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You'd start to boil as the pressure reduced with altitude (eyes popping out and all that) so I guess you'd have to pack a big overnight bag to carry all the gear (oxygen, spacesuit, food)..! I wonder how long it would take?
Space starts about 60 miles up (definitions vary). OK, a 60 mile ladder climb would be very hard work but there's no reason why (with a strong enough ladder) you couldn't go by car. Modern racing cars generate downforce to help them corner at speed. In some instances this is more than the weight of the car. If you got one of these cars and drove it up a curved ramp fast enough (this things going to take some fuel and a big engine) then onto a vertical flat plate (the "ladder") you could drive up into space in much less than an hour. Remember to take a parachute. (I'm banking on the fact that, as you go up, while there's less air to create the "downforce2 that holds you to the ladder there's also less gravity and less drag so you can go faster. I'm not sure this would work.OK, let's try to get round that problem if you are prepared to modify the car a bit then any car could do the job provided that it had a low enough gear. You would need something to hold you onto the "ladder" a big magnet and a steel ladder would work. Remember to pack enough air for yourself and the car's engine.
So, some sort of counterbalance structure - Or how about one of those magnetic monorailways - but as the weight increases, does this not mean that there has to be some sort of escape velocity? Or perhaps not, as the vehicle is actually pulling on something.
The racing car theory - yes I've often heard the quote about downforce, and that it would be possible to drive the car upside down with it sticking to the ceiling - now, why hasn't anyone built an upside down road to test this? It would make formula 1 more interseting!