**MW output
balloon engines to meet renewable energy targets.**

Ian Edmonds, www.solartran.com.au

**
Introduction**

In September 2007 the Federal Government set 30,000 GWHr as the renewable energy target for 2020. In view of the paucity of ready-to-go renewable generation other than wind power it is likely that some 4000 new wind turbines will need to be installed to meet this load. Suitable Australian wind power resources lie primarily on a narrow band of elevated sites around the Southern coastline of NSW and Victoria, Fig 1. Unfortunately, this band overlaps some of the most scenic and populated areas of Australia. Proposals to site large wind farms in this region are being met with increasing hostility by Australians concerned by the visual and audible impact on the natural environment. Wind resource drops sharply with distance from the coast and inland Australia is, in the main, unsuitable for wind power.

FIG 1. The Australian wind resource.

The solar radiation resource inland is, however, very high and engines driven by hot air such as the solar updraft tower, Fig 2, have been proposed for the inland region. A 50 kW solar updraft tower was built at Manzanares in Spain in 1981 with an installation cost, at that time, of about $20/W and an overall efficiency of 0.1 %. In 2002 a much larger solar updraft tower (200 MW, now scaled back to 50 MW) was proposed for construction in NSW by the Australian company Enviromission.

FIG 2. Artists impression of a 200 MW solar tower engine (Thomas and Davey 2004).

A dozen 50 MW, 500 m high solar updraft towers similar to that illustrated in Fig 2 would go a long way to meeting the 30,000 GWHr target for 2020. However, there are serious technical and economic difficulties involved in implementing solar tower technology. The principal economic problem is the financial risk in committing about half a billion dollars to construct the first tower. The principal technical problems are associated with the tower height and the thermal efficiency of the tower engine. In common with all engines the thermal efficiency is limited by the temperature difference of the heat sources between which the engine operates. In particular the maximum efficiency is given by 1 – T2/T1 where T1 is the temperature of the source delivering heat to the engine and T2 is the temperature of the source into which the engine rejects heat. A solar updraft tower operates in the atmosphere where the temperature declines linearly with height at about 6.5 degrees C per km. Thus a 500 m high tower engine operates over just 3.2 degrees temperature difference and the thermal efficiency is correspondingly very low – about 2%. When collector loss (about 50%) and turbine loss (about 50%) are included the overall efficiency of a 500 m high solar tower is about 0.5%. Clearly this low efficiency can be improved by increasing the height of the tower and, initially, a 1 km high tower was proposed for NSW. However the cost of a tower increases roughly as the height cubed and structure cost and technical difficulty preclude towers much higher than 500 m.

Hot air balloons, Fig 3, operate to altitudes exceeding 20 km and should, in principle, be capable of incorporation in an engine to generate power at relatively much higher thermal efficiencies. This note outlines the concept, the theory and predicts the performance of balloon engines in the 50 kW to 0.5 MW range.

FIG 3. A Cameron Z-1600 balloon being charged.

**
Concept of the reciprocating balloon engine**.

The envelope of a balloon is tethered via a windlass to a motor/generator, Fig 4. The balloon is charged with hot air obtained by drawing ambient air through a glazed solar collector that encloses black pipes filled with water. When fully charged the balloon is allowed to ascend with the buoyancy force doing work on the generator. At some predetermined height a large fraction, typically 80%, of the remaining air is vented, the buoyancy is reduced and the balloon is hauled back to ground level by the operating the motor/generator as a motor. The system delivers, via the motor/generator, an electrical power output to a storage battery or to the electrical grid.

Fig 4. Concept of the operation of a balloon engine.

**
Theory of the balloon engine.**

The buoyancy force developed by a hot air balloon is given by

F_{b}
= Vg(r
–r_{i})
– M_{b}g

where V is the balloon volume, g gravity,
r the density of the
ambient air, r_{i}
the density of air in the balloon and M_{b} is the mass of the balloon
envelope. The density of the ambient air depends on the pressure p and
temperature T and can be found from the expression
r = pM/(RT) where M is molecular weight of air and R is the Gas Constant.
Air temperature T declines linearly with height and the air pressure p declines
exponentially with height according to well known relations so the variation of
ambient air density with height can be found. As the balloon is open at the
lower end the air pressures inside and outside are the same. Assuming adiabatic
expansion of the internal air a simple relationship T_{i} = T_{c}(p/p_{0})^{(1-1/}^{g)}
relates the internal temperature T_{i}
to the pressure p. T_{c} is the temperature of the charge air and p_{0}
is the air pressure at ground level. Knowing p and Ti the internal air density
r_{i}
may be found using r_{i}
= pM/(RT_{i}) and therefore the buoyancy force, F_{b}, versus
height, can be found. As the rising balloon is lifting a rope and is also
opposed by an air friction drag force the drive force at the generator windlass,
F_{d}, is given by

