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  *  
    (Top)
  *  
    1History
    Toggle History subsection
      +  
        1.1Double wall fallacy
      +  
        1.221st Century
  *  
    2Principle
  *  
    3Material constraints
    Toggle Material constraints subsection
      +  
        3.1Compressive strength
      +  
        3.2Buckling
  *  
    4Atmospheric constraints
  *  
    5In fiction
  *  
    6See also
  *  
    7References
  *  
    8Further reading

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Vacuum airship

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From Wikipedia, the free encyclopedia
Hypothetical airship concept
[220px-Flying_boat]Francesco Lana de Terzi's flying boat concept
c.1670

A vacuum airship, also known as a vacuum balloon, is a hypothetical
airship that is evacuated rather than filled with a lighter-than-air
gas such as hydrogen or helium. First proposed by Italian Jesuit
priest Francesco Lana de Terzi in 1670,^[1] the vacuum balloon would
be the ultimate expression of lifting power per volume displaced.
(Also called "FLanar", combination of F. Lana and the Portuguese word
"flanar," which means wandering.^[2])

History[edit]

From 1886 to 1900 Arthur De Bausset attempted in vain to raise funds
to construct his "vacuum-tube" airship design, but despite early
support in the United States Congress, the general public was
skeptical. Illinois historian Howard Scamehorn reported that Octave
Chanute and Albert Francis Zahm "publicly denounced and
mathematically proved the fallacy of the vacuum principle"; however,
the author does not give his source.^[3] De Bausset published a book
on his design^[4] and offered $150,000 stock in the Transcontinental
Aerial Navigation Company of Chicago.^[5]^[6] His patent application
was eventually denied on the basis that it was "wholly theoretical,
everything being based upon calculation and nothing upon trial or
demonstration."^[7]

Double wall fallacy[edit]

In 1921, Lavanda Armstrong disclosed a composite wall structure with
a vacuum chamber "surrounded by a second envelop constructed so as to
hold air under pressure, the walls of the envelope being spaced from
one another and tied together", including a honeycomb-like cellular
structure.^[8]

In 1983, David Noel discussed the use of a geodesic sphere covered
with plastic film and "a double balloon containing pressurized air
between the skins, and a vacuum in the centre".^[9]

In 1982-1985 Emmanuel Bliamptis elaborated on energy sources and use
of "inflatable strut rings".^[10]

However, the double-wall design proposed by Armstrong, Noel, and
Bliamptis would not have been buoyant. In order to avoid collapse,
the air between the walls must have a minimum pressure (and therefore
also a density) proportional to the fraction of the total volume
occupied by the vacuum section, preventing the total density of the
craft from being less than the surrounding air.

21st Century[edit]

In 2004-2007, to address strength to weight ratio issues, Akhmeteli
and Gavrilin addressed choice of four materials, specifically I220H
beryllium (elemental 99%), boron carbide ceramic, diamond-like carbon
, and 5056 Aluminum alloy (94.8% Al, 5% Mg, 0.12% Mn, 0.12%Cr) in a
honeycomb double layer.^[11] In 2021, they extended this research; a
"finite element analysis was employed to demonstrate that buckling
can be prevented", focusing on a "shell of outer radius R > 2.11 m
containing two boron carbide face skins of thickness 4.23 x 10^-5 R
each that are reliably bonded to an aluminum honeycomb core of
thickness 3.52 x 10^-3 R".^[12] At least two papers (in 2010 and
2016) have discussed the use of graphene as an outer membrane.^[2]^
[13]

Principle[edit]

An airship operates on the principle of buoyancy, according to
Archimedes' principle. In an airship, air is the fluid in contrast to
a traditional ship where water is the fluid.

The density of air at standard temperature and pressure is 1.28 g/L,
so 1 liter of displaced air has sufficient buoyant force to lift 1.28
g. Airships use a bag to displace a large volume of air; the bag is
usually filled with a lightweight gas such as helium or hydrogen. The
total lift generated by an airship is equal to the weight of the air
it displaces, minus the weight of the materials used in its
construction, including the gas used to fill the bag.

Vacuum airships would replace the lifting gas with a near-vacuum
environment. Having no mass, the density of this body would be near
to 0.00 g/L, which would theoretically be able to provide the full
lift potential of displaced air, so every liter of vacuum could lift
1.28 g. Using the molar volume, the mass of 1 liter of helium (at 1
atmospheres of pressure) is found to be 0.178 g. If helium is used
instead of vacuum, the lifting power of every liter is reduced by
0.178 g, so the effective lift is reduced by 14%. A 1-liter volume of
hydrogen has a mass of 0.090 g.

