Factor Safety

I have received many favorable comments and questions on the previous paper on 4130n and was requested to continue.

First let us get one big misunderstanding out of the way for good. Heat treating steel does not change Young's Modulus. http://en.wikipedia.org/wiki/Young%27s_modulus

No matter how much you may think that a chassis made from 4130n is more flexible than a chassis made from heat treated tubing, it just isn't so.

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Part two: Factor of Safety

So you are out for a hike in the Grand Canyon. It's a nice day, you've just had lunch, and are working your way back to the rim when the Coyote and Road Runner go zipping by at warp 7. You are distracted and slip, fall, and sprain your ankle. No problem, you just whip out your iPhone, call the rescue group, give them your location, Visa number, and wait. In short order the helicopter shows up overhead and starts to lower a net. When it gets down, you see it is attached to some line not much bigger than dental floss. Screaming to the guy hanging out of the helicopter, you ask what is going on. He says, "how much do you weigh?". You reply, "about 200 with all my gear." He replies, "No worries, this cord is good to about 250 pounds." "No way", you reply. "Do you have anything stronger." He drops the net again, this time attached to something only a bit larger in diameter. "How much is this good for?" you ask again. "The tag says about 350 pounds, is that OK?". "What if it gets nicked on a rock? What if my leg catches a branch? What if that bear grabs me on the way up?" you reply. He then drops down another net attached to some line, again only slightly larger. "What is this good for?" you scream. "About 450 pounds" he replies. Realizing that the bear has now headed your way, you scream back, "Send the net down on something with a Factor of Safety of at least ten. "What is a Factor of Safety?" he replies. Suddenly, for some unknown reason, the bear has split, your ankle feels great, and you have just found a nice stick that looks just like a crutch. So you wave them off and proceed to go hobbling along.

So now ask yourself, what strength line would you have been satisfied with to dangle below a helicopter?

Now the definitions:

Factor of Safety: http://en.wikipedia.org/wiki/Factor_of_safety

"Factor of safety can mean either the fraction of structural capability over that required, or a multiplier applied to the maximum expected load (force, torque, bending moment or a combination) to which a component or assembly will be subjected. The two senses of the term are completely different in that the first is a measure of the reliability of a particular design, while the second is a requirement imposed by law, standard, contract or custom. Careful engineers refer to the first sense as a factor of safety, or, to be explicit, a realized factor of safety, and the second sense as a design factor, but usage is inconsistent and confusing, so engineers need to be aware of both.

Appropriate design factors are based on several considerations. Prime considerations are the accuracy of load and wear estimates, the consequences of failure, and the cost of over-engineering the component to achieve that factor of safety. For example, components whose failure could result in substantial financial loss, serious injury or death, usually can use a safety factor of four or higher (often ten). Non-critical components generally have a design factor of two. An interesting exception is in the field of aerospace engineering, where design factors are 1.50 – 3.00 because the costs associated with structural weight are high. This low design factor is why aerospace parts and materials are subject to more stringent quality control. A Factor of Safety of 1.0 implies no "over-engineering" (not exceeding design requirements)."

That Wiki definition is good, but let's take a look at some examples. I would not take the chance of hanging from a line with a breaking strength of 450 pounds when my gear and I were about 200 pounds. NO WAY! I would like to see a breaking strength of at least 1000 pounds and preferably 2000 pounds. Makes sense, right? Yes, let's proceed in draining a bit more out of the Loch and see why.

Let us first start with a simple example. You are hanging a cheap piece of driftwood art, (domestic sediment), in an unused part of your unused formal dining room. It weighs 20 pounds, there is nothing under it that could get hurt if it falls, and it is the last thing you want to be doing right now. So you grab a hook, screw it directly into the drywall, use some mystery twine that breaks at 22 pounds, and your done. If it falls, who cares?

Example two is a small engineering company who's contract is to suspend their mega-ton nuclear powered neon sign over one of the busiest streets in the Windy City. There is ice, wind, rust, and many other gremlins trying to pull that sign down on the people walking below. Weight is not a factor in the support system so this problem calls out for a Factor of Safety of 20...? Maybe even 50.

