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Description  |
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FIELD OF THE INVENTION
The present invention generally relates to photothermal devices. More
specifically, the present invention relates to photothermal devices which
controllably heat and cool a gas to thereby control the pressure and
density of the gas so as to produce acoustic or mechanical pressure.
BACKGROUND OF THE INVENTION
Devices which controllably produce acoustic or mechanical pressure are well
known. Acoustic devices, such as loudspeakers, convert electrical energy
into mechanical energy. An electrical energy signal is typically applied
to the magnetic coil and diaphragm assembly of the speaker which causes
the diaphragm to vibrate and thereby generate acoustic or sound waves in
response to the electrical signal. One disadvantage of this conventional
approach is that the sound is generated from a single point source, i.e.,
the speaker itself. This type of sound often does not sound as realistic
as sound generated at different locations in space.
An alternative acoustic device is known, wherein a laser beam is used to
convert an electrical signal into sound. Such a device is disclosed in
U.S. Pat. No. 4,641,377 to Rush et al., the contents of which are
incorporated by reference herein. The device disclosed in the Rush et al.
patent is a photoacoustic speaker which produces photoacoustic sound by
modulating the intensity of the laser beam in accordance with an
electrical input signal. The modulated laser beam output is passed into an
enclosed gas absorption chamber containing gas which absorbs the laser
beam signal. The gas is heated as it absorbs photons of the laser output
wavelength and produces photothermic pressure waves corresponding to the
electrical input signal. Because the intensity of the laser beam varies
according to the electrical input signal, the heating of the gas is not
uniform, but rather, varies with the intensity of the electrical input
signal. The absorbing gas is thus heated proportionately according to the
electrical input signal. The heating and subsequent cooling of the
absorbing gas produce pressure waves which propagate radially outwardly.
The photothermic pressure waves produce sound when they impinge on the
walls of the enclosed chamber.
Rush et al. indicate that the enclosed chamber may be a room and that the
absorbing gas may be air. However, it should be noted that according to
the Rush et al. patent, the disclosed device only produces sound exterior
to the enclosed chamber and this is a result of the vibration of the
chamber walls. Essentially, the Rush et al. device operates along the same
lines as a conventional speaker, using the chamber walls as the vibrating
diaphragm in order to produce sound pressure waves external to the
enclosed chamber. In this manner, the Rush et al. device is capable of
producing only a column of sound emanating from the diaphragm, i.e., the
chamber wall.
Also known are mechanical or electromechanical devices which control the
position and movement of objects in an air environment. One class of such
devices is magnetic levitation devices in which an object is suspended in
air or propelled along a predetermined course. These devices typically
utilize magnets or electromagnets to create a repulsive force which is
used to counteract the gravitational force and/or to provide a propulsion
force.
Also known are acoustic devices which operate to process sound, such as for
example, noise cancellation or reduction devices. Automobiles or other
machinery often generate excessive amounts of noise which are either
unpleasant or exceed proscribed noise levels as mandated by governmental
or safety regulations. One approach to reducing or eliminating the noise
source is to generate an equal but opposite noise source, i.e., one which
is equal in magnitude but opposite in phase, i.e., 180.degree. out of
phase. Ideally, the acoustic waves from the original noise source and the
generated noise source combine to cancel each other. Practically however,
total noise elimination cannot be achieved, since there is some delay in
generating the out of phase noise source because it is often generated as
a continuous sample based on the original noise source. Thus,the generated
noise source is not truly 180.degree. out of phase. This is not the case,
however, where the original noise source may be modeled a priori, thus
allowing for the real-time generation of a 180.degree. phase shifted noise
source.
SUMMARY OF THE INVENTION
According to the present invention, a novel apparatus is provided for
controllably heating and cooling a gas. This type of apparatus, also known
as a photothermal device, may be used to heat and cool a gas in order to
alter and thereby control the acoustic, mechanical or optical properties
of the gas itself or objects under the influence of the gas. For acoustic
applications, the photothermal device may be used to generate
three-dimensional spatially-located sound corresponding to an electrical
audio signal. Also, the photothermal device may be used to generate a
three-dimensional sound shield around a noise source in order to prevent
the propagation of sound waves from the noise source.
