 
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these don't help unfortunately
 
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