Merrymaker_Mortalis wrote:One thing I am not sure about is: At what point is it more appropriate for a bend on the track to have a bank of 45* ( \ ) as opposed to 90* ( | ) to minimise rider discomfort?
Is that question even easily answered cold?
That's a difficult question to answer from a purely physics standpoint; in general, and from personal experience of coasters, I'd say that high speed corners require steeper banks; that way the added centripetal force holds the body more upright, counteracting gravity pulling the person down.
...I had written out a very long, detailed summary of work-energy and the forces acting on a coaster, but then I realised that it probably would be of only limited use to you. So instead, I will embark on a quick summary of probably the most important force in rollercoaster design- centripetal force.
Newton's second law tells us that to change the direction of a coaster's velocity requires an acceleration, and that acceleration requires a force to cause it. When an object is travelling round in a circle (or part of a circle), the direction of its velocity is constantly changing. By way of an example, if you imagine one of the tips of the tails on Kapol's signature perpetually spinning round, at one moment it'll be moving downwards, then it'll spin round and start moving towards the left, then it'll spin some more and suddenly it's velocity is directed upwards. The direction of its velocity is changing, and this requires it to be accelerated inwards towards the centre of the circle. This is centripetal acceleration, and requires centripetal force to cause it.
(Centrifugal force is what our bodies 'feel' as a sort of opposite of centripetal force, as we feel ourselves being thrown outward with the same force causing us to be accelerated inwards. It's more complicated than that, but isn't relevant right now)
Centripetal force is important partly because it is one of the best ways of subjecting a coaster and its occupants to lots of acceleration, or controlling the acceleration & resultant force acting on the coaster. The formula for centripetal force is F=(mv^2)/r, where m is the mass of the coaster, v is its velocity and r is the radius of the curve it's travelling round; that's why the 'ideal' vertical loop for a train is more elongated than a circular loop, so that as the train slows down (v decreases) the track curves more steeply (r decreases) so the amount of centripetal force acting on the body stays constant. That way, you only get 'hang time' similar to what you would get from being projected straight up and falling straight back down, which feels 'right' for the coaster's occupants (that's an awful explanation, but I'm trying to keep things vaguely simplistic).
From that, it's best to deal with things on a case-by-case basis; the only general rule worth remembering is that tight, fast turns (where centripetal force is high) will need lots of track supports to cope with all the centripetal force required. So... sorry if that wasn't as enlightening as you might have hoped, I suggest if you've got anything more specific you want to know you ask it as a specifically phrased question