Investigations in to weight-saving for tongue
First I’d like to start by suggesting that the Australian guidelines are pretty close, but may be slightly, to significantly unconservative. I say this because I am aware that trailer designers use an over-the-road factor of 3gs and an off-road factor of 5gs when analyzing the stresses in trailers. What I found in my case, assuming a 20% maximum tongue weight is that I got a higher moment than the Aussies did. Now there are lots of assumptions (primarily how much of the trailer’s weight is on the tongue) that go into the calculation and it’s probably OK for the over-the-road trailer, but in the case of Dave Nathanson and his off-road trailer, it likely results in under-sizing the tongue. Had Dave used the off-road 5g factor, he would have calculated much more moment and this would have resulted in a more robust tongue. The calculation for determining the bending moment is pretty simple (some of the other structural calculations are a bit more math-intensive) and I think most capable of using it. The steel sizes can then be looked up in the Tongue Strength Sheet after the moment is calculated.
Step 1 – tongue weight
Interestingly, since these little teardrops have a lot of weight in the aft, should you leave your 5 gallon water jug or 80Lb cooler at home, your tongue weight can go up significantly. What I did was use the trailer balance spreadsheet to calculate the tongue weight depending on what was loaded into the trailer. I started full up and estimated that I’d have about 50 Lb on the ball. Then I started unloading stuff out of the back – water, ice chest, propane, etc. The weight went up to nearly 80 Lb. Since that didn’t include any misc crap in the sleeping area, which would make the weight go up further, I decided to use 100 Lbs as the maximum that the ball would see. This also corresponds to 20% of the trailer weight, which I don’t think is too crazy and this offers what appears to be a nice wide tongue load range.
Calculating the moment is quite simple, it’s just the weight times the distance from the ball to where the trailer makes contact.
In my case, since my trailer will not be going off-road [on purpose anyway]:
M = tongue weight * dist from ball to tear contact point * gfactor
M = 100 * 42 * 3 = 12,600 in-lb
The Australian method comes up with:
M = 500 * 42 * .5 = 10,500 in-lb
This is 20% less than the actual calculation yields. Since I only assumed a maximum of 20% on the tongue, this method could be unconservative. I think the Puffin, for instance, had a tongue weight that exceeded 20%, or was that the time he forgot to remove the jack stands (I could be ‘dis-remembering’ that). The good news is since you are unlikely to encounter an actual 3g dip in the road the 20% difference in the calculation methods won’t likely result in a catastrophic failure of the tongue. Still, 3gs are what the real guys use, for the trailer anyway (according to the trailer design handbook I read many moons ago when I designed a BIG trailer for a guy to haul a bulldozer on). Enter this in the FWIW dept. Anyway, since it’s such a simple calculation, why not use it? I believe that what they have done to make it easier for the fabricator is to try and simplify it by making an assumption about the percent of the total trailer weight that is on the ball -- in this case 16.6%. If an 800 Lb trailer had 160 Lb on the tongue -- that would be 20%. The problem is you have a truly off-road trailer the tongue will likely be undersized. The loading between highway and off-road is certainly not going to be the same. I remember clearly that the handbook recommended 5gs for off road. I can only imagine where some guy with a 4WD would drag that hapless tear! In the end, you should weigh the tongue once you load up (or not load up – with stuff just in the cabin like AC mattress misc.) and double check the tongue strength based on the actual weight and g-loading rather than to assume anything.
Step 2 – calculating the stress
The stress is independent of the material. It’s a function of the load and the geometry. Here we luck out, if using a rectangle or square section, because the stress is very easy to calculate (angles are more complicated, but the data needed use usually in a chart, and doesn’t actually have to be calculated) for either of these two sections.
The general equation for stress (bending) is f = Mc/I
Where f is the stress, M is the moment, c is the distance from the section centroid to the outer edge, which in the case of the square or rectangle is just ½ the height, and I is the moment of inertia.
The moment of inertia for a solid section is: I = 1/12 * b * h^3
Where b is the width and h is the height.
To get the moment of inertia of a hollow section in the case of a square or rectangle, we just calculate the outside and subtract the inside:
I hollow rectangular section = 1/12 *(b outside * h outside ^3 – B inside * h inside^3)
This, for a square, the equation further reduces to:
I hollow square section = 1/12 * (h outside^4 – h inside^4)
Let’s use uber-ultra as example
At 12,600 in-lb, looking at the tongue strength sections listed in the table, we could go with a 2”x2”x.125 or a 2”x3”x.083 (14gage) The weights are similar, but with the advantage that the height gives the Moment of inertia in the calculation (h cubed), the taller section is just a bit lighter. Let’s calculate the stress in either section:
2x3 rectangular section (wall is .083 thick -- 14 gage):
I 2x3x14 gage = 1/12*(2 * 3^3 - 1.834 * 2.884^3) = .8339 in^4
f bending = 12,600*1.5/.8339 = 22.6 Ksi
2x2 square section (wall is .125 thick)
I2x2 = 1/12*(2^4 - 1.75^4) = .5518 in^4
F bending = 12,600*1.0/.5518 = 22.8 Ksi
The stress is the same, but the section that is taller and thinner is lighter
The 2x2 section weighs 3.05 lb/ft and the 2x3 section weighs 2.67 lb/ft
Hummmh.
