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Specs on unit say 2,900lb hitch weight, 13,400lbs shipped weight.
My truck has a 9,900lb GVWR, 20,000lbs GCWR, so it appears that I am over on the GVWR by 1240, and over on the GCWR by 1680, with this particular unit.
Am I doing the math correct?
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No. Begin with the GVWR of the trailer. Assume you'll load it to the gunwalls, and that actual hitch weight will be 20 percent of GVWR. Folks that start with some weight other than the GVWR of the trailer are just fooling themselves. A year or so down the road a CAT scale ticket will slap them back to reality.
Example: If the trailer's shipping weight is 13,400, the trailer GVWR is probably 16,000 pounds. So assume your wet and loaded trailer is going to gross 16,000 pounds. 20 percent hitch weight is 3,200 pounds.
Your truck weighs 8,240 before you tie onto the trailer. Add 3,200 for a GVW of 11,440. 1,540 pounds over the GVWR of your tow vehicle. A few hundred pounds overweight is understandable, but 1,540 pounds overweight means there is an idiot somewhere whispering in your ear.
Add 16,000 to 8,240 and your GCWR is 24,240. 4,240 pounds overloaded. That's not so bad if you have a hot-rod engine and BTS tranny doing the work, along with stock-size tires. But with your 35" tires, it's crazy.
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Any suggestions, on how to make this work, short of buying a new truck?
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Of course. Buy less trailer. With your 8,240 pound truck and 9,900 GVWR, you have 1,660 pounds available for hitch weight. A smaller trailer would have about 17 percent hitch weight, so the max trailer GVWR you should look at is about 9,700 pounds.
Yes, they make 5ers that have a GVWR of less than 9,700 pounds. Mine has a GVWR of 7,900 pounds. My previous 5er had a GVWR of 6,000 pounds.
But if you insist on a 16k trailer, then you need a lot more truck than your pre-2005 F-350 SRW to tow it with.
16k trailer plus 9k tow vehicle is 25,000 pounds needed GCWR. Ford makes them with 26,000 GCWR and more. But they are not SRW pickups and they don't have a 3.73 rear axle ratio or big tires.
3,200 pounds hitch weight plus 9,000 pounds tow vehicle is 12,200 pounds required GVWR. The 2005-up F-350 DRW longbed diesel has 13,000. But it has only 23,000 GCWR unless you add the TowBoss package to make it meet you needs of 25,000 GCWR.