Square vs Wide Turning abilities

[Mk.32]

Hi everyone,
With all the bridges this year the wide frame is quite popular however it does have the disadvantage of being easier to tip over.

We were thinking of using a square base [27x27inch] to allow us to fit 3 bots on the bridge but not have it tip as easily.

However how well would a square frame turn compared to the wide?

[Cuog]

It should be able to turn faster but with less power compared to a wide bot.

But could you explain how it would be less prone to tipping? It would appear to me that given the same height you would be just as likely to tip forward/back as a wide bot, and now given that you've cut down on your width, it would be easier to tip side to side than a wide bot.

[Djur]

Hi everyone,
With all the bridges this year the wide frame is quite popular however it does have the disadvantage of being easier to tip over.

We were thinking of using a square base [27x27inch] to allow us to fit 3 bots on the bridge but not have it tip as easily.

However how well would a square frame turn compared to the wide?

Square bases have the same (or a even slightly smaller) wheel base than a wide robot. There really isn't much advantage to having a 27" square robot.

[Mk.32]

It should be able to turn faster but with less power compared to a wide bot.

But could you explain how it would be less prone to tipping? It would appear to me that given the same height you would be just as likely to tip forward/back as a wide bot, and now given that you've cut down on your width, it would be easier to tip side to side than a wide bot.

We were thinking that the fact the wheels are closer together would make it less likely to tip, but are not sure. Could anyone clarify this?

[Ninja_Bait]

These threads might help a little. They're physics quizzes from ether (both of which I "won", may I add). The first tells you the torque (applied to the wheel) required to start a square, 4wd, robot rotating. The second is the same problem, but for all rectangular robots:

http://www.chiefdelphi.com/forums/showthread.php?t=98947
http://www.chiefdelphi.com/forums/showthread.php?t=98971

The result for the second is that tau=muNr/sqrt(f^2+1) where f is trackwidth over wheelbase. You can see that for a square bot, f equals 1, which yields the solution to ether's Quiz 5. A narrow bot (f<1) requires more torque and a wide bot (f>1) requires less torque. You can apply the same principles to other tank drive setups, too.

As for tippiness, changing your trackwidth will give you no boons. All the tipping forces are in the plane formed by the vertical direction and forward direction. A two-dimensional robot will act the same as a three-dimensional robot that is infinitely wide in this case.

If you want to go wide, go all the way.

[hollings]

This all depends on where the center of gravity is on your robot.

[Ether]

This all depends on where the center of gravity is on your robot.

For an explicit treatment where the CoM (Center of Mass) is offset aft of the CoG (Center of Gravity), see this link:

http://www.chiefdelphi.com/forums/showthread.php?t=99089

[Ninja_Bait]

Shhh.... that's quiz 7 (http://www.chiefdelphi.com/forums/showthread.php?t=99089&highlight=quiz+7).

The torque analysis doesn't change; a smaller trackwidth, ceteris paribus, requires more torque to turn.

Nor does the tipping analysis. A thin bot is as likely to tip when driving up the bump as a wide robot when they have the same center of gravity relative to their geometric center. It's more likely to tip side-to-side as well, as Cuog has said.

EDIT: ether beat me to the link, but here's the analysis anyway.

[DonRotolo]

We were thinking of using a square base [27x27inch] to allow us to fit 3 bots on the bridge but not have it tip as easily.

However how well would a square frame turn compared to the wide?
OK, so to summarize: A 27" square robot will tip at least as easily as a wide robot, and turn at least as poorly as a narrow bot. The worst of both worlds!

I say go for it.:p