Relationship between altitude and max MPH

You'll need a book with the ICAO standard atmosphere tables. Finding the altitude where the atmosphere is 25% less dense is easy. The part about going faster is dependent on the power curve of the engine, the drag curve of the airframe, and how both are affected by altitude.
Do you have enough information about the aircraft and its engine to begin working these out?


Steven Fahey, CET
"Simplicate, and add more lightness" - Bill Stout

No, it's just a hypothetical question. Let's say it was a rocket flying horizontally with a given amount of thrust, and a nice slender Cd. Or, whatever example would stabilize the variables to give some indication of how the thinner air lessens the work needed. Would a 25% reduction in atmosphere equal a 25% reduction in effort to do the same mph? That's more to the point of what I'm trying to find out.

Is there less work needed?

You're assuming that the lessened draw reduces power requirements, but commensurately, your lift would presaumbly decrease as well.

TTFN

From the table below the density will be 25% lower at approx. 9500 feet. Use density ratio, which is a ratio to density at altitude to that at sea level.
In order to create the same lift at altitude, for a given indicated air speed (IAS), you have to have a higher velocity. It is called true air speed (TAS), which is IAS corrected for temperature and density. For your rocket cruising at 100 mph IAS, the TAS at 9500 and standard temperature for that altitude (-3.8C) would be 115mph. Your drag would be reduced by the lower density but would be offset mostly by the increase velocity (varies as velocity squared). Most of the time you get a reduction, but nowhere near 25%. Normally power or thrust also decrease with altitude.
Cheers!

This is the issue faced by high altitude aircraft too. As altitude increases then to maintain the same aerodynamic pressures on the wings the TAS must increase proportionally.

The speed of sound also decreases at altitude and for this aircraft there is an altitude where the decreasing speed of sound curve crosses the increasing TAS curve.

The aircraft must fly above a certain TAS or it stalls, so at high altitude the Devils Corner is that triangle where a slight increase in speed means it breaks the sound barrier and the wings fall off but flying a bit slower means it stalls then one wing drops and goes faster, breaks the sound barrier and the wings fall off.