Traveling from Holmfirth towards Sheffield, and when you get to Langsett on the A 616 you get a sign Sheffield 16 miles. Carry on a good few miles past Underbank, still heading towards Sheffield, when you get to Stocksbridge near the new Fox Valley, there's a sign saying Sheffield 21 miles. Further on, at Wortley 18 miles. Bonkers. If you were new to the area you'd be gutted travelling all that way to get further away from your destination. Wortley is in fact about 8 miles away from Sheffield. Just thought I'd share that fascinating story.
And, moments before the 18 mile Sheffield one, if you come off at Wortley and onto the A629, you get a sign which says Sheffield 8 miles. Tbf, I think the 18/21 miles assume you're going via the M1. I can't explain the Langsett one though, unless it assumes you're going via Stocksbridge.
That reminds me of the feeling I get on my long walks. No matter how much I plod on, I don't seem to get any nearer the mandatory pub at the end of the walk.
Fairly sure the road from Brid to Scarborough used to do that (might still do). You drove about 5 miles and the distance increased by about 10. Maybe the signs take into account the back roads - surely its shorter to go through Outibridge to Hillsborough than continue along to Tankersley or take the A629?
I would go through the Wortley Wormhole, it's only a fraction of an inch that way. I went through it in June last year but think I came out into an alternative universe.....