Re: What would happen to an object/person hitting atmosphere suddenly at speed?

Greetings:

Reference: Schaum's Outline Series, Theory and Problems of College Physics,
7th edition McGraw-Hill 1979

Your question is related to the study of Aerodynamics which is one branch
of the general science of Fluid Dynamics. This is one of the most difficult
sciences to mathematically model. For this reason scientists and engineers
still use experimental measurements in wind tunnels and pressure measurements
in the flow systems to gather design information for aircraft, jet engines,
rockets, and space vehicles. Wind tunnel testing is an expensive procedure
and pressure measurements on actual vehicles operating at ultrasonic speeds
are most often conducted in flight tests in place of wind tunnels. Experiments
on the X-15, the world's fastest aircraft, the Space Shuttle, and the SR-71
Blackbird can give us some idea of what would happen in your thought
experiment.

In 1968 the X-15 probably reached about Mach 6.72 (4,554 miles per hour,
7,327 km per hour) during a dive from high altitude. You can read about the
X-15 program and see pictures of the aircraft on the following web sites:

air-and-space.com

The SR-71 Blackbird spy plane set the speed record for jet powered aircraft
that take off under their own power. The Lockheed SR-71 Blackbird is, to date,
the fastest airplane ever to streak across the sky, even though it's more than
30 years old. Capable of speeds over 2,200 miles per hour (3,540 km per hour),
Mach 3, the SR-71 can fly at altitudes above 80,000 feet (24.4 km). The SR-71
is made from the metal titanium to withstand the 2000 degree red hot
temperatures that the wings reach while cruising at 80,000 feet.

http://www.pbs.o rg/wgbh/nova/barrier/machines.html

http://users.cihost.com/at a/aircraft.html

The vehicle in your thought experiment is traveling at 10,000 meters per
second (22,374 miles per hour) which is about 30 times the speed of sound
(Mach 30) and you are flying in dense surface level air not in the thin air
in at the edge of space. At velocities greater than about 480 kilometers per
hour ( 300 miles per hour) air is modeled as an incompressible fluid similar
to water only with less density. The density of dry air in your question at
the surface of the earth is about 1.185 kilograms per cubic meter.

Hypersonic vehicles generate at least two shock waves, one from the leading
edge of the vehicle and one from the trailing edge of the vehicle. This is
why we hear two sonic booms when the Space Shuttle lands. At velocities greater
than Mach 3 the shock wave causes the air molecules to dissociate into a hot
plasma gas which surrounds the vehicle. The Gemini, Mercury, and Apollo
spacecraft experienced this during there loss of signal (LOS) phase when
radio communications are not possible during reentry. These spacecraft are
capable of heating to thousands of degrees for a few minutes where your
wooden space craft would disintegrate at about 200 degrees C (400 degrees F).
Thus the atmospheric friction and the plasma shock wave would turn you vehicle
and its pilot into a hot plasma gas in a few seconds, very similar to a meteor
entering and burning up in the thin upper atmosphere.

To estimate the drag forces that the vehicle will encounter let us use Impulse
and Momentum (I&M) techniques that are used in similar physics problems in the
reference. However, in this case the drag forces and g loading will be
underestimated but will give us an order of magnitude guess.

Let us model your vehicle to have a nose cone with a 15 degree angle between
the surface and the vehicle axis (30 degree total angle). The nose cone is
followed by a cylinder with a 1.6 meter (63 inch) diameter in which the pilot
can sit or recline. This vehicle presents a drag cross sectional area of
2 square meters to the air stream.

An impulse causes a change in momentum: The change in momentum is equal to
the impulse in both magnitude and direction. Thus, a constant force (F) acting
for a time (t) on a body of mass (m) changes its velocity from an initial
value (Vi) to a final value (Vf) then

Impulse = change in momentum

F * t = m * (Vi - Vf)

We will first use the vehicle as our frame of reference and assume that it
is standing still and that the air is rushing toward it at Vi = 10,000 meters
per second (as in a wind tunnel). The mass of the air that will hit the nose
cone will be the volume of one second of air times the density of the air.

m = 10,000 meters/sec * 2 square meters * 1.185 kg per cubic meter
m = 23,700 kg (52,400 lbs, 26.2 tons)

We will assume that the air particles will bounce off of the nose cone like
ping pong balls and travel in a straight line 30 degrees from the vehicle axis
after hitting the 15 degree nose cone (In reality the air particle trajectory
would be bent around the body of the vehicle by the air flow surrounding the
vehicle).
Thus in our model the component of the final velocity (Vf) of the air flow
relative to the vehicle axis will be:

Vf = Vi * cos 30 = 8,660 meters /sec

Using I&M the force on the nose cone during the first second will then be:

F *t = m * (Vi - Vf)
F * 1 = 23, 700 kg * (10,000 m/s - 8,660 m/s) = 31,758,000 Newtons

This force (F) on the nose cone will be directed into the vehicle normal
(90 degrees ) to the surface. The force F can be decomposed into a
compression force (Fc) normal to the vehicle axis and a drag force (Fd)
parallel to the vehicle axis.

Fc = F * cos 15 degrees = 30,675,873 Newtons
Fd = F * sin 15 degrees = 8,219,575 Newtons

We can now use Newton's Laws of Motion to calculate the deceleration
of the 5,000 kg vehicle after the first second in the air bubble:

F = m * (-a)
thus -a = F/m = -8,219,575 / 5,000 = -1,644 meters per second squared
or -1,644 / 9.8 = -167 g

One pound = 4.45 Newtons, therefore the compression force on the vehicle
is a crushing 30, 675, 873 / 4.45 = 6.9 million pounds force!

As I stated earlier this model is a low ball estimate because it neglects
the force required to generate the shock waves and the frictional force of
the turbulent boundary layer around the vehicle. However, a human being
loses consciousness at about a 10 g force and a 100 g force ruptures the
heart and major blood vessels. So our simple low ball model tells us that
the pilot will probably be dead during the first second, hopefully before
he is crushed and incinerated into a plasma.

Best regards, Your Mad Scientist
Adrian Popa