Code center > Suggestions
Tie Forces
Numsgil:
As I promised for too long and didn't do, here's the tie forces problem for a tie moving through a medium:
Let's pretend the tie is a solid block of length L; It's mass is considered to be the mass of the two bots it connects plus it's own mass, which is uniformly distributed along the length. So it's sort of like a dumbell in mass distribution.
m1 = 1st bots mass
m2 = 2nd bots mass
mL = mass of rod
Thus total mass = m1 + m2 + mL
The position vector of the center of mass of this rod is going to be:
x1 = position vector of bot 1
x2 = position vector of bot 2
xc = (m1*x1+m2*x2)/(m1+m2)
The velocity of the center of mass is going to be:
v1 = velocity vector of first bot
v2 = velocity vector of 2nd bot
vc = (m1*v1+m2*v2)/(m1+m2)
Okay, that's all pretty standard. First I'd like to show Carlo's Algorithm:
1. v3 = (v1+v2)/2
2. you = (x2-x1)
3. Force Magnitude = Ft = swim constant * (v3 x you) (that's a cross product). I assume you all remember the swim constant in the physics panel? This is what it did.
4. Force's vector to apply to bots is Ft * <uy, ux> (that is, it's reverse of you).
Now, I don't know if you caught it or not, but there is small error in this algorithm:
1. Assumes drag on the tie is linearly related to velocity. It is not under certain circumstances.
2. Does not slow a tie that is rotating about its center since the average velocity is zero, even though most of the tie is moving. This is the one I found most disturbing.
I seem to have several pages of notes at this point, and I'm not sure what all they do. Let me reread them and post later today about what things I tried that I was having trouble with.
Basically, just to keep you interested, I was going to calculate the force on a subsection of length, called dL, and then integrate it across the length L.
Numsgil:
Okay, second part:
The force on a cylinder moving through a liquid is Av^2*length where:
v = velocity perpindicular to the cylinder.
A = density of liquid * Cd(v) * radius of cylinder
Cd = Coefficient of drag, between [0,1], and is sort of a black science in the real world. It is dependant on velocity. I have a piece wise function for determining it.
I was thinking that I'd take A * integral(V(dl)^2*dl) where V(dl) = velocity of tie at some length dl and dl is the integrating factor for length along tie.
But I get bogged down in the math, and my head explodes. What a mess.
I can find a good enough approximate value for A I believe. The hard thing is figuring out how to handle the v^2*length thing.
Right now, this is what I'm doing (using the stuff I defined above):
a = v1 x you
b = v2 x you
V(dl) = a + (b-a)/L * dl
which is simply the equation for a point-slope line with y intercept a and slope (b-a)/length.
PurpleYouko:
--- Quote ---But I get bogged down in the math, and my head explodes. What a mess.
--- End quote ---
My head exploded a long time ago. That is why I never really got into tie physics. It is a complete nightmare :wacko:
Numsgil:
I tried it again today during class. I thought the 3 months since I worked on it would give me perspective.
Instead I just re-realized how incredibly difficult the damn problem is.
If nothing else, I can always use Carlo's old algorithm.
Botsareus:
If nothing, thats the most brillient peace of string phyz I ever read. Working on it already. If I have qustions I let you know
Navigation
[0] Message Index
[#] Next page
Go to full version