All,
Just a quick note about my idea for a personal ?jet? powered by a
rotary engine ducted fan -- call it the "Rotor fan." In my last few
posts I?ve thrown up a lot of figures about power, thrust etc, with
some calculation errors along the way, which has probably confused
things. Here is a summary that should clarify things and put them
into context vis a vis the Diamond D-jet.
The D-jet is a single-engine fanjet airplane that is now
undergoing certification. The specs, which are preliminary and
probably optimistic, give a gross weight of 5,110 pounds, a useful
load of 2,240 lb., and a fuel capacity of 1,740 lb, leaving a
full-fuel payload of 500 lb. -- a little on the short side for a
five-seat airplane, even compared to the
600 pounds payload you get with one of the new high-performance
singles like Cirrus or Columbia.
The D-jet is powered by a Williams FJ-33 fanjet engine rated at
1,300 pounds of static thrust at sea level. That is enough power,
according to Diamond, to give the plane a maximum cruise speed of 315
knots at its 25,000 ft. ceiling and a time to climb of 15 minutes, or
about 1,700 feet per minute. The airplane?s range is given as 1,350
nautical miles at an economy cruise speed of 240 knots.
Provided that the certified airplane actually delivers those
numbers, this is what we need to shoot for with the Rotorfan personal
jet. In outward appearance the Rotorfan will be similar ? it will have
a duct buried within the fuselage with an exit nozzle somewhat bigger
than the D-jet?s, and exiting from the aft fuselage similar to the
D-jet. Two intake air scoops will be side-mounted, as on the
D-jet. The rotary engine will be mounted forward of the duct in an
engine compartment separate from the duct and will drive the fan via
short driveshaft. The fan will be located at the front of the duct,
aft of the intakes. The duct will be about 48 inches long, which is
similar to the FJ-33 duct length of 47 inches. The fan diameter of 20
inches will give a helical tip speed of mach 0.825 at 7000 rpm, at an
aircraft true airspeed of 315 knots at 25,000 feet. This compares to a
fan diameter of 17.3 inches on the FJ-33
http://en.wikipedia.org/wiki/Williams_FJ33.
The big question is: How much power does our rotary engine need to
make in order to keep up with the D-jet? And can the rotary
realistically make that kind of power?
To get an answer, we need to figure out just how much power the
D-jet is making in terms of thrust and then convert that to
horsepower, because that?s the only way we can compare its power
output to the rotary.
We first need to know the drag of the D-jet at its cruise speed.
Diamond doesn?t tell us that, but thrust equals drag in straight and
level flight, and we can figure out the thrust of the airplane based
on its fuel burn and cruise speed. To get fuel burn we divide the
airplane?s range, by its speed: 1,350 nautical miles divided by 240
knots means the D-jet can stay aloft for 5.625 hours. Assuming that
Diamond has included the standard NBAA fuel reserve of 45 minutes, we
add 0.75 hours to get a total of 6.375 hours, about six hours and 20
minutes. Dividing the fuel weight of 1,740 lb. by this figure, we get
a fuel burn of 274 pounds per hour, just under 40 gallons per hour.
(This does not take into account the higher fuel burn used at takeoff
and climb, so actual cruise fuel burn will be a little more).
Now that we know fuel burn we can solve for engine thrust. To do
this we need to know the engine?s thrust specific fuel consumption,
which is the standard measure for turbine engine fuel efficiency and
comparable to brake specific fuel consumption for piston engines. The
FJ-33 has a TSFC of about 0.5 at sea level, which means it makes one
pound of thrust for each half pound of fuel burned.
But since jet engine thrust decreases with altitude, specific fuel
consumption goes up. At 25,000 feet, the FJ-33 can only make about 530
pounds of thrust at full power. But the engine is also burning less
fuel at that altitude because of the lower air density. Assuming a
TSFC of 0.8 at 25,000 feet, and knowing that the D-jet burns 274
pounds per hour at its economy cruise of 240 knots, we find that it is
making about 340 pounds of thrust, or about 64 percent of full power.
In order to figure out how much power our rotary engine needs to
make we need to convert that 340 pounds of thrust to thrust
horsepower, using the equation:
THP = thrust in pounds * speed in feet per second / 550
This gives us about 250 thp. Now all we need to know is how much
brake horsepower out rotary needs to make in order to produce 250 thp.
Since thp is simply brake horsepower times propeller or fan
efficiency, we can easily find the answer if we know our fan
efficiency.
And therein lies the big question: How much propulsive efficiency
can we get from our small diameter fan duct? Airplane propellers
routinely deliver efficiency of 80 percent to 85 percent, but it is
believed that fans cannot approach this level. Paul has mentioned a
figure of 60 percent, which is from the Kuchemann and Weber book.
This may or may not be the most we can expect to see. There are
reasons to think that much higher efficiency could be achieved.
Even if we assume the worst and take that fan efficiency of 0.6 as
an upper limit, we find that our rotary would need to make about 400
bhp at our economy cruise power setting and over 600 bhp at our full
power setting at 25,000 feet. This is within reach of a 4-rotor
boosted engine.
