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Re: The Bike Problem:  As I believe Chales 2nd told his scientists, "The only solution is to try it and see", which I did this morning using my late 1940s/early 1950s Ernie Clements (See  https://en.wikipedia.org/wiki/Ernie_Clements ) with the lugless frame made with Reynolds 531DB tube.  Look at the way he’s cut the tubes to fit exactly and faired in the braze.  It must have looked like a piece of jewellery when new.  I’ve no idea if it’s the frame he rode in the 1948 Olympics, but that’s what I tell people.  So far no one’s called my bluff.  Age has its privileges.  

The answer is, it's almost unsolvable.  Push the top pedal forwards; the bike goes forwards.  Put the pedals horizontal and push down on the front pedal, and the bike goes forwards.  But push back on the low pedal at the bottom of its stroke with the wheels on the ground, and the bike doesn’t want to go anywhere.  Eventually, if you push hard enough, the bike will start to go backwards, but only at the expense of the pedal forcing itself forward against your push.  It’s like pushing with all your strength against an immovable wall, your body moves backwards away from the wall.  DaveP

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