DRAG CALCULATION FOR ADDITIVE MANUFACTURED CONICAL NOSE UNDER VARIOUS NOZZLE SIZES USING FDM

This is a project to establish a relation between the drag force and diameter variation for a 3D printed conical structure that was printed for about 10.1 cm, using open source FLASHFORGE 3D printer. It is established that there is an almost linear increase in drag force for the increase in diameter due to the lower accuracy produced by higher diameter nozzles. The actual size of head for a Saturn five rocket was considered to comparison, and the value of 10.1 m.

The diameter increase results in almost quadratic increase in the frontal area, which further has directly proportionality to the drag force experienced. Thereby, there is almost a linear increase with the slope of about 1.25 for the curve.

This means that the increase in radius will result in corresponding increase in the drag force, but the slope being above 1, it is essential to maintain the compromise between both radius of rocket to carry the payload as well as the drag force experienced. The drag force indirectly sums up the fuel load in the rocket, meaning that there would be an optimal point between both the amount of fuel carried and the amount of payload carried.

clear all
close all
clc

% frontal area measured in case of CNC finishing
%data collected from printing 3 samples in FLASHFORGE 3D Printer for cones with diameter of 10.1 cm
disp('The common sizes of nozzles are: 0.15 mm, 0.25 mm, 0.35 mm and 0.4 mm')
disp('variation of 0.16 mm for every 0.1 mm increase in nozzle size - trial made with 3 cones printed')
%diameter of Saturn 5 rocket (in meters)
diameter_saturn_CNC=10.1;
%assume the diameter of the object remains the same for the additive manufacturing with 0.1 mm nozzle
%increase in diameter of about 0.16 mm for every rise in 0.1mm nozzle
%diameter in cm
% so diameter will have values differing in 0.16mm implying that it is divided into 62 values for 10 cms.
dia=linspace(1010, 1020, 62.5)
radius= dia/2;

%frontal area calculation for Saturn 5 conical tip to prevent drag 
%calcaulation formula obtained from NASA website (https://www.grc.nasa.gov/WWW/K-12/rocket/sized.html)
frontal_area= radius.*radius*3.14159265359;

%drag coefficient calculation
%data taken from NASA website (https://www.grc.nasa.gov/WWW/K-12/rocket/shaped.html)
disp('coefficient of drag for various nozzle cones as suggested by NASA are:');
disp('sphere = 0.07');
disp('prism = 1.14');
disp('bullet = 0.295');
disp('The most used is bullet type head ');
coeff_drag=0.295;

%density of air (kg/m^3)
density=1.225e-6;

%velocity of rocket to escape earth gravity (Ve = (2GM/r)^.5 ). Escape velocity is 11,186 m/s = 11118600 cm/sec
velocity=1118600;

drag_force_experienced=0.5*density.*frontal_area.*velocity.*velocity;

disp('So as you can see, there is a huge variation on the drag force experienced by the rocket ship');
%plot to describe the variarion 
plot(dia,drag_force_experienced, 'color', 'r');
set(gca, 'fontsize', 14)
grid on
xlabel('diameter of the rocket head')
ylabel('drag force')