✍ Ping-Pong Anemometer

3D printed...

Sphere anemometers are simple devices that use the wind drag force on a sphere to determine the wind speed by equating the weight of the sphere with the drag force in a pendulum like configuration.

The drag force is the force that a sphere feels when traveling with a certain speed latex2png equation in a viscous fluid (relatively to the fluid, in our case air). This forces depends on the relative velocity between the air and the sphere, on the density of the air latex2png equation, effective area in contact with the fluidlatex2png equation and an adimensional coefficient latex2png equation called the drag coefficient. In this case this force amounts to

latex2png equation

Note that the drag coefficient latex2png equation is a geometric factor and is usually determined experimentally. For a sphere, for high enough Reynolds numbers, the drag coefficient is around 0.5.

Apparently this kind of anemometer was invented in 1900 by G. Daloz. Modern versions includes a ping-pong ball.

Equating the weight of the sphere

latex2png equation

with the drag force in a pendulum like configuration for a given equilibrium position one gets

latex2png equation

and for the velocity:

latex2png equation Where D=2 R is the diameter of the ping-pong ball.

Given that a ping-pong ball has mass of 2.7g and a typical diameter of 40mm one gets for the density rhoball=2.7/(4*pi/3*2^3)~0.081 g/cm^3

and thus

latex2png equation

Here's the OpenSCAD file:

// Author: Tiago Charters de Azevedo
// Maintainer: Tiago Charters de Azevedo

// Copyright (c) - 2016 Tiago Charters de Azevedo (tca@diale.org)

// This program is free software; you can redistribute it and/or modify
// it under the terms of the GNU General Public License as published by
// the Free Software Foundation; either version 3, or (at your option)
// any later version.

// This program is distributed in the hope that it will be useful,
// but WITHOUT ANY WARRANTY; without even the implied warranty of
// MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE.  See the
// GNU General Public License for more details.

// You should have received a copy of the GNU General Public License
// along with this program; if not, write to the Free Software
// Foundation, Inc., 51 Franklin Street, Fifth Floor,
// Boston, MA 02110-1301, USA.


// Gravity aceleration
g=9.8; //(m/s^2)
rhoair=0.001225; // (g/cm^3)
// pi
pi=3.1415926;

/*Drag coeficiente
.5 sphere
see: https://en.wikipedia.org/wiki/Drag_coefficient
*/
Cd=.47;

// Ping-Pong
D=.04; // (m)
mball=2.7; // (g)
A=pi*pow(D/2,2);
rhoball=mball/(4*pi/3*pow(100*D/2,3));// 0.081; // (g/cm^3)

// Font size
fsize=4;

R=100;
h=2;

coef=1;//3.6*0.621371;
module slice(h=2){
    difference(){
        cylinder(h,R,R,center=true,$fn=64);
        translate([0,2.5*R/2,0]){
            cube([2.5*R,2.5*R,2*h],center=true);}
        translate([2.5*R/2,0,0]){
            cube([2.5*R,2.5*R,2*h],center=true);}}}

module vscale(){
    for(alpha=[0:5:89]){
        v=coef*sqrt(pi*g*rhoball*pow(D,3)*tan(alpha)/(3*A*Cd*rhoair));
        rotate([0,0,alpha]){
            translate([-R*.99,0,-0]){
                rotate([0,0,-0]){
                    linear_extrude(height=h,scale=1,twist=0,convexity= 0){
                        text(str(floor(v*10)/10),size=fsize,font="Arial Black:style=Bold",center=true);}}}

            translate([-R*.8,-1*0,h/2]){
                sphere(h/2,center=true,$fn=64);}}}

    translate([-R*.7,-1*0,h/2]){
        sphere(h/2,center=true,$fn=64);}


    translate([0,-R+2,0]){
        rotate([0,0,90]){
            linear_extrude(height=h,scale=1,twist=0,convexity= 0){
                text("m/s",size=fsize,font="Arial Black:style=Bold",center=true);}}}}

//difference()
{
    intersection(){
        union(){
            difference(){
                slice();
                cylinder(10,R*.7,R*.7,center=true,$fn=64);}
            translate([0,-R/2,0]){
                cube([6*h,R,h],center=true);}
            translate([-R/2,0,0]){
                cube([R,6*h,h],center=true);}}
        cylinder(10*h,R,R,center=true,$fn=64);}
    vscale();}


cylinder(h,3*h,3*h,center=true,$fn=64);

difference(){
    union(){
        cylinder(3*h,h,h,center=false,$fn=64);
        translate([0,0,3*h]){
    sphere(h,center=true,$fn=64);}}
    translate([0,0,2.5*h]){
        rotate([0,90,0]){
            cylinder(3*h,1,1,center=true,$fn=64);}}}
Palavras chave/keywords: anemometer, ping-pong, 3d printer

Criado/Created: 08-05-2016 [18:12]

Última actualização/Last updated: 23-01-2017 [09:16]


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