I tend to do both, (braking and down shift).
One thing I have been thinking about though... I am teaching my girl friend to drive at the moment, over here in Sweden we need to attend a 3 hour training lecture to be approved as a 'teacher'.
They are big on what the call eco driving - Part of which is thE use of engine braking (down shifting). Does that save fuel? Cant really figure it out.
On a side note, thdespito promote skipping a gear when accelerating, despite a long winded debate with the instructor, I am sure that doesn't save fuel either. yeah you dint accelerate as hard, but you accelerate for longer.
Braking turns you kinetic energy into heat, changing down at least stores some of it in the flywheel & other moving engine parts. Driving in the highest gear possible is generally the most economic as the lower revs equate to less friction losses. Power is also directly related to the amount of fuel/air mixture going through the engine; lower revs mean you need more mixture per rev, so a more open throttle and higher combustion chamber pressure, which also help mpg (à la diesel). Of course, if you miss out a gear, you'd usually have to take it to higher than optimum revs in the lower gear before you change up - so more useful in an unladen hgv than a Mini.
Hehehe...yes but for how long and how much? Certainly not enough to be of use for anything, and ultimately only turns that kinetic energy into heat. I'd have to disagree that power is directly related to the amount of fuel entering the engine, there is a lot more to be considered such as BMEP and cylinder scavenging.
If only the rest were as simple as you suggest, but it's not.
Remember, people desire power but they drive torque.
Yes...fuel injected cars cut fuel when on the over-run, but if you say coasting, coasting used to me rolling with the car in neutral or the clutch dipped. That certainly won't save juice. Some say it's against the law in the UK, but it's probably off the books now with the number of vehicles that are designed to coast.
i do know for a fact that whilst I have enjoyed getting 53 MPG at an average speed of 72 MPH (as calced by the computer) from a 150 hp merc common rail, I don't enjoy someone who piss farts about in and out of gear - this is a very Chinese thing, and having sat with a coach driver who would try and coast down a hill and half way up the other side, to miss 3 gears and get stuck behind a lorry for 2 miles going back up the other side, I had a desire to launch a pork and chilli dumpling at the back of his head every time he tried it......