On a random side note; why is that harder wheel compounds that make a ride run faster also make it run rougher? In my head, that would go against everything I know about energy transfers in physics, but I’ve often heard it said that harder wheel compounds make a ride run rougher.
With my physics head on, surely a rough/rattly ride transfers energy into rattling the train, which would leave less energy left over to be transferred into kinetic energy and therefore make the ride slower when it runs rougher/more rattly? Energy is not gained or lost and can only be transferred to different energy sources, so with that in mind, surely energy being channelled into rattling the train would take away kinetic energy and make the ride slower, no?
Also, wouldn’t wheels made of a harder material be less prone to developing things like small fractures on the exterior of the wheel, which I know to be a common cause of a slightly more rattly ride?
A harder wheel decreases rolling resistance, you should know this Matt having just passed your driving test and why it is important to make sure your tires are at the correct pressure.
More rolling resistance = more energy is lost.
Less rolling resistance = less energy is lost.
A softer or less inflated wheel increases the rolling resistance, increasing fuel consumption as the engine has to work harder to maintain a set speed. The same applies to a bicycle too, ever tried riding one with under inflated tires? It requires much more effort, as more of the energy to put in, is being absorbed by the increased rolling resistance. Exactly the same principles apply to a coaster too, the only difference being in a car the momentum forward is from an engine, in a coaster it is from potential energy. But the energy lost through rolling resistance is exactly the same.
Harder wheels / tires absorb less shock, so make the train rattle. The energy used to create a rattle is far far less than the energy used by increased rolling resistance due to softer wheels. This is why it doesn't work the way you think it does. The rattle per say doesn't come from the potential energy either in the same way, it is more transferred, you go over a bump, that bump will transfer across and rattle the train, hard to explain. Think of it like going over a pothole, you haven't used any more fuel than normal to go over the pothole than what you would usually use, but the car has rattled like hell as you went over it. Similar principles.
My cycle rattles like hell when I have the tires inflated really high which you could liken to hard compound wheels on a coaster, but the bike is WAY easier to cycle, and it maintains a higher speed for much longer when I stop peddling.
EDIT: One more reply, I would say a harder wheel would be more prone to cracks as the energy isn't being absorbed and toning the force down. The very reason why large structures such as coasters, bridges and skyscrapers are designed to flex and move with the weather and from live loading forces applied to them, is so that they don't break and snap, causing catastrophic failures. Much better to move and absorb the energy and transfer or dissipate it in a more friendly way to the structure.
The most impressive video in action of this principle, is this video of HUGE skyscrapers swaying quite heavily in the 2011 Japanese earthquake. The buildings are swaying hugely to absorb the energy of the earth quake, they are designed to do this, if they did not do this, they would have collapsed out right - kind of like how a hard coaster wheel would crack over time due to not absorbing the energy. These buildings stand strong to this day. No structural damage occurred, whereas building that were designed to be more ridged and 'hard' have collapsed time and time again in earth quakes with half of the magnitude that this one in Japan had.
From: https://www.youtube.com/watch?v=HB2jgJJG2is
this is the 3rd weekend we’ve planned to go and she’s starting to lose patience 
