Benny and Aaron pretty much summed it up nicely. Aaron is exactly right that the weight on the tongue is not the same as the weight on the rear axle and the front axle does get unloaded. This is where the lever arm stuff comes in (the weight on the rear axle would logically be greater than the weight on the tongue, due to the lever arm). The fact that the summation of the truck alone and the summation of the truck plus trailer load do not add up exactly is also a point of confusion. I'm not familiar with grain scales. Do I assume that you get independent weights for each axle? If so, I would throw out the totals and calculate totals from the axle weights alone.
In that case, the truck weighs 6,080 pounds and the weight with trailer is 10,060 pounds. Simple math tells us the trailer weight is 3,980 pounds. (That sounds about right for a C22 and trailer, no?). The loads on front axle, rear axle and trailer axle are 3,300, 3,460, and 3,300 pounds, respectively. That sounds pretty well balanced. By simple subtraction, the weight on the tongue is 680 pounds (3,980 - 3,300). There is no need for lever arm calculations to determine weight on the tongue. The lever arm calculations would be used to find out how much is loaded on the rear axle and how much is unloaded from the front axle ... but we already have the axle weights so what would be the point of doing the calculations? Theoretically, the distance between front and rear axle would need to be 4.85 times longer than the distance from the tongue to the rear axle for these weights to be right. If the wheelbase of the truck is 10' then the extension of the bumper and tongue is a little more than 2'. Again, this sounds reasonable.
The only troubling aspect is that the tongue weight is about 17% of the total, which is a little high, I think we all agree. Perhaps moving the boat back several inches wouldn't be a bad idea.
OTOH, if the axle weights are off and the totals are more correct, this would throw off the calculations above and perhaps indicate a lighter tongue weight by about 300 pounds. In that case the tongue weight might be in a good range. This can only explain the rear axle weight being 800 pounds greater if the lever arm from axle to tongue is longer.
I think you need to find out why there is such a large error in the weights and it would also help do a check on calculations if you knew the distance between truck axles and distance between the ball and the rear axle. These (and correct weights) are all you need to calculate the additional load on rear axle and reduced load on front axle.
If the trailer axle is rated for 3,500 pounds, why is this a problem? The axle weighed in at 3,300 pounds when it is loaded on the truck, so I don't see a problem there.
I'm not familiar with trailer extensions, but the fact that the extension has been repetitively loaded and unloaded without any permanent deflection seems to indicate that the flex you see isn't a problem. If the stress resulted in strain, then I'd be more worried. I-beams are designed to take a load with limited deflection. Square tubes are not. They are going to flex. It doesn't mean that it is going to bend. Maybe sometime down the road, but if you are sliding that thing in and out without any unexpected friction, what is the worry? If you feel you need to stiffen it up, why not just insert some bar stock inside the tube and call it a day? Bar stock on the bottom would be most helpful, but fastening it would certainly be a problem to solve. There must be some practical solutions.
In that case, the truck weighs 6,080 pounds and the weight with trailer is 10,060 pounds. Simple math tells us the trailer weight is 3,980 pounds. (That sounds about right for a C22 and trailer, no?). The loads on front axle, rear axle and trailer axle are 3,300, 3,460, and 3,300 pounds, respectively. That sounds pretty well balanced. By simple subtraction, the weight on the tongue is 680 pounds (3,980 - 3,300). There is no need for lever arm calculations to determine weight on the tongue. The lever arm calculations would be used to find out how much is loaded on the rear axle and how much is unloaded from the front axle ... but we already have the axle weights so what would be the point of doing the calculations? Theoretically, the distance between front and rear axle would need to be 4.85 times longer than the distance from the tongue to the rear axle for these weights to be right. If the wheelbase of the truck is 10' then the extension of the bumper and tongue is a little more than 2'. Again, this sounds reasonable.
The only troubling aspect is that the tongue weight is about 17% of the total, which is a little high, I think we all agree. Perhaps moving the boat back several inches wouldn't be a bad idea.
OTOH, if the axle weights are off and the totals are more correct, this would throw off the calculations above and perhaps indicate a lighter tongue weight by about 300 pounds. In that case the tongue weight might be in a good range. This can only explain the rear axle weight being 800 pounds greater if the lever arm from axle to tongue is longer.
I think you need to find out why there is such a large error in the weights and it would also help do a check on calculations if you knew the distance between truck axles and distance between the ball and the rear axle. These (and correct weights) are all you need to calculate the additional load on rear axle and reduced load on front axle.
If the trailer axle is rated for 3,500 pounds, why is this a problem? The axle weighed in at 3,300 pounds when it is loaded on the truck, so I don't see a problem there.
I'm not familiar with trailer extensions, but the fact that the extension has been repetitively loaded and unloaded without any permanent deflection seems to indicate that the flex you see isn't a problem. If the stress resulted in strain, then I'd be more worried. I-beams are designed to take a load with limited deflection. Square tubes are not. They are going to flex. It doesn't mean that it is going to bend. Maybe sometime down the road, but if you are sliding that thing in and out without any unexpected friction, what is the worry? If you feel you need to stiffen it up, why not just insert some bar stock inside the tube and call it a day? Bar stock on the bottom would be most helpful, but fastening it would certainly be a problem to solve. There must be some practical solutions.
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