1922

DESIGN: Electrotor-SloMo ~ Rotor - Disk - 2 Blades vs. 3 Blades

Advantages of;

	2-blade Rotors	3-blade Rotors
Portability ⁽¹⁾	Portability ⁽¹⁾
Storability ⁽¹⁾	Storability ⁽¹⁾
Field Assembly ⁽¹⁾	Reduced field assembly ⁽¹⁾
Vibration:		Reduced vibration during forward flight ⁽²⁾
		Reduced vibration during maneuvering ⁽²⁾
Aerodynamic Efficiency ⁽³⁾	Aerodynamically more efficient ⁽³⁾
Gyroscopic Precession:	Slower, which is good ⁽⁴⁾	Less mass x shorter squared radius ⁽⁵⁾

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Notes:

2-blade per rotor will not require that the blades be removable for ground transportation, and the storage space will be less.
This is the result of the absolutely rigid rotors. The most objectionably vibration frequency for a pilot is 15 cycles/sec. At 700 RPM, 3-blade rotors will produce a rotor induced vibration of 35 cycles/sec, whereas 2-blade rotors will produce a rotor induced vibration of 23 cycles/sec. For additional information see; [Rotor Induced Vibration] below.
2-blade rotors should be more aerodynamically efficient; at least with a larger diameter they will be.
An advantage for the 2-blade rotor may be that slower rotational speed means the precessional frequency [caused by flight control change] increases and this should mean a weakening of the GP.
An advantage for the 3-blade rotor is the smaller mass and a shorter radius squared.

Efficiency: A slower RPM (and larger solidity ratio) will result in a more efficient aero-rotor. However, a faster RPM will result in a more efficient motor.

Blade Count Consideration: The tooling could be made for 2-blade rotors then they could be used later to produce for 3-blade rotors with greater thrust requirements

Power Requirement Comparison - 2-blade vs. 3-blade:

3-blade rotor will reduce the moments on the bearings and distribute this moment more equally around the circumference of the bearing races and the motor's air gap.

3-blade rotor will reduce the moment and increase the frequency of the vibration when weight-shift is applied, particularly at slow RRPM speeds.

3-blade should make it a little less effort to weight-shift due to the narrower chord.

Blades are probably going to be removable for storage and transportation therefore the 3-blade layout should not be detrimental.

3 bladed rotors are less efficient then 2 bladed rotors, however, more power can be obtained from the motor if it is run faster. This is because higher torque increases engine heat where as higher speed does not.

All specifications are the same except for; the RRPM (tip speed is the same), the number of blades, and the rotor diameter.

The following table is for comparison. ~ For current values see; Helicopter - Disk and Power Specifications for Intermeshing Configuration

Rotor Efficiency:

	Electrotor: ~ Interleaving 2-blades / rotor	Electrotor: ~ Interleaving 3-blades / rotor
Gross Weight:	300 lbs	300 lbs
Blades:	4	6
Radius:	6.0 ft	6.0 ft
Chord:	0.667 ft	0.5 ft
Taper:	0.0"	0.0"
Aspect Ratio:	11.1	11.1
Disk Area (one rotor):	113.1 ft²	113.1 ft²
Total Disk Area:	128.1 ft²	128.1 ft²
Effective Disk Area:	160.7 ft²	160.7 ft²
Twist:	-10º	-10º
Pitch:	9.38º	8.75º
Disk Loading:	2.34	2.34
Blade Loading:	18.7	16.7
Rotor Solidity Ratio:	0.125	0.140
Stagger:	1.25 ft	1.25 ft
Rotor Speed:	700 rpm	700 rpm
Tip Speed:	440 ft/sec	440 ft/sec
Power Momentum:	15.8 hp	15.8 hp
Power Combined:	17.37 hp	16.8 hp

Notes re Above Table:

The 4-blade rotors obviously require less power because their Solidity is greater.
Reducing the RPM and increasing the Pitch (or increasing the solidity) will reduce the power requirement of both.
When the 4-blade rotor is taken to 0.75" chord and the solidity of the two columns is equal the power combined is also basically equal. This implies that the blade count has no effect on the efficiency. ~ Strange.

