If we re-engineered the German V-2 to launch a man, how high would it go?

Question

Using the German V-2 rocket dimensions, how high would it fly with today’s technology? It used 6 tons LOX, 4.5 tons alcohol and was 46’ high, 5.5’ across, 28k lbs launch weight, with 1 ton pay load: http://www.ww2guide.com/vweapon.shtml
Suppose we allow 1 ton for a Mercury-style crew capsule and 1 human occupant. Replace the riveted steel, say with titanium. Use a better fuel and better rocket engine. Could we get it in orbit using today's methods and materials?

The real question is, does anyone here know how to do the math?

Answer 1

The V-2, when used as a space research vehicle, was capable of ascending about 50-60 miles straight up, and never got anywhere near an orbital insertion velocity.

But the boys at Peenemunde got a lot of things right, and considering that they had to work everything out from scratch, what they accomplished was phenomenal. Werner VonBraun sketched the basic arrangement for a liquid cooled, liquid fueled, turbo-pump fed rocket engine on a napkin in a Berlin restaurant in about 1938, and his idea was so pinpoint right on that it has never been improved upon significantly.

The main engines of the Space Shuttle are built according to that napkin design, with minor refinements. So in a large sense all space vehicles to date are re-engineered V-2s.

Re-working the original V-2 within the confines of its dimensions would produce a launch vehicle capable of perhaps 10 to 15 percent greater performance than the original, giving a sub-orbital sounding rocket at best.

But the re-engineering was done, nonetheless. The Mercury Atlas launch vehicle was as good a "re-engineered V-2" as you are going to get.

Answer 2

It was alredy done- The apollo space programme!