The bigger problem though is takeoff thrust. Mark has mentioned
that the little Williams probably makes the equivalent of about 800 hp
at full sea level power, and this is not unreasonable. This is more
than we could hope to get from even a 4-rotor boosted engine. Assuming
the most we could safely make from a 4-rotor engine is 600 hp, it
means we are making only three quarters the power of the Williams at
sea level. But assuming we have a boosted engine, we can probably
carry that power to our ceiling of 25,000 feet, where we will have
rough parity with the fanjet. We see here that the higher we go, the
more we close the gap with the fanjet.
But there is one important factor that plays to our advantage and
that is fuel weight. Our much lower fuel burn means we can carry much
less fuel and our airplane can be significantly lighter. That means
that we can hope to match the D-jet?s thrust to weight ratio of about
4 -- gross weight of 5110 pounds divided by 1300 pounds thrust -- with
a lower output engine.
Since takeoff thrust is the most difficult parameter for our
rotary engine to match, we have to try to reduce airplane weight to a
value that will give us a comparable thrust-weight ratio. Assuming we
can make 1000 pounds of static thrust with our 600 bhp engine, we
would need an airplane weight of 4000 pounds to match the D-jet's
thrust-weight ratio of 4. That is probably not possible. Because our
4-rotor engine is at least 200 pounds heavier than the Williams, we
would need to eliminate about 1300 pounds of fuel weight in order to
do that.
That would leave us with just 450 pounds of fuel, which is not
enough. So how much fuel weight can we eliminate? Assuming our very
efficient turbocharged or turbocompound engine has a reasonable BSFC
of 0.4, the 400 or so hp we are making at our economy cruise would
burn about 160 pounds of fuel, less than 60 percent of the Williams
engine fuel burn of 274 pounds. So if we want the same range our fuel
capacity can be 60 percent of the D-jet, or about 1000 pounds.
That?s a savings of 700 pounds of fuel weight, but since our
engine weighs 200 pounds more, we have a net saving of 500
pounds. Roughly speaking we now have an airplane with a maximum gross
of about 4500 pounds and a thrust to weight of about 4.5. That's not
bad. We can probably shave a little bit more weight by making the
structure a little lighter, to compensate for our lighter gross
weight, but it?s not going to be much.
So summing things up, we have an airplane that is probably going
to have a bit longer takeoff roll than the D-jet, but will actually
perform better up high. Assuming the same lift to drag ratio, our
lighter weight will give stronger climb and higher top speed. (We need
less lift and therefore less angle of attack, and hence less induced
drag, to fly a lighter plane at the same airspeed).
We will have great fuel economy, burning only 60 percent of the
fuel it takes to fly the D-jet. Plus we have the flexibility of a
piston plane to fly at low altitudes at the same low fuel burn.
Turbines simply can?t do that. Even the most fuel efficient turbine
gulps gas down low, making short hops something that you just don?t
do, unless you don?t mind whipping out your wallet at every gas pump
you pass.
This advantage alone is not to be underestimated. So even with
just this rough comparison -- and assuming the dismal fan efficiency
of 60 percent -- it is clear that a rotorfan ?personal jet? is not an
unfeasible idea. If we could get our fan efficiency up to about 70 or
75 percent, this airplane could be a world beater. We could use a much
lighter 3-rotor engine, much less fuel weight again, lighter aircraft
structure, etc. We could also scale this idea down as George Wright
has suggested, right down to a single-seater like the Mini-Imp.
I'm going to give this a little more thought and try to figure out
what kinds of fan efficiencies we might hope to achieve, based on what
the efficient little fanjets of today are doing. I have a feeling that
even the little Williams with its 17-inch fan is getting well over 60
percent efficiency.
Regards,
Gordon.
> > Pretty good summary Gordon. I have not checked all
your
> numbers but it looks good. You have certainly spent
a
> lot of time thinking about it.
> > One thing going against the duct is skin friction
> drag is prop. to the square of the velocity so if
you have
> a high velocity duct exhaust you are paying a price.
> > That is one reason the eff. of the duct is so bad.
> > Paul Lamar ...No rotor no motor.
>
Gordon
It sounds like an interesting concept and the devil
will be in the
details.
Perhaps you have spoken to Monty about this as well?
I think he was
thinking along the same path for his plane design.
Paul's 1997 design
posted a few days ago had a unique way of diverting
some of the thrust
through the radiators thereby killing two birds with
one stone. If done
well
then the 680 Hp. 26B engine would cool well and the
expanding heat out
the
exhaust would help to evacuate the duct. It will take
years to get the
duct
tested well so perhaps an all aluminum engine will be
happening by then
and
hence bringing your gross weight down further.
Doug Fir
Cooperstate bound
doug,
all aluminum engines are available now, just very
expensive. racing beat has aluminum housings for 13b
and 20b engines. front housing $1200, intermediate
housing $1750, rear housing $1425.
gary
midland, tx
Gary,
try and buy one! They have been notoriously hard to get.
Bill Jepson
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