F_{d}
= F_{b} – mgh - (1/2)C_{d}rAv^{2}

where m is the mass per unit length of the rope, C_{d} is the drag
coefficient of a sphere (C_{d} = 0.1), A is the cross section area of
the balloon and v is the velocity at which the balloon is constrained to ascend
and descend (taken as 5 m/s in the present case).

From the above expressions it can be shown that an average temperature difference between the internal and external air of about 30 C will occur during operation to altitude 3000m. Thus considerable heat loss is expected and this calls into question the assumption of adiabatic expansion and compression during the ascent and descent of the balloon. However if the balloon is black it receives a considerable radiant input from direct and reflected sunlight that, calculations show, largely balances the heat loss leading to approximately zero nett heat transfer. In fact solar balloons (Ballon-solaire 2007) can remain aloft all day and accomplish long, high, flights powered only by solar radiation, Fig 5.

FIG 5. A solar balloon of about 100 kg lift. FIG 6. Small windlass and generator-motor unit to take a 100 kg breaking strain line.

**
Predicted performance.**

To illustrate the practicality of the balloon engine a commercially available
balloon envelope was used to predict performance. The Cameron Z-1600, the large
balloon shown in Fig 3, has a volume of 45,000 cubic metres (equivalent to a
sphere of diameter 44 m), an envelope mass of 513 kg and costs A$220,000
(Purvis, 2007). The tethering rope has mass per unit length 0.118 kg/m and
breaking strain 85 kN. The ambient ground air temperature is at 15 C and when
the charge air is drawn through the collector the air is heated to 60 C. After
charging the balloon ascends at 5 m/s for 10 minutes doing work on the
generator/motor. At 3,000 m 80% of the remaining air is discharged and the
balloon is hauled in by the motor reaching ground level after another 10 minutes
when the volume the remaining air in the balloon is 7,000 cubic metres. Thus the
recharge volume required each cycle is 38,000 cubic metres. This is delivered
by four 0.55 kW fans each delivering 7.5 m^{3}/s in 22 minutes. The
force versus distance cycle (Fig 7) encloses an area corresponding to a work
output of 121 MJ. As the heat input in the recharge air is 2,100 MJ the thermal
efficiency is 121/2,100 = 0.058 or about 6%. Averaging over the recharge, ascent
and descent phases of the engine operation (a total of 42 minutes) and including
the fan energy for recharge the average power output of this balloon engine is
48 kW.

Fig. 7. Force – distance graph for a 44 m diameter balloon engine charged with 60 C air and discharging 80% at 3000 m. Average power output 48 kW.

The power output of a balloon engine scales as diameter cubed whereas the envelope mass and friction losses scale as diameter squared. Therefore there should be significant benefits in larger engines. To illustrate the point the diameter of the balloon was scaled by a factor of two up to 88 m. A similar cycle to 3,000 m gave the force versus distance diagram illustrated in Fig 8. The work output is 1.0 GJ, the thermal efficiency is 0.059 or about 6% and the average power output over a cycle is 0.44 MW.

Evidently, doubling the balloon diameter increases the average power output by close to a factor of 10. This suggests a 180 m diameter balloon would generate 4 MW and a 360 m diameter balloon 40 MW.

Fig. 8. Force – distance graph for an 88 m diameter balloon engine charged with 60C air and discharging 80% at 3000 m. Average power output 0.44 MW.

**
Discussion.**

Preliminary cost estimates (based on the envelope cost being 50% with the remaining components, collector, drive train, generator/motor and tether rope accounting for the other 50%) suggest a system installation cost of $9/W for a 50 kW engine and $4/W for a 0.5 MW engine. These costs are similar to the costs of other renewable energy systems such as wind power and photovoltaic power. The installation cost of the 50 kW Manzanares solar updraft tower was $20/W in 1981. The marked cost difference between an updraft tower engine and a balloon engine is due to three factors. (1) A tower is a steel or concrete structural component. The material and assembly cost is high and increases rapidly with height. A balloon envelope is formed from thin, relatively low cost material which is essentially self supporting in operation. (2) The balloon engine operates at about three times higher efficiency than an equivalent output tower engine therefore the glazed collector can be much smaller in size. (3) The balloon engine utilizes components sourced from well established industries. Namely the recreational hot air ballooning industry, the rope industry and it utilizes a high torque, low frequency drive train between the windlass and generator similar to that used by wind turbines. Much of the drive train technology for wind turbines in the 10 kW to 1 MW range should be directly transferable to balloon engines in the same power range.

