# Math Questions

Discussion in 'Hangar Flying' started by choppergirl, Sep 21, 2018.

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1. Sep 21, 2018

### choppergirl

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Fabricating a 4 ft trailer extension. How I'll square it up to weld it together:

Cutting square holes today to bolt mount it with square tubing and battleship plate steel.

Is there a formula or rule of thumb to determine the ratio of how far back the wheels need to be on a pull trailer to prevent harmonic wobble vibration of the whole trailer at highway speeds?

If I add 4' to my trailer, it will be 14' from the hitch to the pivot point of the wheel carriage, and 8' from the pivot point of the wheel carriage back to the rear end of the trailer.

I'm wondering, will I luck out and that be far enough back from the center of gravity of the trailer to prevent disasterous wibble wobble of the whole trailer, so that I don't have to create a new pivot point mount and move the whole carriage back a few more feet.... or....

Floor lenght of the extended trailer would be 19.5'... so roughly... 11.5' of floor ahead of the pivot point plus hitch in front of that, and 8' behind pivot point. Not a huge ratio difference, I know, but still behind the center of the trailer floor body by 1.75'. Is that pushing it?

~

I suppose, as a note to self, once the trailer is enclosed, I should remember to put my plane in tail first, so the main weight of the plane (engine and all) is at the rear of the trailer instead of the front.... to further add more weight behind the wheels to the rear of the trailer and alleviate the situation, rather than worsen it. Or wait, maybe it should be the other way around, with more weight between the trailer wheels and truck wheels, to add braking power. I'm guessing this is about as much about trailer loading management as it is about wheel location, and in the video the guy has his weight inside the trailer all forward or all back.

~

I was able to fix my wire welder feeding/spurting problem by removing 2' of the feed line tube that goes to the gun and adding some corrugated plastic reinforcement tube around it. As the welder was designed, it was just too long of a feed tube and causing too much friction, esp. with the kinks the line got over time. Works like a charm now, at least, for what it is, a bargain basement welder. New modified welder.

Last edited: Sep 21, 2018
2. Sep 21, 2018

### pictsidhe

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The wheels need to be behind the cg. No, I don't mean ChopperGirl sitting up front
Since boats are tail heavy you may get away with stretching the frame backwards. Check you have some weight on the hitch each time you set off and you should be good, I like ~5% of the trailer weight, but many prefer more and will no doubt yell at me for suggesting that. Move the load around to get the hitch weight about right. It's normal to have the empty trailer with the cg in front of the wheels. Too much weight on the hitch is also bad. When I've built trailers, I weld the axle on last so I can tweak the empty balance just so. Some deft work with a 4 1/2 grinder will likely have your axle off in an hour if need be.

Has autumn come early in GA?

3. Sep 21, 2018

### lr27

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When I extended a small trailer to make it into a boat trailer, I stretched both the front and the back. I think the total, loaded weight is about 300 to 400 lbs. As I recall, the tongue weight felt like maybe 30 lbs or so. I may have calculated or measured it, but if so, I've forgotten. In any case, it seems to behave on the highway.

I have an ancient book called "Royce's Trailer Boating" which agrees with pictsidhe. It says 5 percent tongue weight up to 1500 lbs, then 7 percent. However, cars and tires were different in 1960, so perhaps the optimum is slightly different. Still, I doubt you'd get into trouble.

4. Sep 21, 2018

### mcrae0104

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Look here for info on trailer stability. His other articles on trailer design are good reading as well.

For the math question, how much weight will be on Dorothy's mains and tail wheel, and how much distance is there from her nose to the mains, and mains to the tail wheel? You would also want to know the unloaded weight on the hitch and on the wheels when the trailer is empty. (Of course, you probably don't know this until it's done, but estimating will work.) With this, you can figure out the CG.

I have to get to work right now but I'll make some diagrams and show you the math when I have some time this evening.

