> Ok, I found a formula for the power in compressed air.
> Pair [W] = Qv [m^3/sec] * Press [kgf/m^2]
> 300bar is ~3x10^6 kgf/m^2

Your calculations are probably approximately correct BUT they rely on a
statement by the manufacturer that was accidentally misleading AND there is
a need to alter your formula to account for the practical situation.

Firstly, the stated tank volume of 90 m^3 was (probably) intended as the
volume of gas at ambient after expansion (or before compression). The real
tank volume is less than a cubic metre. (Note the size of the car itself is
probably in the order of 5 cubic metres. They correct this error somewhere
on their site (in the FAQ?). For the E=QP formula to apply the pressure used
must be maintained throughout the "work stroke" represented here by the
Volume. (You use m^3/sec which is the instantaneous power but if you take
total volume and remove the time term you get total available energy).

Secondly, if you have a cylinder with a piston in it and you apply the
maximum pressure and the piston moves by the volume stated then the work
done would be equal to QP as you state.

This is a restatement of the well known formula

        work = force x distance.

Here volume = area x stroke.
Force = area x pressure
So work = Volume x pressure = area x stroke x pressure
= force x stroke
= force x distance.

With a gas, when you compress it from Pambient to Pmax then the average or
effective pressure is related to the natural logarithm (ln) of the pressure
ratios. For example if I compress air from 1 bar to 10 bar the effective
pressure is ln(10/1) = 2.3. ie the average pressure is 2.3 bar. This makes
sense if you consider the pressure on the piston as it moves down the
cylinder. After it has moved 50% of the way the pressure has double. After
it has moved 75% of the way the pressure has risen by 4 times. The maximum
pressure occurs only at the very end.

So, if you increase pressure from 1 bar to 300 bar the EFFECTIVE pressure =
ln(300)
BUT ln(300) ~= 6 !!!
A 300 bar "charge" expanding to ambient will only provide a MEAN pressure of
about 6 bar. This astounding result again makes sense when you look at the
pressure in the cylinder as you expand it.
Take a cylinder of 299 units volume and a "head" space of 1 unit volume. At
full expansion you have 300 units. At full compression you have 1 unit. Now
make it a 300 unit cylinder to make the sums very slightly easier.

Now start expansion.
At zero stroke you have 300 bar. At 1/300th of the stroke you are down to
150 bar (already) as volume has doubled. At 2/300 of stroke it's 100 bar. At
3/300 or 1% of stroke its 75 bar. And so it goes on. At 50% of stroke
pressure is about 2 bar ! You need a very special expansion engine to handle
such wide expansion ratios efficiently.

It actually gets worse. Intuitively we may feel that P1V1 = P2V2.
Unfortunately the gas laws state
PV^gamma = constant.
(Gamma is the specific heat of the gas at constant pressure compared to that
at constant volume).
For a perfect gas (and air is close enough) gamma = 1.414 ( = root two).
This reflects the equal division of energy between l=kinetic and potential
energies - heat and pressure. In most cases the heat of compression is lost.
Real thermodynamicists may wish to put on hobnail boots and take task with
how I have described this but the principles are essentially as stated.

 Nice online tutorial in fluid dynamics here


http://www.cfdrl.uc.edu/WebPage/Courses/comp_flow/cf_index.html


The outcome of all this is that the available power is far less than it may
have appeared. Recalculating to see how little may leave you surprised.




        Russell McMahon







> Ok, I found a formula for the power in compressed air.
>
> Pair [W] = Qv [m^3/sec] * Press [kgf/m^2]
>
> 300bar is ~3x10^6 kgf/m^2
>
> Assuming you need 10hp to move the car at about half the max. speed (for
> max. efficiency) you need 8kW for 6 hours (300km at 55km/h, half the max.
> speed). That's 21600 seconds. Assuming 20bar equivalent pressure in the
> motor (I just picked that number for reasonable end pressure in the tank -
> 20 bars is about ten times the pressure in a usual shop air end hose and a
> usual working pressure in many pneumatic circuits):
>
> Qv = Pair [W] / Press [kgf/m^2] = 8000/204000 = 0.04 [m^3/sec]
>
> for 21600 seconds:
>
> V = 864 [m^3]
>
> which at 300 bars (15 times more than 20bars) are:
>
> V1 = 57.6 [m^3]
>
> which is less than their 90m^3 tank and very credible because I assumed
> 100% efficiency and theirs is lower, about 64% (based on the ratio of
> their tank volume and V1 above).
>
> There would be the small problem of keeping the whole thing from
> *freezing* stiff, this requires about 6-7kW of heat *input* while working
> (remember expanding gas cools it down). This is what they use the
> compression of atmospheric air for I think.
>
> Recharging the thing would require the same energy input (assuming 100%
> efficiency as above but with their tank volume). Eg 6-8kW for 12 hours,
> probably more like 6-8kW for 14-18hours to account for efficiency. 300bar
> compressors do not grow on trees so I suppose it comes with the car (maybe
> the motor is reversible and they have an electric motor to drive it).
>
> Guy Negre was a F1 mechanic in a previous life I think, and he must know
> what he is doing.
>
> I liked the idea of soy oil lubrication ;-).
>

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