The design of the engine is best understood by following the engine cycle drawing attached here.  Readers should have some understanding of engine cycles for existing two stroke, four stroke, and diesel cycles. The inlet and outlet valves of the engine are, preferably, microprocessor controlled. The valve design for the FAE must be of a gate valve, ball valve or similar design. This valve design is necessary to enable a vacuum to be maintained in the cylinder under engine braking.  Actuation of the valves can be by stepper motors, pneumatic actuators, or solenoids and controlled by an engine control unit (ecu).

It is intended that the engine operates at high temperatures and high pressures for maximum efficiency. The retention of heat within the engine and within the storage tank is also important for efficiency; ceramic materials may help in this quest. 

    Basic Calculations for Power and Mass of Air

    No of cylinders    = 4
    Operating Pressure     = 1MPa
    Piston Diameter    =80mm
    Crank Stroke        =80mm
    Swept Volume        = pD2 /4 x stroke
                = 0.000402 M3

    Work done by down-stroke of one piston
    Work        =  pressure x change in volume
            =  1MPa  x .000402 M3
            =  402 Joules
    Work done by four pistons = 402 Joules x 4 = 1.61 KJ

    Power            =  work done over time 
    Power at 1000RPM     =  1.61KJ x 1000 RPM / 60 seconds
                =  26.8 kW
    Mass of air consumed at 1000RPM at full power in one hour in 20?C
        Mass     =  PV/RT
             =  1MPa x 102.54M3 / 287 x 293K
             =  1219 kg

            Various Methods of measuring Efficiency

   Carnot Efficiency is a measurement of the utilisation of the thermal energy contained in fuel. Petrol engined vehicles typically run at 30% or so Carnot efficiency. The remaining 70% of the energy of the fuel is lost as rejected heat.

Electric vehicles can utilise 80% or more of the energy stored in the battery.

I have not calculated a figure for the Carnot efficiency of the FAE. It all depends on the time span that the compressed air is stored and the insulation quality of the storage tank and engine. If these losses can be minimised then the FAE can run at very high levels of Carnot efficiency.

It may be noted that Carnot efficiency does not take into account the kinetic energy recovered by regenerative braking systems.

    Energy Density
         of various fuels per. Wikipedia

    Uranium 235      79,000,000 Mega Joules/Kilogram
    Petrol             47.2 MJ/kg
    Coal            24 MJ/Kg
    Wood            16.2 MJ/Kg
    Li-ion Battery        0.72 MJ/Kg
    Compressed Air    0.5 MJ/Kg
    Lead Acid Battery    0.1 MJ/Kg

Whilst this chart shows up the obvious comparative disadvantage of compressed air and battery power compared to fossil fuels; it also shows compressed air compares favourably to battery power as a means of energy storage. Whereas a 1000 Kg battery pack weighs the same fully charged as when half charged, a compressed air tank fully charged at 1000Kg may weigh only 600 Kg when half charged (assuming 100Kg weight of tank).

   Carbon footprint / Greenhouse Gas emissions. From website, the CO2 emissions from petrol cars are;

  3.15Kg/ Litre for ongoing fuel usage and extraction costs
      0.75Kg/Litre  -  for construction and maintenance of cars

Assuming a fuel consumption of 8Litres/100Km (or 12.5 km/Litre), the CO2 output of an average car is;

    0.252Kg/Km fuel use
0.060Kg/Km construction and maintenance.

A compressed air car is assumed for now to have the same construction and maintenance costs as a petrol car; the ongoing fuel costs is dependent on the means by which air is compressed and on the efficiency of the compressor. A typical 240V workshop air compressor outputs 289 Litres of air compressed to 1.1 MPa and draws 2.25 KW. In one hour of operation this compressor will generate 17,340 Litres or 17.34 M3 of compressed air. My preferred means of powering the air compressor is by solar panels, wind generators or windmill (where the compressor is driven directly by the wind rotor) .

If we assume that a compressed air car is fuelled for a 100Km commuter run and uses an average of 26.8 KW during the run. The 26.8KW is my guess as to the average power demand of the car for this trip given normal traffic conditions.  The amount of air consumed is 102.54 M3 per 100 km(per earlier calculations). The workshop compressor will need to run for 5.91 Hours to produce this air.  (Regenerative braking energy recovery is ignored for now).

