Modeling a wingsuit base jumper's speed

[v42Waeger]

Homework Statement

Model a base jumper based of a video in which is clear he has three phases the first is a free fall for 7 seconds, then he opens the wings of his suit which causes more fricition and continues to 'fly' for a whole minute at 125mph speed and at last he opens his parachute till he reaches the ground.

Relevant Equations

any formulas related to gravity and fricition which are needed to model the movement in the program.

Fgravity = m*g
Ffriction = k*A*v^2
Ftotal = Fgravity - Ffriction
a = Ftotal/m
v = v+a*dt

if t<7 then Fgravity>Ffriction
if 7<t<67 then v =55,88 (meters per second)
if t>67 then A = 45 (square meter)
if t>67 then Fgravity<Ffriction

the t defines the seconds the first 7 seconds are the free fall (phase 1) then till 67 seconds into the movement he 'flies' and after that he opens his parachute. This is not the exact way i put it in the program but the way i translated it to english.

 

[Cutter Ketch]

unfortunately reality is more complicated. During both the wing suit portion and the parachute portion (unless it’s an ancient dumb parachute) he really is flying. By flying I mean that the wing suit and parachute generate a force which is in a significantly different direction than just opposed to the direction of motion through the air. In this case you need to think more like an airplane rather than just free fall with drag.

You know the force of gravity. You don’t have any power, so there is no thrust. That leaves the force generated by the flow of the relative wind over the airfoil and body. In analyzing flight, the force of the wings (and fuselage, or in this case body) is generally broken into two pieces: one component in the direction opposite the direction of motion through the air called drag, and a component perpendicular to the motion called lift. The amount of drag and lift depend on the speed of the body through the air, the angle of attack (how the body or wing is angled relative to the relative wind) and, of course, the shape of the body and/or wing. It takes a lot of analysis to relate the relative wind speed and the angle of attack to lift and drag. For a simulation you would need tables relating these. The shape can also cause torques. This is how you fly. The pilot alters the shape creating an imbalance of force about the center of gravity resulting in torques that allow him to roll, pitch, and yaw. Again, careful analysis or measurement are required to relate shape changes to torques, and these must be determined over the full range of speed and angle of attack parameters.

Anyhow, if you can determine the lift and drag and torque for a variety of shape configurations, relative wind speeds, and angles of attack, (not easy) then it is a relatively simple matter to calculate linear and angular accelerations and continue in small steps through time.