/** This program calculates the effect of the Coriolis force on a kicked
    football.  (Or any other projectile).  It models the effects of the
    Coriolis force in 3 dimensions.

    For the equations and coordinate system used, see:
    https://en.wikipedia.org/wiki/Coriolis_effect#Rotating_sphere
*/

// Initial velocity components
veast  = 0 m/s
vnorth = 6.0015 m/s  // Less than this, ball stops short
vup    = 0 mph

// Initial positions    
east  = 0 yards
north = 0 yards
up    = 0 inches   // Initial height above ground.

timestep = 0.01 s

omega = 1 revolution/day      // Rotation rate of the earth

latitude = 33.63326 degrees // Atlanta airport

useCoriolis = true            // Change this to see with/without Coriolis effect.

t = 0 s
while north < 726 m and vnorth > 0.001 m/s
{
   t = t + timestep
   
   // Eastward component
   if useCoriolis
      aeast = 2 omega (vnorth sin[latitude] - vup cos[latitude])
   else
      aeast = 0 m/s^2

   speed = sqrt[vnorth^2 + veast^2]

   // Friction always works *opposite* of direction of rolling, so we
   // calculate friction components for each velocity component.
   vangle = arctan[veast, vnorth]  // Angle east of north
//   println["Angle is " + (angle->"degrees")]
   aFriction = -0.0248 m/s^2
   aFrictionEast = aFriction sin[vangle]
   aFrictionNorth = aFriction cos[vangle]

   veast = veast + aeast timestep + aFrictionEast timestep
   east = east + veast timestep
   
   // Northward component
   if useCoriolis
      anorth = 2 omega (-veast sin[latitude])
   else
      anorth = 0 m/s^2


   vnorth = vnorth + anorth timestep + aFrictionNorth timestep
   north = north + vnorth timestep

   speed = sqrt[vnorth^2 + veast^2]
   
   // Upward component
   // Rolling, so no upward acceleration
   aup = 0 m/s^2

   //if useCoriolis
   //    aup = aup + 2 omega (veast cos[latitude])  // Add coriolis effect upwards
   
   vup = vup + aup timestep    // deltaV = a t
   up  = up + vup timestep     // deltaDistance = v t

   println["t: "     + format[t, "s", 3]       + "\t" +
           "East: "  + format[east,"m",3]     + "\t" +
           "North: " + format[north,"m",3] + "\t" +
           "Speed: "    + format[speed,"m/s",3]]
}

if north < 726 m
   println["*** Ball stopped short. ***"]