I don’t know that you’d be able to shrink everything. Those bags of pretzels can’t get much smaller.
<homer>
mmm…nanopretzels
</homer>
Yep, I’ve seen guys fly model aircraft with miniature jet engines. It’s very impressive to see. And the sound is incredibly accurate with respect to their full sized cousins.
[They’re all miniature turbo fans these days…I’d love to see some of the old timey mini pulse jets in action.]
[nitpick]The mini-jet I saw is much smaller than a 2 foot diameter - the widest part of the thing was about 2-3 inches. [/nitpick]
Just wanted to clear up the size issue - accuracy counts! Have no idea how fast anything in it spins - I’m strictly a piston-pilot at this point, don’t know nuthin’ 'bout jets.
Still damn impressive, though.
Like all othe turbines, they drink fuel like fish drink water. Not a whole lot of flying time on the fuel tank, which seems to be a problem with the little jets - keeping enough fuel on board to get useful time out of the engine.
Pulse jets for models are available, but aren’t widely used (even banned by several R/C clubs) for two reasons: it’s difficult to make an effective throttle for a small one, so they get dangerously fast (260 mph!); and they’re really loud.
Yep, Gunslinger, I know pulse jets are still available. But as noted, they’re banned by many R/C clubs and not widely used - hence my comment about how I’d love to see one in action 
Sorry to pop back in again, but my ‘human’ was simply wrong – heavier-than-air, powered, sustained, controlled was the milestone the Wright brothers achieved. Others (and even themselves) had flown in a powered craft before. Not that it’s not the most important event in aviation - all those factors had to be there to show that the experience could be (somewhat) safely repeated.
Yeah, I remember when I had my first joint…
I apologize if my quick skim missed the direct mathematical answer you requested. Please be aware that the following is approximate.
A 747-400 is 231ft 10 inches long, and masses 339,000lb (passenger version, empty) I don’t know its total volume, but the passenger and cargo bays have ca 25,000 cubic feet of combined usable volume, and total fuel tank volume is over 9000 cubic feet, so allowing the cockpit/lounge deck, mechanicals, double-wall shell and bulkhead volume, engine nacelles, and other unaccounted volumes in the wings and tail, I think that 50,000 cubic feet is not an unreasonable guess
Your hypothetical model would be 1:116 scale. It would have 1/(116^3) or 1/1,560,896 the volume and weight of a “real” 747-400, or 55.352 in^3 of volume weighing 3.475 oz (or, in metric, 907 cc and 98.5 grams) for a net overall density of 0.1086 g/cc [which is less than 1/3 the density of compressed waste cardboard according to the US Department of Energy]
By comparison, oxygen has a density of ca. .0007138 g/cc (16g/22,415cc at 1 atm pressure and 32F/0C) and nitrogen is 7/8 as dense (allowing us to disregard the fact that the published figures for a 747-400 disregard an implicit bouyancy from atmospheric air)
The scaled down model would be roughly 150 times as dense as air - exactly the same as a real 747 (since weight and volume scale identically with the cube of the length) However, the wing surface area scales down with the square of the length, so the ratio of the wing surface area to mass is 116 times that of the ‘real’ 747 . This is the oversized lift-to-weight ratio the early responses alluded to.
However, not all aerodynamic factors scale identically - e.g. the size and magnitude of normal atmospheric turbulence cells (or any turbulence) is constant, regardless of the craft flying through it. The mini747 would be dramatically affected by trivial turbulences. Slamming a door in your room might make your modelplummet as if it were flying through turbulence. A normal up or downdraft might make it act as if it were caught in a microcell (which has caused crashes off the end of runways on approach) Increased surface to mass ratios giveth and they take away, too.
Such a plane would not fly at all identically to the original. That’s why a paper glider (which has far less wing surface area per gram than any ‘full-scale’ aviation glider, much less any powered airplane) can ‘fly’ well, unpowered, at a few miles per hour, but ‘real world’ airplanes need speed ranging from US highway speeds to Indy 500 speeds or more to take off (A two-seat Cessna 150 typically takes off at ca. 50-55 mph; the steam catapults on a US aircaft carrier throw fighters off the deck at 165 mph; a 747-400 takes off at 180+ mph [more when heavily laden, or in hot and humid, or high altitude airport conditions)
Thanks KP. That was the specific type of conversion I was looking for. Wow, 3.5 oz for a two foot long model seems pretty light. I thought it would be much heavier.