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This was my lumpy route
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You're going to end up crossing a lot of the High Weald which is not flat. I reckon you could probably net out at just over 2000m climbing if you finesse the route a bit.
That'll probably send you down more busier roads though, to miss the sharper elevation of the smaller lanes. So there's a balance to be struck, as they're less fun especially if you're less experienced.
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https://ridewithgps.com/routes/39632158
This is my best shot. Go on your way to Brighton but then swing east before Turners Hill and then try and make the most of the space between the Weald and the South Downs. I can't speak for the roads down there, look a terrible tangle, but there might be some usable ideas in there. Only issue is that it's a fair bit longer than 200k, more like 250k. With some A/B road compromises in that route you could probably get it down to 225km. For the inexperienced I'd say too many hills is worse than too far.
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I did this three years ago, was a lovely route, but a but far (you'll need to amend the outward leg but the return is alright). I did it on tired legs from another 200 the day before, but I was preparing for PBP, so...
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hippy
honk
youramericanlover
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@TTM
I'm trying to route the flattest 200k I can from SE London down to Eastbourne and back, so thought I'd check here for inspiration. The only chat I could find was @hippy trying to build the lumpiest version possible, whereas I need to do the opposite. I'll be riding with a group of mixed ability and worry anything much more than 2000m total climbing could end up being a loooooong day and not much fun for some. Is it doable?