The present invention operates on the principle that when a gas is heated,
it gains energy and expands. Conversely, when the heat is removed, it
loses energy and contracts. A laser source is used to provide infrared or
other frequency light energy to the gas at the location to which it is
directed, causing the gas to heat at that location and expand, thereby
converting the laser energy into acoustical or mechanical energy. In this
manner, sound may be generated along the length of the laser beam by
modulating or turning on/off the output of the laser beam in accordance
with the frequency characteristics of a desired audio signal. If two or
more lower power laser beams are made to intersect at a point in space so
that their combined heating effects are sufficient to heat the location in
space, multi-dimensional spatially-located sound may be generated. In a
preferred embodiment, three lasers forming a tri-axial laser energy source
"deposit" energy at specific points in three-dimensional space creating
acoustic sources at those points. The present invention may also be used
to provide a three-dimensional acoustic barrier using a tri-axial laser
energy source to produce a holographic or pseudo-holographic effect for
the production and/or cancellation of sound in a controlled, specified
manner.
The present invention may also be used to controllably heat and cool a gas
to thereby provide mechanical energy or force. In one embodiment according
to the present invention, the controlled heating and cooling of the gas
may be used to establish standing waves. These standing waves are static
and stationary, in that despite ongoing propagation of sound, there exists
in a given space close to the source, molecular pressure zones created by
the regular peaks and valleys of the standing wave. The standing waves may
thus be used as sound barriers or even physical barriers. In the case of
physical barrier, the standing wave is created with sufficient energy to
counteract the opposing mechanical force. In this manner,
photothermoacoustic levitation may be achieved. Similarly, if the standing
wave is created with sufficient energy greater than the opposing
mechanical force, then photothermoacoustic propulsion or motion may be
achieved.
BRIEF DESCRIPTION OF THE DRAWINGS
Other objects, features and advantages of the invention discussed in the
above brief explanation will be more clearly understood when taken
together with the following detailed description of an embodiment which
will be understood as being illustrative only, and the accompanying
drawings reflecting aspects of that embodiment, in which:
FIG. 1 is a block diagram of a three-dimensional sound generation apparatus
according to the present invention;
FIGS. 2A and 2B is a block diagram of an alternative embodiment of a
three-dimensional sound generation apparatus according to the present
invention;
FIG. 3 is a transmission graph showing energy transmission efficiency in
the range of 0.5 to 2.0 microns;
FIG. 4 is a transmission graph showing energy transmission efficiency in
the range of 500 to 1000 microns;
FIG. 5 is a transmission graph showing energy transmission efficiency in
the range of 10 to 2 microns;
FIG. 6 is a transmission graph showing energy transmission efficiency in
the range of 4 to 5 microns; and
FIG. 7 is a force-displacement graph showing force requirements for
levitation as a function of height.
DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS
According to the laws of thermodynamics, all energy can be reduced to forms
of heat. Molecular, nuclear, chemical, electrical and acoustic energy can
be quantified as a function of heat. At a temperature of zero Kelvin, all
forms of energy cease because molecular, atomic and sub-atomic activity
ceases. The human ability to detect light at different wavelengths as
different colors occurs because the eyes have "target" cells which have
evolved so as to detect energy in a given range of frequencies. The human
eye cannot detect ultraviolet light or higher frequency energy, nor can it
detect infrared radiation or lower frequency energy; however, energy at
these frequencies does exist.
In the infrared region, light and heat are synonymous. The particles of
energy radiated are photons. Since lasers typically emit coherent light,
or light at a single frequency, lasers are particularly well suited for
producing an extremely narrow beam of controlled, modulated infrared
light. The laser is a photonic oscillator which takes electrical energy
and converts it into light of one specific frequency or wavelength. It is
a photonic device because it emits photons, as opposed to radio waves or
gamma rays. It is an oscillator because there are electromagnetic waves of
only one frequency or wavelength generated within the device, at a more or
less constant or periodic rate. The single wavelength output of the laser
is well suited for conveying information. Just as radio waves have
embedded in them acoustic frequencies that can be converted back into
sound, the laser output can be modulated by turning it on/off at varying
rates to recreate particular frequencies, thereby producing sound. The
laser output is modulated by mixing the optical or light waves with lower,
variable frequencies, such as audio frequencies. Thus, the modulated laser
output is analogous to a modulated carrier wave in radio. The outputs of
multiple lasers may be combined in order to produce more intense
heating/cooling.
