Well, the simplest and safest way is to buy Ultranav (
www.ultranav.com) for your jet and let it figure out those performance numbers.
But since you probably want to figure out how to do it the old fashioned way here’s a couple of different ways that performance problem can be run.
The safest and easiest way is to go to your second segment climb gradient chart and find a weight that allows you to maintain your required climb gradient at the top of the climb. In your example just find a weight that lets you do 5.7% on the 8000’ chart. The problem with this method is that it unnecessarily restricts your takeoff weight*.
Another method is to go to your second segment climb gradient chart and find the altitude between your top of climb and field elevation (i.e. if T/O fields at 4000’ top of SID is 8000’, so use 6000’) and find the weight at 6000’ that lets meet the climb requirement. I call this the median altitude method.
A final method is to find a weight that lets you meet the climb requirement at field elevation add that to the weight that lets you meet the climb requirement at the top of climb and divide by two (i.e. at 8000’ you can T/O at 22,500lb and get 5.7%, but at sea level you can go at 30,000lb so you use 26,250lb as your maximum take off weight). I call this the median weight method.
*Reason this is unnecessarily restricting is that for the first part of you climb you will be exceeding your required performance. Let’s say you can only be at 75%MTOW at 8000’ and meet a 5.7% (350per nm) climb gradient, but at sea level you can be at 98% of MTOW and meet a 5.7%, if you take off at sea level at 75%MTOW you will be climbing out much better than 5.7%, thus exceeding the climb requirement.