Andrew: ...and I thought I did obsessive spreadsheets! Wow. Good work!
Shrug: don't give up on trying to pre-calculate the tongue weight. The tongue weight on the Road Toad turned out to be pretty much what I had calculated (~15% unloaded, ~10% loaded), which is good considering the axle brackets were welded on before powdercoating and it'd be a real pain to have to move them
For what it's worth, here's how I did it. It's a little more complicated to explain than to actually do.
As an example, assume a 10-foot long trailer body that is a rectangular box (some adjustments would have to be made to calculations for teardrop shape). Now assume said trailer weighs 1,000 lbs and the weight is distributed fairly uniformly because of the box shape (chassis and body thrown together here for simplicity). Weight is 100 lbs. per foot of body length.
I used a starting point of the spindle center (not axle) at 3.75' (45") from the rear of the trailer body and 6.25' (75") from the front of the body. I have an additional 4.4' (53") length from the front of the trailer body to the center of the hitch ball.
Then I calculated the force moments by taking the total weight over the behind-spindle center and front-of-spindle center sections as acting as a point load 1/2 way from their respective distances from the spindle center. The tongue weight is a point load at the distance from the end of the tongue to the spindle center.
So:
Behind spindle-center moment: (3.75 ft. x 1/2) x (100 lbs./ft. x 3.75 ft.) = 703 ft .lbs.
Front of spindle-center moment: (6.25 ft. x 1/2) x (100 lbs./ft. x 6.25 ft.) = 1,953 ft. lbs.
Moment acting at end of tongue = 1,953 - 703 = 1,250 ft. lbs.
Tongue distance from spindle center: 6.25 + 4.4 = 10.65 ft.
Tongue weight = 1,250 ft. lbs. / 10.65 ft. = 117 lbs. = 11.7% of total trailer weight of 1,000 lbs.
Of course, we haven't considered the weight of the tongue itself and some other items in this simplification. We could refine our calculation by adding some other point loads for the bulkhead, galley cabinets, water tank, battery, propane tank. etc., by calculating their distance behind or in front of the spindle center. Set everything up in a simple spreadsheet and then play around with your initial assumed axle/ spindle center placement until you get the tongue weight/percentage that you want.
For example, assume an additional 175 lb. point load on the rear end located 2.5' (30") from the spindle center (437.5 ft. lbs.) and an additional 70 lb. point load for the tongue box and contents located 9" in front of the main body or 7' (84") from the spindle center (490 ft. lbs.). This is a net increase of 52.5 ft. lbs. (490-437.5) acting on the tongue, or an increase in tongue weight of 5 lbs. (52.5 ft. lbs./ 10.65 ft.).
This will all probably become clearer if you sketch it out. Sounds more complicated than it is.
The same concepts can be used to estimate the tongue weight by measuring the weight at the front jack. Or to figure out the strength of gas supports you need for the hatch.
For example, if the measured weight (using a scale) at the tongue jack is 150 lbs., and the distance from the tongue jack to the spindle center is 109", and distance from the center of hitch to the spindle center is 127" (tongue jack is 18" behind center of hitch), the tongue weight can be calculated at ((109*150)/127) = 129 lbs.
Or, if you have a 4-foot long hatch that weighs 50 lbs., you could calculate it as a 50 lb. point load acting 2 feet from the hinge for a 100 ft. lb. moment. If two hatch supports support the hatch 5" from the hinge, they would need to support a total of 240 lbs. (100 ft. lbs. /(5/12) ft.). Add 10% for temperature fluctuations and you get 264 lbs., or 132 lbs. for each gas support. Therefore, 150 lb. supports would work fine in this case and 120 lb. supports would be too weak.
Hope this helps.
Rik