Dangerous Top Heaviness

[GoTurtleGo]

Is there a math formula or ratio for figuring out how to keep your foamie/teardrop from blowing over? Wider than tall is a little too vague to be helpful. For example, are a mere four inches wider than tall sufficient for safety? And having it be heavier on the bottom rather than the top is self-evident, but, for example does building a basement make you a little safer if you are tall?

This came up again recently when folks were concerned with someone's planned build. And someone calculated the ratio and said it was not sufficient to make it safe. But, as per usual, I cannot remember who or where this discussion took place. Any one remember who the calculator was?

I would love some feedback.

Thank you,

Kathleen

[GPW]

Lot depends on the shape of the roof too , rounded roof , the wind blows over it, flat roof (Box) the worst ... Side area , center of gravity , all things to consider ... but the old no higher that wide is a good rule of thumb .... not written in stone , varying with many factors , such as , are the wheels on the outside of the cabin , or under the cabin (wheel stance ) ... Lots of little things to mill over , better if you carry all the heavy stuff down low on the floor ... or the 500# of Beer ballast ... or soda pop..

I believe Catherine and twins was the one that had the blow over... and it's been some time now ..

[NMMarauder]

I can answer this one.

An object will always tip over when the center of gravity is outside of its outermost support. Here is a diagram to clarify.



We can see that the center of gravity is still on the correct side of the tire about which it is tipping. The force of gravity (noted as F1) will right this trailer and it will land on its wheels.



In this diagram we can see that the center of gravity is on the wrong side of the tire about which it is tipping. Gravity is going to tip this trailer onto its side. Sorry my labeling of X1 is so messy.

So here is where the common rules of thumb come into play. The wider the trailer is, the harder it is to tip it so far that the center of gravity passes the outside support. Also, if the center of gravity is very low, this makes it harder to tip the trailer so far that the CG passes the outside support. To sum up: if you don't want your vehicle to tip, make it wide and keep the center of gravity low. But that's not very helpful because it doesn't give you numbers you can work with to predict when your trailer might tip. So let's look at another diagram.



In this diagram F2 is the force due to the wind. The wind applies force to the whole side of the trailer but it can be summed up as a single force acting through a single point. It is acting through point Y2. F2 x Y2 creates a moment (which is just a word that means twisting force) and that twisting force wants to tip the trailer about point Q. (This assumes the tire isn't going to just side which is probably a good assumption) Let's call this moment the "tipping" moment.

F1 is the force due to the weight of the trailer and it is acting through its center of gravity which is at X1. F1 times X1 creates a moment that wants to keep the trailer on its tires. Let's call this moment the "Restoration" moment.

So as long as the restoration moment is greater than the tipping moment, all is well and the trailer stays safely on its tires. When the moments are equal then it is the start of danger so let's try to find out when that occurs.

Let's look at the variables in question:

X1 is the horizontal distance from the center of the trailer to the outside of the tire (in ft), assuming that you build your trailer symmetrically so that the center of gravity isn't skewed to one side of the trailer. I think I chose the center of the tire for my calcs.
F1 is the weight of the trailer in lbs.
Y2 is the point through which all of the summed up wind forces acts (in ft). This can be tricky to determine for anything other than a simple shape (such as a box). What you want to find is the centroid of the shape. If you use something like SketchUp to draw your designs, there is a way to let it find the centroid for you. Anyway.... for our example let's assume you are building a box trailer. The centroid would be at 1/2 the height of the box.
F2 is the force due to the wind. This one is complex enough that I'll explain it below.

F2 = Area of the side of the trailer x Pressure from the wind x The coefficient of drag of the trailer side. In condensed form it looks like this: F2 = A x P x Cd

The area of the side of the trailer is calculated in square feet. Again this get's tricky if you have something other than a simple shape. This is another value that I let SketchUp calculate for me. For a box trailer it would simply be width x height
The pressure from the wind is calculated by this equation:

P = 0.00256 x V^2 (That's a number, 0.00256 times the velocity of the wind squared) where velocity is measured in miles per hour.

Finally Cd is the coefficient of drag for your shape. This is another tricky variable to define. It totally depends on the shape and it has to be determined in a wind tunnel. The best you can do is estimate it based on some of the values in the table below.



So at this point it would be wise to put all of this in a spreadsheet so that you can play with the numbers. But what you really want to know is "At what point does the left side of the equation below equal the right side"

F1 x X1 = A x 0.00256 x V^2 x Cd x Y2

I was going to put some example numbers in but I'm not sure that would be all that helpful. It comes down to playing with Trailer weight, trailer width, surface area of the side of the trailer, trailer height (because a taller trailer will have a larger Y2 value), wind speed and picking a Cd. I chose 1.17 as a value but only because I was pretty sure my trailer shape would have a lower Cd than that. I like to know the worst case scenario.

Anyway... I hope that my explanation was helpful.

[KCStudly]

That is about the best, most understandable explanation that you can get. Great job laying it out, NM!

[GoTurtleGo]

Thank you NM. That is a very helpful explanation, despite my rusty math brain, but I understand it enough to start the spread sheet and collect my facts and best guesses. I can then see that if what I desire is practical. Your drawings are perfect.

By the way NM is one of my favorite places on the whole big wide earth. You are privileged to live there.

Also thanks GPW for the reminder of all the rules of thumb. I'll make a list of those too so I can keep them properly in mind as safe checks.

