I will play devils advocate here.
I am basing my duct eff. on Kucheman and Webers book, Aerodynamics of
Propulsion real data. Last chart.
I got bad news for you Gordon. The smaller the duct dia. the worse
the efficiency. That is the rational behind the high by pass turbo fan.
Take a look at this thrust chart. Notice the high by pass turbo fan is
more efficient
through out the speed range than the pure jet. In fact the big debate
now in air
liner engine design is to use and even larger fan and gear it to save
fuel. The core
engines are still in the duct. Perry Mick's engine was largely out side
the duct with
a long e-shaft extension. See the gif.
http://www.bridgingworlds.com/duckt.htm
The most efficient propulsion system is to accelerate the largest mass of
air possible only a little faster than the aircraft speed.
Your assumption of the .7 TSFC of the Williams is unfounded and undocumented
so far. The last chart is closer to the real world. Do you mean BSFC for the
Williams based on equivalent thrust HP? Show us your source.
One last thing. Most biz jets will fly at 40,000 feet no problem. Huge
advantage when
it comes to weather and MPG. The turbo compound rotary has years to go
before it can fly at 30,000 feet.
My having said all that does not mean nobody should try it. IMHO it is a
real
engineering challenge and beyond almost everyone except perhaps a large
aero space
firm. Now a days the big engine manufacturers are still making significant
changes in turbo ducted fans due to the pressure to reduce air liner
fuel consumption.
It is close but so is the turbo prop. People like jets for different
reasons.
One is the smoothness. Two is the long TBO. Three is above the weather. Four
is the status. If you have money to buy the biz jet the cost of fuel is
inconsequential.
Paul Lamar
Gee Paul,
You're going to play devil's advocate? What a switch.
About the duct diameter, yes the smaller diameter is generally less
efficient because of the reason you said: "The most efficient propulsion
system is to accelerate the largest mass of
air possible only a little faster than the aircraft speed."
In order to achieve the same thrust with a smaller diameter, the
airstream has to be moving faster. That's why a pure jet is least
efficient, and a high bypass ratio turbofan is more efficient.
However, look at the relative sizes here. A 24-inch fan is actually
bigger than the small Williams engine. So compared purely to the
Williams engine my 24-inch fan will be more efficient, especially since
there is no engine inside the duct.
Look at the nozzle exit diameter of bizjet engines. You have to be
talking about a pretty big plane if you are talking 24 inches. These are
engines that are producing thousands of pounds of thrust.
So relatively speaking my 24 inch fan is actually more efficient than
the high-bypass engines. The slipstream speed going through that duct
will not be very much faster than the airplane airspeed. As a ratio, it
will be a much lower than that of the bizjet engines.
There is also a point where the wetted area starts coming into play and
becomes the dominant factor -- moreso than the speed and diamter of the
propulsion stream. Think of the small plane I am proposing with a 24
inch fan and then scale that fan and duct up to a bizjet. The fans would
have to be huge, maybe four or five feet in diameter. Imagine the size
of those nacelles. It would be like hanging the nacelles from a 747 on a
Citation. Such a thing could not even hope to fly simply because of the
huge wetted area.
So this question of efficiency is one of relative sizes. Yes, the jets
are getting better efficiency by increasing the fan diameter, but this
works only up to a point.
With my 24-inch duct on that plane I am actually beyond that point and
making the fan bigger will only make things worse. That's why I believe
making the fan even smaller will actually be an improvement.
Yes, I was talking about BSFC and equivalent horsepower on the Williams
engine. I have no idea what this figure might be for the Williams
engine, but I have heard the figure 0.69 thrown around as the state of
thea art for high bypass engines.
But talking about equivalent BSFC on jet engines is not really a good
practice. It's much better to stick to TSFC for jets. I believe state of
the art TFC for high bypass turbofans is around 0.5 TSFC at sea level.
At 25,000 feet it would be about 1.25.
And speaking of calculations, I just found another mistake in my last
post. (Sorry about all the mistakes, I'm putting this stuff up there
without really checking it...)
In trying to figure out how much power a rotary would have to have in
order to equal the perfromance of the Williams, I figured out the long
range cruise thrust of 330 pounds.
I mistakenly translated this figure directly into brake horsepower,
rather than first calculating thrust horsepower.
So, 330 pounds of thrust equals at 275 mph (240 knots) equals 240 thrust
horsepower. (Using the equation THP = thrust in pounds * speed in feet
per second / 550.
So now we can calculate how much brake horsepower we need to make 240 THP.
If we assume a fan efficiency of 75 percent, we get 322 brake horsepower.
So if this is our 62 percent power long range cruise, our 100 percent
takeoff power would be 520 horsepower.
This is probably a bit more than you would want to push a 3-rotor
engine, but 450 hp should be doable.
This means that our fuel consumption figures also go down dramatically.
Long range cruise at 62 percent power and 240 knots would give a fuel
burn of 130 pounds of gasoline per hour, or 21 gph.
This is spectacular. That means that with 150 gallons of fuel on board,
our range would be considerably longer than the D-jet -- but with 800
pounds less fuel weight.
That lower weight means our 450 hp 3-rotor could give us a comparable
power loading as the turbofan D-jet.
You mentioned flying at higher altitudes. Yes this has advantages for
weather flying and fuel efficiency, but that height is a whole'nother
ball game for pilot training and capability. Flying at 25,000 feet is
much more reasonable from a safety perspective for the average
owner-pilot and a single-engine plane.
Besides, the fuel efficiency of our rotary is so much better than a jet
that it makes hardly any difference. Turbine engines have to fly high.
Even turboprops burn a lot of gas below 10,000 feet. Our ratary fan on
the other hand will fly as frugally as a piston single down low, while
keeping up to the small single-engine jets at FL250.
Sounds pretty good to me. Yes, I agree that if you have the money to buy
a bizjet you have the money to buy gas for it. But we're talking here
about personal use planes. Even if I could afford to buy a $1.5 million
D-jet, I would still have to have a pretty big wallet to keep those
tanks filled.
If you can make a rotary fan plane that does eveything the D-jet does
and does it just as smooth and civilized, and at half the price, you
will really have something. And keeping it in fuel will not be much more
than a turbocharged Columbia or Cirrus.
And yes, I know the turbocompound rotary is not there yet, but a
turbocharged rotary would be pretty close and that's pretty much there now.
Regards,
Gordon.
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