MAX ball shot trajectory

[Nitroxextreme]

I know that most teams must be working out the math as to how far they actually can shoot the ball with a 12 m/s speed

I'm sure that people are also playing around with the concept that if you are moving forward when shooting you will have a faster speed and hence longer trajectory

However, I believe that if you are really planning on shooting the "long shot" your not gonna want to be moving because even if you can shoot it really accurate standing still once you move there will be almost no accuracy.

So who has figured out the ideal angle and hence the maximum trajectory?

[Donut]

Part of that depends on what height your shooter is at. We were originally planning on a higher shooter, I was getting that with a shooter 54" off of the ground shooting the ball at 12 m/s at a 45 degree angle, you would be able to land the ball in the goal from just under 45', without air resistance. With air resistance my guess is the maximum range will be somewhere within a few feet of 40'.

[racsan12345]

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.

For more calculations refer to my
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 = initial angle + .5)
{
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) //To change height difference, change the 1.3 (meters).
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;
}

[Donut]

Originally Posted by racsan12345

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.
}

Why are you using a starting velocity of 12.8 m/s? I believe we're limited to 12 m/s.

[Tatsu]

Racsan, your calculations dont make sense

once the ball reaches maximum trajectory, drag DECREASES ay not increases it.. so the plus sign there doesnt make sense.. you need an if statement.. if vy is negative, then change the sign on drag.

Anyway my data say

.798 radians at 9.97 meters launched at 12 m/s

The only simplifying assumption I made was that
drag in x direction = dragcoef*vx^2 rather than taking the sine of the drag.. its accurate enough I believe.

Tatsu

[Kevin Sevcik]

The easiest way to figure the direction of the drag is Fx = Fd * Vx / V, actually. You need all those numbers anyways. Back on the topic of the thread, though, I get a maximum range somewhere around 30 to 35 feet depending on your Cd assumptions. It's all terribly approximate because our ball might be rough enough for the Cd to start at .2 when the ball is traveeling 12 m/s. Then jump up to .416 as it slows down.

[racsan12345]

Originally Posted by Tatsu

Racsan, your calculations dont make sense

once the ball reaches maximum trajectory, drag DECREASES ay not increases it.. so the plus sign there doesnt make sense.. you need an if statement.. if vy is negative, then change the sign on drag.

Tatsu

Tatsu,

When v_y is negative, it makes atan(v_y/v_x) makes theta negative, thus making sin(theta) negative. So you wouldn't need that if statement.

[binary_sandman]

shooting the ball into the top goal is very Probable the ball itself is 7in the goal is 40in more tham 4 times the size;
traveling at 11.9meters per second to be safe;
39.041984feet per sec which can be made from the middle of
the field (in theroy).
conclude this there is a good chance this will work esp.
we have already programed Autonomous and most of
drive motors
{1388 all the way}

[Tatsu]

racsan - agreed. sorry, my mistake

[Lil' Lavery]

45 degrees is the angle that will give you the greatest maximum range from the goal, but that's is not the only factor to be considered. Because the goal has a top there is a period where you cannot shoot, as your shot would be hitting above the goal at that point. Also, because of the wall there is a period where your shot will hit the wall before it can get high enough to pass through the goal.
Thus why I suggest a variable angle.

[ThomasP]

You don't need variable angle to get a better range of shots, you can have variable force to have the same effect.

[lukevanoort]

Although this isn't entirely on topic, make sure that you don't end up too far above the minimum. The goal slants forwards just a little bit, so any power over what you need to score it and it'll smack the top of the goal and fall onto the platform.