Example three is launching a small rocket with a small scientific payload, to 600,000 feet. This sounding rocket has a Factor of Safety of 1.3 because if it had a Factor of Safety of 1.4, it might only get to 400,000 feet and that is with no payload. So in Aerospace, Factor of Safety is always low. All parts have to be designed, built, and tested to carry its designed load plus the safety factor. Spot on. No less, no more. This is one reason why rockets cost so much

Example four is a design for a manned submersible to venture down to the Mariana Trench, about 36,000 feet deep. The pressure at that depth is 15,620 psi. Since the submersible can not go any deeper, and the spherical hull will be accurately made, one could reason that a factor of safety of just over 1.0 would suffice, except that no one in their right mind would get in the thing.

The desired Factor of Safety depends on many things.

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Structural Loads: http://en.wikipedia.org/wiki/Structural_load

On a Top Fuel or Funny Car, loads from acceleration, aerodynamics, exhaust thrusts, engine torque, etc. are known. Some better than others. Loads that result from engine / clutch failures, tire failures, bumps in the track, skating across the lane, crashes into the wall, etc. are not that easy to determine.

Assuming you know the maximum loads during a better than average pass, how much beyond those known loads would you desire your structure to experience and still survive? Just a bit? Two times? Five times?

Now what about the maximum loads during a CRASH? What would you want the Factor of Safety to be above those loads? Well, the problem is that those loads will never be known, and in the words of a very respected chassis builder, "Show me the crash and I'll build you the car." This is where the implementation of a Factor of Safety is crutial.

On my FEA* model, the Top Fuel chassis has, at 330 MPH, 59F, 29.92, 1.8g's, 9000 ft. lb. torque, a section of chassis at a particular location has a compressive load of 13,812 pounds. The material 4130n has a tensile yield of 63,100 pounds per square inch. The area of a 1.375 x .058 wall tube is .240 sq. in. So, 63,100 x .240 = 15,144. Can you see it now?

Therefore, under maximum load there is a tube on the chassis that has a Factor of Safety of only 1.1. So you and your gear are being lifted up out of the canyon by a line with a breaking strength of 220 pounds. Now what happens if that bear grabs your leg?

*FEA: Some do not trust analysis, especially when it is done on computers. This is undoubtedly due to the lack of understanding of FEA computer models, and their use in engineering. The computer does not "design" the car. The engineer designs the car and FEA is the tool to do the analysis. It also could be done on paper, but with great difficulty and time. Does Boeing just knock together a new jet transport? No, it is extensively engineered to a degree beyond imagination. During flight testing, it is not to determine if it will fly or not break, but to see how close the actual performance is to that predicted by the model. Usually to less than a percent. While it is true that no computer model will be as accurate as the real thing, computer models are far superior to eyeball engineering. Understand that the model is just that, a model. It is only as accurate as the input load sets, which are difficult to determine with high accuracy, but can be determined to good accuracy. There is also the problem of accurately reproducing the car in the model. Even the cars themselves have manufacturing differences.

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Uncertainties:

An engineer designing a new structure faces several uncertainties:

• Loads are not known to an exact value. • Material properties have some variation. • Computer models, though a good representation of the structure, are still mathematical abstractions of the real world. • The generated model may not be a perfect representation of the structure. • Unknowns: Some physical events will have an effect on the structure, but the magnitude of that effect is unkown. The appetite of the bear perhaps? • The designer or analyst may have missed a load case. • Defects may be introduced in the manufacturing process. Really?

Face it. There will always be something you didn't think of. A Factor of Safety is used to account for these uncertainties.

A chassis should first be designed with adequate Factor of Safety for the nominal expected loads during operation. Just like the wing on that plane you just flew on. Then one designs for the anticipated loads regarding events such as tire shake and disintegration, crashes, etc.

The loads during a pass are not high in a Top Fuel or Funny Car chassis. A load of 13,812 as previously mentioned, is not large. Large loads are in the spar caps of an open class sailplane pulling 6g's. We're talking close to 200,000 pounds of compression and tension in the spar caps! Yes, go back and count the zeros. And I won't even mention the spar on the jet flying overhead. But the small load of 13,812 pounds in the TF chassis member I mentioned has high STRESS, because there is hardly any material there. Alloy 4130n is a great material, but it's not Kryptonite. Most TF and FC chassis in the 80's, with small fuel pumps and magnetos, were built with 1.375 Ø .058" wall, the same used today with huge fuel pumps and magnetos!!!! Can you hear me now?

