## Aerodynamic rotor (optimal number of blades)

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brötchen
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### Aerodynamic rotor (optimal number of blades)

So i have been reading all sorts of blogs,wikipedia articels etc. about UAVs and, especially rotor-wing type UAVs, which got me thinking about what factors influence rotor design.
to me it seems that the most important aspect of a rotor that is intended for UAV is efficiency which, in this case means maximum specific impulse.
according to my limited understanding of aerodynamics and physics specific impulse should increase as the amount of air that is moved increases which would mean a higher number of blades would increase efficiency as the surface area of the rotor, and therefor the amount of air influenced at any given time, is increased. but why than is it that most small helicopters and rotor-wing UAVs only use 2 or 3 blades and wind turbines usually only use 3 blades as well?
wouldn't more blades improve performance/endurance/MTOW?

jmorgan3
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### Re: Aerodynamic rotor (optimal number of blades)

I can't find anything specifically about blade number in my textbooks, but wikipedia has a couple of leads. The article on wind turbines has an uncited section which gives a plausible explanation of the various trade-offs.

The article on propellers links to a 1943 Popular Science Article which briefly describes the trade-offs as applied to high-powered fighters.
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gorcee
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### Re: Aerodynamic rotor (optimal number of blades)

Each rotor is essentially a wing. And each wing creates both lift as well as drag. So adding rotors increases drag, which increases the load on the engine. Smaller helicopters have less powerful engines, due to both size, weight and cost constraints.

brötchen
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### Re: Aerodynamic rotor (optimal number of blades)

The wikipedia page you linked states that there is a "diminishing return" and goes on to claim that there is a 6% increase in efficiency when increasing blade count from 1 to 2 which confuses me as i would have thought that having twice the blade area would mean twice the power.

Moose Hole
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### Re: Aerodynamic rotor (optimal number of blades)

In iRobot (the movie) they had a ceiling fan with one curved blade, and a counterweight on the opposite side. I think that's more about style than efficiency though.

gorcee
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### Re: Aerodynamic rotor (optimal number of blades)

It should also be mentioned that rotors don't work by "pushing air downwards." Although there is a downwash component, and an associated momentum transfer, a rotor is just a spinning wing, and lift is primarily obtained by creating a pressure difference between the upper and lower surfaces of the rotor.

jmorgan3
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### Re: Aerodynamic rotor (optimal number of blades)

brötchen wrote:The wikipedia page you linked states that there is a "diminishing return" and goes on to claim that there is a 6% increase in efficiency when increasing blade count from 1 to 2 which confuses me as i would have thought that having twice the blade area would mean twice the power.

Remember that an airfoil changes the velocity field of the air all around it. The two blades are basically in each other's downwash, meaning that neither can individually extract the power that a single blade can.
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thoughtfully
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### Re: Aerodynamic rotor (optimal number of blades)

It's hard to be balanced with a single blade, though.

Blades also add weight. Might not be important in a wind turbine or watercraft, but it matters a lot to things that fly.

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Korrente
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### Re: Aerodynamic rotor (optimal number of blades)

I don't build aircraft, I just operate them so I may be wrong on some points, but here's how I simplify the issue to myself:

It's primarily torque and drag. Think about a 2-bladed rotor (as in one blade on each side) that has a good mass but it's not huge and the engine is able to spin at maximum RPM without issue. Also it's balanced easily and the anti-torque rotor doesn't have to spin terribly fast to counteract that force.

When you get into turbine aircraft they have the power to drive those four/five/six/nine big blades around and are willing to accept the added drag just because they have the excess power to overcome it and make the most of the added lift.

So your question comes down to what kind of RPM you want and how powerful your engine is.

Also, more blades (especially with propellers) usually means you can run at a lower RPM and generate less noise.

Jakell
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### Re: Aerodynamic rotor (optimal number of blades)

I thought that the video on this site of a mono-copter was pretty cool.

I have read that for fairly small things, a single blade can be most efficient, and as you scale them up, the increased available force becomes worth the extra weight and drag. Sadly, I can not remember where I read this...
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Carnildo
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### Re: Aerodynamic rotor (optimal number of blades)

Jakell wrote:I have read that for fairly small things, a single blade can be most efficient, and as you scale them up, the increased available force becomes worth the extra weight and drag. Sadly, I can not remember where I read this...

For driven rotors (eg. airplane propellers), the optimal number of blades is determined by how powerful the driving system is: if, at maximum power, the blade tips are moving faster than the speed of sound, you need more blades. (Sometimes you can make the blades longer instead, but space constraints don't always permit this.)

p1t1o
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### Re: Aerodynamic rotor (optimal number of blades)

gorcee wrote:It should also be mentioned that rotors don't work by "pushing air downwards." Although there is a downwash component, and an associated momentum transfer, a rotor is just a spinning wing, and lift is primarily obtained by creating a pressure difference between the upper and lower surfaces of the rotor.

Lift is directly proportional to the downwash.

It is purely that momentum transfer keeping you up.

That is not to say that pressure gradients are not involved - however, it is more true to say that lift is purely obtained by forcing air downwards, though you cannot do this without creating pressure gradients.

gorcee
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### Re: Aerodynamic rotor (optimal number of blades)

p1t1o wrote:
gorcee wrote:It should also be mentioned that rotors don't work by "pushing air downwards." Although there is a downwash component, and an associated momentum transfer, a rotor is just a spinning wing, and lift is primarily obtained by creating a pressure difference between the upper and lower surfaces of the rotor.

Lift is directly proportional to the downwash.

It is purely that momentum transfer keeping you up.

