Download or view CoriolisBall.frink in plain text format
/** 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. ***"]
Download or view CoriolisBall.frink in plain text format
This is a program written in the programming language Frink.
For more information, view the Frink
Documentation or see More Sample Frink Programs.
Alan Eliasen was born 19966 days, 22 hours, 3 minutes ago.