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There's some logic behind this tip: less fuel = less weight and so less fuel needed during acceleration.
Half filling the tank will save you some fuel (and make the fill-ups feel less expensive) but it increases the risk of you becoming stranded without fuel. Some drivers are incredibly efficient at ensuring they fill up before they absolutely have to, most though, are not. Are the small savings worth risking being stuck on the side of the road?
Anywhere you can find a forum post asking whether Tesco petrol is better than BP, you'll see a post by someone who lives near a fuel-depot. They see tankers from all the different companies going in, and decide that all fuel stations must therefore be selling the same fuel.
Because, a fuel depot could never store more than one option could it?
The thing that differs between brands and supermarkets (and within the respective groups) is the additives. These are added, to order, when the tanker is filled and can make a huge difference to the performance of your vehicle. Each vehicle differs, so there's no one correct answer (though we've found Shell generally gives the lowest cost per mile). Engines like to be clean, so the presence of additives can preserve them as well as improve efficiency.
Some seem to think that it's a good idea to realise minor fuel efficiency savings by removing the spare tyre from their car.
It's true that by removing the weight, your vehicle will be a little more fuel-efficient as a result. The trade-off, though, is that you might well find yourself stuck in a dangerous situation for longer than is necessary as a result. No-one wants to change a flat on the side of the motorway, but it's still far better than having to wait on the hard shoulder because you discarded your spare to save a few pence.
Price is an important factor and it's psychological impact should not be underestimated, but there's more to saving money on fuel that price per litre.
What we're truly interested in is the price per mile, and to find this you need to know what economy your vehicle gets when running that fuel. If it's 5p a litre cheaper, but works out 0.5p a mile more expensive (because you get worse economy) then you're actually losing money, not saving it.
You also need to factor in the journey to the fuel station, we used to know someone who drove his Mercedes 15 miles to Asda to save 5p a litre vs the Tesco 5 miles away.
Giving his Merc a generous cost of 25p a mile, he'd have needed to buy 100 litres of fuel just to break even (10 mile round trip to Tesco = £2.50, 30 mile round trip to Asda £7.50, difference £5.00/0.05 = 100 litres). In a car with an 80 litre tank he was burning money whilst trying to save it.