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 19967 days, 12 hours, 12 minutes ago.