3.3 Accelerated Motion and Life
37
system is shifted in space, its momentum is conserved. Angular momentum of a
system will be fixed if the system dynamics do not depend on the system’s angular
orientation. Energy conservation in a system follows if that system behaves the same
way starting at any time, provided its initial conditions are reproduced.
Charge conservation results from a so-called ‘gauge’ symmetry, which is an
invariance under any shift in the phase of the wave functions describing the particles
coupled with the addition to the fields interacting with those particles by a gradient
of that phase times the charge of the particle in the field.
3.3 Accelerated Motion and Life
Who studies petrified dinosaur droppings? Answer: A fecescist.
—wcp
Accelerations which affect humans are usefully expressed in terms of ‘g’, the
gravitational acceleration of freely falling bodies near the surface of the Earth
(g = 9.80665 m/s squared or about 32 feet per second squared). Since the dawn
of aircraft, the human physiology during high and low acceleration has been of
significant interest. Flying a plane into a steep dive and then pulling out can cause
pilots to black out. Flying a large aircraft on the path and speed of a projectile thrown
high into the air produces “zero g” for those floating inside. Table 3.1 indicates some
effects on a person whose body is parallel with the direction of various accelerations.
3.3.1 High-g
A little kinematics shows that the minimum deceleration per unit ‘g’ after a sudden
stop such as in a collision or after a fall can be found from v 2 /(2g x), where v is
the initial speed and x the stopping distance. If a car hits a solid wall, the stopping
distance may only be a little more than the thickness of an airbag, maybe three feet.
At 60 mph (88 ft/s), the stop produces about 40 g’s. A person will take only about
70 ms to stop from 88 ft/s to zero speed in 3 ft. Car air bags are designed to deploy
before decelerations exceed 20 g’s, and inflate in less than 30 ms.
A typical elevator will generate less than a 15% change in the force of the floor on
the passengers, i.e. the effective ‘g’ is (1.0±0.15) g. Amusement rides are generally
designed to keep riders below 3 g’s, although some have reached 6.5 g’s. The Apollo
astronauts felt about 4 g’s after liftoff. Test pilots encounter 20 g’s lasting a few
seconds. In 1954, Col. John Paul Stapp survived 46.2 g’s for 1.4 s in a decelerating
rocket sled. 20
20 Data from Nick T. Spark, The Story of John Paul Stapp, the Fastest Man on Earth, Wings and
Airpower Magazine, p. 53, Republic Press, Cal. (Jul 2003).
37
system is shifted in space, its momentum is conserved. Angular momentum of a
system will be fixed if the system dynamics do not depend on the system’s angular
orientation. Energy conservation in a system follows if that system behaves the same
way starting at any time, provided its initial conditions are reproduced.
Charge conservation results from a so-called ‘gauge’ symmetry, which is an
invariance under any shift in the phase of the wave functions describing the particles
coupled with the addition to the fields interacting with those particles by a gradient
of that phase times the charge of the particle in the field.
3.3 Accelerated Motion and Life
Who studies petrified dinosaur droppings? Answer: A fecescist.
—wcp
Accelerations which affect humans are usefully expressed in terms of ‘g’, the
gravitational acceleration of freely falling bodies near the surface of the Earth
(g = 9.80665 m/s squared or about 32 feet per second squared). Since the dawn
of aircraft, the human physiology during high and low acceleration has been of
significant interest. Flying a plane into a steep dive and then pulling out can cause
pilots to black out. Flying a large aircraft on the path and speed of a projectile thrown
high into the air produces “zero g” for those floating inside. Table 3.1 indicates some
effects on a person whose body is parallel with the direction of various accelerations.
3.3.1 High-g
A little kinematics shows that the minimum deceleration per unit ‘g’ after a sudden
stop such as in a collision or after a fall can be found from v 2 /(2g x), where v is
the initial speed and x the stopping distance. If a car hits a solid wall, the stopping
distance may only be a little more than the thickness of an airbag, maybe three feet.
At 60 mph (88 ft/s), the stop produces about 40 g’s. A person will take only about
70 ms to stop from 88 ft/s to zero speed in 3 ft. Car air bags are designed to deploy
before decelerations exceed 20 g’s, and inflate in less than 30 ms.
A typical elevator will generate less than a 15% change in the force of the floor on
the passengers, i.e. the effective ‘g’ is (1.0±0.15) g. Amusement rides are generally
designed to keep riders below 3 g’s, although some have reached 6.5 g’s. The Apollo
astronauts felt about 4 g’s after liftoff. Test pilots encounter 20 g’s lasting a few
seconds. In 1954, Col. John Paul Stapp survived 46.2 g’s for 1.4 s in a decelerating
rocket sled. 20
20 Data from Nick T. Spark, The Story of John Paul Stapp, the Fastest Man on Earth, Wings and
Airpower Magazine, p. 53, Republic Press, Cal. (Jul 2003).