According to recent studies, zombies use their sense of smell about 73% of the time in the initial tracking mechanism when hunting their prey. Though they might rely on (generally poor) eyesight and sounds while within the vicinity, they will first get to within your vicinity through smell before doing so.
There was some debate about how far the radius of track-by-smell extended, with the a key 1993 Harvard paper1 suggested it was on a potential order of 3.5 miles but there being both conclusions extending this (1997 field report on the popular tv-show Survivalist set the target at potentially as high as 19 miles2) or contracting this (as little as half a mile, according to a New Mexico Biological Study3).
No matter what the distance, you should keep in mind that the threat of being tracked is always in front of you.
It is most likely they are tracking blood scent, though it is possible for them to track sweat4. There has been no conclusive evidence as to whether there is any sort of factual basis behind the "zombies smell fear" urban legend (and its conclusion that you should take Valium to help hide your scent), though one could say that any sort of mental state that increases your heart rate and your sweat production will likely result in a higher tracking radius.
Keep blood scent down. Colognes and perfumes will do little to hide it, and you will have to use so much that your new scent will probably just attract them as well. Ammonia will effectively destroy the odor, but will be damaging to your nose (remember that you can smell them, as well) and skin. Ammonia might effectively work in protecting the lower floor of a house from getting hit, but is not a good personal protection device.
Dress wounds immediately. Cauterization will actually spread the scent, so it might be better to avoid this except when you are in a safe place.
Any time it is cool, your scent will travel slower and you will be less likely to be tracked. Not only will night time temperatures mean that you can stay cool more easily, but they tend to have less winds past the first couple hours of night.
Some hold to the idea that zombies are instinctively afraid of the dark, which may or may not be true. Zombies tend to be more forward and in larger clumps during the day, but then it is possible something else is at work here, so do not rely upon it.
Also, their already poor eyesight means they will have trouble locking in on you, and since the iris of their eyes is at only 40% of the functionality of our own5, you can blind them easily with a handheld flashlight if they do get close.
On the now defunct website RememberDallas.org, there was a long discussion about whether animals were a blessing or a curse. One user, indentified by his call name "MarcSinger", argued fervently that they were a great aid. (s)He listed several key reasons (including a reluctant admittance that they could make a food source in a pinch). The most important of which was that the animal scent helped to overcome the blood scent the zombies would use to track you. Second most important was they would provide necessary companionship.
It would be a disservice to not point out that another of the sites major posters, DalphFMdS, was wholy against the concept of animals as companions. (s)He claimed they were beastly and could turn against the owner. Citing potential for fear and a drain on the resources, DalphFMdS, concluded that it was actually worse to have animals in such situations.
Likely, though, if you are a huge animal fan, and can take care of them, then they should be at worst neutral as a factor in your survival. To use them as a "red herring", keep in mind that animals with stronger smells, such as ferrets, large dogs, goats and even skunks are going to work better than animals without a distinctive odor.
On the aforementioned episode of Survalist, it turns out that the most successful, if grossest, way of avoid zombie scent is to use pieces of zombie by strapping them to your body.
The episode demonstrated the fact that zombies have to be extremely cross range (less than half a meter) before they can get a good lock on you if you have the zombie flesh on, but its not all good. Part of the problem is the fact that people are not sure why it happens.
Though smell might be the central issue, being surrounded by zombies does not protect you. There is also the fact that zombies usually will not eat a dead body past the first few minutes of death. This has lead to the speculation (though never confirmed) that zombies are repulsed by some after effect of the infection. This is at odds with the quickly becoming classic book on Zombology, the Flesh Eaters6, which maintains that any exposure to the zombification virus will lead to a low level of infection which will stay with the person until weeks later. If the infection prevents zombies from being able to smell you, then any person in the vicinity of zombies would be infected, and therefore would be unsuitable for food. Since this is not the case, it is assumed that the premise of Eaters is flawed in this regard. or is not taking into account all factors.
How best to go about this? As digusting as it sounds, it seems a good "smear" is the best way. You are going to need about ten pounds (four kilograms) per one hundred fifty pounds (about 70 kilograms) the person weighs. Either cut it into strips, or grind it up. Depending on how long it has been rotting, either of these tasks might be the best for a given situation. You are going to want to cover as much of your body as possible, though some have suggested that smearing it on your arms and neck, as well as on your upper shirt and lower jeans, will help to prevent the undead from biting you in your most vunerable spots.
Bath regularly. This can keep you alive. Waterways can be your natural friend. Dress all wounds quickly, and focus on healing them up. Not only will infection be bad, there have theories that open wounds in contact with the undead can cause zombification.
Avoid large groups, this will exponentially increase the distance that your smell can be detected. Bodily waste also will increase your danger, so you might want to stay on the move or be near moving water so you can have proper sewage.
Finally, if you do want to bunker down, there is no harm, except to your nose, if you stake a few of the bastards along your perimeter to block the smell.
1: Reicher, Harold and Julia Steingald. "A Systematic Study of the Nasal, Aural, and Visual Abilities of the Animated Dead". Published in the Journal of Sensory Physiology, volume 19. Harvard Press: 1993. pp 1072-1079.
2: Survalist. Episode 309: "Avoiding a Dallas-class Incident". Imagine.
3: Rogers, Gene, et al. "The Politics of Fear in Ghoul Research." New Mexican New Biology, issue 67. NMBS. pp 20-23.
6: Author Unknown. the Flesh Eaters: Fifteen Days Inside a Suburb Turned into Hell. Egoist books: 1995.
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