Wednesday, August 31, 2011

Piston vs. Gas Turbine Engines, Cost

The small 1.3 HP Honda GX35 engine pictured in the previous post retails for around $250.00.  But no company makes a comparable commercially available, mass-produced, small gas-turbine engine.  The only small 5-50 HP gas turbines that fit this description are the after-market turbochargers made for car engines.  A quick check on eBay shows these items for sale at under $200.00. 

I’m not ready to consider this crude price comparison a valid cost OME (order of magnitude estimate), but it does make me wonder.  It does seem to indicate that, contrary to popular wisdom, a gas turbine might be cheaper to make than a piston engine of comparable power output.

The one area where a valid cost OME comparison might be made is in the area of aircraft engines.  Both piston and small gas turbine engines are used to power private planes and small commercial planes.  So with this in mind, I spent several days searching the web, looking for information on piston versus gas turbines.  It seems the accepted wisdom in the aircraft industry is that, at the small end of the power/size scale, pistons are always less expensive than gas turbines.  But for all of my searching, I never ran across any hard numbers to back up this accepted wisdom.

What comparisons I did find, always struck me as apples and oranges.  Here is the problem: the smaller the turbine, the faster it spins and the bigger the gearbox needed to couple the engine to the propeller.  Why is this so?  A turbine blade’s ability to compress/expand airflow is a function of its speed through that air.  As the radius of a turbine gets smaller, its rotational velocity has to go up in order to keep the blade’s speed constant. 

So as a gas turbine is made smaller it will require an increasingly higher gear reduction to couple to the machinery it is meant to drive.  So it would seem to me, that at some point, it would be the size/complexity of a gas turbine's associated gearbox that drives the cost of a gas turbine engine, not the cost of the gas turbine itself.

Impedance Matching is a term that has specific and quantitative expressions when applied to various problems in physics and engineering.  But it can also be used as a general term to describe the problem of coupling any power source to its load.  For the case of mechanical systems such as an engine driving some mechanism, impedance matching often takes the form of a gearbox. 

For example, if you look at the picture of the Solar Turbines GS-350 shown in the last post, you will notice that the gearbox looks to be about the same size as the turbine itself.  An industrial generator is constrained to work at a 60 Hz frequency; hence the requirement for a gearbox to couple the high speed rotation of the gas turbine to that of its much slower, by comparison, attached generator. 

Gearboxes? We don’t need no stink’n gearboxes!  But unlike industrial situations that require a 60 Hz AC source, our robot harvester/tender is going to be DC powered.  Since our gas turbine’s AC generator’s output current is going to be converted to DC, this means that we can let it turn at any speed it wants too.  Which further means that one can build our small gas turbine generator set as a single shaft connecting turbine rotor, compressor rotor and generator assembly [1].  

And without the cost of a speed reduction gearbox, it appears that the cost of a gas turbine might actually work out to be less than that of a comparable piston engine.

[1] Noting that an added benefit of this configuration is that the generator can be used in reverse as the turbine’s starter-motor.

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