    CO2 emissions from power generation are

    Coal 0.955 Kg/KW
    Solar Panel- 0.106 Kg/KW
    Wind Power 0.021 Kg/KW

CO2 output from shop compressor for the 100 km trip is thus;

    Coal Power     5.91 hours x .955 Kg/KW/hour  x 2.25 KW/ Hour = 12.699 Kg/ Hour
    Solar Power     = 1.409 Kg/Hour
    Wind Power     = 0.279 Kg/Hour

Ongoing fuel use CO2 emissions per kilometre for a compressed air car is therefore;

    Coal Power     =0.1270 Kg/Km
    Solar Power     =0.0141 Kg/Km
    Wind Power     =0.0028 Kg/Km

To summarise, a compressed air car put to the same task of a commuter run of 100 km outputs only 50% of the CO2 of a petrol car when the air compressor is powered by a coal powered generator,  and only 4.7% of the CO2 when powered by a wind powered generator.  Accounting for regenerative braking energy recovery of the FAE will significantly improve that figure. Further efficiencies and reductions in greenhouse gas emissions are achievable by using a more efficient means of compressing air than the workshop compressor. 

        Compressed Air Car v Electric Cars

A compressed air car using the FAE engine will have similar performance and range to an electric car because of the comparable energy density.  The FAE engine initially may (or may not) cost more to manufacture than an electric motor, but a compressed air tank will have a lower cost and a much longer life cycle than a battery pack.

At the moment, brush-less DC motors powered by Li-Ion battery packs are leading the field in zero emission vehicles. I hope to show that compressed air vehicles can be competitive and can ultimately be proven to have lower life-cycle greenhouse emissions than a battery powered vehicle.

        Other Compressed Air Engine Designs

In brief outline, some of the other designs that I am aware of,

    MDI This firm started in 1991 and is a well funded company that is working exclusively on its compressed air vehicles. The MDI engine does not have regenerative braking and uses a external combustion process to make up for the lost heat energy.

   Di Pietro Rotary Air Engine This engine also does not have regenerative braking. The FAE engine cycle (which can be applied to rotary engines also) is, frankly, superior to the conventional pneumatic engine cycle of the Di Pietro engine. 

   Permo-Drive Technologies is an Australian firm that has developed a hydraulic regenerative braking system primarily for use in heavy vehicles. In it's original form the system had a separate hydraulic pump and separate motor. Looking at their website now, it appears that they may have blended both pump and motor functions in the same body. The permo-drive system is not intended for, and is not capable of, being the primary means of powering a vehicle.

   Cargine Engineering Camless Combustion Engine This design, of which I am only recently aware (thanks to, is a hybrid pneumatic/combustion engine. This design is very close to a FAE variant that I envisaged in my Patent Application. This company has clearly solved all the engineering challenges in building a prototype that can run at high RPM. As far as I can tell, the regenerative braking cycle is not optimised ,(as it is in the FAE), in that use is not made of vacuum during the down-stroke of the piston.  Volvo, SAAB, Koeningsegg AB, and Lund University in Sweden are partners in this venture.

    Braking force under compression

    Compression ratio 20:1
    Volume at Bottom Dead Centre, V1     = 0.00042223m3
    Volume at Top Dead Centre, V2     = 0.000020106m3
    Intake air pressure, P1        = 101.3 kPa
    Compressed air Pressure P1= P1V1n / V2n
                    = 9,711,924 Pa, 9.7MPa

    Temperature of Working Fluid = T2 = T1(V1/V2)n
                    = 293(20/1)1.5-1
                    = 1310K , 1037C

    Work done on upstroke of piston, W = P1V1 - P2V2
                        = 305J
    Work done at 1000RPM for 4 cylinder engine
            = 305J x 1000RPM/60 seconds/rev x 4
            = 20,333Watts, 20.3 kW

    Braking force under vacuum during the down-stroke of  the piston must be constrained to the tensile strength of the con-rod and con-rod bolts and is controlled by the valve closed duration. I assume that a vacuum  force of 305J could be accommodated, thus the total braking force of a 4 cylinder engine at 1000RPM = 40.6kW. Additional braking force is available by supplementing intake air with air from the compressed air tank.

    Thermodynamic Efficiency

In the 2009 paper Economic and Environmental evaluation of compressed-air cars, Creuitzig et al use the formula

    Overall Efficiency of the compressed air process = Work done under isothermal process/ Work done under Adiabatic process.

    Wiso = P2V1 ln(V2/V1) = 128J
    Wadb= P1V1 P2V2   
            n-1         where n=1.4
        = 488J
    E= 128/488 = 26%

This measure of thermodynamic efficiency limits assumes that all the heat generated by the compression process is dissipated into the atmosphere. In the FAE car  the preferred means of compressing the air is by an on-board electric motor that turns the FAE in a compressor mode; This ensures that all the heat generated by the compression process  is stored (assuming an adiabatic type ceramic FAE).