Right, physics time:
we could probably relate this almost directly to the vehicle's contact surface with the ground and it's weight (not mass; here weight is Fz=m*g)
While Giels equation is correct the classic form is W = m*g, where g is approximately 9.81 on the Earths surface.
Unless Warzone is going to implement wind (of varying strengths and directions) I do not think aerodynamics will do much for Warzone -- a car may weigh 1,200kg, a tank on the other hand, while larger in volume (and surface area) will probably weigh closer to 60,000kg. Since it is not 50 times larger in its surface area and probably goes slower than the car resistance due to drag is going to be a lot lower in proportion to its weight.
Friction between the tracks and the ground however, will be an issue. The equation for this (assuming the object is moving) is F = mu*R, where F is the frictional force in Newtons, mu is the coefficient of friction (normally between 0 and 1) and R is the normal reaction force. So long as there are no external forces acting in the vertical direction (e.g. strings) R = m*g. mu can be worked out for difference surfaces by experimentation (seeing how much force is required to get a smooth block on known mass to move horizontally).
Right, now onto energy and work done. The set of equations you want are: E = 1/2*m*v^2 = Fs. E is the energy in Joules which is equal to half times the mass (in Kg) times the velocity in ms^-1 (metres per second). Notice the squared term, this basically means that to increase your speed from 2ms^-1 to 4ms^-1 takes 4 times as much energy. This is also equal to the Force applied to the object times the change in distance. How does this fit into Warzone? Well we can give each engine an energy output and then using that in combination with the mass of the unit work out its maximum velocity.
Next stop: projectile motion. Everything when dropped from a height on the Earth (so long as it is not too high) accelerates at the same rate in free-fall, that rate is refereed to as g and is about 9.81ms^-2. What does this mean? If I dropped a block of lead and a block of wood (of equal surface area/volume) both would hit the ground at the same time.
A classical example of this is with the monkey and the hunter. A monkey is sitting atop a tree, when a hunter, who has climbed up a neighbouring tree decides to shoot the monkey. The monkey however has lighting quick reflexes and so as soon as the shot leaves the barrel of the hunters gun he lets go of the branch he was holding onto. The question is, what happens to the monkey? Sadly for the monkey the laws of physics are not on his side as the bullet drops at the same rate as the monkey falls, so regardless of the distance between the hunter and the monkey (so long as neither get a chance to hit the ground) the monkey gets hit.
Projectile motion tends to use the following three equations (which are actually the equations of motion, which have many uses). These are:
- v = u + at
- v^2 = u^2 + 2as
- s = ut + 0.5at^2
- u = initial velocity, in ms^-1
- v = final velocity, in ms^-1
- a = acceleration, in ms^-2
- t = time, in seconds
- s = distance travelled, in metres
By making the following assumptions about a projectile (lets say a golf ball):
- The motion is parabolic (so it makes an arc)
- Air resistance is negligible
It is possible to work out how far the golf ball will travel. Todo this we need to take the horizontal and vertical components of the golf balls motion and work with them individually.
Lets assume that a golf ball is hit by a golf club and begins to travel at an angle 45 degrees to the horizontal at a speed of 10ms^-1. Using this we can work out where it will land like so:
In the vertical direction:
u = 10 * sin(45) (remember trigonometry)
s = 0 (the motion is parabolic so in overall the vertical component does not change as we land at the same height we started at)
t = ?
v = ?
a = -9.81ms^-2 (we are going against gravity).
By placing what we know into s = ut + 0.5at^2 we get: 0 = 10 * sin(45) * t - 4.905t^2. Factoring t yields: t * (10 * sin(45) - 4.905t) = 0. So therefore t equals either:
- t = 0
- 10 * sin(45) - 4.905t = 0 => 4.905t = 10 * sin(45) => t = (10 * sin(45)) / 4.905 => 2.883s
We now have the time!
Since there is no air resistance there is also no acceleration in the horizontal direction (Newtons first law). So since a = 0; we get: s = ut. Now we know the time of the flight and so all we need is the velocity:
u = 10 * cos(45)
Giving us: s = 2.883 * 10 * cos(45) = 20.39m. So our projectile will take 2.883 seconds to reach its final destination and will travel 20m in the horizontal direction. Using these equations we can do accurate projectiles in Warzone.