If the laser is held stationary, the amount of heat imparted to the air
will decrease with distance from the laser, i.e., as energy in the beam is
transformed into heat, the beam gets weaker and less energy can be
transmitted to the air located further away from the laser. If nothing is
done, the laser will simply heat a line in space and no sound will be
generated. To generate sound, the laser must be modulated or turned on and
off at a rate that is within the audio band, e.g., DC to 20 KHz. This
causes the air to heat and cool at a desired rate, thus producing a sound
of a particular frequency. The heating and cooling creates pressure waves
at the particular frequency which are equivalent to conventional sound
waves. The sound produced by a single laser beam will be produced along
the laser beam in a linear fashion and will decrease in amplitude as the
distance from the laser increases. The volume of the sound will depend on
the mount of energy in the laser beam. In effect the sound waves will be
cone shaped with the large part of the cone at the laser output.
If two lasers are positioned orthogonal to each other, two orthogonal cones
will be created which will interfere with each other where they intersect.
If they have the same phase and frequency, they will add at the
intersection producing increased sound. If they are 180 degrees out of
phase, there will be cancellation at the intersection and no sound. If the
frequencies are different, but both in an absorption frequency range, the
resulting sound waves will be complex.
If the energy of any one laser is too low to produce significant sound, the
addition of two or more beams at the intersection may be enough to create
sound. A point source of sound can be created by having two or more laser
beams intersect each other. There will be more sound at the intersection
if the lasers are at the same frequency and phase, and the point of
intersection is not too far from the lasers. Further, as the point of
intersection is moved by repositioning the lasers, the apparent source of
the sound will move in space. Naturally, the energy in each beam decreases
with distance, so if the intersection is so far from each laser that the
beam has already lost more than 2/3rds of its strength, the intersection
of three beams will not be sufficient to produce more energy than one beam
at its inception. Therefore, more laser beams may be needed to achieve the
desired effect. Additionally, multiple laser beams may be aligned along
the three axes of space to produce sound in each of the three dimensions,
thus resulting in a generation of a volume of three dimensional sound.
The laser frequency may be set so that it is not readily absorbed by air,
but is instead absorbed by a particular gas. The gas could then be
confined in a chamber and radiated or energized by the laser beams. In
this manner, the sound will be generated in the chamber. If the chamber
were made like a hollow wall, this would cause the position of the sound
to move by moving the laser beam over the chamber wall.
In the transmission of radio waves, a high frequency signal is mixed or
modulated with a set of lower frequencies. Typically, microphones are used
to convert mechanical energy (sound waves) into electrical energy which
are then mixed with the higher frequency carrier wave. At the point of
reception, a tuned circuit of electromagnetic devices designed to resonate
at a specific frequency is used to detect and filter out the carrier wave,
leaving the original electromagnetic impulses. At the receiver, the
electromagnetic impulses are then converted back to acoustic or sound
energy corresponding to the mechanical energy sound waves.
As indicated above, a modulated laser output signal may be used to generate
sound. However, such a system is only operable in an atmosphere which is
appropriate for the reception and absorption of infrared energy. There are
two types of molecules appropriate for the reception of infrared light
energy, while at the same time offering maximum energy transfer. These are
water vapor and carbon dioxide (see FIGS. 3-6). FIGS. 3-6 represent the
points within the infrared spectrum which have the greatest absorption of
infrared energy at specific frequencies or wavelengths. Each Figure
represents absorption at a specific pathlength, i.e., the maximum measured
length or distance from the laser's physical boundaries, which here is 2
meters; an ambient temperature of 296 Kelvin; and an air pressure of one
atmosphere. The charts shown in FIGS. 3-6 have been prepared using
HITRAN-PC software available from the University of South Florida at Tampa
Physics Department.