The main problem with the concept of vacuum airships is that, with a
near-vacuum inside the airbag, the exterior atmospheric pressure is
not balanced by any internal pressure. This enormous imbalance of
forces would cause the airbag to collapse unless it were extremely
strong (in an ordinary airship, the force is balanced by the pressure
of the lifting gas, making this unnecessary). Thus the difficulty is
in constructing an airbag with the additional strength to resist this
extreme net force, without weighing the structure down so much that
the greater lifting power of the vacuum is negated.^[2]^[11]

Material constraints[edit]

Compressive strength[edit]

From the analysis by Akhmeteli and Gavrilin:^[11]

The total force on a hemi-spherical shell of radius R R R by an
external pressure P P P is p R 2 P \pi R^{2}P \pi R^2 P. Since the
force on each hemisphere has to balance along the equator, assuming h
<< R {\displaystyle h<<R} {\displaystyle h<<R} where h h h is the
shell thickness, the compressive stress ( s \sigma \sigma ) will be:

    s = p R 2 P / 2 p R h = R P / 2 h \sigma =\pi R^{2}P/2\pi Rh=RP/
    2h \sigma = \pi R^2 P / 2 \pi R h = R P / 2 h

Neutral buoyancy occurs when the shell has the same mass as the
displaced air, which occurs when h / R = r a / ( 3 r s ) h/R=\rho _
{a}/(3\rho _{s}) h/R = \rho_a/(3 \rho_s), where r a \rho _{a} \rho_a
is the air density and r s \rho _{s} \rho_s is the shell density,
assumed to be homogeneous. Combining with the stress equation gives

    s = ( 3 / 2 ) ( r s / r a ) P \sigma =(3/2)(\rho _{s}/\rho _{a})P
    \sigma = (3/2)(\rho_s/\rho_a)P.

For aluminum and terrestrial conditions Akhmeteli and Gavrilin
estimate the stress as 3.2 [?] 10 8 3.2\cdot 10^{8} 3.2\cdot 10^8 Pa,
of the same order of magnitude as the compressive strength of
aluminum alloys.

Buckling[edit]

Akhmeteli and Gavrilin note, however, that the compressive strength
calculation disregards buckling, and using R. Zoelli's formula for
the critical buckling pressure of a sphere

    P c r = 2 E h 2 3 ( 1 - m 2 ) 1 R 2 P_{cr}={\frac {2Eh^{2}}{\sqrt
    {3(1-\mu ^{2})}}}{\frac {1}{R^{2}}} P_{cr} = \frac{2Eh^2}{\sqrt{3
    (1-\mu^2)}}\frac{1}{R^2}

where E E E is the modulus of elasticity and m \mu \mu is the Poisson
ratio of the shell. Substituting the earlier expression gives a
necessary condition for a feasible vacuum balloon shell:

    E / r s 2 = 9 P c r 3 ( 1 - m 2 ) 2 r a 2 E/\rho _{s}^{2}={\frac
    {9P_{cr}{\sqrt {3(1-\mu ^{2})}}}{2\rho _{a}^{2}}} E/\rho_s^2 = \
    frac{9P_{cr}\sqrt{3(1-\mu^2)}}{2\rho_a^2}

The requirement is about 4.5 [?] 10 5 k g - 1 m 5 s - 2 4.5\cdot 10^{5}
kg^{-1}m^{5}s^{-2} 4.5\cdot10^5 kg^{-1} m^5 s^{-2}.

Akhmeteli and Gavrilin assert that this cannot even be achieved using
diamond ( E / r s 2 [?] 1 [?] 10 5 E/\rho _{s}^{2}\approx 1\cdot 10^{5} E
/\rho_s^2 \approx 1\cdot 10^5), and propose that dropping the
assumption that the shell is a homogeneous material may allow lighter
and stiffer structures (e.g. a honeycomb structure).^[11]

Atmospheric constraints[edit]

