Why a small jet will never beat a turboprop

Sad to read today that Piperjet pulled their project until the market gets better, but better this than I suppose than have the project fail. They are great people-having been a major sponsor at FCA annual meet in Savannah this year.

I was reading Austin Meyers post on the Evolution build when I came across this. According to Austin, this is why a small jet will never beat a turboprop.


From Austin on this link:



http://www.x-plane.com/hardware/evo/evo.html

http://www.x-plane.com/hardware/evo/4_trip_3.html

BELOW IS A (SLIGHTLY UPDATED AND EDITED) EMAIL I SENT TO AN ENGINEER WHEN I WAS CANCELLING THE CAVALLO PROJECT, AND THE REASONS IT (AND ANY OTHER VERY LIGHT JET) WILL SIMPLY NOT MATCH A TURBOPROP OR LARGER JET FOR PERFORMANCE, AS TEMPTING AN IDEA AS A SMALL JET MAY BE:


hi man!

ok i think i am canceling the x-1 project (as it stands, with a single jet), and here is why: the range is just too low, the fuel burn too high, compared to a lancair-4.

when looking at any reasonable figure of merit, the lancair-4 runs circles around anything i can design.

observe these scores, with the lancair-4 p, the lancair propjet, and the x-1 with a pw-610 and a second variant with a pw-615:


X-1 with pw engines:

pw 610: we go 265 kt at 315 pph=265 kt at 46 gph = 5.8 nmpg. range is 673 nm.
pw 615: we go 310 kt at 381 pph=310 kt at 56 gph = 5.5 nmpg. range is 573 nm.


speed in kts * range in nm / fuel in lb = score

lancair 4-P =286*1350/100=3861
lancair propjet =325*1216/150=2634
x-1-610 =265* 673/110=1621
x-1-615 =310* 573/110=1614

the lancairs are FASTER than an x-1 with a pw-610... while going TWICE the distance on the same fuel.

how can i build an airplane that is slower than a lancair, goes half the distance, and would cost twice as much?

as well, part of my plan was to reduce weight and frontal area by pulling out the insulation and interior ammenities... this would result in a plane that is a carbon-fiber shell with a jet engine on it. sounds FUN. BUT, when i spoke to mr. karkow, he reminded me that the noise in global flyer (before they added insulation) was 105 db... that is a between a snow-mobile and a chain-saw. as well, ANR headsets did NOT reduce the noise at all... the ANR systems only work with lower-freq noise! as well, ICE would form on the inside of the craft (including windshield) throughout the flight. upon landing, the ice would melt and water would be sloshing around the cabin of the airplane. every flight. the carbon-fiber shell, attached to the engine, would shake with the engine, causing every bit of the airplane to act like a speaker.

so, to pull out all the interior of the airplane would have you flying in a block of ice making more noise than a snowmobile, with ice melting around your feet following every flight. doing this might save 100 pounds in weight, which would buy you about 15 minutes of cruise fuel.

again, you are in a block of ice making more noise than a snowmobile, ANR headset is ineffective, water is sloshing around your feet after every flight, to give you 15 more minutes of fuel.

in other words, insulation is light, fuel is heavy... you do not get a better airplane by giving up a LOT of insulation since you get only a LITTLE fuel in return.

as well, the lancair guys are faster on half the fuel flow, with very warm, quiet cabins.... whisper-quiet with their ANR's.

for flight exceeding 500 miles, the lancair's are 3 or 4 times faster... since they will not be stopping for fuel like the x-1 pilot would be.

the lancair costs less.. their engines run $100k, the x-1 engine would run $300k or more.


the x-1 would be a laughing-stok to any lancair pilot... how could it not be? look at the figures of merit.

as well, the x-1 is NOT like a thirtieth of a Boeing 737, carrying a thirtieth of the payload (4 people instead of 120) at the same speed and distance.

the x-1 is NOT as good as the lancair (PROP airplane at the same speed and size and range targets)
and
the x-1 is NOT as good as a thirtieth of a boeing 737 (JET airplane scaled up.. a biz-jet is supposed to give airliner speed and altitude in individual-sized servings, providing the same speed and range as an airliner, but smaller).

now, WHY is this?

well, it comes down to 4 fundamentals that i can think of... 2 fundamental reasons the x-1 is not as good as a lancair prop, and 2 fundamental reasons the x-1 is not as good as a thirtieth of a boeing 737.


