Not spur gears, helical gears - apologies for a senior moment.

The intended advantage of 7/8-speed autoboxes is to allow fuel-efficient gear changes without unlocking the torque converter - relegating the torque converter to standing start use only.

It won't change up if doing so will cause the engine to run too slow. It's no good having an engine labouring as this also uses too much fuel.

Whilst many autoboxes have a Tiptronic function function most are controlled so that they will automatically change up of you redline the engine, so there is no huge advantage. I use my tiptronic function when slowing down as a form of engine braking, but only out of habit and enjoyment rather any effort to save fuel.

My current car changes into top gear at about 38mph, so it's always in 3rd gear in urban areas. I'm confident, however, that it would easily pull top gear at 30 when lightly loaded on a road with no gradients.

The most efficient part of the engine operating range is near the point at which an automatic transmission would deduce driver demand for a downshift (ie lowish RPM and high load.

This makes setting up the shift strategy for automatics rather tricky.

The other snag is that torque converters can't transmit power very efficienctly at low speed (otherwise they'd stall the engine!)-so if the torque converter is unlocked at low speed there's no advantage to changing up early because torque converter slip would negate any advantages in reducing RPM.

Engines mated to a torque converter coupling often make use of the damping effect of the fluid to replace the flywheel with a lighter flexplate so it might not be safe to labour the engine at low speed.

Jazz had TC and 7 fixed speed CVT..

A permutation which works very well. The simplistic summary at the start is misleading in my view.

I've only driven two cars with auto transmission. Both are torque converter systems with P, R, N, D, 3, 2, L settings. You can hold the car in the lower gears, but you cannot force it to change to a higher one. My current car changes into top gear at about 38mph, so it's always in 3rd gear in urban areas. I'm confident, however, that it would easily pull top gear at 30 when lightly loaded on a road with no gradients.

I assume that manual override systems, like Tiptronic, mean that you can change up at will. In practise, do you achieve a worthwhile improvement in fuel economy when you force the car to change up a gear in circumstances like those I mention?

Driving my wife's 207 tiptronic auto, it has an annoying habit of hanging on to 2nd at just under 30 MPH around town, so I tend to change manually into 3rd. I don't know what effect this has on economy though - it's pretty poor around town anyway.

Yes, you can force it to change up earlier, but it will only do so when it detects that the engine will not labour, e.g you could pre-select 3rd gear at 20 MPH, but the electronics will delay that change until say 25 MPH..

Similarly, if you leave it in "manual" whilst slowing/coming to a stop, it will change down automatically, but stay in 1st when setting off again. If you forget to nudge it back into Drive or change up manually, cue the screaming engine!

Yes, although the 207 only has 4 gears. Nevertheless, it can't be best for economy to have the engine turning over at about 2600 RPM in 2nd.

Petrol-electric or diesel-electric can be more efficient when combined with regenerative braking and energy storage - i.e. battery.

The battery is a middleman-like all middlemen, he always takes a cut. Sometimes he earns his cut, but you want to cut him out of the equationwhere possible. Hybrid is more an alternative means of propulsion than transmission. The regenerative braking capability is a no-brainer because electric motors are usually fully reversible as generators. The contribution to economy isn't as significant as it might seem and isn't the raison d'etre of hybrid, but it is a feature that's easy understood by the public.