power increases to the cube of speed, so the relative power required is just the ratio of speeds to the power of three. The benchmark here is the average on a normal bike, say 13 mph. Want to travel at 20 mph, then you will need (20/13)^3 times more power (all else being equal). Needless to say, going fast gets VERY hard.
For HR, I validated 2*HR – 80 using my power meter as a reasonable steady-state (i.e., average over some constant effort, rather than just jumping around due to sprint efforts). That means that when I’m chugging along at 140 bpm, my power is 200 watts – I’m usually at about 20 mph on a road bike and 24 mph on a TT bike (more aero). It’s an OK estimate but fails at the extremes (max HR etc..). I have several power meters, including a PowerCal, that uses rate of change of HR to estimate power with a simple regression. I made some more complex ones for fun too.
What my simple sum ignores is the difference in weight – which is not huge, but could be important if the route is not flat. Aerodynamics are assumed to be the same for both bikes.