Considerations re 3-blade Rotors & Slow RRPM, and perhaps Undercamber Airfoil:

The article Computational Investigation of Micro Hovering Rotor Aerodynamics in the April 2010 issue of AMH Journal says ".... micro air vehicles (MAVs) which typically operate between Re = 10³ and 10⁵......" .

For hovering with 3-bladed rotors which have; 5.0 ft Radius, 800 RRPM, 0.5 ft Chord, @ 0.75Radius and 0.33" taper/ft. The Reynolds number = chord (ft) x speed (mph) x 9360. Re = c x MPH x 9360., Re = 0.3125 * 314 * 9360 = 918,450 = 9.1 * 10⁵.

For one rotor of a two-rotor bilateral configuration helicopter, with a GW of 150lb per rotor, the power to hover is 6hp. per rotor by momentum theory and 5.2 hp by blade element theory. [from Prouty]

An interesting aspect related to the Reynolds number is that with tapered blades as the speed of the sectors increase when moving out toward the tip, the chord decreases. Therefore some of the change in the Reynolds Number is mollified.

Rotor Induced Vibration:

Thinking Preamble:

Two gyroscopes, which have their mass equally distributed around their circumference, will have their individual gyroscopic precessions mutually canceled by the rigid frame that joins the two rotors. See picture on OTHER: Flight Dynamics - General - Precession - Gyroscopic and Aerodynamic. This should also apply, in large part, to rotors with 3 or more blades.

However, the 2-bladed rotors will have 2 masses that are located at 180º to each other on the rotor disk.

With fast turning &/or high weight blades, there will be a 2P vibration. Slower &/or light weight blades will reduce the amplitude of the vibrations.

With outside forward rotating Intermeshing -to- Interleaving this vibration should be considerably noticeable during forward flight. This is because the force will manifest itself at the 270º azimuth and this has the shortest moment arm length between the center of the craft and the center of the force. I.e. it may appear like a 4P vibration.

Note that then the rotational speed is very slow (a gyroscope will wobble) the moment and thus the vibration will manifest closer to the azimuth of the force and not 90º later due to the gyroscopic precession. What will the azimuth be for the Electrotor-SloMO????

Vibration: Acceptability graph see OTHER: Aerodynamics - Vibration - Rotor Induced - Overview. The bottom of the bucket (worst frequency) is 15 cycles/sec.

I wonder if this 15 cycles/sec is the worst for the pilot's arm, which will be taking the majority of the vibration. In addition, the length and moment of the front legs, combined with their natural frequency MIGHT offset the 2 or 3P rotor induced vibration. Concern: This reduction in the pilot's perceived vibration will result from flexibility in the front 'legs' and this flexibility in the flight control is a detriment.

2P vibration: The use of rotors with 2 blades, a 6.0 ft radius and a speed of 730 RRPM gives an ideal tip speed of 460 fps. This will result in a 2/rev vibration at ((730 / 60) * 2) =24.3 cycles per second. This is near the worst area of 15 cycles per second, therefore perhaps consider 3-blade rotors, but this may not help much. At a rotor speed of 500 RPM = 8.33 per sec * 2P = 16.66 per sec which is at the bottom of the bucket. Using twisting of the rotor frame for yaw control will probably be VERY objectionable for the pilot's hands and arms.

A 4-blade rotor is a little better (33.33 per second), but not much. Using twisting of the rotor frame for yaw control will probably be VERY objectionable for the pilot's hands and arms.

Perhaps this is an argument for faster rotors, a smaller radius, and without the large chord?? 5'-6" radius and 900 rpm gives a tip speed of 518 fps. With 3 blades the vibration will be an acceptable 45 cycles per second. However, the power requirement will go up.

Alternatively, consider slowing the blades down below 730 RRPM. A 7-ft radius at 600 RPM gives a tip speed of 440-fps (0.4 Mach!). The rate of vibration is (600/60) x 2 = 20 cycles per second. Above the 15 cycles per second and NO GOOD.

Last Revised: August 17, 2011