The conversion of light into sound occurs when specific molecules are
resonated at specific frequencies. These specific frequencies are
indicated as dips in the Figures at or below the 50% mark for
transmission, i.e., the opposite of absorption. The deliberate and
controlled injection of instantaneously variable amounts of heat into
specific molecules (water vapor or carbon dioxide) will create
instantaneously variable degrees of molecular motion or vibration. This
can be analogized to billiard balls striking each other and transferring
energy to adjacent balls. The vibration will occur at such a rate so as to
create perceived instantaneous variations in local air densities, i.e.,
the compression and rarefaction of the air, which will be perceived as
sound.
The laser's optical frequency is modulated by electromagnetic signals input
via a microphone or other electrical audio source. The modulated carrier
is produced at the laser output and is propagated into the atmosphere. The
output variations which occur in the audio frequency range cause
instantaneous variations in local air temperature at specific absorption
points which in turn cause instantaneous variations in local air
densities, resulting in local air compressions and rarefactions which
produce sound waves.
The generation of sound waves, which are actually low-amplitude pressure
waves, will require the laser to produce some variations in local air
temperature from the mean ambient value. Additionally, the temperature
variations established by the laser should be as small as 50 .mu.seconds
to produce audio signals up to 20 kHz, i.e., the range of human detection
of sound. For example, the establishment of a particular sound wave
requiring that the temperature of a 1 cc target zone be increased by 1
degree Kelvin within a 1 .mu.second time interval requires heat Q in the
amount of:
Q=c.sub.v m.DELTA.T (1)
where Q represents the heat energy transferred, c.sub.v is the
constant-volume specific heat for air, m is the air mass, and .DELTA.T is
the temperature change in degrees Kelvin. Substituting the appropriate
values for air gives:
Q=0.716kJ/(kg.multidot.K).times.(1.29.times.10.sup.-6)
Q=0.924.times.10.sup.-6 kJ/cc of air
Thus, the power required to raise the temperature of the 1 cc target zone
by 1 degree Kelvin in 1 .mu.second is equivalent to:
Power=0.924.times.10.sup.-6 kJ/10.sup.-6 sec=0.924 kW or 924 Watts
These power requirements are well within the capabilities of currently
available lasers. Accordingly, heating and cooling of air in times on the
order of 1 .mu.second, i.e., up to 1 MHz operation, may be achieved to
produce sounds up to 20 kHz and beyond using conventional lasers.
The sound waves will be produced in areas or zones where there are
significant targets available to absorb the laser energy. These target
zones are areas of significant laser energy absorption, such as greater
than 50% absorption. The absorption in the target zones occurs for more
than a single frequency of the incident radiation. The target zones thus
have an effective bandwidth of frequencies at which significant absorption
takes place. This use of lasers rum counter to the traditional use of
lasers in communication systems which seek to minimize the absorption of
the laser energy. Essentially, photothermoacoustics relies on the
traditional obstacles to laser transmission to achieve its desired effect
and function.
The modulated laser output may be brought into direct contact with other
modulated outputs to produce complex, multidimensional waveforms. The
combination of these multiple outputs may be used to produce either
constructive or destructive interference of the resultant combined
waveform. In this way, sonic holography, i.e., the three dimensional
visual recording and reproduction of sonic events is possible. Sonic
holography relies on the interactions of waves of varying geometries on
three mutually orthogonal axes to produce a constantly changing three
dimensional sound. In addition to the generation of three dimensional
sound, localization of the sound is also possible by deliberately altering
one or more of the sound components along the three axes to thereby
locationally shift the generation of the sound.
Sound localization may be accomplished by including additional information
in the system signals. For example, a sub-carrier of known frequency,
amplitude and phase may be utilized to convey localization information.
The localization information may be input via a user controlled joystick
whose spatial movements are converted into corresponding laser positioning
signals to cause the laser beams from the multiple sources to intersect at
different positions and heat the air at the intersection, thereby
spatially locating the generated sound at the variable intersection. In
this way, sound may be dynamically localized to a precise
location--something which is not possible at all with conventional fixed
location planar speakers.
Referring now to FIG. 1, therein is illustrated a three dimensional sound
generation apparatus 100 according to one embodiment of the present
invention. Sound generation apparatus 100 includes audio sources 102, 104
and 106 for driving the x, y and z axes, respectively. Alternatively, a
single audio source, such as 102, may be used to drive all three axes.
