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!

Photograph of Wright Brothers propeller reproductions between 1911 (left) and 1903 (right). Propeller lengths are 8 ft. 6 inches.  
Photograph of Wright Brothers propeller reproductions between 1911 (left) and 1903 (right). Propeller lengths are 8 ft. 6 inches.

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 = AE/A0, where expanded area AE = Expanded area of all blades outside of the hub.
  • Developed area ratio = AD/A0, where developed area AD = Developed area of all blades outside of the hub
  • Projected area ratio = AP/A0, where projected area AP = 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’ve prepared following table for kids to have some fun.

#10V/5A15V/5A17V/5A10V/10A15V/10A17V/10A17V/Max A
1N/AN/AN/AN/AN/AN/AN/A
2120016501800N/A (4.40A max)2480 (8.8A max)31003070
3138016001780N/A (6.33A max)290031003300
41360 (4.79A max)172016901360 (4.79A max)2300 (8.89A max)33003450
51300 (4.61A max)170019001300 (4.61A max)2700 (8.31A max)33003400
61150 (4.23A max)155016701150 (4.23A max)2250 (8.25 max)2710 (4.5A max)2710 (4.5A max)
71200 (3.96A max)190020001200 (3.96A max)2480 (3.96A max)3050 (8.36A max)3050
8N/AN/AN/AN/AN/AN/AN/A
9N/AN/AN/AN/AN/AN/AN/A
10N/AN/AN/AN/AN/AN/AN/A
11N/AN/AN/AN/AN/AN/AN/A
121410173018201420 (5.3A max)2920 (9.6A max)32403100
131400178018901580 (5.8A max)300033803300
141370167018001400 (5.1A max)2600 (9.22A max)29003000
X1N/AN/AN/AN/AN/AN/A2200

.. 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 … 😉

3 thoughts on “Propeller science

  1. Very interesting. Would be even better if I understood it all, but my conclusion is that if I need a new propeller for a boat, I will call you! Cheers, Serge

    ……………………………….. -Sent by “either” Robin or Serge. -Mail may be from; acrohc@me.com, acrohc@iCloud.com or acrohc@yahoo.com They are all valid. -Also, any bad grammar or spelling is due to self correcting!!!

    >

  2. Remember that a prop sucks in air, which means the air going past the blades is the sum of the vehicle speed, plus the incoming air speed, and that the angle of the blades needs to be sensible relative to that flow throughout the blade span. My free Fusion360 add-in “Airfoil Tools” has all the math to get that right (plus auto-selecting the correct blade profiles as well): See http://www.foils.pro

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