One big propeller vs. multiple smaller propellers....

[Dusan Stan]

The question is which is better from the efficiency point of view: One big propeller or multiple smaller ones? Or are they the same?
My general impression is that a bigger one will have much more better efficiency as if you consider the following points:
1. lift is proportional to the area of the disk (momentum theory);
2. biggest loses are the tip loses, more propellers, more tips.

How all this changes with shrouded propellers? You eliminate tip loses, but is the assumption that increasing the number of propellers increase the shrouded wetted area and increases losses as well?

 

[russ_watters]

Efficient at doing what? What type of craft? What act? What is the equation/parameter for the efficiency you want?

 

[Dusan Stan]

Sorry; I thought the propeller efficiency is obvious: generating lift with the least amount of power. I do not think the type of craft is important, but let's assume we're talking aircraft.

 

[russ_watters]

Sorry; I thought the propeller efficiency is obvious: generating lift with the least amount of power. I do not think the type of craft is important, but let's assume we're talking aircraft.

The type of craft is important. There is a reason why helicopters and propeller planes have very different sized propellers: propeller planes use their propellers for thrust to move forward and helicopters primarily use them to generate lift to stay aloft. So, which are we talking about?

 

[Ketch22]

Sorry; I thought the propeller efficiency is obvious: generating lift with the least amount of power. I do not think the type of craft is important, but let's assume we're talking aircraft.

This can be a very interesting and sometimes counterintuitive challenge. The power required to just move a propeller is calculated from the surface area in contact with the water. The speed of the expelled fluid is determined by pitch and RPM, which affects the thrust produced. Friction with the liquid is a pure parasitic loss while loss of thrust due to cavitation is a relational loss. Efficiency implies the highest thrust with the lowest energy losses.
I order to find the answer to this question we would need to know; how fast do you want to go, what is the power available, what is the resistance you are working against, and what is the structure supporting your vessel. Too many variables at this point.

 

[Baluncore]

Sorry; I thought the propeller efficiency is obvious: generating lift with the least amount of power.

The propeller needs to be big enough to distribute the power of the motor. I think the issue is not the size and number of propellers so much as the size and number of motors that drive the propellers. The combined efficiency of a motor and propeller combination is a trade-off that will be evaluated over the entire performance envelope of the aircraft, with emphasis on critical safety situations.

 

[Dusan Stan]

Let's separate the stuff here to compare apples to apples:

The question is:
What needs less power to create same amount of lift/trust:
A. an helicopter having:
- One big rotor;
- 2 smaller rotors, assuming disk loading is the same;

B. an airplane:
- one big propeller
- 2 smaller propellers, same disk loading;

C. a boat:
- a single propeller;
- 2 smaller propellers, same disk loading or the equivalent parameter in marine environment.

I'm trying to disregard the efficiency of the engines, one engine vs. multiple engines, transmission, and compare only the way how mechanical energy is transmitted to the medium to create thrust.

 

[Baluncore]

The airfoil blade of a propeller is twisted along it's length to set the optimum angle of attack.
The width and thickness profile changes along the blade to allow for different airspeed and radius.
The area of the transducer disc should make no difference to the lift or thrust per unit area.

For a boat the minimum diameter of the propeller is proportional to √( power / (speed ^1.5 ) )
That says there is no efficiency change with change of size.

A helicopter rotor has little or no twist so the region of maximum lift moves dynamically along the blade. That makes optimum efficiency analysis very difficult.

 

[Dusan Stan]

The area of the transducer disc should make no difference to the lift or thrust per unit area

Should I understand that the lift is the same for the same area? What about the tip and other losses?

 

[Baluncore]

Should I understand that the lift is the same for the same area?

The lift will be the proportional to the total area of transducer discs. Therefore efficiency cannot be size dependent.

What about the tip and other losses?

What about them. Induced drag. More smaller tips = fewer bigger tips.

 

[jack action]

For the airplane case at least, despite these statements:

In general, the larger the prop diameter, the more efficient it will be.

(source: http://www.epi-eng.com/propeller_technology/selecting_a_propeller.htm)

Theoretically the most efficient propeller is a large diameter, slowly turning single blade propeller.

(source: http://www.nar-associates.com/technical-flying/propeller/cruise_propeller_efficiency_screen.pdf)

When reading the whole thing (and the more complete NACA document), we can see that the propeller efficiency is maximum at some value of $\frac{V}{ND}$ where $V$ is the true air speed, $N$ is the prop rpm and $D$ is the prop diameter. So any propeller diameter can give the maximum efficiency as long as it has the proper rpm.

 

[taigame24h]

tks you

 

[Tom.G]

https://www.nasa.gov/langley/ten-engine-electric-plane-completes-successful-flight-test
http://www.nytimes.com/2016/06/18/science/nasa-electric-plane-x57.html?_r=0

 

[Dusan Stan]

Nice information guys!
Returning to the original subject, If you consider the thrust created from the momentum theory perspective, a thin disk having pressure difference acting on the sides of it, Thrust = Disk_Area * Pressure_Difference; The pressure difference is not constant, it diminishes towards the edge where you have air "leaking"

For a single disk:
A = Pi * Radius^2;
Periphery = 2 * Pi * Radius;

For n disks:
A = n * Pi * Radius^2;
Periphery_n = n * 2 * Pi * Radius;

Considering same disk area, we can deduce that the Periphery increases with the sqr(n), so the region of "leaking" air becomes bigger and bigger with increasing the numbers of disks.

Is it wrong to assume that the best case is a single big propeller versus multiple small ones? Is any fault to my logic so far?

 

[rootone]

One big propeller night be more aerodynamically efficient, but multiple propellers has an advantage that by adjusting differential spin rates the propellers can also be used as a part of the flight control systems.

 

[Baluncore]

The pressure difference is not constant, it diminishes towards the edge where you have air "leaking"

The tip losses are called "induced drag". https://en.wikipedia.org/wiki/Lift-induced_drag

Considering same disk area, we can deduce that the Periphery increases with the sqr(n), so the region of "leaking" air becomes bigger and bigger with increasing the numbers of disks.

Is it wrong to assume that the best case is a single big propeller versus multiple small ones? Is any fault to my logic so far?

I think it is a mistake assuming there are only two variables. If the propeller blade is shorter then the tangential velocity will be less. Induced drag is proportional to the square of the velocity. Maybe you will find the square cancels the square root in your peripheral region.

The propeller is an airfoil that has a linear velocity distribution along the radius. A wing is modeled as having the same velocity distribution along the length. The propeller is twisted and the section changed along the radius to optimise lift at all points. A propeller also has elliptical tips to reduce the induced drag. Square cut propeller tips are usually only seen where ground clearance is important. If the tip came to a point, there would be low lifting area pressure difference at the tip, so low induced drag but there would be a greater wetted area.