Last edited: Sep 21, 2018
5. Sep 21, 2018

### narfi

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https://www.synthx.com/articles/trailer-stability.html/

Slight rabbit trail,
I was backing a 206 on floats into the lake when the trailer came off the hitch, the trailer started rolling on its own down the hill with my Boss's plane on it, only thing that stopped it was the hydraulic lines from the tractor to the trailer, my heart was really beating....

Saw a guy tearing down the road beside the runway on his 6wheeler with a trailer full of his grandkids behind him. Just as he went out of sight we heard a huge noise and all ran out to see what happened. The trailer had come off the hitch and the tongue hit the ground and turned the trailer into a catapult to launch the grandkids through the air trying to catch up with him on the 6 wheeler and failing. Luckily kids bounce, so no one was seriously hurt.

Last edited: Sep 21, 2018
6. Sep 22, 2018

### mcrae0104

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There are several ways to do this. What I'll show here is how to find the trailer's CG, the plane's CG, then put them together and find the weight at the hitch and at the wheel pivot. Keep in mind I'm making up numbers for weight, the CG of the plane, etc.

[HR][/HR]
1) Weigh the trailer to see how much is on the wheels and how much is on the hitch. Suppose you get these numbers:

[HR][/HR]
2) Find the CG of the trailer by summing the moments around point H:

Now you know where the trailer's CG is:

[HR][/HR]

3) Now do the same to find the plane's CG--weight on mains & tail, then figure CG location:

[HR][/HR]

4) Put the two CG locations and weights together on one diagram to sum the moments around the hitch and find the reaction at the wheel pivot:

Since you know the total weight and the weight on wheels, you also can find the weight on the hitch, and you have all the information you need: 44% of the weight is on the hitch (at least in this hypothetical example).

[HR][/HR]

5) Another way of looking at it would be to see how far the CG is in front of the trailer's wheels:

[HR][/HR]

6) But what if we turn her around backwards? Maybe it's easier to load & unload tail-first or maybe there's too much weight on the hitch for your pickup; where would the CG be if the plane is turned around? Run through the same process and you find that 13% of the weight is still up there on the hitch, and the combined CG is still ahead of the rear wheels (now 22" instead of 75").

7. Sep 24, 2018

### Fred in Wisc

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Here's a rule of thumb without the math. In general, you want about 10% of the weight of a small trailer on the hitch. More won't really hurt anything, within reason. When you have problems is when the trailer is tail heavy, it's very unstable and prone to whipping around when driving.

8. Sep 24, 2018

### mcrae0104

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Hmm, all the pictures disappeared from my post above... I promise it made more sense with pictures!

9. Sep 25, 2018

### blane.c

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It doesn't have to be that exact for what you are doing provided you are going to carry something reasonably heavy around also, like a tool box, air compressor, or whatever, just figure it out reasonably close and place the tool box were needed to get it to ride right. Batteries, spare tires and other stuff can be located as necessary to fine tune the weight as well. Another thing is you are likely to want to change some things or add some things to the trailer in the future and the weight will shift.

10. Sep 25, 2018

### pictsidhe

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Too much weight on the hitch upsets tje towing vehicle. Ok if it is heavy. But if your trailer weighs over 1/2 as much as the towing vehicle, you want to avoid significant hitch weight. If yiu have a 5th wheel, you can have a lot of weight on the hitch. If not, you can end up with a lot less weight on your front wheels.
Try it if you must. It really does not feel good.

I judge hitch weight with my arm and a guess at my trailer weight. So I am not precise. I arrived at my 5% through trial and error. I have towed with a heavier trailer than tow vehicle and have yet to have any mishaps. Unlike sone of the people who don't think hitch weight matters...
If you have it nicely balanced, you can hardly tell you are towing. Other than the lousy braking and acceleration.

11. Sep 25, 2018

### pictsidhe

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Math time.

Moments.
The sum of moments comes to zero.

With your axle as the reference.

Hitch weight x hitxh distance from axle = trailer weight x cg distance from axle.

You can also calculate the change in hitch weight.

Hitch weight change x hitch distance = added weight x distance of weight from axle.

12. Sep 25, 2018

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