I'll attempt to explain in brief why one should down-shift while braking. Assume that the car in question is a Swift Diesel. It has the following specs:
3rd gear ratio: 1.233
5th gear ratio: 0.725
Assume that you're driving the car at 100kph in 5th gear and that the engine is doing 2000 revs. Armed with the above data, we'll do a few really simple calculations to understand the theory behind:
If the gear ratio is 0.725:1, the driven wheels rotate once every 0.725 rotations of the engine. Which means, in our case, the wheels are rotating at about 2758 RPM (2000/0.725). The aim of braking is to reduce the speed of the wheels, which will automatically reduce the speed of the vehicle. This applies until the point where the wheels don't start locking up.
When 3rd gear is engaged at 100kph, the engine speed rises to 2466 RPM (2000*1.233) and the wheel speed drops to about 1662 RPM (2000/1.233). This is what we want, isn't it? We haven't braked at all but still using the transmission, we have just reduced the speed of the car. Here's the math behind:
At 100kph, in 5th gear, the engine is doing 2000 RPM. When 3rd gear is engaged, the gear ratio is changed from 0.725:1 (for 5th gear) to 1.233:1 (for 3rd gear). So, to get the engine speed, multiply 1.233 with 2000 (to get 2466 RPM) and to get the wheel speed, divide 2000 RPM by 1.233 (to get the reduced speed as 1662 RPM).
Result: Wheels which were rotating at 2758 RPM, are now, after down-shifting, rotating at 1662 RPM--a decrease of more than a thousand RPM. Exactly the result what we expect and need!
THE WORST CASE SCENARIO: Shifting to neutral!
Ok, so what happens when at 100 kph in 5th gear, we shift to neutral? The wheels are freed from the engine and so they start to rotate freely on their own. That is, the wheels continue to rotate at the same 2758 RPM, without slowing down. The momentum of the car will keep carrying it at the same speed. The air-resistance and the tyre friction will slow the car down but this amounts to a very minuscule resistance. The car will stop only after it has traversed a few kilometres of running! Hence the vehicle speed doesn't practically reduce at all! This'll require the driver to put extra pressure on the brakes, which reduces its life as well.
I hope this amply demonstrates that refraining from down-shifting and more seriously, shifting to neutral while braking is STRICTLY NOT A GOOD DRIVING TECHNIQUE. Most drivers, however, are doing this and I hope that they'll change to a better driving style in the future.
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