\section{Other ways of staying up}
\subsection{Airships}
This chapter has emphasized that planes can't be made more energy-efficient
\marginfig{
\begin{center}
\begin{tabular}{@{}c@{}}
{\mbox{\epsfxsize=53mm\epsfbox{../../images/Akron.eps}}}\\
%{\mbox{\epsfxsize=53mm\epsfbox{../../images/Spirit.eps}}}\\
\end{tabular}
\end{center}
\caption[a]{
The 239\,m-long \ind{USS Akron} (ZRS-4) flying over Manhattan.
It weighed 100\,t and could carry 83\,t.
Its engines had a total power of 3.4\,MW, and it could transport 89
personnel and a stack of weapons
at 93\,km/h. It was also used as an aircraft carrier.
% speed 93 km/h range 20,000 km?! 133 km/h maximum
% 8x420kW
% akron was helium filled.
% Spirit of Dubai; photo by Arnold Nayler.
}
}
by slowing them down, because any benefit from reduced air-resistance
is more than cancelled by having to
chuck air down harder. Can this problem be solved by
switching strategy: not throwing air down, but being as light
as air instead?
An \ind{airship}, \ind{blimp}, \ind{zeppelin},
or \ind{dirigible}
uses an enormous \ind{helium}-filled
\ind{balloon}, which is lighter than air,
to counteract the weight of its little cabin.
The disadvantage of this strategy is that the enormous balloon
greatly increases the air resistance of the vehicle.
The way to keep the energy cost of an airship (per weight, per distance)
low is to move slowly, to be fish-shaped, and to be very large and long.
Let's work out a cartoon of the energy required by an idealized airship.
% L = 2R R = L/2
\newcommand{\blimpL}{\ensuremath{L}}
I'll assume the balloon is ellipsoidal, with cross-sectional
area $A$ and length $\blimpL$.
\marginfig{
\mbox{\epsfbox{metapost/blimp.55}}
\caption[a]{An ellipsoidal airship.
}
\label{fig.blimp0}
}%
The volume is $V= \frac{2}{3} A \blimpL$. If the airship floats stably
in air of density $\rho$, the total mass
of the airship, including its cargo and its helium, must be
$m_{\rm total} = \rho V$.
If it moves at speed $v$, the force of air resistance is
\beq
F = \frac{1}{2} \cd A \rho v^2 ,
\eeq
where $\cd$ is the drag coefficient, which, based on aeroplanes, we
might expect to be about 0.03.
The energy expended, per unit distance, is equal to $F$ divided
by the efficiency $\epsilon$ of the engines.
So the gross
transport cost -- the energy used per unit distance per unit mass --
is
\beqan
\frac{F}{ \epsilon m_{\rm total}}& =& \frac{ \frac{1}{2} \cd A \rho v^2 }
{ \epsilon \rho \frac{2}{3} A \blimpL }
\\
&=& \frac{3}{4 \epsilon } \cd \frac{ v^2 }
{ \blimpL }
\eeqan
That's a rather nice result!
The gross transport cost of this idealized airship depends only on its
speed $v$ and length $\blimpL$, not on the density $\rho$
of the air, nor on the airship's frontal area $A$.
This cartoon also applies without modification to \ind{submarine}s.
The gross transport cost (in kWh per ton-km)
of an airship is just the same as the gross transport
cost of a submarine of identical length and speed. The submarine will
contain 1000 times more mass, since water is 1000
times denser than air; and it will cost 1000 times more to
move it along. The only difference between the two will be the advertising
revenue.
So, let's plug in some numbers.
Let's assume we desire to travel at a speed of 80\,km/h (so that
crossing the Atlantic takes three days). In SI units, that's 22\,m/s.
Let's assume an efficiency $\epsilon$ of $1/4$.
To get the best possible transport cost, what is
% 80km/h is 22.2m/s
the longest blimp we can imagine?
The Hindenburg was 245\,m long.
% and was powered by 4400hp.
If we say $\blimpL = 400$\,m,
we find the transport cost is:
\[%beqan
\frac{F}{ \epsilon m_{\rm total}}
% &=& \frac{3}{4 \epsilon } \cd \frac{ v^2 }
% { \blimpL }
\:=\: {3} \times 0.03 \frac{ (22\,\m/\s)^2 }
{ 400\,\m } \:=\: 0.1\,\m/\s^2
% 0.1089
\:=\: \eccol{0.03\,\mbox{kWh/\tkm}}.
% 0.03025
\]%eeqan
% 1\,kWh/\tkm & 3.6\,m/s$^2$
If useful cargo made up half of the vessel's mass, the
net transport cost of this monster airship
would be \eccol{0.06\,\mbox{kWh/\tkm}} -- similar to rail.
% Triton, longest submarine: 136.4 m
% Top speed, submerged: 50 km/h.
% 172 crew.
% Displacement 7773\,t when submerged.
% According to the cartoon,
% 13.9m/s
% 3* 0.03 * 13.9**2 / 136.4
% 0.13\,m/s$^2$, or 0.035\,kWh/\tkm.
