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The ideal propeller has one blade. For obvious reasons, that would be impractical. However, adding more blades causes each blade to operate in each others slipstream/downwash.

How to quantitatively estimate this interference?In other words, what is the real angle of attack and airflow speed seen by each blade

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  • $\begingroup$ Question seems incomplete @toshi-ba $\endgroup$ – rauberdaniel Jun 30 at 19:30
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    $\begingroup$ Single-bladed props with counterweights actually do exist. $\endgroup$ – quiet flyer Jun 30 at 21:34
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    $\begingroup$ There's a pun to be made here about the question completeness and single-blade props, I'm sure. $\endgroup$ – AEhere supports Monica Jul 1 at 10:39
  • $\begingroup$ just completed the question. sorry i signed up while typing the question $\endgroup$ – toshi ba Jul 1 at 18:47
  • $\begingroup$ The problem with this question is that you are asking for an estimate of something without defining the nature of the metric in which you want your answer. The last sentence is also a different question. $\endgroup$ – Juan Jimenez Jul 2 at 13:43
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For a simple 2D approximation, you can do it in a similar way to how you would analyze the effect of wake on a tailplane or any other body, i.e. by solving the flow field around both at the same time. Since the movement of the blades is cyclical and the flow is subsonic, each blade affects both the ones ahead and the ones behind it. Therefore, you would would need to solve for an infinite number of blades simultaneously so that the one in the middle would have a realistic airflow, but since the effect of the N-th blade will tend to nill, a good approximation can be had with just a few blades on either side of the studied one.

The process would look like this:

  • Choose the spanwise station of the blade you are interested in and the operating point (rpm and forward velocity) you want to study. These will give you the effective angle of attack for the blade station.

  • Knowing the angular blade spacing around the hub, the spanwise station you selected, the rpm and the forward velocity, find out where the first airfoil will be relative to the second one in a 2D representation.

  • Solve the flow field for an effectively infinite number of airfoils spaced this way. In practice solving for a relatively small number of blade instances will provide a good approximation of the real flow on the central blades in the series, as the ones on the edges are only used to provide boundary conditions resembling the real world case: Streamlines in a compressor blade cascade, from Yershov et al.

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  • $\begingroup$ thx for the answer. instead of studying the whole flow field, can i analyse the blades as series of diffusers/channels, (which would be the spaces between them) $\endgroup$ – toshi ba Jul 5 at 12:06
  • $\begingroup$ A "series of diffusers/channels" is essentially the same, it all depends on how you postulate your boundary conditions and how closely they need to match the real world, i.e. how far away from the blade do you want to take effects into account. $\endgroup$ – AEhere supports Monica Jul 5 at 12:09
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It's possible to calculate the losses for a given configuration, but it's not an easy task. Meanwhile, there is a hundred years worth of testing and experience with propellers, so if you have a classic prop design and want to know typical trends, you can find most of the results in the literature.

One of the best classic sources on this topic is NACA-TR-640 (1938!)

I'll quote one graph from it that is directly relevant to the question:

Power coefficient per blade

As can be seen, adding an otherwise identical blade causes a power loss of maximum 6-8% per blade (in static conditions, at zero speed), and very little (1-4%) in normal flight conditions.

Comparison of the respective propulsive efficiency curves (Fig.35 in the work) is even more interesting: the difference is even smaller, and in some regions (when the blades stall) the multi-blade props can be more efficient than two-blade ones.

In practice, when you need to absorb extra power from the engine and are constrained by the diameter, you have to increase solidity of the prop. You can do it either by adding blades or by increasing the blade chord. The paper demonstrates that adding blades is better in terms of efficiency. Thus the premise "The ideal propeller has one blade" is not necessarily true, given the realistic constraints.

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Power loss due to swirl is up to 10% of the applied power, depending on the applied thrust. From Prouty, Helicopter Performance, Stability and Control.

enter image description here

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