Backpacker -you have just proved yourself wrong
the 3 times rule also takes into account distance. Something you have completely missed out on.
Your calculations have just given differing rated of descent so the 3 times rule does not come into effect.
Before you retort back. Can you just confirm that the rule of thumb is 'I have to lose 10,000' so i need about 30 miles'. If so, where is that on your calculations above. We use that for about 250 knots in the descent rate about 1500fpm. Do that at 60kts and its 333 fpm, for the same 30 miles travelled. All I am trying to get across is that it clearly is a good rule of thumb for faster aircraft but is mathematically incorrect for smaller one. The figures prove that without question.
If you use the 3times rule. What is the ROD, because you must have a second constant for it to work. You cannot have 3times the height, then vary ROD as it makes a mockery of it.
If you don't take distance into account, especially in faster aircraft, you will just fly past the airport too high/low, whatever.
For cessna's and the like i used to taech groundspeed/distance = minutes and divide by altitude to lose. So yes, I like to keep it simple when its right.
Again, just go a check the formula in a nav book somewhere that takes into account the above and then come back to me and tell me I am wrong or right.
Your last comment about specific aircraft ROD, I was not questioning anyone about.