*** Is it possible that a problem that should have been solved with structure was unsuccessfully addressed with material selection?

4130n 1.375 x .058 wall weighs .068 lb. per inch. Cross sectional area = .240 sq. in.

4130n 1.500 x .095 wall weighs .119 lb. per inch. Cross sectional area = .419 sq. in.

For every 10 feet of tubing changed from 1.375 x .058 to 1.500 .095 results in an increase of 6 pounds. Hey, don't some cars carry a lead weight in the front? That weight would be much better applied at structure. If you need help maintaining balance when shifting weight around, contact me.

Now by no means am I suggesting that 1.500 .095 wall is the size material to use. It has just been mentioned to show what an increase of that amount changes does to the weight of the car. You may, as a driver or crew chief, decide to increase the Factor of Safety more, using the next common size tubing which is 1.500 .120 wall. (cross section .520 sq. in., weight = .165 lb. per inch)

Regarding that section of tubing in the Top Fuel chassis loaded to 13,812 pounds compression, lets take a quick look at changing to 1.500 x .095 wall. The cross sectional area of .419 sq. in., gives it a capacity of: 63,100 * .419 = 26,483. This gives that section of tubing a Factor of Safety of 2.0. Wow, not as much as one would think for 1.500 x .095 wall tubing! And that is just for the maximum loads on a clean pass. Toss in some tire shake, bumps in the track, radical steering, inaccurate alignment of frame members when welded, and eventual wear and tear... well, you get the idea.

But this is for loads during a pass, not tire failure, uncontained engine failure, or crashes. It would be prudent to have an additional Factor of Safety proportional to the accuracy of their estimated values.

But here is something to keep in mind. The cases of chassis Factor of Safety aforementioned, are to 4130n material yield. To reach ultimate strength, (complete breakage), the Factor of Safety is higher. This is why a material with high elongation is important. Materials which are tough and deformable have an ultimate strength which is higher than their yield strength which gives them a natural Factor of Safety, not to bending, but total failure.

Remember, the specifications for chassis construction are minimums. Maritime law issued in 1894 stipulated a minimum of 16 lifeboats, enough for 962 passengers, on ships of 10,000 tons or more. On the RMS Titanic, the White Star Line exceeded the regulations by providing an additional four lifeboats thus increasing the capacity to 1,178. The RMS Titanic had capacity for 3,547 passengers, but only had 2,224 passengers on it's final voyage.

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Buckling: You don't mess around with hornets or buckling.

http://en.wikipedia.org/wiki/Buckling

"In engineering, buckling is a failure mode characterized by a sudden failure of a structural member subjected to high compressive stresses, where the actual compressive stresses at failure are smaller than the ultimate compressive stresses that the material is capable of withstanding. This mode of failure is also described as failure due to elastic instability. Mathematical analysis of buckling makes use of an axial load eccentricity that introduces a moment, which does not form part of the primary forces to which the member is subjected."

****"A sudden failure of a structural member"****

Yes, you don't mess around with buckling. It gives you no warning. A structure has to be designed for buckling with plenty Factor of Safety. FEA beam model will work just fine.

From the Wiki definition: "In 1757, mathematician Leonhard Euler derived a formula that gives the maximum axial load that a long, slender, ideal column can carry without buckling. An ideal column is one that is perfectly straight, homogeneous, and free from initial stress."

http://en.wikipedia.org/wiki/Euler-Bernoulli_beam_equation

I do think we all agree that there is no part on the car that is an "ideal column". So Euler's formula has to be given lots of Factor of Safety. There are some really long lengths of inadequately supported tubing loaded in compression on a Top Fuel chassis. This has to be dealt with in any new design. A Funny Car is not so bad.

In closing, do consider an adequate Factor of Safety when designing the new class of chassis for 2008. Only proper professional analysis can determine the proportionally correct amount of material in each member of the chassis. This is not rocket science, but it IS science.

...and please remember the bear.