Propeller science

Propellers are planned as an essential tool for powering our blimp propulsion. A good understanding of the science behind those will make a difference between making the project’s numbers black or red. Blimp’s cruising speed needs to be as efficient as possible, while they also need to be powerful enough to provide necessary lift off power for emergency situations.

So let’s ask the Wikipedia first. Wikipedia, what actually is a propeller?

A propeller is a device with a rotating hub and radiating blades that are set at a pitch to form a helical spiral, that, when rotated, performs an action which is similar to Archimedes’ screw. It transforms rotational power into linear thrust by acting upon a working fluid, such as water or air.

Wikipedia

Even Wright brother’s first air-plane had one!

Now, reading through all that Wiki, you’ll reach the part describing the propeller geometry characteristics:

• Pitch ratio PR = propeller pitch/propeller diameter, or P/D
• Disk area A₀ = πD²/4
• Expanded area ratio = A_E/A₀, where expanded area A_E = Expanded area of all blades outside of the hub.
• Developed area ratio = A_D/A₀, where developed area A_D = Developed area of all blades outside of the hub
• Projected area ratio = A_P/A₀, where projected area A_P = Projected area of all blades outside of the hub
• Mean width ratio = (Area of one blade outside the hub/length of the blade outside the hub)/Diameter
• Blade width ratio = Maximum width of a blade/Diameter
• Blade thickness fraction = Thickness of a blade produced to shaft axis/Diameter

… all that reads very educated and is for me quite difficult to see which value will have an impact on our performance and how much it actually matter as there is a too many variables I can’t predict. So I took it a bit step sideways and prepared a tiny science project. Let’s use our code from OpenScad and generate some random-ish propellers and test how they operate in our intended EDF scenario!

I took our already-existing propeller code:

module edf_prop(leafs, twist, rot){
  //Nose
  Tx(-2)
  Ry(90)
  difference() {
    Tx(0){
     scale([1,1,1.3])
     sphere(1.55);
     cylinder(h = 2, r1 = 1.55, r2 = 1.55, center = false);
    }
    
    Tz(0.5)
    cylinder(h = 2, r1 = 1.45, r2 = 1.45, center = false);
    
    Tz(-1.2)
    edf_lead_in_hole();
    
    scale([1,1,0.4])
    Tz(1.3)
    sphere(1.45);
    vent_holes();
    
    Tz(-0.2)
    cylinder(h = 0.3, r1 = 0.45, r2 = 0.45, center = false);
  }

  //Inner tube Wraps
  nw = 12;
  for(w=[0:360/nw:359])
  Rx(w) {
    T(-2,1.45,0)
    Ry(90)
    cylinder(h = 2, r1 = 0.07, r2 = 0.07, center = false);  
  }

  *Tx(-0.1)
  Ry(90)
  TubeSimple(0.1, 1.5, 1.5, .1);
  
  //Propeller
  Tx(-1) {
  difference () {
    for(w=[0:360/leafs:359])
      Rx(w)
      proprep(tip_scale=1.48, L = 1.5, r = 4, twist = twist, rot = rot, naca = 1408);
      //delimiter
      Tx(-1)
      Ry(90) {
        TubeSimple(3, 4.4, 4.4, 0.6);
        cylinder(h = 2, r1 = 1.5, r2 = 1.45, center = false);
      }
    }
  }
}

And generated 14 scenarios:

T(0,-4,-4)
prop_to_print("1", "8/-30/-20", leafs = 8, twist = -30, rot = -20);
T(0,-4,-12)
prop_to_print("2", "12/-30/-20", leafs = 12, twist = -30, rot = -20);
T(0,-4,-20)
prop_to_print("3", "16/-30/-20", leafs = 16, twist = -30, rot = -20);
T(0,6,-4)
prop_to_print("4", "8/-40/-20", leafs = 8, twist = -40, rot = -20);
T(0,6,-12)
prop_to_print("5", "12/-40/-20", leafs = 12, twist = -40, rot = -20);
T(0,6,-20)
prop_to_print("6", "16/-40/-20", leafs = 16, twist = -40, rot = -20);
T(0,16,-4)
prop_to_print("7", "8/-50/-20", leafs = 8, twist = -50, rot = -20);
T(0,16,-12)
prop_to_print("8", "12/-50/-20", leafs = 12, twist = -50, rot = -20);
T(0,16,-20)
prop_to_print("9", "16/-50/-20", leafs = 16, twist = -50, rot = -20);
T(0,26,-4)
prop_to_print("10", "8/-60/-20", leafs = 8, twist = -60, rot = -20);
T(0,26,-12)
prop_to_print("11", "12/-60/-20", leafs = 12, twist = -60, rot = -20);
T(0,26,-20)
prop_to_print("12", "8/-50/-10", leafs = 8, twist = -50, rot = -10);
T(0,36,-4)
prop_to_print("13", "12/-50/-10", leafs = 12, twist = -50, rot = -10);
T(0,36,-12)
prop_to_print("14", "16/-50/-10", leafs = 16, twist = -50, rot = -10);

Code above generates 3D models like this:

Separated per picture, you can list through the gallery below. Each model has its ID, number of blades, blade angle and twist angle value.

Rendering and transforming it into STL model and consequently into a 3D printer code (GCODE) took a while, while actual printing took … days, but result was worth it!

Next stage is to collect some data on how each propeller behaves. We’ve designed a see-saw test-bed.

I prepared following table for kids to have some fun.

#	10V/5A	15V/5A	17V/5A	10V/10A	15V/10A	17V/10A	17V/Max A
1	N/A	N/A	N/A	N/A	N/A	N/A	N/A
2	1200	1650	1800	N/A (4.40A max)	2480 (8.8A max)	3100	3070
3	1380	1600	1780	N/A (6.33A max)	2900	3100	3300
4	1360 (4.79A max)	1720	1690	1360 (4.79A max)	2300 (8.89A max)	3300	3450
5	1300 (4.61A max)	1700	1900	1300 (4.61A max)	2700 (8.31A max)	3300	3400
6	1150 (4.23A max)	1550	1670	1150 (4.23A max)	2250 (8.25 max)	2710 (4.5A max)	2710 (4.5A max)
7	1200 (3.96A max)	1900	2000	1200 (3.96A max)	2480 (3.96A max)	3050 (8.36A max)	3050
8	N/A	N/A	N/A	N/A	N/A	N/A	N/A
9	N/A	N/A	N/A	N/A	N/A	N/A	N/A
10	N/A	N/A	N/A	N/A	N/A	N/A	N/A
11	N/A	N/A	N/A	N/A	N/A	N/A	N/A
12	1410	1730	1820	1420 (5.3A max)	2920 (9.6A max)	3240	3100
13	1400	1780	1890	1580 (5.8A max)	3000	3380	3300
14	1370	1670	1800	1400 (5.1A max)	2600 (9.22A max)	2900	3000
X1	N/A	N/A	N/A	N/A	N/A	N/A	2200

.. it sort of took weeks to get this done, but we’ve finished it! 🙂 As you can see there, prints 1,8,9,10,11 didn’t print properly, so they were not test. Still I think it all gave us some indication on what we are dealing with.

Having a fun, we’ve also added the X1 model – which is just a simple 2-blade propeller.

Putting it all in a graph – turbines 3,4,5 and 13 are clearly standing out.

Long story short – our winner is number 4! 8 blades, 40′ blade twist and 20′ blade rotation.

Oh, and I almost forgot – we had a bit of fun while doing that as well. Sebi asked what would it be like to throw in a paper napkin … 😉