That is not to say that pressure gradients are not involved - however, it is more true to say that lift is purely obtained by forcing air downwards, though you cannot do this without creating pressure gradients.

Yes, but it is something of a mis- conception that lift is created solely by the downwash itself. It's somewhat inaccurate to think of a wing (or rotor) as generating lift purely by shoving air down; even though the downwash terms appear in the computation of the coefficient of lift, the overall picture of lift is still a (dynamic) pressure times area type of relationship.

In other words, it's not completely correct to say that things fly just by pushing air down without any consideration of the formation of the pressure field and its associated issues. The untrained observer won't really understand the difference.

p1t1o
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### Re: Aerodynamic rotor (optimal number of blades)

Hmm. It just sounded like you were dismissing the massflow and momentum transfer a fair bit, it sounded like you were implying that you could generate lift without moving air downwards, it almost sounded like *gasp* you were referring to equal transit time *spit*

Forgive me for falling into your "untrained observer trap" but is not "formation of a pressure field" the technical term for "forcing the air downwards" in any case?

Perhaps we are getting confused by a chicken/egg scenario, at the moment I am thinking purely in terms of reactionary forces whereas if you are an engineering type (am i right?) then I'm guessing for you the pressure gradient comes first, and the subsequent motion of the air is almost a secondary effect?

I hope I'm not speaking out of turn

gorcee
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### Re: Aerodynamic rotor (optimal number of blades)

p1t1o wrote:Hmm. It just sounded like you were dismissing the massflow and momentum transfer a fair bit, it sounded like you were implying that you could generate lift without moving air downwards, it almost sounded like *gasp* you were referring to equal transit time *spit*

Forgive me for falling into your "untrained observer trap" but is not "formation of a pressure field" the technical term for "forcing the air downwards" in any case?

Perhaps we are getting confused by a chicken/egg scenario, at the moment I am thinking purely in terms of reactionary forces whereas if you are an engineering type (am i right?) then I'm guessing for you the pressure gradient comes first, and the subsequent motion of the air is almost a secondary effect?

I hope I'm not speaking out of turn

The important considerations depend purely on context.

If I'm looking at the maximum takeoff weight of an aircraft, then the relevant piece of information is that we need [imath]L=\frac{1}{2}\rho U^2 S C_L > W[/imath] at some takeoff velocity [imath]U=T_{to}[/imath].

If I'm designing the wing for that aircraft, then I need to consider all of the factors that go into computing that [imath]C_L[/imath], which includes downwash and vorticity, 3-D wing effects, etc.

If I'm designing the control system for this wing, then the pressure fields become more important once again. The forces on the control surfaces are the relevant factors, and these are most immediately related to the pressure distributions around the control surface. Remember that force is pressure times area, and when looking at design considerations that are largely concerned with F=ma in its various forms, pressure is usually the thing we care about most.

In other words, a naive reader might look at a pure momentum transfer argument and say, "well clearly we can get more efficiency if we just angle the wings more to push more air down." Sadly that's not how it works, because even assuming that we're not getting flow separation, it neglects the effect of drag, which is much more easily understood as a pressure-related phenomenon.

p1t1o
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### Re: Aerodynamic rotor (optimal number of blades)

gorcee wrote:
p1t1o wrote:etc etc etc

etc etc etc

Haha, ok I think we're on the same "how sh*t flies" page I was just initially shocked at your earlier statement!

gorcee
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### Re: Aerodynamic rotor (optimal number of blades)

p1t1o wrote:
gorcee wrote:
p1t1o wrote:etc etc etc

etc etc etc

Haha, ok I think we're on the same "how sh*t flies" page I was just initially shocked at your earlier statement!

A couple other comments, not directed at you, but for anyone who might be watching the thread:

One of the cautions against using a pure downwash/momentum argument is "how does a plane fly in level flight?" Obviously, the wing is producing lift, and in doing so, is generating a non-zero downwash component. So there is a momentum in this fluid heading earth-ward, but where is this momentum conserved? The vehicle isn't going up since it's in level flight. So the momentum must be conserved elsewhere in the flow field. And it is, in trailing vortices (and tip vortices, though there is still a momentum conservation in 2-D flow in say a wind tunnel where there is no space between the tunnel walls and the wing tips).

So for level flight where the vehicle has no net vertical momentum, it's definitely apt to say that the vehicle is being suspended by a pressure field acting upon the wing with exactly the same force as the force of gravity acting against it.

Zamfir
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### Re: Aerodynamic rotor (optimal number of blades)

One of the cautions against using a pure downwash/momentum argument is "how does a plane fly in level flight?" Obviously, the wing is producing lift, and in doing so, is generating a non-zero downwash component. So there is a momentum in this fluid heading earth-ward, but where is this momentum conserved? The vehicle isn't going up since it's in level flight. So the momentum must be conserved elsewhere in the flow field. And it is, in trailing vortices (and tip vortices, though there is still a momentum conservation in 2-D flow in say a wind tunnel where there is no space between the tunnel walls and the wing tips).

That's a good point, but I would say that any argument in favour of either "pressure" or "momentum" helps to sustain confusion. Much better to stress that pressure and mass flow are two sides of the same coin, like pushing against a wall and the wall pushing you.

IMO, a good starting point to "why do wings generate lift"is to ask "why not?". Shapes affect the flow around them, and for a non-symmetric shape it would be a special case if those flow fields did always balance out their net forces. Poisson flow is such a special case, but for realistic flows you would expect that most shapes generate a net force, and that some produce a lot of net force.

That takes the issue out of an ever-deepening series of "yes, but why" questions, and instead shifts to the much more mundane question of "why are wings particularly useful generators of force".

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