There are further complementary aspects between balloon engines and wind turbines. It is envisaged that balloon engines would be used at times of low wind, in particular during still, hot days in summer when peak air conditioning loads are high. In this way balloon engines would complement wind turbines which would not be contributing power to the grid in these conditions. At other times, in particular windy conditions and night time, balloon engines would be stored in the discharged state at ground level. This complementary delivery of renewable power during both still and windy conditions should help compensate for the imbalances in the supply grid due to the variability of wind power and should, in fact, allow for a higher component of wind power within power networks than is currently feasible. Another complementary aspect is that balloon engines have similar modularity and similar scalability as wind turbines. Thus it is envisaged that balloon engines would evolve through the kW to MW range in a similar way to wind turbines and would, similarly, be utilized in farms of modules with the important difference that balloon engine farms would be situated in the dry interior rather than in the coastal region.

The balloon engine is a big reciprocating engine with a capacity of 45,000 m^{3},
a stroke of 3 km and a frequency of 1 rph. However in many respects the balloon
engine is similar to other reciprocating engines such as the two stroke petrol
engine. The autonomous operation of a balloon engine will need to be worked out
during its evolution. However, as many types of reciprocating engine operate
autonomously at frequencies very much higher than 1 rph autonomous operation of
balloon engines does not seem insurmountable.

With the single balloon engines described above the time during the upstroke/downstroke phase is used to heat storage water in the glazed collector which is closed during this time. As the time for the charging phase is about the same as the time for the upstroke/downstroke phase operation of a two-balloon double-acting engine is also possible. In this case when one balloon is in the upstroke/downstroke phase the other balloon is being charged.

The power output of the balloon engine scales as balloon diameter cubed whereas the cost of the principal component, the balloon envelope, scales as diameter squared. This suggests that, for the balloon engine, the installed cost per Watt of output varies as the inverse of the balloon diameter. As the principal component of the engine, the balloon envelope, is self-supporting and self-erecting there seems to be no inherent constraint on increasing the size of the balloon engine other than the necessity of operation within the 10 km altitude range of the troposphere. This contrasts with other types of renewable energy engines such as the solar updraft tower or the wind turbine where the principal component of the engine has to be supported against gravity, by a structure the cost and installation of which increases rapidly with height.

**
Preliminary trial****.
**

It is envisaged that preliminary trials of the balloon engine will utilize a balloon envelope of about 15 m diameter (Fig 5) providing a lift of about 100 kg at a charge air temperature of 60 C. The envelope illustrated is actually a solar balloon. However, the smallest commercially available hot air balloons are about the same size. The envelope will connect to a small windlass - electric motor unit similar to the type used for kite fishing (Fig 6). The windlass illustrated takes 2km of 100 kg breaking strain line limiting the operational height of the balloon engine to about 2 km. Initial trials will have the air heated to the required temperature with a propane burner and will provide data on lift versus temperature, ascent and decent rates, power input and output, venting procedures, heat loss, effect of wind and other data. Separate trials will be conducted to determine optimum collector geometries for the supply of air at the rates and temperatures required for the engine.

** **

**
Conclusion.**

The concept, mode of operation and elementary theory of reciprocating balloon engines that operate over heights of several thousand metres with thermal efficiencies greater than 5% has been described. Preliminary performance and cost estimates for engines in the 50 kW to 0.5 MW range suggest the installed cost per unit power output is similar to that of other renewable energy systems and decreases with system size. As opposed to other engines there appears to be no inherent limitation on engine size. It is envisaged that the engines would be operated as summer peak supply units to complement wind turbines in a renewable energy supply system. Support is being sought from within the wind industry to trial the first balloon engine.

**
References **

**
**

Ballonsolaire 2007. http://perso.orange.fr/ballonsolaire/en-index.htm

Purvis N. 2007 www.cameronballoons.com private communication

Thomas M. H., Davey R. C., 2004. The solar tower: large scale renewable energy power station development. 19 World Energy Congress, Sydney, Australia. www.ph.unimelb.edu.au/~roger/261-07/solar-tower.pdf