Sound generation apparatus 100 also includes lasers 112, 114 and 116 for
the x, y and z axes, respectively. Lasers 112, 114 and 116 are powered by
power supply 120. Localization of the outputs of lasers 112, 114 and 116
in the x, y and z directions is provided by phase, amplitude and frequency
variable sub-carrier generators 122, 124 and 126, respectively, which may
also include mechanical positioning devices to aim the lasers in different
directions to change the position of the source of the sound. The outputs
of lasers 112, 114 and 116 may optionally be provided with lenses (not
shown) for directing their respective outputs.
The sound generation apparatus according to the present invention may be
modified to include a feedback system to dynamically and instantaneously
adjust the operation of the apparatus in response to air currents,
humidity and altitude changes, and user/operator preferences. In the case
of photothermoacoustic applications, the feedback system is designed to be
capable of fast frequency response and typically utilizes infrared
sensors. Such a system is illustrated in FIGS. 2A and 2B. The
photothermoacoustic sound generation device 200 illustrated in FIGS. 2A
and 2B is similar to the apparatus 100 shown in FIG. 1. Accordingly, only
the major differences between the two systems are labelled in FIGS. 2A and
2B and discussed herein.
Referring now to FIGS. 2A and 2B, therein is shown a three dimensional
sound generation apparatus including a sensor 230 for monitoring the
focused sound field output of the x, y and z axis lasers. Sensor 230 may
be a microphone or other sensor capable of detecting the focused sound
field. Alternatively, it may be an infrared detector that picks up the
infrared energy focused at the sensor by the lasers, which energy is
related to the heat, and thus, the sound generated at the sensor.
The output of sensor 230 is input to feedback module 240 which provides
appropriate control signals to control module 242. Control module 242 is
used to adjust the input audio signal, e.g., from function generator 252,
phono 254, VCR 256, tuner 258, or any other appropriate audio input
source. RF generator 250 is used to generate the radio frequency carrier
signal which is then modulated by the signals from function generator 252.
Control module 242 controls the amount of audio and/or function generator
252 signals injected into the system; control the phase, frequency and
amplitude of each of the subcarriers from the RF generator; and facilitate
the size and location of the sound field. It should be noted that the
output signal from sensor 230 is a three channel composite signal
conveying information about the x, y and z axes. Also, feedback module 240
is connected directly to RF generator 250. Feedback module 240 is also
connected to preamplifier/mixer 244 in order to correct any detected audio
frequency drift.
According to an alternative embodiment, the present invention may be used
to controllably heat and cool a gas to thereby provide mechanical energy
or force. The controlled heating and cooling of the gas may be used to
establish standing waves. These standing waves may be static and
stationary, in that despite ongoing propagation of sound, there exists in
a given space close to the source, molecular pressure zones created by the
regular peaks and valleys of the standing wave. The standing waves may
thus be used as sound barriers or even physical barriers. In the case of a
physical barrier, the standing wave is created with sufficient energy to
counteract the opposing mechanical force. In this manner,
photothermoacoustic levitation may be achieved by creating a counteracting
force equal and opposite to the gravitational force acting on a body.
Similarly, if the standing wave is created with sufficient energy greater
than the opposing mechanical force, then photothermoacoustic propulsion or
motion may be achieved. For example, once the gravitational and frictional
forces are negated, propulsive force may be applied in order to set and
maintain an object in motion.
The magnitude of the levitation force may be calculated using certain
applicable laws of thermodynamics. The gas in which an object is to be
levitated or propelled according to the present invention may be a gas,
such as air. At ambient conditions, air is known to behave in a manner
characteristic of an ideal gas, the concept of which greatly simplifies
the prediction of gas behavior over broad ranges of temperature and
pressure.
Ideal gas theory is based upon certain assumptions about the physical
nature of a gas, including: (1) that the molecules which make up the gas
are identical and in a stable state; (2) the molecules may be modeled as
hard spheres which obey Newton's laws of motion; (3) the total number of
molecules is large, with the resulting large number of intermolecular
collisions maintaining the overall distribution of molecular velocities
and the randomness of the motion; (4) the volume of the molecules is a
negligibly small fraction of the total volume occupied by the gas, a
plausible assumption given the fact that gas volumes may be changed
through a large range of values with little difficulty, and that when a
gas condenses the volume occupied by the liquid may be thousands of times
smaller than that occupied by the gas; (5) no appreciable forces act on
the molecules except during a collision; and that (6) intermolecular
collisions and collisions with the walls of any container are completely
elastic, thereby conserving molecular momentum and kinetic energy.
