Re: Nerf ball starting at 12m/s 45 degree angle ending at 8ft 6in w/ air resistance
 

Aerodynamic drag is definitely a factor for a fluffy object like a Poof ball. It's not an extremely large factor, but it has a real and noticeable effect.

Re: Nerf ball starting at 12m/s 45 degree angle ending at 8ft 6in w/ air resistance
 

You're kidding right? You lose around 4 meters to air resistance fireing 45 degrees from 0 -> 0 at 12 m/s. This is fairly nontrivial. Initial deceleration is easy to calculate

F= 1/2 Cd * rho * A * v^2

for a poof ball, thats's about

F= 7.52e-3 * v^2

F= 1.08 Newtons.. that may seem insignificant.. but the poof ball is light..

F=ma=1.08 , so taking m = .18 kg we get a = 6.016 m/s^2 deceleration..

yes, that's about 2/3rds g, that's nontrivial.

Re: Nerf ball starting at 12m/s 45 degree angle ending at 8ft 6in w/ air resistance
 

You drive a Honda Scion, dont you?

(Aerodynamics ?! we dont need no stinking aerodynamics! :^)

Re: Nerf ball starting at 12m/s 45 degree angle ending at 8ft 6in w/ air resistance
 

ugliest...vehicle...ever...

Re: Nerf ball starting at 12m/s 45 degree angle ending at 8ft 6in w/ air resistance
 

Btw, the 2-dimentional version of calculation is done.

check the programming section for my mathematica notebook its called something like traj.zip.. gimmie a day and I'll also upload the raw data in CSV form.

Re: Nerf ball starting at 12m/s 45 degree angle ending at 8ft 6in w/ air resistance
 

For launching 4.5 feet to 8.5 feet:

Please input the initial velocity in meters per second: 12.8
Please input the coefficient of drag (0.07 - 0.5): 0.416
The uber best range is 14.7775 meters at an uber angle of 47 degrees.


C++ Code:
#include <iostream.h>
#include <math.h>

int main()
{
// float i = cos(x); x is in radians
// float i = atan(x); i is in radians arctangent

float x;
float y;
float v_initial = 12.8;
float v_x;
float v_y;
float initial_angle;
float theta;
float drag;
float area = pow((3.5 * 2.54 / 100), 2) * 3.14159;
float mass = .206; //kilograms
float C_D; //Coefficient of Drag
float a_x;
float a_y;
float increment = .01; //Incrementing time
float best_range;
float rad_conv = 2.0 * 3.14159 / 360.0;
float uber_best_range = 0;
float uber_angle = 0;

cout << "This program will calculate the maximum range and best angle to launch a 7 inch diameter poof ball." << endl << endl;
cout << "Please input the initial velocity in meters per second: ";
cin >> v_initial;

cout << "Please input the coefficient of drag (0.07 - 0.5): ";
cin >> C_D;

for(initial_angle = 10; initial_angle <= 80; initial_angle++)
{
x = 0;
y = 0;
v_x = v_initial * cos(initial_angle * rad_conv);
v_y = v_initial * sin(initial_angle* rad_conv);
best_range = 0;

do
{
theta = atan(v_y/v_x);
drag = .5 * C_D * area * sqrt(pow(v_x, 2) + pow(v_y, 2));
a_x = drag / mass * cos(theta);
a_y = drag / mass * sin(theta) + 9.8;

v_x = v_x - a_x * increment;
v_y = v_y - a_y * increment;

x = x + v_x * increment;
y = y + v_y * increment;

if(y > 1.3 && v_y < 0)
best_range = x;

}while(y >= 0);

cout << "At " << initial_angle << " degrees, the best range is " << best_range << " meters." << endl << endl;

if(best_range > uber_best_range)
{
uber_best_range = best_range;
uber_angle = initial_angle;
}

}

cout << "The uber best range is " << uber_best_range << " meters at an uber angle of " << uber_angle << " degrees.";

return 0;
}

--Ownage

Re: Nerf ball starting at 12m/s 45 degree angle ending at 8ft 6in w/ air resistance
 

nice, nearly identical code, different language.

(btw, you might want to run it for <1 degree increments)

Re: Nerf ball starting at 12m/s 45 degree angle ending at 8ft 6in w/ air resistance
 

Have I been trolled?

The Scion Xb is Toyota's ugly cube. Honda's ugly cube is the Element.

Re: Nerf ball starting at 12m/s 45 degree angle ending at 8ft 6in w/ air resistance
 

971 got .41 ish as our Coefficient of drag (using wind-tunnel testing). Can we assume this is verified. Also, I don't know if this has been explained, but the "rho" in the drag equation is air density, generally around 1.2 kg/m^3.

Re: Nerf ball starting at 12m/s 45 degree angle ending at 8ft 6in w/ air resistance
 

.41 matches prediction. prediction is .416 with flow of 12m/s