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Staying over night, have bike, but need route.
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Some of the tarmac roads are so rough and covered in mud that they might as well be considered as gravel routes. Depends which side of the city you are staying, but you could consider making your way on roads to the airport, where there is quite a good museum (which will probably be closed) but you can wander around the Vulcan and a few other relics, then make your way via Brampton through the lanes towards Gilsland and Birdoswald along Hadrians Wall. If you've time make your way onto the Spadeadam ranges, which are more spectacular the further you go. All on tarmac, but you'll get dirty!!
As above, a friend lives Brampton way and heads out through the Spadeadam ranges on his gravel bike quite a bit. Not been but sounds pretty dramatic country...
<i> https://www.sustrans.org.uk/find-other-routes/reivers-cycle-route</i>
Mostly on road, but it avoids the main roads.
It might be a wee bit far to ride from Carlisle, but if you drive to, say, Lanercost (12th c. priory) and start from there - Gilsland - out past the ranges past Butterburn to the end of the tarmac at Keilder Forest - take bridleway on left through forest (much of this bit has been felled) - leave bridleway and go through ford on left after a couple of Ks (you might get wet) and then follow fire road to Bull Cleugh gate at edge of forest - descend rough track to tarmac - then go back South to Lanercost on this road, via Bewcastle (13th c. ruin and 8th c. Anglo-Saxon cross in church yard (signposted) and past Askerton Castle (A Pele tower attached to a farm). Plenty of history and good views(on a good day, obvs). Â