# Vacuum airship

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 displacement lift power.

## History

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.[2] De Bausset published a book on his design[3] and offered \$150,000 stock in the Transcontinental Aerial Navigation Company of Chicago.[4][5] 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."[6]

In 1921, Lavanda Armstrong discloses 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, however leaving some uncertainty how to achieve adequate buoyancy given "walls may be made as thick and strong as desired".[7]

In 1983, David Noel discussed the use of geodesic sphere covered with plastic film and "a double balloon containing pressurized air between the skins, and a vacuum in the centre".[8]

In 1982-1985 Emmanuel Bliamptis elaborated on energy sources and use of "inflatable strut rings".[9]

In 2004-2007 Akhmeteli and Gavrilin address choice of materials ("beryllium, boron carbide ceramic, and diamond-like carbon" or aluminum) in honeycomb double layer craft to address buckling issues.[10]

## Principle

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 helium gas with a near-vacuum environment and 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 however is that with a near-vacuum inside the airbag, the atmospheric pressure would exert enormous forces on the airbag, causing it to collapse if not supported. Though it is possible to reinforce the airbag with an internal structure, it is theorized that any structure strong enough to withstand the forces would invariably weigh the vacuum airship down and exceed the total lift capacity of the airship, preventing flight.[citation needed]

## Material constraints

From the analysis by Akhmeteli and Gavrilin:[10]

The total force on a hemi-spherical shell of radius ${\displaystyle R}$ by an external pressure ${\displaystyle P}$ is ${\displaystyle \pi R^{2}P}$. Since the force on each hemisphere has to balance along the equator the compressive stress will be

${\displaystyle \sigma =\pi R^{2}P/2\pi Rh=RP/2h}$

where ${\displaystyle h}$ is the shell thickness.

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

${\displaystyle \sigma =(3/2)(\rho _{s}/\rho _{a})P}$.

For aluminum and terrestrial conditions Akhmeteli and Gavrilin estimate the stress as ${\displaystyle 3.2\cdot 10^{8}}$ Pa, of the same order of magnitude as the compressive strength of aluminum alloys. Akhmeteli and Gavrilin note, however, that this disregards buckling, and using R. Zoelli's formula for the critical buckling pressure of a sphere

${\displaystyle P_{cr}={\frac {2Eh^{2}}{\sqrt {3(1-\mu ^{2})}}}{\frac {1}{R^{2}}}}$

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

${\displaystyle E/\rho _{s}^{2}={\frac {9P_{cr}{\sqrt {3(1-\mu ^{2})}}}{2\rho _{a}^{2}}}}$

The requirement is about ${\displaystyle 4.5\cdot 10^{5}kg^{-1}m^{5}s^{-2}}$.

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

## Atmospheric constraints

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 ${\displaystyle k_{\rm {L}}<{\sqrt {1-{\frac {P_{\rm {int}}}{P}}}}\cdot L_{\rm {a}}}$, where ${\displaystyle P_{\rm {int}}}$ is pressure within the sphere, while ${\displaystyle k_{\rm {L}}}$ («Lana coefficient») and ${\displaystyle L_{\rm {a}}}$ («Lana atmospheric ratio») are:[11]

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

where ${\displaystyle P_{\rm {atm}}=101325}$ ${\displaystyle Pa}$ and ${\displaystyle \rho _{\rm {atm}}=1.22}$ ${\displaystyle kg/m^{3}}$ are pressure and density of standard Earth atmosphere at sea level, ${\displaystyle M_{a}}$ and ${\displaystyle T_{a}}$ 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 ${\displaystyle L_{\rm {a}}}$ big enough to surpass ${\displaystyle k_{\rm {L}}}$ for such materials as some composites (below altitude of ca. 15 km) and graphene (below altitude of ca. 40 km). Both materials may survive in the Venusian atmosphere. The equation for ${\displaystyle L_{\rm {a}}}$ shows that exoplanets with dense, cold and high-molecular (${\displaystyle CO_{2}}$, ${\displaystyle O_{2}}$, ${\displaystyle N_{2}}$ type) atmospheres may be suitable for vacuum airships, but it is a rare type of atmosphere.

## In Fiction

In Passarola Rising, novelist Azhar Abidi imagines what might have happened had Bartolomeu de Gusmão 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.

## References

1. ^ "Francesco Lana-Terzi, S.J. (1631-1687); The Father of Aeronautics". Retrieved 13 November 2009.
2. ^ 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.
3. ^ De Bausset, Arthur (1887). Aerial Navigation. Chicago: Fergus Printing Co. Retrieved 2010-12-01.
4. ^ "Aerial Navigation" (PDF). New York Times. February 14, 1887. Retrieved 2010-12-01.
5. ^ "To Navigate the Air" (PDF). New York Times. February 19, 1887. Retrieved 2010-12-01.
6. ^ Mitchell (Commissioner) (1891). Decisions of the Commissioner of Patents for the Year 1890. US Government Printing Office. p. 46. 50 O. G., 1766
7. ^ US patent 1390745, Lavanda M Armstrong, "Aircraft of the lighter-than-air type", published Sep 13, 1921, assigned to Lavanda M Armstrong
8. ^ David Noel (1983). "Lighter than Air Craft Using Vacuum" (PDF). Correspondence, Speculations in Science and Technology. 6 (3): 262–266.
9. ^ US patent 4534525, Emmanuel Bliamptis, "Evacuated balloon for solar energy collection", published Aug 13, 1985, assigned to Emmanuel Bliamptis
10. ^ a b c 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
11. ^ E. Shikhovtsev (2016). "Is FLanar Possible?". Retrieved 2016-06-19.