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Inspired by building a new drone, I got lost in curiosity. What if I have a fixed length of rotor blades and a target amount of lift I want to, well, lift. How do you calculate the number of blades?

I have read a lot about disk loading and was intrigued by this answer (https://aviation.stackexchange.com/a/32252/44213) which found a correlation between diskloading and amount of blades (or lift per blade). It made me wonder; is it actually possible to calculate the number of blades? If it matters (and I guess it does) I want to use a naca0012 airfoil.

Searching around I did find the relation between the number of blades and decreasing efficiency/lift per blade when you add a blade. Also the fact that is would be easier to lengthen the blades is something I found. But if lengthening is not an option, how can you actually calculate this? And, to complete the question disturbing me, what effect does a second disk (like the chinook) have on these calculations?

Any help is much appreciated. Any links will be read thoroughly.

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Determining the number of blades is one of the steps in designing the main rotor of a helicopter, but not the first one. The main rotor design process is an iterative process with quite a few input parameters, which depend on the mission type:

  • Max. TO weight
  • Max. speed
  • Installed engine power
  • Autorotation performance
  • Noise
  • Manoeuvring g
  • Blade profile
  • Blade area
  • Vibratory loads

Using these inputs, the design process determines:

  1. Rotor diameter. This determines the disk loading: lower disk loading results in better hover performance and auto-rotational performance, higher disk loading in better cruising flight performance.
  2. Tip speed. As close as possible to the drag divergence speed in cruise, also a limiting factor in selecting rotor diameter.
  3. Rotor solidity. How much disk area is actually occupied by blade area, determined by blade stall limits in manoeuvres. Increasing the rotor solidity requires more engine power, but increases the blade stall margin.
  4. Number of blades. Mostly based on dynamic criteria, less on aerodynamic ones. The Bell 212 shows that rotor solidity can be increased by using wider blades, but using more blades minimises vibratory loads and the noise per blade passing.

The rotor design process is quite broad, and can best be found in the theory books which also contain statistical data to aid the initial stages. The plot below is from Leishman and shows that light helicopters have a blade length of about 4 meters, apparently a good length for this weight and mission type.

enter image description here

The overlapping twin rotor disks of the Chinook result in one rotor operating in the wake of the other, reducing efficiency and requiring more disk area. So total disk loading will reduce.

Two good books on helicopter stuff: Helicopter Aerodynamics, Stability and Control by Ray Prouty, and Principles of Helicopter Aerodynamics by J. Gordon Leishman.

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  • $\begingroup$ Thanks so far. What I try to understand is, what does an extra rotorblade actually add in lift, percentage wise? And what should be deducted for the overlapping disk area at e.g. the ch47? It surprised me that the diskloading/m2/blade for many helicopters is about 8.7, but for the ch47 it is 15,3. Do you have some gestures to help me understand? BTW: I start thinking from scratch, so the other parameters can be dependent variables. $\endgroup$ – Arie Jan 30 at 10:32
  • $\begingroup$ “... what does an extra rotorblade actually add in lift, percentage wise?” Depends on what we are comparing, add a rotor blade to a rotor that can already lift a helicopter means we’re only adding drag if we don’t keep total blade solidity equal. The disk loading per blade is not a main initial aerodynamic design parameter and we cannot look at only that without considering all other related parameters. The answer you link to suggests that blade loading is a main design parameter, which is not really how it works. $\endgroup$ – Koyovis Jan 30 at 19:52
  • $\begingroup$ OK, I think I understand what you mean; normally the blade is designed to fit the needs of the rest. But, what if you want to design a drone and have to work with available blades. Not to be picky, I just like to understand the matter and sometimes I end up thinking the other way around than it is normally done. It helps me to understand why. Sorry for that. $\endgroup$ – Arie Jan 31 at 21:34
  • $\begingroup$ Some calculations here $\endgroup$ – Koyovis Jan 31 at 23:40

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