North of Piccadilly Circus

You think thats bad? You should try the NB curve just before Paddington.

I would expect that the rough ride is due to increased wear on the tracks due to the tight curvature of the bends.

(Just increasing the portion of spam here) That's OK. Please let me know if you notice any inaccuracies. Despite the fact that they are based on signalling diagrams, there were initially quite a few mistakes . DLR coming very soon! SSLs whenever I have the time.

Baker St to Finchley Road NB Metropolitan is terrible. At some points it feels like the train wheels are bouncing off the rails! On supposedly ballasted track the beds are as hard as concrete.

Off topic. Track curves with less than 200m radius are classed as tight curves and will often have lubricating devices fitted before a curve. It relies on train wheels to spread lubricating grease onto the running surface of the head of the high rail. This increases the life of rail and cuts down on maintenance.

When the Victoria line was opened in the 1970s, track lubrication was taken off the track and onto the trains and was applied through a train mounted graphite rod. Being entirely underground, the line lacks natural lubrication through rainfall and conditions are very dry. It was soon found that the track required more intensive maintenance with some sections requiring rerailing in a matter of weeks. Eventually track mounted lubricators were retrofitted.

Gauge corner cracking rail defects were commonly found on the Vic. GCC was found to be the cause of the Hatfield derailment and the risks of GCC were relatively unknown at the time. This sparked an intensive investigation by LU and led to the introduction of new types of ultrasonic inspection equipment.

The Met is rather "lively and bouncy" along that section, but the Bakerloo seems to grate around the mentioned bends as if it had square wheels.

I wonder how often the track on sharp curves has to maintained or replaced compared to straight or slightly curved track?

The next generation of Bakerloo Line stock could do with steerable axles IMO.

Sounds like a tight track gauge and the noise is a result of the wheel flange in contact with the rail.

As said before curved track needs to be greased to reduce rail and wheel wear. Check rails are also used to reduce the force exerted by the outside train wheels on the high rail. This restrains the inside train wheels on the low rail from moving sideways towards the four foot reducing side cut on the high rail. So these extra maesures require more maintenance!

Rail transposing or 'turning' used to be an option for worn rails. The contact area between rail and train wheel is small and limited to one side of the rail head. To save on material costs the rail used to be taken out and reversed and the unworn part of the head would then be presented to the train wheels. This practice was banned after the Hammersmith derailment. The defective rail had been turned at some point and an investigation had revealed that it had been a factor.

Track gauge is slightly wider on curves. Gauging for bullhead RBH95 and flatbottom FB113A rail differ slightly (sorry but we work in metric only!) and are as follows:
straight BH = 1432mm
curved BH = 1435mm
straight FB = 1435mm
curved FB = 1438mm
This wider gauge also applies to junctionwork.

I'm not in a position to answer your question q8 but by considering the physics of a train and some simple track design rules we might be able to point ourselves in the right direction.

A train travelling round a curve will experience a centrifugal force. If the outer rail is lifted above the level of the inside rail then the train experiences less outward force. This difference in rail level is the cant and varies up to 150mm. To achieve equilibrium and eliminate the outward force sufficient cant is required. However, this is limited to maintain stability (to avoid wheel unload) of the train and is not always achievable and there is still a remaining outward force. Too wide a gauge would allow the train wheels which are at a set distance apart to move under the outward force and could cause the outer wheel flange to "climb" over the high rail and derail the train. Check rails are used to reduce the risk but brings us back to the problem of rail wear and noise.

This outward force varies according to track radius and speed and therefore limiting speed would be a consideration. Track designers use different formulae to calculate the line speed limit around curves taking into account curvature and cant. They could of course design curves and transitions to safely operate at higher speeds but are limited by existing infrastructure such as tunnels and junctions.

IMHO trains and curves don't mix well. What you have a is a straight rigid train car with rotationally stiff bogies being forced around a curve which is not good for both the train wheels and the track. This was looked at a few years ago and resulted in initiatives to improve track lubrication and the brought about the wheel profile examination sheds at the depots amongst other things.

Sorry to ramble on but I've got a question too. Someone told me that train axles don't have differential speeds like in a car and when going round a curve train wheels are being forced to travel at different speeds. It would be because the inner and outer wheels are covering different distances. Can anyone shed any more light on that?

Trains indeed DO have a differential action to allow the outer wheel to travel further.

The action is created by the design of the wheel tread. It is not flat (obvious!) but neither is it a single straight angle. If you get close enough (to any train axle) you will see the profile starts at a small angle then becomes steeper as it approaches the wheelflange. This gives a greater radius for a wheel whose flange is close up against the outer rail (of a bend) and hence the differential action.

The primary differential is given by the 1:20 coning of the tread. This provides for slightly different inner and outer tyre circumferences, the idea being that the wheelset will take up an optimum position on slightly curved track (and will also not 'hunt' on straight track). See here for a scale example of the prototype shape.

Russ