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Nutty - there is no way on earth I can eat or drink riding up hill - I'll choke for sure. Are you really able to eat whilst climbing?
<slightly O/T for this board, but I'll answer anyway.>
Yes, I can eat and drink quite happily whilst climbing.
I have found, for me (so YMMV) that whilst I can blast the downhills and maintain a good speed on the flat, the effort uphill just doesn't provide the returns.
On Wednesday I blasted the first 2 miles home, flat, and had an AV speed reading of 20mph. I wasn't tired or out of breath. I then turned uphill for the first of the minor ascents, and for the same effort the bike slowed to 15 or 16 mph. Dropping the effort right down I cruised quite happily at 13 to 15mph.
This is typical for me, hence me not seeing the benefit of really putting the hammer down, sweating out all my liquid and getting both dehydrated and into oxygen debt just to travel an extra 2 miles per hour.
Instead I prefer to drop the effort down slightly, keep flowing, and therefore cover the longer distance in the same average speed as I don't have to stop/slow to recover from the uphill sections.
On a really long/steep uphill, such as Ditchling Beacon on the FNRTTC I purposefully go into a low gear right at the start and then ride at a pace that I can maintain without getting breathless until I get to the top. On some rides I've trundled past the faster boys near the top of the climb whilst they are gasping for air and I'm still as fresh as a daisy. Think Tortoise and Hare. Plus, as I said, because I'm not gasping for air I'm quite happy getting a maltloaf out of the pannier (yes I can do that whilst riding too) and eating it; thus saving the necessity to stop and refuel.