'Solidity' is indeed a valid prop parameter, think its the frontal area of the blades / swept area of the baldes (i.e. disc area).
More blades or wider chord, higher solidity
Contra-rotating prop, doubles it I imagine
I'm stabbing a bit here, being much more than 20 years ago..
But solidity would be increased to absorb more power from the same diameter (disc area), e.g. Spitfire prototype started off with a 2-bladed fixed pitch prop just under 10' diameter, ended up with either 5-bladed Rotol prop of 10'6" or in the Seafire's case, a contra-rotating prop with 2 sets of 3 blades.
This because power went from about 900 HP on the prototype to something like 2,200 Hp (maybe more) in the later Griffon engined versions Seafire) and yet prop diameter was severely constrained by layout and undercarrige length - hence increasing solidity.
Efficiency I think comes down to the difference between inflow and outflow velocity, very much like a turbojet VS turbofan, where the lower outflow velocity of a fan (but over a greater area) increases the efficiency.
A higher solidity prop would increase the ratio Vout/Vin, decreasing efficiency, one really wanting a smaller change in velocity added but over a larger area.
Propulsive efficiency isn't about how much air you can throw behind you and how much energy you can add to it, it's about how little energy you use to add a 'given amount' of energy to the propulsive medium (air)
However, I'm sure tip-speed comes into this as well, as anywhere near transonic conditions will ramp up the prop blade drag and reduce efficiency...
Having just opened Aerodyanmics for Engineering Students, Houghton & Brock..
Ideal Froud efficiency of an airscrew = 2V/(Vs+V) where V is the freestream velocity and Vs is the final velocity in the screw's wake, so as that increases efficiency reduces, Vs being in the denominator.
Another form of that formula is V/Vo (where Vo is the velocity in the plane of the disc, less than Vs but of course greater than V, the free-stream velocity)
Any real airscrew will have an efficiency less than the ideal Froude of course, but that is the basis of propulsive effciency, and a higher solidity will increase VS and reduce efficiency.
Nice to know it sort of fits my gut instinct expressed above
And hope that helps a bit