A vacuum airship should at least float (Archimedes law) and resist
external pressure (strength law, depending on design, like the above
R. Zoelli's formula for sphere). These two conditions may be
rewritten as an inequality where a complex of several physical
constants related to the material of the airship is to be lesser than
a complex of atmospheric parameters. Thus, for a sphere (hollow
sphere and, to a lesser extent, cylinder are practically the only
designs for which a strength law is known) it is k L < 1 - P i n t P
[?] L a {\displaystyle k_{\rm {L}}<{\sqrt {1-{\frac {P_{\rm {int}}}
{P}}}}\cdot L_{\rm {a}}} {\displaystyle k_{\rm {L}}<{\sqrt {1-{\frac
{P_{\rm {int}}}{P}}}}\cdot L_{\rm {a}}}, where P i n t {\displaystyle
P_{\rm {int}}} {\displaystyle P_{\rm {int}}} is pressure within the
sphere, while k L {\displaystyle k_{\rm {L}}} {\displaystyle k_{\rm
{L}}} (<<Lana coefficient>>) and L a {\displaystyle L_{\rm {a}}} {\
displaystyle L_{\rm {a}}} (<<Lana atmospheric ratio>>) are:^[2]

    k L = 2.79 [?] r s r a t m [?] P a t m E [?] ( 1 - m 2 ) 0.25 {\
    displaystyle k_{\rm {L}}=2.79\cdot {\frac {\rho _{s}}{\rho _{\rm
    {atm}}}}\cdot {\sqrt {\frac {P_{\rm {atm}}}{E}}}\cdot (1-\mu ^
    {2})^{0.25}} {\displaystyle k_{\rm {L}}=2.79\cdot {\frac {\rho _
    {s}}{\rho _{\rm {atm}}}}\cdot {\sqrt {\frac {P_{\rm {atm}}}{E}}}\
    cdot (1-\mu ^{2})^{0.25}} (or, when m \mu \mu is unknown, k L [?]
    2.71 [?] r s r a t m [?] P a t m E {\displaystyle k_{\rm {L}}\approx
    2.71\cdot {\frac {\rho _{s}}{\rho _{\rm {atm}}}}\cdot {\sqrt {\
    frac {P_{\rm {atm}}}{E}}}} {\displaystyle k_{\rm {L}}\approx 2.71
    \cdot {\frac {\rho _{s}}{\rho _{\rm {atm}}}}\cdot {\sqrt {\frac
    {P_{\rm {atm}}}{E}}}} with an error of order of 3% or less);
    L a = r a r a t m [?] P a t m P {\displaystyle L_{\rm {a}}={\frac
    {\rho _{a}}{\rho _{\rm {atm}}}}\cdot {\sqrt {\frac {P_{\rm
    {atm}}}{P}}}} {\displaystyle L_{\rm {a}}={\frac {\rho _{a}}{\rho
    _{\rm {atm}}}}\cdot {\sqrt {\frac {P_{\rm {atm}}}{P}}}} (or, when
    r a \rho _{a} \rho_a is unknown, L a = 10 [?] P a t m P [?] M a T a
    {\displaystyle L_{\rm {a}}=10\cdot {\sqrt {\frac {P_{\rm {atm}}}
    {P}}}\cdot {\frac {M_{a}}{T_{a}}}} {\displaystyle L_{\rm {a}}=10\
    cdot {\sqrt {\frac {P_{\rm {atm}}}{P}}}\cdot {\frac {M_{a}}{T_
    {a}}}}),

where P a t m = 101325 {\displaystyle P_{\rm {atm}}=101325} {\
displaystyle P_{\rm {atm}}=101325} P a {\displaystyle Pa} {\
displaystyle Pa} and r a t m = 1.22 {\displaystyle \rho _{\rm {atm}}=
1.22} {\displaystyle \rho _{\rm {atm}}=1.22} k g / m 3 kg/m^{3} kg/m^
{3} are pressure and density of standard Earth atmosphere at sea
level, M a M_{a} M_a and T a T_{a} T_{a} are molar mass (kg/kmol) and
temperature (K) of atmosphere at floating area. Of all known planets
and moons of the Sun system only the Venusian atmosphere has L a {\
displaystyle L_{\rm {a}}} {\displaystyle L_{\rm {a}}} big enough to
surpass k L {\displaystyle k_{\rm {L}}} {\displaystyle k_{\rm {L}}}
for such materials as some composites (below altitude of ca. 15 km)
and graphene (below altitude of ca. 40 km).^[2] Both materials may
survive in the Venusian atmosphere. The equation for L a {\
displaystyle L_{\rm {a}}} {\displaystyle L_{\rm {a}}} shows that
exoplanets with dense, cold and high-molecular ( C O 2 CO_{2} CO_{2},
O 2 O_{2} O_{2}, N 2 N_{2} N_{2} type) atmospheres may be suitable
for vacuum airships, but it is a rare type of atmosphere.

In fiction[edit]

In Edgar Rice Burroughs's novel Tarzan at the Earth's Core, Tarzan
travels to Pellucidar in a vacuum airship constructed of the
fictional material Harbenite.

In Passarola Rising, novelist Azhar Abidi imagines what might have
happened had Bartolomeu de Gusmao built and flown a vacuum airship.

