Cannon Shot Questions - Some Physics

[Halsafar]

Alright, I made a little diagram of the situation.
Now, this is suppose to be 3D, but the screeny is a 2D Example.

I understand the following:
- Calculate intial Force based on the yaw of the turret and the pitch of the cannon (angle and up angle).
- vV = vU + (vA * t); I can calculate the velocity and have it accelerate
- vGravity += (0,-9.81,) * Mass; Apply that to the velocity vV += vGravity;

Things I need explained:
- How to apply wind force? is wind force a vector? how come it is always explained in a scalar? do the weather channels take the magnitude of the wind vector?

- Will the simple accelerator and gravity application above cause the parabola effect as a cannon shot should.

- How do I calculate the terminal velocity and apply it? as in the velocity at which an object stop gaining downward speed (right?).

- Does wind resistance or gravity or both apply to acceleration force? or the current velocity?


Thanks in advance,
Halsafar

[Halsafar]

I have the application built, now all I need are the above questions answered.

This is a project to aid in the design of my next game. I will be posting the source and all of this physic demo probably tomorrow if I can get this sorted out today.

[wossname]

I'd just have a vector for the 4 main things...

1. Cannonball position
2. Cannonball velocity
3. Gravity
4. Wind

Use the cannon to set the initial velocity to some large quantity (i assume you are using metres per second as your units?) with the appropriate angle. then for each time step add both the wind and gravity to your velocity (taking the mass of the projectile into account using simple acceleration laws) then simply add that resultant velocity to the position of the cannonball. That should be all there is to it.

You might want to give the wind vector a more accurate feel by adding the [reverse of the cannonball velocity] to it. This will give a more accurate 'local windspeed'. I haven't worked out the appropriate math for that though.

Wind resistance effect would be hardly noticable for something like a cannonball, given its large mass and small volume and surface area. Terminal velocity (due to gravity) for a cannon ball is significantly greater than that of, say, a cricket ball.

I'll do the math now and get back in an hour or so...

[Halsafar]

I figured that much myself. Applyin wind resistance to the velocity bugs me a bit tho.

A ball will continue to accelerate at the same force, gaining velocity of course.
Wind resistance applys only to velocity doesn't make sense, you think it would also slow the acceleration.

This application has to apply to a cannon ball and a golf ball...two round objects of completely different mass.

[Halsafar]

I give my ball an acceleration and an initial force to apply to the acceleration...like the explosion in the cannon.

Gravity applies to the current velocity right?
So -- some accelerations could very well lift a cannon ball up forever?
This seems to happen, if I hit the ball with enough force it NEVER comes down because the acceleration in the y direction is way greater than the cumulated gravity vector.

[azteched]

A cannonball is only accelerated by the cannon for a small time, during the firing process. After that the main forces on it are gravity, and air resistance.

The cannonball will only never come back down if its velocity just after firing is greater than the Earth's escape velocity - you can easily calculate the escape velocity by considering energy conservation.

You seem to have the idea that the cannonball is accelerated upwards during flight - this isn't true - the upwards force and acceleration only applies during the firing process.

[Halsafar]

Yes I did recently read an article which confirmed all youve said.

The ball is fired at a 45 degree angle for example, it has inital upward acceleration but the pull of gravity immediatly begins to apply to the acceleration as soon as it leaves the barrel.

So, I have a question.

Doing physics (assume we are in a vacuum):
Is it accurate that a CannonBall: (all is measured in milliseconds)
Mass - 113.0f kg
ShotForce - 20km/ms
Angle - 90 Yaw, 45 Degree Pitch (face north, arc cannon at 45 deg up)

According to the near realistic app i've built:
Ball Travels: 4.11km, peak height 0.75km


Edit: The average weight of a cannon ball is 491.4kg or 30 pood (1 pood = 16.38 kg). My application is an attemp to create an environment for any ball.

[azteched]

20km/ms

Do you mean 20km/s, as in 20 000 m/s?

At that speed it'll go into space!

(I think the escape velocity for earth is around 13km/s)

[Halsafar]

Yah -- That flaw is obvious.

Anyone want to check my math for me?

//Get time -- the time passed between the frames -- in milliseconds
t = m_Timer.GetDelta();

//Apply Gravity
m_vBallAccel.y += m_vGravity.y; //(-9.81 / 1000) -- the time is applied next

//Continue to accerate velocity
m_vCannonBallVel += m_vBallAccel * t;

//Determine displacement -- first new position then the true displacement
Vector vDisplacement = m_vCannonBallPos + (m_vCannonBallVel) +
m_vBallAccel*0.5*(t*t);
vDisplacement = vDisplacement - m_vCannonBallPos;

//Deal some collisin detection, then add the displacement to the CannonBallPos


Edit: I do not think I have this down right.

[azteched]

Vector vDisplacement = m_vCannonBallPos + (m_vCannonBallVel) +
m_vBallAccel*0.5*(t*t);

It's simpler than that:

DisplacementThisInterval = (Average Velocity over Interval) * dt

You can approximate the average velocity by (NewVel + OldVel) / 2. Or just use NewVel, it probably won't matter unless you're going for actual physical modelling (but in that case the whole discussion is a bit moot).

[Halsafar]

what is dt?
t is time. whats d? distance?

I am going for real physics.
I am writing a tiny physics simulator, where you fire a ball from a cannon, you get to set all the variables of the ball and the force of the blast.

The project is to prepare for my next game I plan to create. If you can assist me that would be great. As of now I am working in a vacuum, so I need to find the proper velocity, acceleratin, gravity equatins -- the realistic ones. All I can locate is the corner cutting equations for most games.

[azteched]

dt is a time interval, in maths/physics you use d(something) to represent a small amount of it (a differential) - so dt is a short time interval.

[Halsafar]

As d as in Delta as in that triangle with a thick side...
You know, after all the physics sites I've been studing, none have notation...I always just assumed d was delta..

[azteched]

(delta)t = "a small but finite time interval"

dt = "an infinitesimal time interval"

dt is a differential. If you want to know more, read up on calculus.

I am going for real physics.

Again, how real? You will have to cut corners at some point.

[Halsafar]

Real enough to simulate close to perfect golf.
I am not going to simulate wind currents but I do intend on creating wind.
I do intend on putting spin into the equation and how the air effects it, how the spin effects its bounce.

I just cannot seem to find the ideal website to study from....I think I may finally have one tho.

No I am not making a golf game, and I am not going to take into consideration the mis-shapen sphere's either. Like a golf ball has dimples to aid its spin and keep it in the air longer. A spinning golf ball with dimples in the air travels FARTHER than in a vacuum. But I will always assume what is being fired is a perfectly round shape.