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Push-pull configuration aircrafts usually feature identical engines and propellers working only in tandem for multiple reasons like higher speed, better climb rate, reliability, cost, ease of maintenance, etc.

It may sound unpractical for piston engines were saving fuel will not outweigh the downside of one engine being a dead weight but may be a good idea for lighter electric or a combo, where engines may also be optimized for different propellers.

Can it be possibly beneficial to have tractor prop for take-off:

  • blown lift
  • no FOD risk
  • less noise outside

and pusher specifically optimized for cruising:

  • larger diameter as no ground clearance issue
  • no parasite drag
  • more stability
  • less noise in cabin

Benefits to consider:

  • efficiency
  • higher achievable speed
  • higher altitude
  • still two motors for redundancy

Problems:

Stowing nose prop.
Foldable prop should be cheaper than VP.

Less take-off power.
Electric motor for tractor could drive 4-bladed prop at peak power.

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  • $\begingroup$ What do you want to do with the set of props not optimized for the current flight speed? Let it windmill? Put it into a bay ? Keep it as a non optimised propeller still trying to power the aircraft? Let them acts as airbrakes? (Feathering seems to be excluded as you don't want pitch variability enabled) $\endgroup$ – Manu H Dec 6 '19 at 11:00
  • $\begingroup$ whatever will be the optimal solution. Putting into a bay / folding would be probably the best one for low speed prop to minimize drag for a high speed one and windmill may work for a cruise prop as it is only for a short time period $\endgroup$ – Anbu Agarwal Dec 6 '19 at 13:48
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    $\begingroup$ To stow a propeller while continuing to use the engine you will need a clutch, which is usually a heavy and relatively complicated piece of equipment. $\endgroup$ – AEhere supports Monica Dec 6 '19 at 15:23
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    $\begingroup$ I would expect an engine to weight even more than a clutch, but yes, multiple loads on a single engine are not impossible. $\endgroup$ – AEhere supports Monica Dec 6 '19 at 16:32
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    $\begingroup$ The best option is a horizontally locked pusher propeller and winch launching. Landing will be in unpowered glide. No deadweight from second engine. $\endgroup$ – Peter Kämpf Dec 21 '19 at 10:04
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This doesn't specifically answer the question in the title, but from the body of your question I would say it's possible, if you had an electric push/pull configuration with a motor in the nose and one in the tail, or at the back of a fuselage pod with booms like a Cessna Skymaster.

The aft facing motor could use simple fixed pitch folding propeller that folds aft and trails in the slipstream when not being driven (popular with motor gliders) and it would be used only for take off and climb, with climb-optimized pitch. In cruise that motor could be shut off and its batteries assigned to the front motor and its blades would fold into a near zero drag trail position. The front motor could have a fixed pitch prop optimized for cruise.

The key issue would still be worst-case climb performance. It would have to be able to make enough thrust on the single cruise pitched prop at the front to climb decently if the back motor failed. Possibly if the front electric motor had some sort of emergency boost feature, where it's torque could be temporarily increased (enough to get its coarse pitched propeller up to red line) for a certain number of minutes without overheating, would be sufficient for single engine safety, with the rear propeller folding back on its own for you.

For single engine performance on the rear motor, you might get away with just a brake for the front propeller to stop it from windmilling if its motor failed. Not as good as feathering, but far less drag than windmilling.

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