# Angle/Trajectory

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• 12-14-2003
JaWiB
Angle/Trajectory
I've been trying to figure out how to calculate a trajectory based on angle and speed, like you might do for artillery or something...

From what I've read so far, you can calculate x and y positions like this:

y = y_velocity*time - 9.8*t^2/2
x = x_velocity*time

Is that correct?

Where I'm lost is how to get the x and y velocities based on the angle to the ground and the force that is applied...

Anyone have any ideas, or is there a better way to do this?
• 12-14-2003
XSquared
Assuming that you are on flat ground, then the x velocity is v*cos( theta ), and the y velocity is v*sin( theta ), where v is the overall velocity, and theta is the angle.
• 12-14-2003
JaWiB
Does that mean that the x and y velocities will be the same? That doesn't sound right...
• 12-14-2003
XSquared
Whoops. The y velocity is v*sin( theta ).
• 12-14-2003
JaWiB
Ah, got it. Thanks
• 12-16-2003
JaWiB
A bit of a bump, sorry, but I tried to translate this into code, and it seemed best to put this in the original thread. Heres where I've got:
Code:

```float y_v; float x_v; float v=20 float Start; float theta=45 float y_v_0=0; //...get start time Start = GetTickCount(); //...calculate x and y initial velocity x_v=v*cos(theta*3.14/180);  //cos and sin take radians y_v_0=v*sin(theta*3.14/180);//degree->radian= theta*pi/180 //...Move the object (this section is being called over and over in a loop) float t=(GetTickCount()-Start)/CLOCKS_PER_SEC; //basing it on time y_v=y_v_0-9.8*t; BallX=x_v*t; BallY-=y_v;```
When I run the program, my ball (that's the object) moves in a parabola, but the angle looks more like 80+ degrees than 45 degrees...Any idea where I'm going wrong?
• 12-16-2003
Silvercord
firstly i don't know what clocks per sec is

secondly the distance travelled taking acceleration due to gravity into account is the average velocity for a time period multiplied by the time passed. Basically, change that -9.8t to -4.9t^2, the t^2 in this case is the time passed since the last time you moved the ball.

9.8t gives the instantaneous acceleration but not the distance travelled.

It works like this:

distance travelled = Vav * time

Vav = (speed1 + speed2) / 2

speed1 = 9.8t (assuming t is still the time OF THE OLD FRAME)
speed2 = 9.8(t+deltat), delta t is the time that passed this frame

it ends up being equivalent to 4.9t^2, as I stated above.

EDIT: Just so you know, this is how I do it in my 3D computer game, and it works perfectly
• 12-16-2003
VirtualAce
Just increase your y velocity by a set amount - it does not have to be exactly what gravity is or you could figure out what gravity's acceleration would be in relation to your world and your desired framerate.
• 12-16-2003
Silvercord
yeah, bubba's solution sounds like it might be easier, but i know mine works.
• 12-16-2003
VirtualAce
Yeah yours does....but I got that idea from Andre Lamothe and he has a point. Who cares what gravity really is...as long as it looks real enough no one will know.
• 12-16-2003
JaWiB
Well in this case I want to keep it consistent with gravity...The only way I've been able to get my path to look right (not sure if it is truly correct) was like this:
Code:

```float Dt = t; float O_y_v = y_v; t=(GetTickCount()-Start)/CLOCKS_PER_SEC; y_v=y_v_0-9.8*t; float d = ((O_y_v+y_v)/2)*(t-Dt); //Old y vel + y vel / 2 == average //d = vt and new_time - old_time = total_time //d = (old_y_vel + new_y_vel)/2 * (new_time-old_time) BallX=x_v*t; BallY-=d;```
Only problem is it doesn't move at the correct speed...I don't understand! Now what am I doing wrong?

Edit: Ah, I think I understand the problem...acceleration is 9.8 m/s^2, and I am assuming a pixel is a meter...

Ah, my brain hurts...there must be a way to speed it up without changing the actual path...no matter, I'll think of it eventually...Thanks, guys, and be sure to correct me if I'm wrong :)
• 12-17-2003
Silvercord
Jawib, I think all you need to do is figure out a conversion from world units (in your computer program), to feet. I've got a macro called FEET, so when I want 32 feet I do FEET(32), and that is what just calculates the conversion from feet to world units. Otherwise I'm looking at your code more closely, it's hard to read.

Quote:

Yeah yours does....but I got that idea from Andre Lamothe and he has a point. Who cares what gravity really is...as long as it looks real enough no one will know.
Okay, I thought you were referring to something different

EDIT:
Jawib, I think I found some errors in your code. I re-wrote it. Here's what I updated, it shows what i was trying to explain, and I tried commenting for you. You may need to change 9.8 to something that offers a conversion from meters to arbitrary world units in your program
Code:

```//discard for now //y_v=y_v_0-9.8*t; //float d = ((O_y_v+y_v)/2)*(t-Dt); //Old y vel + y vel / 2 == average //d = vt and new_time - old_time = total_time //d = (old_y_vel + new_y_vel)/2 * (new_time-old_time) //float O_y_v = y_v; //old y vel float oldt = t; //this is the 'old time' from last frame t=(GetTickCount()-Start)/CLOCKS_PER_SEC; //total # seconds passed since start time float        deltat = t-oldt; //time now minus time last frame float        d = ((9.8*oldt) + (9.8*(oldt+deltat))) / 2; //average velocity d *= deltat; //average velocity multiplied by time, I put this on a second line to make it more readable BallX=x_v*t; BallY-=d;```
• 12-17-2003
JaWiB
Well what I had worked...all I had to do was make time move faster:
Code:

`t=(GetTickCount()-Start)/CLOCKS_PER_SEC*Speed; //I set speed to 6.5`
I'm pretty sure it was accurate too...I made it so I can change the velocity and angle from within the program and it looked right

Anyway, maybe I'll try your method when I get home.
• 12-17-2003
Silvercord
may i see it? I'd like to just mess around with someone else's code :)
• 12-17-2003
JaWiB
Well if you want...I'm not the best at writing beautiful code though...Anyways I was using my own tga file loader class and you will have to change the path/file name if you want the object to show up. I didn't include my "ball" image, since it sucks
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