I am more of a draw-it-all-on-gridded-paper kind of girl because the process of using my hands informs my brain better than using the computer. Apparently I have a primitive brain.

Thank you guys! I'm excited to have this information in hand.

[Mary C]

so.... the issue at hand is how much weight is inside on the floor, Where you are driving ....high bridges, wind storms in New Mexico, OK tornadoes or where the next hurricane will make landfall. it helps to know the projected wind velocities and the thunderstorms height. Then factoring the width vs height and the other stuf above (I am not too smart with math) I think a glass of wine is in order.....oops it is my ballast. now to get out my calculator.....yep two bottles over so I am ok. I guess NM did a great presentation I can be honest and say the pictures were a great help for my next build. kinda reminds me of how my trailer looked in the barn when I was painting the bottom...

Mary C.

[GPW]

Naturally , the very Best thing to do is NOT drive during BAD weather... Like a sailboat =... there are days when you Don't go sailing ... If you find yourself in a dangerous weather condition , pul over , preferably behind a large building , leeward of then storm ...

[Fred Trout]

do NOT drive during BAD weather

^^ agree with this

[Mary C]

I know one thing for certain with mine it would not just tip on its on.....it took a block and tackle to get it up so I could paint the underside..I refuse to worry I will look for a building and park away from the wind but that will not work on the bridge......but I will just go anther way. He He..

Mary C.


Sorry Turtle, I just couldn't help myself.

[GoTurtleGo]

I do remember Eagle's fears about the big bridge near her home and the wind on it. After I finished reading the big thread, I dreamt about that once - being blown over the side of a bridge! So, no one needs to persuade me to stay out of the wind. Catherine's first foamie was a BIG lesson in cautiousness.

And ballast and wine and beer barrels - got it!

[WizardOfOdds]

Excellent analysis and explaination!
Very glad to see the technical aspects explained with a little bit of math and physics.
I also like the pen/paper drawings rather perfect PC generated graphics.
Keep up the good work, we need more of this.

One caution I might add:

Finally Cd is the coefficient of drag for your shape. This is another tricky variable to define. It totally depends on the shape and it has to be determined in a wind tunnel. The best you can do is estimate it based on some of the values in the table below.

The table shows the Cd against a HEAD wind for each of the several side profiles shown. Most tear drop trailers have flat vertical sides and uniform width top to bottom and front to back. So it seems to me the closest simple shape to use for a SIDE WIND is a rectangular block. That is, that nice smooth tear drop shape might give a small Cd against a head wind, but we are dealing with a side wind in the tip-over analysis. Just my 2 cents.

[GPW]

In all the time we’ve been here ,there’s only one trailer that we know of that has blown over and that was Catherine’s and it was very tall and narrow ... and aside from twisting the frame a bit , the only damage to the cabin was a little “rub” ... easily fixed on the spot .

[angib]

Yes, the analysis above does appear to mix side and longitudinal drag forces. But it doesn't matter much as it is all very theoretical - in reality, it is the combination of forward motion and sidewind airflows that matter and they are nothing like the two separate airflows added together (which is how sailing boats can sail). Also, the faster most trailers are towed, the greater the aerodynamic lift force on the trailer body - even if the trailer has 10% hitch weight when stationary, there will be a speed above which the hitch weight goes negative. The lift force will be a third force trying to overturn the trailer.

With vehicle aerodynamics, a simple answer is often a wrong, or at least inaccurate, answer - rocket science is pretty basic compared to vehicle aerodynamics. Add in that every trailer's behavior will change hugely, depending on the vehicle towing it, and simple answers are not easy to come by.

[KCStudly]

... but barring all of that, it does make sense to at least look at the most basic aspects, will it tend to tip over sitting still in a broadside wind? Despite that being hitched up will likely affect the angle of wind once it starts tipping, and despite the dynamic aspect of trailing wind and lift, at least the simple math above, (what us in the trade like to call a "dumb idiot" check) is a starting point.

If it fails this simple math "test" at low-"ish" wind speeds then things will probably only get worse underway. If it passes with flying colors, suggests that your good up to 100 mph side wind (an exaggeration), then at least you have some confidence that you will be okay under most reasonable weather conditions.

As always, when the weather is unreasonable, hunker down. I plan to carry a big roll of 550 cord and a bag of tent stakes as std. camping equipment. Not only will they be useful for shade tents and tarp flies, but in a bad situation I might even be able to stake and/or tie the dam thing down.

[WizardOfOdds]

Perhaps some read

“Yes, the analysis above does appear to mix side and longitudinal drag forces. But it doesn't matter much as it is all very theoretical -”

and

“... but barring all of that, it does make sense to at least look at the most basic aspects, will it tend to tip over sitting still in a broadside wind? “

to at odds against each other, but I actually agree with both, here’s why.

Granted, no simple freshman physics analysis is going to give accurate answers to even the side-wind only analysis. But it is does make sense to at least look at the basic aspects because it probably is accurate enough to compare two or more designs or situations.

For example, you can compare numbers for two different designs you are considering and use the predicted tipping wind speed (that just adequate to tip each) as an indicator of which is better. Or you can compare the numbers of your candidate design against a design which is known to have an unacceptable sensitivity. Or what if you just change one aspect (say axle over/under switch which changes heights), how much does it change the tipping wind speed? In these and many other comparisons, I would use just such an analysis.