OpenSCAD code to create organ pipe feet, customisable for size and shape
Aim: Produce a foot that must print without supports, based on these premises:
- Walls will be thick enough to support PVC pipe while organ being moved, eg on a cart over rough ground
- PVC pipe will be used for the resonating pipe
- The pipe will be stopped, not open
- Frequency will be given
- Mouth height calculated using frequency in this formula (stopped pipe) MH = [3.018 - 0.233 ln f]^5 (MH = Mouth Height; f = Frequency; ln = natural log)
- Flue (the slot in the languid through which air is blown) needs printing at high resolution for accuracy
- flue_width is calculated from the Ising formula (link below)
- Stem diameter, inside diameter of the stem connecting to the windchest
- Foot length - from windchest to mouth to resonator = user's choice
- Upper lip offset - achieved by aligning flue on languid [(https://www.colinpykett.org.uk/physics-of-voicing-organ-flue-pipes.htm#Offset)]
References:
- [Formula using windsheet width (the thickness of the air stream coming from the flue) to get Ising's number at https://www.mmdigest.com/Tech/isingform.html and https://www.rwgiangiulio.com/math/wst.htm [Beware, Imperial units] windsheet_thickness = (I^2 * f^2 * ρ * H^3) / 2P I = Ising's number; p = air density; P = air pressure; H = mouth height ]
- Mouth height: a = 440Hz, stopped MH = 8.1 (https://www.rwgiangiulio.com/math/mouthheight.htm)
- [Pipe length is: flue to stopper base - the pipe width + stopper pipe_length = 3386 / f - pipe_internal_diameter (plus a bit of headroom?) (https://www.rwgiangiulio.com/math/pipelength.htm) (https://www.ccoors.de/webpipecalc/)]
- Upper lip offset: (https://www.colinpykett.org.uk/physics-of-voicing-organ-flue-pipes.htm#Offset)