Hey all,
I've been trying to figure something out about slaloms
and getting myself confused. All of the stuff on
course design I've seen (e.g. RHJ's notes) treat a
car's path though a slalom as a series of semicircular
arcs connected together, presumably with the car
traveling at a constant speed.
Problem is this: At the junctions between arcs, the
car would have to have an instantaneous change in
lateral acceleration from full-left to full-right in
order to make this work. That obviously isn't
possible. The only way to get smooth changes in
lateral acceleration would be to have the car take a
sinusoidal path through the slalom, which looks a bit
different. Is this a better model of the car's path?
Reason I'm asking is, I'm attempting to work out a
physical explanation for whether a narrow car is
faster through a slalom than a wide one. I know
empirically that tends to be true, but I'm thinking it
might not be solely due to the smaller side-to-side
distance traveled. I tried using the semicircle
assumption and the math got WAY ugly.
Anyway, TIA for any help or references y'all can give
me.
Craig "yeah, I KNOW I should get out more" Blome
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