Here, from a paper in the Public Record Office, are Saunders Roe's proposals in 1958/9 to use the SR53 as a research vehicle.
The drawing has been somewhat tidied up and simplified, but shows all the essential details.
The diagram starts at the bottom right, illustrating what had been achieved to date with manned balloons, the Canberra (which then held altitude records), and the Bell X2. The 3 contours show what the basic machine could do with minimal uprating. Then we see a big jump if the aircraft is air launched from a Valiant, with maximum altitude of 45 miles. After that the jet engine is removed and replaced by 55% more rocket fuel, then finally we have the "ultimate development".
But a lot of this is fantasy. Without small rocket thrusters the aircraft controls would become ineffective above about 100,000ft. If instead, the vehicle goes for speed - Mach 4? - it does not have the airframe to cope. Aerodynamic heating would necessitate steel or titanium rather than aluminium, although apparently soe design work was done at Saunders Roe on stainless steel leading edges, etc.
The Bristol 188 was designed to operate in these regions, but was less than successful. As an answer to the X-15, the SR53 would not have been up to it.
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