Would a 2nd row of distributed props on a 2nd staggered wing of a biplane increase its efficiency? Would a 2nd row of distributed props on the rearward wing of a biplane with 25% gap and 150% negative stagger increase the efficiency of a biplane ULTRALIGHT, 25MPH, Re 500K? ( rear wing is 25% lower than forward wing, 150% rearward)

Both wings would have distributed propulsion from several props along their span in tractor configuration.

Forward wing props see a prop inlet speed of V1, or aircraft speed.

Forward wing sees V2 ( exit speed of prop), (assume an increase in speed of 50%, based on prop size, Hp using prop formula) V2=150%V1

Calculate forward wing size based on 150%*V1*k1

k1= efficiency/coverage factor of Wing1

Props of 2nd (rear) wing would have a inlet speed of V2, but an exit speed of V3 ( assume another 50% increase)

2nd wing sees a speed of V3=150%V2=150%(150%V1)=225%V1. 

Calculate rear wing size based on 225%*V1*k2

k2=efficiency/coverage factor of Wing2

An interesting note: average leading edge airspeed over wings is (150%+225%)/2=190% of aircraft speed!! ( if this proposed theory is correct)

Is this correct, at least conceptually? See side view of configuration below.
Source: nap.edu

Not really no. The velocity off a propeller does not shoot straight back, rather in circular motion (shown above and below).


Source: High-Lift Propeller System Configuration Selection for NASA's SCEPTOR Distributed Electric Propulsion Flight Demonstrator, NASA

From the conclusion of that NASA report on span-wise propellers generating lift:


  A potential constraint on the design of the high-lift propellers system is the total thrust. If large amounts of lift augmentation are required from the propellers, then high thrust values from the high-lift propellers are likely. If these propellers produce excess thrust, then the aircraft will be unable to sustain flight at the desired speed. This implies that drag producing devices may need to be added to the aircraft or the primary propellers operated as windmills to produce additional drag.


Applying the same conclusion to the biplane, thrust will be wasted, and possibly will work only in a limited angle-of-attack range for the prop-boosting-prop-boosting-wing idea.


Own work; variable pitch blade

Note that a very fast stream before a propeller leads to [forward] thrust losses due to the propeller's angle-of-attack (shown above). And the less efficient the thrust becomes, since the momentum change will be harder – propellers add little velocity to large amounts of air, in fact, the pressure rise (a thrust measurement, which also is indicative of the mass flow) is around only 2% for propellers.