
Oh a very nice subject indeed, and quite frankly I won't be able to give you any easy answers.
The 737 can descend in many ways by using the autopilot, but only 1 of them is modelled in the stock 737's: the vertical speed mode.
By using the V/S thumbwheel you can select a RoD (rate of Descent) that will maintain a constant angle. Throttles are not at full idle, we're conducting a
partial throttle descent here.
First let's assume your descent speed will be around m.76/300
I noted you were already aware of the 3:1 method to determine how far away from the airport you should start your descent....for the 737 add an extra of 5nm to slow from 300 to 250kts when passing 10.000ft. That should be fine.
So you know which technique to use (V/S) and how far away you will begin to descent...now we only need to find out what your initial Vertical speed will be.
Take your groundspeed, divide it by 2 and add a zero and 10%.
So if you have a GS of 440kts, half of that is 220...add 10% (12) =240
Add the zero= 2400
Your rate of descent will be 2400ft/min...but then you got to let speed bleed off at 10.000ft. This is in general 35nm from the airport. At 250kts