Since both of these are well under the 31.5 Ksi allowable for strength either can be used, but with an 8 ft piece of tongue, the 2x3 section is 2.6 Lb lighter.
Since the stress doesn’t change due to material, we are able to make a straight material substitution and save some weight with some decent aluminum.
Aluminum Square Tube is produced primarily in 6063 and 6061 alloys. It has square defined corners on both the inside radius and outside radius.
6063-T52 is the lower strength of the two alloys and is generally produced in thinner wall sizes but has better corrosion resistance and finishing qualities than 6061.
Fty = 21Ksi, Ftu = 27Ksi
6061-T6511 has more strength for structural applications requiring high strength yet a light weight material.
Fty = 35 Ksi, Ftu = 42Ksi
As can be seen from the above numbers, the 6061-T6511 is as good as the steel (now some steels are WAY better, but this ain’t one of them); so, we COULD make a direct substitution for the steel with the 6061-T6XXX. However, after much searching, I could not find either of these sizes in 14 gage, which is a pity – that would be the maximum weight saving for metallic. Oh well, if someone finds a source for the 14 gage 6061 in a 2x3 size, do let me know.
So, we still have a couple of choices. We could make a direct substitution for the 2x2 stock, since the stress is below the aluminum allowable.
Density of aluminum = .101 lb/in^3
Density of steel = .284 lb/in^3
8 ft steel 2x3 = 21.36 lb
8 ft alum 2x2 = 9.09 lb
That’s a savings of 12.27 lb – not insignificant.
If you could manage to find the 2x3 14 gage aluminum, the weight would be a mere 7.6 Lb with a weight savings of 13.8 lb.
The 8 ft aluminum tongue runs about $45 dollars, excluding shipping, but as weight goes, this one seems pretty cheap.
Having said all of that, there is one consideration not yet addressed and that is stiffness. While it is correct that the aluminum weighs about 1/3 of the steel. Unfortunately it also had only about a third of the stiffness. What does that mean. It means more displacement for the same load – approximately 3 times as much. This means that the trailer will be a little more lively (bouncy). The deflection at 300 lb (of course this is the maximum design-to load) is .82 inches (FEM derived) with the 2x2 steel, therefore, the aluminum would displace 2.4 inches for maximum design-to condition. Maybe it’s not that big of a deal, since we really hope never to see that kind of a sinkhole in the road, but even at 1 g the deflection is .82 inches -- seems kind of high.
Hmmmm..
OK, there is still a little something up my sleeve. How about if we sacrificed a little bit of the weight for a lot more stiffness. How about we go back to the 2x3 section and instead of the 14 gage, which is apparently unavailable anyway, we go to the 11 gage (.12 wall thickness) which is actually available.
I 2x3x.125 = 1/12*(2*3^3-1.75*2.75^3) = 1.4671 in^4
f 2x3x.125 = Mc/I = 12,600*1.5/1.4671 = 12.88 Ksi
Now that stress is LOW – we could even use the sort of crappy 6063-T52, and the deflection, compared to the steel 2x2 is pretty similar:
deflection = 1/3 (PL^3)/EI
deflection 2x2 steel = 1/3(300*42^3)/((29e6*.5518) = .46 in
deflection 2x3 alum = 1/3(300*42^3)/10.3e6*1.4671) = .49 in
Since I'm pretty confident that the 2x2 steel would work, and considering the deflection is pretty darn close the 2x3x.12 Al should be OK as well.
The actual deflection will be slightly larger as the beam isn't perfectly fixed, but is gives us a relative comparison between the two.
The weight saving is still 21.36 – 11.57 = 9.8 lb and the stress very low and the deflection acceptable. I can tell you folks in my business would nearly kill to save 10 lb.
I won't go into too much detail about the composite beam I was investigating (like I didn't go though too much detail already!), but suffice it to day that unless you were willing to spend a lot on graphite to get the stiffness higher, it's just too flexible out of fiberglass. I was able to configure it so that the stresses were all acceptable and the weight low; but, the deflections were much larger than either the aluminum or steel – so much so that I don't think a glass only beam-type tongue would work (Andrews large nose of a tongue might well, but not a standard beam) – it would be way too bouncy.
I'll post a picture of the models of the beams when I get a chance -- it's past midnight and my brain is fading...
Well a couple of things are demonstrated: the amount of weight to be saved is a function of the overall loading, and the higher the loads, and or heavier the trailer, the more weight-saving potential exists. For a really light trailer, there isn't as much weight to save because the overall weight the react the smaller loads is less to begin with. In the first posting, with a longer overhang, and more moment, the ultimate weight-saving is more significant. Mostly, what happens when everything gets really light, is that the very thin gages that could be tolerated, don't even exist (or would be expensive to custom make); so, though you could theoretically reduce the weight, a lot, practically, you may not be able to reduce as much as theory suggest (but you can still save a significant amount). If you have a light trailer, follow the second posting, if you have a heavier trailer, follow the first.