% http://news.bbc.co.uk/1/hi/sci/tech/769642.stm
% cargolifter is meant to carry 160 t at 100 km/h and is 260m long
% http://www.guardian.co.uk/world/2007/nov/20/theairlineindustry.japan
% 75m long tokyo
\amarginfig{t}{
{\mbox{\epsfxsize=53mm\epsfbox{../../images/ekranoplanBelyaev.eps}}}\\[0.1in]
{\mbox{\epsfxsize=53mm\epsfbox{../../images/ekranLunInCruiseBelyaev.eps}}}\\
\caption[a]{The \ind{Lun} \ind{ekranoplan} --
slightly longer and heavier than a Boeing 747.
Photographs: A. Belyaev.}
}%
\subsection{Ekranoplans}
The \ind{ekranoplan}, or water-skimming wingship,
is a ground-effect aircraft:
an aircraft that flies very close to the surface of the water, obtaining its lift
not from hurling air down like a plane,
nor from hurling water down like a hydrofoil or speed boat,
but by sitting on a cushion of compressed air sandwiched between its
wings and the nearby surface. You can demonstrate the ground effect
by flicking a piece of card across a flat table.
% ; curling the leading edge
% of the paper upwards a little may help.
Maintaining this air-cushion requires very little
energy, so the ground-effect aircraft, in energy terms, is a lot like a
surface vehicle with no rolling resistance.
Its main energy expenditure is associated with air resistance.
Remember that for a plane at its optimal speed, half of its energy
expenditure is associated with air resistance, and half with throwing
air down.
The Soviet Union developed the ekranoplan as a military transport vehicle and
missile launcher in the \ind{Khrushchev} era.
% 550 ton, 125 ton, 400 ton Lun-class carry 100 t cargo
% According to \tinyurl{4p3yco}{http://www.fas.org/man/dod-101/sys/ship/row/rus/903.htm},
% Lun: eight NK-87 turbofan engines rated at 28,660 lb trust each
% that is 13000kg do I multiply by g? Yes
% 127 kN total 1000 kN
% max takeoff weight 400t exactly
% 341 mph cruise
The Lun ekranoplan could travel at 500\,km/h, and the total thrust of
its eight engines was 1000\,kN, though this total was not required once
the vessel had risen clear of the water.\nlabel{LunE}
Assuming the cruising thrust was one quarter of the
maximum; that the engines were 30\% efficient;
and that of its 400-ton weight, 100 tons were
cargo, this vehicle had a net
freight-transport cost of \eccol{2\,kWh per ton-km}.
% 1000000 newtons / 4 / 0.3 / 100 tons in kWh per ton-km
% picture with helicopter: A. Belyaev
% picture: A. Belyaev
% source http://www.se-technology.com/wig/html/main.php?open=showcraft&code=0&craft=26
% \tinyurl{47wvvs}{http://www.se-technology.com/wig/html/main.php?open=showcraft&code=0&craft=26}
I imagine that, if perfected for non-military freight transport,
the ekranoplan might have a freight-transport cost about half that of
an ordinary aeroplane.
% modern ekranoplan companies
%The AF8/SF8 built by Fischer Flugmechanik and AFD (Germany) for Flightship Ground Effect
% (Australia) 2001.
% The Hoverwing HW2VT scale prototype of 80 seat ferry by Fischer Flugmechanik
% The TY-1 by China Academy of Science and Technology (China)
% Amphistar/Aquaglide by Centre of Ekranoplan Technologies ALSIN (Russia)
% 747 is 360t takeoff weight
% hovercraft? 45 knots typical
% 160 tonnes 60 knots 1968 cross-channel hov. BH4
% BHC SR-N4 The world's largest non-military hovercraft, carrying 418 passengers and 60 cars
% The first SR-N4 had a capacity of 254 passengers and 30 cars, and a top speed of 83 knots (154 km/h/96 mph).
% wave-piercing catamarans use less fuel
% To maintain speed the engines were upgraded to four 3,500 shaft horsepower (2,610 kW) Rolls-Royce gas turbines
% mark 3: up to 60 cars and 418 passengers (112 t maximum)
% 4 hours, uses 2800 imperial gallons
% cruise: 111 km/h
% energy cost 1: assume engines 30% efficient
% 4 * 2610 kW / 0.30 / (111 km/hour) / 418 in kWh / km
% 75 kWh per 100 pkm
% energy cost 2:
% 2800 imperial gallons * 10 kWh / litre / (111 km/hours * 4 hours) /418 in kWh/km
% 69 kWh per 100 pkm
% freight energy cost:
% 2800 imperial gallons * 10 kWh / litre / (111 km/hours * 4 hours) /112 in kWh/km
% 2.6 kWh per tkm.
% preferred image
% jpeg2ps SRN4_Hovercraft_Mountbatten_Class0C.jpg > SRN4_Hovercraft_Mountbatten_Class0C.eps