Turning Radius

[Rick TYler]

Al and Alan, wouldn't it be more correct to say that those are the minimum possible turning radii? Because steering in this case uses the slip angle of the wheels to generate turning force (I know that's a sloppy way of wording it...) won't the actual radius will always be greater than the theoretical minimum? On a low friction surface (like Lunacy) I would think it would be much larger than the minimum, with the radius increasing with robot speed.

[PWHSrobotics]

thankyou for the help, are there any equations that I can get closer to 'actual' turning radius from the min theoretical radius?

[Al Skierkiewicz]

Rick,
In cases where the robot is already moving you are correct. And in the case of a fast moving robot with the ability to have a small turnig radius (at a stopped condition) would approach infinity at it's maximum speed. i.e. it would hit a wall or field border before turning. In cases where the robot is stationary but turning, the minimum would be the turning radius but I think it still would be affected by the trailer hitting the back of the robot.

[Rick TYler]

Originally Posted by Al Skierkiewicz

In cases where the robot is stationary but turning, the minimum would be the turning radius but I think it still would be affected by the trailer hitting the back of the robot.

I loved Al's last comment so much that I think it should be spotlighted. We have these conversations all the time: "Here's the incredibly complex calculation of how the system would work based on physics and mathematics, but the noise level is so high (or the real world will intrude in imperfect ways, like a trailer hitting a robot) that we are going to take that 27.3991 mm calculation and just turn it into 'a big old hunk of 2-inch square tubing.'"

And this, my Padawan robot builders, is also engineering.

On the original question, doing the velocity, thrust, friction, and slip-angle math for describing turning radii at different speeds is well beyond the ability of my rusty math. Sorry.

[MrForbes]

For the theoretical aspect, just make a scale drawing with the wheels at various angles, and see where the lines intersect, as Al suggested.

For the practical aspect, put the trailer on it and drive it on FRP and see what happens. Strange things, I guarantee!

[IKE]

Originally Posted by Rick TYler

Al and Alan, wouldn't it be more correct to say that those are the minimum possible turning radii? Because steering in this case uses the slip angle of the wheels to generate turning force (I know that's a sloppy way of wording it...) won't the actual radius will always be greater than the theoretical minimum? On a low friction surface (like Lunacy) I would think it would be much larger than the minimum, with the radius increasing with robot speed.

Al and Alan are correct assuming very small slip angles. This would be relatively low speed small input stuff on regolith.

Rick is really on to something. One other thing to consider is how the back wheels play into this. If they are going the same speed they will induce higher slip angle. Racers often call this Push because the back wheels are pushing the forward wheels to induce understeer (or less steer than requested). However depending on CG location and the actual manuever you attempt, you could also get Oversteer. The grossest exageration of this is the guys that do drifting, rally, or Dirt track stuff.

Gelespie (spell?) has a vehicle dynamics book that is excellent at talking about how these equations may be applied and simplified (bicycle model). Assuming reltively small slip angles, the bicycle model works well for the system you have. I.E. Take the angle off of straight. The tanget of this angle times the radius of curvature is equal to your wheelbase. Thus to find the radius of curvature:

WB=wheelbase
angle=angle off of straight that your wheels are turned.

WB/(atan(angle))=radius of curvature

If you have extra weight available, place it in different locations on your machine. This should help change the oversteer/understeer effects you might get. In general the trailer will produce understeer effects (this is what I am seeing in most videos), unless you really crack the whip, and then it could result into an oversteer condition.