FUNDAMENTAL REASONS SMALL JET WILL >>>NEVER<<< BE AS GOOD AS A BIG JET:

1:
let's start with an airbus a-380.. a huge plane that goes maybe 8,000 miles at mach 0.85 or so.
it weighs 1.2 million pounds and has length and breadth of 250 ft
now let's say we want to build a small jet.. a plane that is 1/10th the size.
this plane will have length and wingspan of 25 ft.

this light jet plane is
1/10 as long
1/10 as tall
1/10 as wide

that should give a plane that is one one-thousandth the volume
that should give a plane that is one one-thousandth the weight
that should give a plane that has one one-thousandth the thrust (to push one one-thousandth the weight)

so, we have a plane that is like an airbus a-380, but with one one-thousandth the weight and thrust and fuel-burn, right?

WRONG!!!!!!!!!!!!!!!!!!!!!!!!

the frontal area and wetted area of our airplane is ONE ONE-HUNDREDTH THAT OF THE AIRBUS, NOT ONE ONE-THOUSANDTH!!!!!!!!

scale the airbus down by 10x and you have one one-hundredth the frontal and wetted area, not one-one-thousandth!

so, your new scaled-down plane has one-one-thousandth the thrust, but one-one-hundredth the (parasite) DRAG!!!!!

so we have TEN TIMES THE DRAG PER UNIT THRUST!!!!!
again: scale down an a380 by a factor of 10, and you have ten times the parasite drag per unit thrust, all else being equal!!!!!

speed goes with square root of drag, so we should expect to fly at a speed fraction of the square root of 10, or about one THIRD the speed.

if we have identical endurance (one-one-thousandth the thrust, one one-thousandth the fuel, would give the same endurance!) but one third the speed, we will clearly have ne third the range.

so, if we managed to do everything as well as an airbus a-380 scaled down, we would still only have one THIRD the speed and range!!!!!!!!!!!!!!!!!!!

this rules makes a very light jet impossible, since very light jets need to have near-airliner performance to perform like jets.

2:
it gets worse.
jets do well because they have a high bypass ratio... teeny little turbines spinning at huge rpm driving giant, slow-turning fans
these teeny fast turbines give huge compression and efficiency, these high bypass ratio fans give huge propulsive efficiency.. so we just scale it down, right?

WRONG!

if the turbine or compressor tolerance is 0.02" for blade-radius on the airbus, and we scale the engine down by 10x in every dimension, our part tolerance is STILL 0.02" since that is the best part we can make... that is now TEN TIMES THE ERROR on an engine that is one-tenth the size. in other words, the smaller engine has ten times the losses due to manufacturing tolerances. this means that you can NOT have a big fan with a small turbine.. the losses due to imperfections in the geometry of the engine are TEN TIMES GREATER, so the turbine can not be one tenth the size in each direction... that turbine is too small to work efficiently! remember, A FEW GRAINS OF SAND GOING INTO THIS ENGINE WOULD BE THE EQUIVALENT OF THROWING BAGS OF GRAVEL INTO THE ENGINE OF THE A-380.

so a small engine can NOT be as good as a big one, because the manufacturing tolerances become 10x as large, so the turbine must be larger, so the bypass ratio must be lower. (a larger turbine is by definition a lower bypass ratio, if the total air going thru the engine is held constant)





ok, so, our very light jet that is a scaled down airliner goes 1/3 the speed of an airliner,
going 1/3 the distance,
and actually does WORSE than the above because the the bypass ratio is lower because the turbine cannot be that small.
so now we are down to 250 knots or so.. maybe 300 knots if we put a bigger engine on and sacrifice even more range.

guess who flies alongside us if we are flying in a jet at 300 mph?

this brings us to our NEXT 2 fundamentals:


FUNDAMENTAL REASONS A 300-MPH JET WILL >>>NEVER<<< BE AS GOOD AS A 300-MPH PROP:

