John Kallend Ph.D. Professor, Department of Mechanical, Materials Professor, Department of Mechanical, Materials and Aerospace Engineering Illinois Institute of Technology

Physics and Skydiving? You must be kidding! Gravity Laws of motion Aerodynamics Air density, pressure, temperature Design of Equipment and Instruments Materials for equipment.

Deflecting air forwards causes the skydiver to move rearwards (Newton’s 3rd law).

Forward motion is achieved by deflecting air backwards

Twisting the body deflects air to the side and allows the skydiver to turn and steer.

A modern parachute has two surfaces and is inflated by air entering the front. When inflated it has the shape of a wing. It flies forward three feet for every foot it descends.

The parachute flies forward at around 30mph, and descends at 10mph. It is fully steerable, like a glider. Control lines attached to the canopy pull down the rear to (a) deflect air downwards and (b) increase drag. This slows the jumper down for landing.

FREEFALL! HOW FAST DO YOU GO? What is “Terminal Velocity”?

Drag = 0.5  A C d v 2 Gravity = mg Fall rate is controlled by the balance between gravity and air resistance

Drag = 0.5  A C d v 2  is the density of the air (1.23kg/m 3 at sea level)  is the density of the air (1.23kg/m 3 at sea level) A is the frontal area of the object C d is the “drag coefficient” which measures how streamlined and slippery the object is v is the velocity

Forces Acting on 70Kg Skydiver Terminal Velocity

Drag = 0.5  A C d v 2 Gravity = mg Fall rate is controlled by the balance between gravity and air resistance

Velocity vs Time after Jumping from 4,300m

Distance vs Time after Jumping from 4,300m

How to Change Fall Rate 1.Change Cd (body position, jumpsuit) 2.Change mass (weight vest, tandem) 3.Change area presented to the wind 4. Change air density (altitude)

The skydiver can control fall rate by changing frontal area and drag coefficient Large area exposed to wind, high C d terminal velocity 110, to 130 mph, Small frontal area, low C d, terminal velocity > 300mph

Air density varies with altitude  ( h )  (0) e h

Terminal velocity increases as air density decreases So you go slower the farther you fall!

Hollywood Skydiving Clips from “Point Break” IIT DOES NOT CONDONE THE USE OF BAD LANGUAGE IN THE MOVIE CLIPS! SPOT THE PHYSICS ERRORS

At 125 mph it takes approximately 5 seconds to fall 1000ft. It takes about 10 seconds to reach terminal velocity, which also covers 1000ft. SO - a jumper leaving a plane at 12,000 feet will take 65 seconds to reach the ground. OR A freefall lasting 4 minutes must exit the plane at an altitude of 47,000 ft even if we ignore the increase in terminal velocity due to the extreme altitude (in fact, it’s 59,000 ft if you account for this).

Ever feel left behind? In a 125mph freefall, a skydiver who leaves 1 second late will be left 180 ft behind his or her partner(s) A jumper who waits 8 seconds will be 1,440 feet behind (about the height of Sears Tower).

HOW ABOUT THOSE DRAMATIC RESCUES? Two skydivers holding on to each other will fall at about 1.4 times the speed of a solo jumper (175mph or 260 ft/sec). (175mph or 260 ft/sec). The parachute takes about 2 seconds to slow you down, so the deceleration is 260/2 = 130 ft/sec 2 which is 4g. If the person weighs 140lb they will have to be able to hold on with a force of 700 pounds! Not very likely!

Projectile Motion ! v vyvyvyvy vxvxvxvx  D  DxDx DyDyDyDy mg

D = - k v 2 = -k (v x 2 + v y 2 ) D x = - k (v x 2 + v y 2 ) v x /  (v x 2 + v y 2 ) m dv x /dt = - k v x  (v x 2 + v y 2 ) Similarly m dv y /dt = - k v y  (v x 2 + v y 2 ) -mg

Avoiding Mid-Air Collisions 2-d Model 2-d Model

Thank you for your attention. Physics Rules!