|MadSci Network: Engineering|
It is a bit surprising that very little work has been done in the field of tire failure analysis to understand the nail puncture failure mechanism. I believe most experts have concluded from the empirical evidence the following things: 1. It is obviously possible 2. Whenever anything is possible and the conditions for it arise often, it is bound to happen. So as long as there are nails on the road (often near construction sites) and cars driving over them, it is only a statistical matter of time before someone gets a flat. What this reasoning fails to address is trully understanding the mechanism by which it happens. One way this could be done would be by mounting some high speed cameras on a car near each of its tires and driving at various speed ranges over pavement sparsely covered with nails, then analyzing the footage as soon as a few failures have been recorded to see if they have anything in common. Alternatively, a model could be constructed (or purchased at a toy store) and scale models of pavement and nails would be required. I typically try to do experiments (or find published results) to answer scientific questions, however, it's easy to see the high cost of carying out this experiment. For this reason, I will attempt to answer in a speculative way. Keep in mind that for this answer to be "science" it is still missing the experimental aspect, and I would rather leave that up to those with a budget. When a nail is driven into a tire, it is safe to assume that it happens in the first contact. The reason for this assumption is that the surface of the tire is compliant (bouncy like a spring) so as soon as contact has been made and the nail is lodged in the thread, if no puncture exists, repeatedly pushing on the nail will not make any progress, rather it will push against the compliant surface of the tire (which makes a "tent" around the nail") with no energy being transfered to the tire (no puncture). The part of the nail that sticks out will simply be polished flush over time against the surface of the thread. Remember that pushing on an elastic object (like a spring) causes energy to be absorbed by the spring, only to be released once the force is relieved. And energy would have be spent in the puncture. Also, the hardness of the tire is unlikely to suddenly be reduced to allow the nail to penetrate in a subsequent rotation. Finally, the force driving the nail can be assumed to be about the same on each rotation (a fraction of the car's weight, as distributed according to its dimensions, acceleration rate and grade of pavement, all of these are parameters that change slowly from one tire rotation to another during normal driving, and can be assumed to be about the same) This is easy to test: Push on a Ballon with a nail with a certain force. If it is not broken in the first attempt, push again with the *same* amount of force. It is not likely to suddenly break if pushed again with the same force a second time. The force will have to break thru a "threshold" for the puncture to happen. So the nail will either fall out, stick sideways on the thread, or penetrate immediately, upon contact. With this understanding, I would speculate that the nail must be standing in a position that allows penetration upon first contact. The only way I can see this happening is by realizing that asphalt is rarely flat. At dimensions similar to a nail's size (about 1 1/2 inch), the pavement's surface is highly uneven. Thus, the conditions necessary for a puncture would be easy to imagine: A nail must have fallen on the pavement in such a way that the head was in a valley, the tip was raised at an angle just high enough for puncture, and the head was supported so it does not slide away. Finally, the tire must have aproached the nail so that its tip met a gap between the thread blocks. This way, the surface making contact with the tip is approximately smaller circle than the surface tracing the road (the thread). This makes the minimum angle required for puncture even lower than if the nail met the surface of the thread. You can easily ilustrate this to yourself: Find a round object with a smaller concentric circle drawn on its own surface, and a ruler. Perhaps an LP record? Pretend the outer edge of the record is the tire's thread surface, and that the label represents the inner surface in a thread gap. This is highly exagerated, but illustrates the point by increasing the observed effect. Hold the ruler at an angle (you could try about 30 degrees) If the pencil met the outer edge of the record, asuming it stuck, there is a certain ratio of forward travel to downward travel for the contact point, You can "eyeball" this ratio and remember it. This ratio varies with the angle at which the ruler is held initially. For example, if the ruler is held flat, there is no forward motion or downward motion and the ratio cannot be calculated. As the ruller aproaches flatness, there is more down motion than forward motion of the contact point. If, instead, the ruler is imagined to stick to the "label's" edge, the ratio of forward motion versus downward motion at the contact point is different; in fact, higher!. My assumption is that for a nail that is sitting at a shallow angle, the higher this ratio, the greater the likelyhood for a puncture, because the tire's contact point is traveling a little more in the direction the nail is capable of penetrating (along its axis) Of course, in the case of a tire this effect is much more reduced because both circles are close in diameter. Also, the contact patch is elastic, a significant difference from the LP record and ruler model. Elasticity would lower the tire so that the distance from the contact patch to the center is lower than both the outer diameter and the thread gap diameter. I will leave it up to you to come up with an experiment to model elastic rotation. Experimentation would be needed to find out the minimum angle required for puncture. Notice how easy it is for nails to land with a slightly raised tip by throwing some nails on ordinary pavement. Try this several times since, this being a random event, all you need to observe is that it happens with a certain likelyhood. Even 1 in 100 is enough for a puncture. Another possibility is that someone vandalized your car, the nail was driven in when you drove away, and the tire held its pressure for a while, just long enough for you to park the car with the nail hidden under the tire's contact patch, before you actually found it (thus making it seem that vandalism was unlikely.) But accidents like this do happen and are quite likely under the right circumstances. As far as the likelyhood of 2 nails been driven at once, I can only say that if they landed on the same area of the pavement, they could have been subject to similar conditions of that area (a valley at their head) and that they fell from a container that held many of them (perhaps a small spill) Hope this answers your question, Your mad scientist, -Aurelio
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