1:
the thrust we get from air is the momentum-change: amount of air we grab times how much we accelerate it
the fuel flow we put into the air is the kinetic energy: amount of air we grab times how much we accelerate it SQUARED
therefore, for any propulsion system to be efficient, it must take a LOT of air and accelerate it a LITTLE.
thus, all else being equal, the HUGE prop of a lancair is inherently more efficient than the tiny compressor of a mini-jet


2:
an internal-combustion recip engine gets the same compression ratio no matter how fast it turns. set the throttle to idle, take-off, cruise, descent, approach, or holding-pattern... it makes no difference: if the compression ratio of the engine is 7:1, you will get that compression ratio at all power settings: 7:1... the compression ratio is realized no matter how fast or slow the engine is turning... the piston still covers the same sapce in the cylinder, regardless of speed.

the JET engine, though, must turn at 100% rpm to get it's designed compression.. if the jet turns 1% less rpm than redline, compression is lost, and efficiency with it... the compression is caused by the dynamic pressure on the blades... 1% less speed on the blades is 2% less compression across them, with the resulting loss in efficiency. you can only run a jet on-design at 100% rpm... any speed less and the efficiency falls apart... no surprise that going to low power settings still involves huge fuel-flow... a jet engine at low power is losing compression! a jet engine at low power is like a recip engine that is losing compression and needs to have it's pistons replaced!!!!!!!!!!





so there you have it. 4 fundamental laws of physics that prove that a VLJ can't work:

-a plane that is 1/10th the size has 1/1000 the weight and thrust, but 1/100 the parasite drag, so will go about 1/3 the speed, all else being equal
-a plane that is 1/10th the size will have 10 times the manufacturing error in size-ratio, resulting in a larger turbine and therefore lower bypass ratio

so the small jet cannot go as fast as the a big jet, so we are down to 300 mph, so comparing to props:
-a plane with a jet takes a smaller bite of air than a plane with a prop, so cannot have the same propulsive efficiency
-a plane with a jet cannot run at lower power settings for much of the flight, like a prop can, without huge losses, because the compression ratio i only maintained at 100% rpm


these are 4 FUNDAMENTAL LAWS that keep a VLJ from becoming a reality.


ok, enough about physics.

lets talk about emotion.

vern raburn had a bajillion dollars and the term 'disruptive technology' in his arsenal... show me a pilot that does not love the term 'disruptive technology'.
he claimed that he could make vljs with this 'disruptive technology'... 2 majors bits of this 'disruptive technology' were friction-stir welding and small jet engines.
which fundamental, listed above, is overcome by friction stir welding? he attached pieces of metal together in a slightly different way. attaching pieces of metal together in a slightly different way. ok. fine. got it. which fundamental, listed above, does that work around? what on earth does that do to make the airplane faster, or use less fuel?

the other 'disruptive technology' was a small jet engine. everyone loved that the engine was so SMALL. the engine is so small and light, it MUST be good! well, look at fundamental #1 in section #2 above... the SMALLER the jet engine, the WORSE IT IS!!!!!!!! IT GRABS LESS AIR! the smaller it is, the more the air must be accelerated, so the more the kinetic energy that must be imparted to it, so the more the fuel flow must be.

so vern's plane was supposed to have disruptive technology to break barriers. the friction stir welding is totally immaterial and irrelevant to flight performance, and the small engine is the exact OPPOSITE of what you need for efficiency... the smaller the engine is, the WORSE it is!


ten thousand pilots thought that with enough money and engineering and use of the word 'disruptive technology' we could side-step the laws of physics.
BS!


the payload, speed, and range of the eclipse-500 and the x-1 cavallo prove that VLJ's just don't work as well as turboprops or larger jets.

to do what the eclipse is supposed to do, you have to buy a piaggo avanti... fundamental #1 in section #2 above proves it.
there can be no airplane that is 1/10 the size of an airliner but still gives the same performance... fundamentals #1 and #2 in section #1 above proves it.
if i want to travel far as fast as i can go in a small plane, then fundamentals #1 and #2 in section #1 above prove that i can only go half the speed of an airliner, and fundamentals #1 and #2 in section 2 above prove that i have to do it in a lancair-4P or lancair Evolution.