Gyrobike

[Captain Canada]

That last one is pretty cool !

[Weaver]

But if you have a chain drive to the rear wheel, you're then going to have to turn that drive through 90 deg to turn the prop, which is going to add back in much of weight, cost complexity etc, that you're blaming the shaft drive for. Bear in mind that the simplest shaft drive engines (BMW flat twins, etc) also have an in-line crankshaft, which is inherently aligned with the prop. What I think you need is this style of engine, with a new gearbox on the back that has two output shafts, one going to the back wheel and one going to drive the prop. It's probably still going to need a chain to get the drive up from from the gearbox level to the prop axis, but that's always going to be a problem if you want the engine low down at the front and mechanical transmission.

[zenrat]

How about belt drive rather than chain.
The hovercraft we used at the poo farm had a Rotax microlight engine mounted low in the hull with the fan driven by a 3" belt.

[Weaver]

How about belt drive rather than chain.
The hovercraft we used at the poo farm had a Rotax microlight engine mounted low in the hull with the fan driven by a 3" belt.

Yes I thought of that too. Those Lockheed Q-Star quiet  recce aircraft used in Vietnam had a very large, very slow turning prop whose speed was reduced, and axis raised, by using a V-belt system, and that was a 210 bhp flat six engine.

[NARSES2]

The hovercraft we used at the poo farm

Now there is something I would want to steer well clear of 

[zenrat]

The hovercraft we used at the poo farm

Now there is something I would want to steer well clear of 

[steelpillow]

What I think you need is this style of engine, with a new gearbox on the back that has two output shafts, one going to the back wheel and one going to drive the prop.

It certainly needs something like that. The drive also needs splitting and feeding to two independent clutches before the main gearshift. The easy way to do that is to take them off opposite ends of the crank shaft.
The gear shift pedal needs mounting direct onto the gearbox and a long actuating lever is a bad idea, so that rather suggests a low-set engine in either a bike arrangement or a long chassis with the engine-gearbox flipped over so the engine lies behind the rider and the rear wheel behind that. A flat-twin or flat-four would avoid the cylinders being flipped upside-down. There was a flight-rated version of the Norton rotary, that'd be nice! But the long chassis is obviously heavier. Either arrangement suggests a propeller drive (pair of chains or shaft?) up the other side to a 90 deg bevel gearing onto the prop shaft.
I would not like a belt drive if it can be avoided. It's always prone to slipping at these power levels. A rare enough event nowadays, but a lot more dangerous on an autogyro than on a ground-hugging or unmanned vehicle (even if it has only poo to float on!).

By the way, thanks all for your comments, I am finding them really useful.

[zenrat]

Wankel engines are a solution in search of a problem.  The Norton rotary in the F1 street bike was a particularly unreliable piece of kit.  I wouldn't trust one to power a manned aircraft.

This photo is of a Moto Guzzi powered drone. 
GUZZI by Fred Maillardet, on Flickr
Note that the drive to the prop is taken from the front of the engine meaning that the "normal" clutch and gearbox could be retained.

[Weaver]

Nice one Fred - I didn't know about the Guzzi drone engine.

Now here's a thought. The Honda CX500/650 engine was also an across-the-frame V-twin, but it was notably shorter than the 'simple' Guzzi layout because it had it's clutch on the front of the engine and the gearbox alongside it instead of behind it:



Since the clutch is driven by a gear from the crankshaft, I see no reason why you couldn't have two clutches on the front of the engine: one driving the gearbox and one driving a jack-shaft on the other side that takes power to the start of the prop drive-train.

Steelpillow: I think you're over-estimating the problems of long gear linkages: they should be fine if they're properly designed:

1. Aircraft designers manage to get 'feel' into manual flying controls despite them being linked to the control surfaces by very long and convoluted systems of rods, wires and pulleys,

2. Some bikes have had quite convoluted gear linkages and still been perfectly rideable, the Moto Guzzi being a case in point. Also, since a sequential motorcycle gearbox is a one-axis lever instead of a two-axis gate, you can easily operate it via a system of Bowden cables. The old Vespa scooters had just such a system, with the gearshift being on a left-hand twistgrip. You needed to make sure that the cable tension and adjustment was spot-on for 'feel', but it worked just fine.