I hate to admit I made a classic freshman mistake - I lost sight of the problem.
The OP wanted to predict changes in tongue weight due to weight added to the back of the trailer. You are right in that you do not need F1 for that analysis.
In my work this summer I was trying to predict how much of the WDH load is transferred back to my trailer axles, and it was that load transfer that I had in mind when I was looking at your formulas. But again, you don't need that for the OP's answer.
We pull a TT that weighs 7600 lbs total that sits on two 3500 lb axles. While it doesn't bother me to overload the Tundra chassis by 3-400 lbs, those trailer axles are built to a price point and are easily the weakest link in our rig. We replaced all the tires with the highest load range 5 weeks after the unit was delivered because they were going to be running right at their load limit.
I actually have a spread sheet that calculates all the axle and tongue loads based on what we put where, and everything that goes into the rig gets weighed (drives my DW nuts - an added bonus). If we get too close to the axle limits I'm going to move something to the truck bed or leave it home. Yeah, I'm compulsive about the load on my trailer axles.
Anyway, perhaps we've saved some brain cells today. At least this was more engaging than watching I Love Lucy reruns. Happy trails!
