Pan Pipes and Whistles

Introduction

Pipes and whistles use a resonating air column that’s open at one end and usually closed at the other. The length of these resonating columns are a quarter of a wavelength (plus a small fudge factor).  So, different frequencies (pitches) are determined by the column length according to the relation:

 Frequency*Wavelength=Velocity (of sound)

Note: a pipe with one closed end resonates at a quarter of a wavelength.  If it’s open at both ends the resonance is at half a wavelength. Closed pipes produce lower frequencies for a given length.

The SCAD Programs

If you don’t have access to the Open SCAD program you can download a free copy at:  

http://openscad.org/

To customize your pipes or whistles, edit the SCAD file(s).  You could make a copy and rename it if you’re worried about messing something up or just download another fresh copy.  There are two modules in the “pan_pipes” program.  The main module called “pan_pipe()” contains variables that set the parameters for the pipes.  In the whistles program the main module is called “pan_whistle()”.  The first variable choice is “rin” that sets the inside radius of each tube (in mm).  “Gap” in the “pan_whistle()” routine sets the distance between the venturi and knife edge to adjust the length of the high velocity air band.   Then “wall” determines the wall thickness of the tubes (you could try 1mm for faster printing if your printer is well tuned). The “band” variable sets the length of adhesion pads printed at each end of a pipe for adhesion to the bed while printing.  The switch variable “adhesion” can turn on additional adhesion side wings if you have problems or may be printing with ABS.  Note: adhesion > 0 adjusts the wing spread.  Finally, “num_sides” is the number of sides on the tubes.

The design programs allow for two octaves of pipes/whistles starting at A4 (i.e. 440 Hertz) as the basis for customizing a pan pipe/whistle array.  The lowest frequency was determined by the printer bed size.  One quarter wavelength of 440 Hertz sound is about 195 mm and that just fits across an 8” (200 mm) printer bed.

In the main module you’ll find a frequency array called “freq_array” that lists the semitone frequencies for a chromatic scale.  It also lists the number of each frequency entry in the array (i.e. a list of pointers for you programmers).  To select the desired pipes, the number of the frequency listed in the “freq_array” are entered into the array variable “pipes”.  This determines which pipes are chosen and the order they will be arranged for printing.  So, if you choose, the order of the pipes may be mixed up into any order.   So copy the line with the “pipes” variable, then comment out the original and select the number of the frequencies you want in your design (note: enter the numbers separated by a comma).

After editing “and saving” the file, run OpenSCAD by pushing the F5 key (Preview) which executes the module command at the bottom of the file.  If you like the design, push the F6 key (Render) followed by the F7 key (Export as STL).  Your custom design is now ready to slice and print.

Printing

I sliced the files with a 0.25mm layer height, 2 vertical shells, and used 4 top and bottom horizontal shells for a 0.5mm nozzle.  I had infill set at 15% but didn’t see many cases where this was employed.  When printing with ABS I found problems with bed adhesion.  There is considerable thermal cooling (tension) forces in the filament tracks along the length of the pipes.  To minimize this, the pipe “wall” thickness was reduced to 1.5mm, the “band” variable was increased that set the length of adhesion pads at each end of the pipe and the adhesion variable set to greater than zero (0).  The thermal stresses across the width of pipe set doesn’t seem to be as much of a problem due to the short printing runs in that direction (until the printing connects the tops of the pipes).

Hints

If you are printing with PLA you may only need a minimal length of the “band” variable for adhesion purposes.  Note: setting the “band” variable longer than a pipe length can produce an unusable design.

If your pipe set contains any of the longest pipes, you could position them in the center of the array i.e. for example, “pipes[8,0,12];” and then rotate the STL file 45 degrees for better bed placement.

The pipes may need tuning if the frequency isn’t correct.  Geometric factors can change the effective pipe length.  Adding or subtracting a small amount to the “fudge” variable can correct this.  Note: in the whistles program “fudge” also adjusts the pipe length to account for the gap air column in the mouthpiece.  Since the velocity of sound varies with temperature that may also need correcting.

Choosing an odd number for the “num_sides” means the top wall of the pipe will print lengthwise instead of bridging.  This can produce a smoother inside finish.

The smallest useable “rin” value seems to be around 4mm for the lower tones. 

A sweet spot for “gap” (length of the air band) seems to be around 6mm or 7mm.

I found that it took more air to make a sound with the pipes than with the whistles. 

You’ll need to blow all the whistles together in the locomotive “Air Chime” for a realistic effect.

Design Discussion

It’s recommended that the width of a resonant pipe be about 1/10 that of the length.  This rule of thumb is aimed at minimizing the effect of the pipe wall on the vibrating air column.  Unfortunately, the design programs have used a fixed inside radius “rin” (half the diameter of the pipe) for all pipes as an expedient in the program calculations.  When the Open SCAD program runs it echo’s the approximate length of the pipes selected. So as an approximation for the optimum pipe diameter the average of the lengths could be used to determine (an optimum) “rin” for the pipe radius.

Whistles use a venturi to shape a band of air and increase the flow velocity across a knife edge.  Air flow from one side of the knife edge leads to a resonant cavity and the other side leads to an exit port.  The venturi air flow restriction is why whistles need less air when compared to pipes.  To understand how a whistle oscillates consider that the band of air is divided by the knife edge.  The portion that enters the resonant cavity tends to compress the air in that column due to the momentum of the air stream.  After peak pressure, the air starts moving out of the cavity and deflects the band of air toward the exit port.  The pressure in the cavity drops and at some point the air band is not deflected towards the exit port but sucked toward the cavity side to fill the partial vacuum in the resonant air column and the cycle repeats.

There were a number of pitfalls in designing whistles (a kilogram of plastic worth).  I initially tried using a horizontal air band and knife edge for ease in printing but couldn’t get a smooth venturi surface due to the ripples in the bridging filaments.  The whistles went “hiss”.  On later reconsideration, the problem may have been the size of the gap between the venturi and the knife edge.  This distance sets the amount the air band can be deflected by the pressure changes in the resonator.

I switched to a vertical air band with exit air ports on the top and bottom of the whistle.  The whistles can be fine-tuned with a fixed distance variable called “gap” in the “mouth_piece()” module.  Note: “gap” is preset to 6mm which works well with “rin=5mm”.  But as “rin” is increased the “gap” may need to be adjusted for optimum performance.  Changes in the “gap” varies the effective length of the air column in the “mouth_piece()” section which will affect tuning.  A tuning factor correction may need to be added/subtracted from the “fudge” variable in the “pan_whistle()” module to fine tune the frequency.  There is a crude tuning approximation in the “fudge” variable to adjust the pipes frequency to that of the whistles but have not been compared to a reference frequency.

I had adhesion problems with the pan pipe design printing with ABS.  Increasing the “adhesion wings” helped but still didn’t produce a clean print. The whistles printed considerably better with the extra wings.

Enjoy !!!!