Using these basic assumptions of ideal gas theory, the following equation
can be derived, which relates gas pressure P, gas density p, and the
molecular root-mean-square speed or average molecular speed V.sub.rms :
P=1/3.rho.V.sup.2.sub.rms (2)
Since the average molecular speed is not a readily measurable macroscopic
quantity, additional thermodynamic equations are required to readily solve
for the pressure P. One such equation is the following expression for RMS
particle velocity in an ideal gas:
##EQU1##
where the Boltzmann constant k=1.38.times.10.sup.-23
J/molecule.multidot.K, T is the absolute temperature in Kelvin, and m is
the mass of a single molecule in kilograms.
The internal energy U of an ideal gas is also related to temperature
according to the following relationship:
U=3/2NkT (4)
where k is the Boltzmann constant identified above, U is the internal
energy of the gas in Joules, N is the number of gas molecules, and T is
the temperature in Kelvin.
Combining the above expressions for V.sub.rms and U (Eqs. 3 and 4) yields:
##EQU2##
Combining P=1/3.rho.V.sup.2.sub.rms (Eq. 2) and V.sub.rms =.sqroot. (2
U/mN) (Eq. 5), the resulting equation is:
P=2/3(.rho.U/mN) (6)
However, since the gas density .rho.=(Nm/V), where N is the number of
molecules, m is the mass per molecule, and V is the volume occupied by the
gas, the following equation relating pressure P, internal energy U, and
gas volume V can be formulated:
P=2/3(U/V) (7)
Equation 7 is useful in that it yields the energy requirements for any
desired pressure increase. As an example of the use of Equation 7, assume
that it is desired to increase the pressure of 1 cubic millimeter of air
from one atmosphere to five atmospheres. Solving the equation for internal
energy U, and using P.sub.i and P.sub.f to represent the initial and final
pressures, respectively, the energy required for this pressure increase
may be calculated as follows:
.DELTA.U=3/2(P.sub.f -P.sub.i)V=3/2›(5-1).times.10.sup.5
pascals!.multidot.›1.times.10.sup.-9 m.sup.3 ! or .DELTA.U=0.6
milliJoules/cubic millimeter
With absorption spectra in multiple bands approaching 100%, the addition of
the above amount of energy should produce the desired pressure increase.
The levitation of objects which may vary widely in mass, and hence weight,
requires the application of a pressure of sufficient magnitude. The
desired pressure should be sufficient to allow the object to be lifted off
the ground without resulting in an excessive and uncontrolled vertical
acceleration. Determination of the required pressure may be accomplished
by performing a force balance on a disk-shaped volume which, for
illustrative purposes, will serve as an example of an object to be
levitated. The relevant characteristics of the disk are its volume V,
circular face area A, thickness t, and mass density .rho..sub.m. The
pressure which gives rise to the net force on the lower surface of the
object shall be designated as P.sub.net. The derivation of an expression
for the required levitation pressure P.sub.net begins with the following
equation relating disk mass and density. Specifically, the mass is
equivalent to the product of mass density, .rho..sub.m and volume, V or tA
:
m=.rho..sub.m V=.rho..sub.m tA (8)
To accomplish levitation, the net vertical force exerted by the pressurized
air under the object must be greater than the object's weight in order to
overcome the gravitational force acting on the object. The relationship
between these forces may be expressed mathematically as follows,
incorporating the definition of pressure as force per unit area, or P=F/A,
and taking into account that weight is equal to the product of mass and
the local acceleration due to gravity:
P.sub.net A>mg (9)
Incorporating Equation 8 yields:
P.sub.net A>.rho..sub.m tAg (10)
or by canceling area:
P.sub.net >.rho..sub.m tg (11)
where g=9.81 m/sec.sup.2 is the local acceleration due to gravity. The
result is an expression for the minimum pressure required to levitate an
object of a given mass density and thickness, independent of surface area.
