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How significantly is fuel economy affected by having an unladen roof-rack on the car?
It would depend on the type of roof-rack fitted.
The more modern slim-line rails would have little affect however, the bigger bulkier racks could, in certain conditions, definitely increase fuel consumption.
Over a long period the savings would slowly add up however I’m not so sure you would notice significant savings on a week to week basis.
Remember, fuel savings are about a lot of things combining to make a significant difference.
How a car is driven is by far the best way to increase or decrease fuel consumption.