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Check my Tie Drag work

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Numsgil:
http://www.darwinbots.com/WikiManual/index...ew_tie_paradigm

Tell me if I'm doing the physics wrong.  I feel pretty confidant in the math since I used Maple to integrate and just copied and pasted.  The only thing fudged is finding the coefficient of drag since it chagnes depending on velocity.  I just use the average speed (absolute value of velocity) since my table of CD values isn't a function but, well, a table.

Please please PLEASE check my work if you're physics inclined.  The physics was really challenging the entire time, and I did my best, but I'm not confidant.

This work should let ties act as useful wings for instance.

Sprotiel:
There's nothing obviously wrong in your derivation, though your awful notations make it hard to understand. Your assumptions, on the other hand, are weird: where does your drag coefficient table come from? It's not like there's an obvious correspondence between DB units and real world physical units. And why do you want to use such a table? It makes more sense to me, phycally and computationally,  to have a fixed, user-selectable, value for the drag coefficient.
Another questionable assumption is the fact that drag is proportional to v^2. In the real world, it's only valid when turbulence is the dominating factor in drag while I would argue that it's more natural to consider that in DB we're in a situation where viscosity is dominant, which means that drag is proportional to velocity.
I'll try to redo the tie physics section so that it's easier to understand, but it would be easier if you installed the LaTeX extension to Mediawiki.

Numsgil:
The drag coefficient is determined by the Reynolds number, which is dimensionless.  Reynolds numbers that are low are viscous, whereas reynolds numbers that are high are turbulent.

While I could limit the simulation to only viscous drag, and make several calculations probably alot easier, I see no reason not to make it more general.

Reynolds number.
----------------
As to the metric of the Darwinbots universe:

distance - twip
time - cycle
mass - "Mass" (it's called a mass)
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What about my notations are awful?  The wiki doesn't have math script so I couldn't use that.  How would you do it differently?  The math script stuff is impossible to install.  There are easily 6 different things I have to set up and get running.  If anyone finds a tutorial on setting up math support on a wikimedia that doesn't involve me installing 6 different programs, I'd be very appreciative.

Numsgil:
Here's the java calculator I use to "borrow" CD values based on Reynolds numbers.

http://www.fluidmech.net/jscalc/cdre01.htm.

Sprotiel:
The fact that the Reynolds number is dimensionless doesn't change anything. How do you determine the fluid's density and viscosity? Another problem is that it's only the magnitude of Re that's important, not its precise value. We don't have orders of magnitude differences in the scales intervening in DB physics - so it's not really useful to compute it for each tie at each step. And yet another problem is that Re isn't a local quantity: it applies to a complete system.

For the math extensions, have you read this?

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