The required pressure is independent of surface area since the same
pressure must be applied to the entire surface regardless of its area. For
example, if the disk is 0.01 meters thick, has a circular face area of 0.1
m.sup.2, and is made of stainless steel having a mass density of
.rho..sub.m =8,000 kg/m.sup.3, then according to Equation 11, the net
pressure is:
P.sub.net >(8.times.10.sup.3 kg/m.sup.3)(0.01 m)(9.81 m/sec.sup.2)
P.sub.net >7.85.times.10.sup.2 Pascals(N/m.sup.2)
In the earlier example discussed above, it was determined that an energy
input of approximately 0.6 mJ/mm.sup.3 would produce a P.sub.net of
4.times.10.sup.5 Pascals, or more than five hundred times that required to
lift the object.
Energy requirements for levitation, in contrast to pressure requirements,
are dictated by the lower surface area of the object. The relationship
between surface area and required energy input may be derived by
considering the amount of work done in lifting an object to a particular
height. The most general definition of mechanical work, which allows for
variation in both force and direction of travel, may be expressed
mathematically in vector notation as follows:
##EQU3##
This equation yields a value for the amount of work W.sub.AB done by a
force F while moving an object along a displacement vector r from point A
to point B. In the present invention, the relevant displacement for
calculating the work done in lifting an object is the vertical
displacement, designated as y. Since the levitation force is also aligned
vertically, the vector Equation 12 simplifies to the following scalar
equation, with the levitation force F expressed as a function of vertical
displacement y:
##EQU4##
The levitation force F(y) is equal to the product of the net pressure under
the object, P.sub.net, and the object's circular face area A, which is
constant. The limits of integration are y=0, representing the object at
rest on the ground, and y=h, which will represent its final levitation
height. Making the appropriate substitutions into Equation 13, and using
W.sub.lev to denote the work done in levitating the object, yields:
##EQU5##
Since area A is constant, Equation 14 becomes:
##EQU6##
Equation 15 shows that the work performed, and hence the energy required,
to levitate an object is directly proportional to its lower surface area.
The process of levitating an object from the ground to assume some desired
equilibrium (motionless and unaccelerated) height h will require that the
levitation force F(y)=P.sub.net (y)A vary in magnitude from a value
slightly above the object's weight to a value slightly below the object's
weight, before settling at a magnitude equal to the object's weight when
height y=h has been achieved. A plot of the desired variation of
levitation force as a function of vertical displacement is shown in FIG.
7. The force-displacement curve of FIG. 7 should provide slight
accelerations and, hence, the desired level of control during the process
of levitation. The initial increase in the levitation force F(y) is
required to lift the object off the ground, after which F(y) settles to a
value equal to the object's weight to ensure a constant velocity during
the process of levitation. Shortly before reaching the desired height h,
the levitation force is decreased to a value slightly below the object's
weight in order to decelerate the object to zero velocity. At y=h, the
object hovers motionless in a condition of equilibrium between weight and
levitation force.
Continuing with the example discussed above, assume a disk volume of 0.001
m.sup.3 and an average levitation force equal to the object's weight (a
reasonable approximation based on the above discussion). Using .eta. to
denote the working efficiency of the device, the energy required to
levitate the stainless steel disk to a height of 2 meters, assuming
.eta.=0.5, is as follows:
##EQU7##
Substitution into Equation 16 results in:
E.sub.lev =(1/0.5)(8000 kg/m.sup.3)(0.01 m)(0.1 m.sup.2)(9.81
m/sec.sup.2)(2 m)
E.sub.lev =3.139.times.10.sup.2 J or 313.9 J
The assumed working efficiency of the device is 50%. Given an energy input
of 313.9 J, the device will levitate the 8 kg stainless steel disk to a
height of 2 meters. The volume of air which is heated under the object to
be levitated corresponds in shape to the surface area of the object times
a height of up to approximately 500 millimeters.
A sound barrier may be created in accordance with the present invention by
surrounding a noise source with high pressure zones which sufficiently
impede the propagation of sound waves emanating from the sound source.
While the invention has been particularly shown and described with
reference to a preferred embodiment thereof, it will be understood by
those skilled in the an that various changes in form and details may be
made therein without departing from the spirit and scope of the invention.
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