Spherical vacuum body airships using the Magnus effect and made of
carbyne or similar superhard carbon are glimpsed in Neal Stephenson's
novel The Diamond Age.

In Maelstrom^[14] and Behemoth:B-Max, author Peter Watts describes
various flying devices, such as "botflies" (named after the botfly)
and "lifters" that use "vacuum bladders" to keep them airborne.

In Feersum Endjinn by Iain M. Banks, a vacuum balloon is used by the
narrative character Bascule in his quest to rescue Ergates. Vacuum
dirigibles (airships) are also mentioned as a notable engineering
feature of the space-faring utopian civilisation The Culture in
Banks' novel Look to Windward, and the vast vacuum dirigible
Equatorial 353 is a pivotal location in the final Culture novel, The
Hydrogen Sonata.

See also[edit]

  * Aerostat

References[edit]

 1. ^ "Francesco Lana-Terzi, S.J. (1631-1687); The Father of
    Aeronautics". Archived from the original on 24 April 2021.
    Retrieved 13 November 2009.
 2. ^ ^a ^b ^c ^d ^e E. Shikhovtsev (2016). "Is FLanar Possible?".
    Retrieved 2016-06-19.
 3. ^ Scamehorn, Howard Lee (2000). Balloons to Jets: A Century of
    Aeronautics in Illinois, 1855-1955. SIU Press. pp. 13-14. ISBN 
    978-0-8093-2336-4.
 4. ^ De Bausset, Arthur (1887). Aerial Navigation. Chicago: Fergus
    Printing Co. Retrieved 2010-12-01.
 5. ^ "Aerial Navigation" (PDF). New York Times. February 14, 1887.
    Retrieved 2010-12-01.
 6. ^ "To Navigate the Air" (PDF). New York Times. February 19, 1887.
    Retrieved 2010-12-01.
 7. ^ Mitchell (Commissioner) (1891). Decisions of the Commissioner
    of Patents for the Year 1890. US Government Printing Office.
    p. 46. `50 O. G., 1766'
 8. ^ US patent 1390745, Lavanda M Armstrong, "Aircraft of the
    lighter-than-air type", published Sep 13, 1921, assigned to
    Lavanda M Armstrong 
 9. ^ David Noel (1983). "Lighter than Air Craft Using Vacuum" (PDF).
    Correspondence, Speculations in Science and Technology. 6 (3):
    262-266.
10. ^ US patent 4534525, Emmanuel Bliamptis, "Evacuated balloon for
    solar energy collection", published Aug 13, 1985, assigned to
    Emmanuel Bliamptis 
11. ^ ^a ^b ^c ^d US application 2007001053, AM Akhmeteli, AV
    Gavrilin, "US Patent Application 11/517915. Layered shell vacuum
    balloons", published Feb 23, 2006, assigned to Andrey M Akhmeteli
    and Andrey V Gavrilin 
12. ^ Akhmeteli, A.; Gavrilin, A.V. (2021). "Vacuum Balloon-A
    350-Year-Old Dream". Eng. 2 (4): 480-491. doi:10.3390/eng2040030.
    {{cite journal}}: CS1 maint: multiple names: authors list (link)
13. ^ Zornes, David (2010). "Vacua Buoyancy Is Provided by a Vacuum
    Bag Comprising a Vacuum Membrane Film Wrapped Around a
    Three-Dimensional (3D) Frame to Displace Air, on Which 3D
    Graphene "Floats" a First Stack of Two-Dimensional Planar Sheets
    of Six-Member Carbon Atoms Within the Same 3D Space as a Second
    Stack of Graphene Oriented at a 90-Degree Angle". SAE
    International. SAE Technical Paper Series. 1. doi:10.4271/
    2010-01-1784.
14. ^ Watts, Peter. "Maelstrom by Peter Watts". Rifters.com.

Further reading[edit]

  * Alfred Hildebrandt (1908). Airships Past and Present: Together
    with Chapters on the Use of Balloons in Connection with
    Meteorology, Photography and the Carrier Pigeon. D. Van Nostrand
    Company. pp. 16-.
  * Collins, Paul (2009). "The rise and fall of the metal airship".
    New Scientist. 201 (2690): 44-45. Bibcode:2009NewSc.201...44C.
    doi:10.1016/S0262-4079(09)60106-8. ISSN 0262-4079.
  * Timothy Ferris (2000). Life Beyond Earth. Simon and Schuster.
    pp. 130-. ISBN 978-0-684-84937-9.
  * Le defi de Cyrano ; un ballon gonfle avec du vide : Fabrice David

*
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