Egg Movement: How to Simulate an Egg's Movement on a Level Plane

[burrkie]

Hi guys,

Im trying to create a simple application for a college project based on an egg moving around a level plane. I've looked around and I've been finding it very difficult to find any equations to simulate the movement of an egg. If anyone has any ideas or could point me in the right direction that would be brilliant.

 

[Danger]

Welcome to PF, Burrkie.
I'm a total amateur, with no education, so I might be off-base here. My first thought, though, is that you should be able to treat the egg as if it were a simple cone. If it is raw, though, I really haven't a clue as to how the fluid dynamics and weight transfer of the white and yolk will affect the movement.

 

[Molydood]

I think the key will be with modelling the location of the centre of gravity relative to the contact patch of the egg on the surface, as that is what will effect its inclination to roll one way or the other.

 

[Andy Resnick]

Hi guys,

Im trying to create a simple application for a college project based on an egg moving around a level plane. I've looked around and I've been finding it very difficult to find any equations to simulate the movement of an egg. If anyone has any ideas or could point me in the right direction that would be brilliant.

I would suggest starting with the simplification that the eggshell is rigid with a shape described here:

http://en.wikipedia.org/wiki/Oval

And the egg is filled with a simple viscous fluid and a solid sphere, maybe locate the centroid of the yolk at the centroid of the half-sphere of the shell. Make the yolk neutrally buoyant to the white, or even better, pretend that it is anchored in place. Then you can use basic kinematics to model the rotation, rolling motion, etc.

 

[mikeph]

Hmmm... interesting. my approach would be to model the egg as influenced at all times by just two forces, equal in magnitude and direction, but one acting on the centre of gravity and one on the point of impact, as described by a position on the surface of the egg (maybe try it as an ellipsoid at first?). Then I believe you can completely describe the state of the system by the position and velocity of this point of contact, (theta, phi) and (d(theta)/dt, d(phi)/dt).

As a solid body, I guess you'll only need three pieces of information to describe the system- the three moments of inertial of the egg along three orthogonal axes. Maybe you can do a coordinate transform to keep the egg fixed and the forces of varying magnitude? This problem may be very difficult, even non-linear?

Try to find the equations.edit- I hadn't even considered fluid motion in the middle. That is certainly a chaotic problem...

 

[Molydood]

...you should be able to treat the egg as if it were a simple cone.

why is that, out of interest?

 

[Danger]

why is that, out of interest?

Just experience. If you roll an egg, it invariably circles around in the direction of the pointy end. Taking a line from the surface through the pointy end to the blunt end gives a slope. Taking a line from the contact patch straight up to the first line and connecting the lines, using the surface as the third line, gives a wedge, which is essentially the bottom (radius?) of a cone.
None of that is the least bit scientific, of course. All I know is that when I see an egg rolling around I think of a cone.

 

[Molydood]

I see were you are going with that one now, it's one very specific case out of all the possible motion states. At least I follow you now, at first I had no idea how a cone could be used as a simple model of an egg!
:-)

 

[Bob S]

Determine whether a raw egg and a hard-boiled egg roll the same. If they do, then you can use rigid-body equations with the three principle moments of inertia (two are the same) to determine equations of motion.
Bob S
[added] The egg's center of mass is directly above the point of contact when it is not rolling. But the center of rotation (gyration) is not at the center of mass, and this may lead to the difficulty in rolling an egg without a wobble.

 

[James Leighe]

This is not a simple project IMO (i'm a programmer by profession).

There are many non-trivial problems you will have to solve. The only questions I have right now is what input and what output do you expect from your program and in what language is it written?

Is it going to be something like...
Enter the starting position of the egg, using some matrix or quaternion, and the time and it will tell you the poisition of the egg at that time? Or will it run until the egg is a rest and initialy will be given some kind of impulse along with it's starting position and rotation?

 

[Danger]

I agree that the problem isn't simple, but I'm not a computer guy. My only attempt at programming was teaching my Atari 800 to play poker, and the damned thing cheated until the day it died.

 

[Andy Resnick]

Hmmm... interesting. my approach would be to model the egg as influenced at all times by just two forces, equal in magnitude and direction, but one acting on the centre of gravity and one on the point of impact, as described by a position on the surface of the egg (maybe try it as an ellipsoid at first?). Then I believe you can completely describe the state of the system by the position and velocity of this point of contact, (theta, phi) and (d(theta)/dt, d(phi)/dt).

As a solid body, I guess you'll only need three pieces of information to describe the system- the three moments of inertial of the egg along three orthogonal axes. Maybe you can do a coordinate transform to keep the egg fixed and the forces of varying magnitude? This problem may be very difficult, even non-linear?

Try to find the equations.


edit- I hadn't even considered fluid motion in the middle. That is certainly a chaotic problem...

If the egg is hard-boiled (solid), there's only two independent axes of rotation (the egg is rotationally symmetric). Solid body rolling, with as you say the contact force and center of gravity creating a torque (force couple). That's fairly easy, I would think.

With the viscous fluid/solid yolk, it's still not hopeless- there's no free surface, and the fluid obeys the no-slip boundary condition at the shell and the yolk. But yes, the flow is time-dependent and three-dimensional. OTOH, egg white is a viscoelastic material, so maybe it could be approximated as an elastic solid (no flow, but stress still propogates within the material). Either way, doing this using FLUENT or some other FDTD code shouldn't be too bad (as in a few months work or less)

 

[burrkie]

First off, thank you for so many quick replys, secondly, I was hoping to get the egg rolling without a fluid centre to begin with, the application needs to have an egg on a solid, level surface, and the user can change the angle of the surrface. Because making an egg roll down a surface and at set angle would have just been too easy... again this is why I've seeked help, and by the looks of things its an interesting topic!

 

[mikeph]

Ahh... that's interesting if the surface is at an angle. If the egg is perfectly orientated, it will roll straight down, but if it's slightly sideways it could do all sorts of things. The weight is no longer in the same direction as the normal force.

 

[Danger]

Af the egg is perfectly orientated, it will roll straight down

Speaking again from the viewpoint of a high-school dropout, I respectfully disagree. My experience with eggs on an inclined plane (and don't even ask why I have this experience) is that they act like little pendulums. The fat end goes foremost, and the whole thing rolls back and forth sideways with a bit of downward movement on each swing. This, of course, relies upon the slope angle being shallow enough that the egg doesn't just slide down.

 

[mikeph]

Sorry, I was talking in my self-imposed approximation of an ellipsoid. You are right I think, in that an actual egg rolling down along its "equator" (minimum great circle) will have the centre of mass at one side, so it will swing.