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Does it make sense that the lower a router is to the floor, the worse my reception?
When my router is on the floor directly, I get terrible reception (even none) in my room which is 40 feet away. When it is a foot up, it gets much better. Does this make any physical sense? What it the typical geometric shape of the wifi coverage? Is it a fixed radius with the wireless router at the center or does it plume out?
All the above answers miss the mark a little.
The closer your antenna is to the floor, the closer it is a ground plane.
In electromagnetics, the ground plane is very important - it determines the total performance of the antenna system. Sometimes a ground plane with well defined characteristics is essential (eg aircraft landing systems use huge big metal rods on the ground and pinned in, to ensure a good ground plane).
In the case of something like wireless LAN, the nature of the floor material has a big impact. For example, there are huge differences in the electro-magnetic properties of a timber floor over a cavity vs a reinforced concrete floor. The concrete is full of steel which can form a form of Faraday cage (ie not much will go through it). However if you are on the same level, and not trying to get the signal THROUGH the floor, then its far more likely that you are just seeing absorption in the floor.
In this case instead of the floor being part of a ground plane that forms an integral part of the radiating properties of the antenna, its just a big sponge.
Think of the floor as a low impedance path (lower than the air), and so the propagating wave is much happier to zap around in the floor than in the air.
Systems like wireless LAN always have range quoted in open air (usually with the equipment mounted 1 metre off the ground), because this is the only means of getting a repeatable range measurement.
These systems don't rely on reflection (as stated by one of the other answers), reflections are really bad in RF systems, they causes peaks and troughs (nulls), and in the null you can see received signal power drop by a factor of several hundred (in RF speak, > 20 dB nulls are common). Just moving equipment a couple of inches can change performance. If you see this, you had reflections and suffered from a multi-path null.
A great many modern WiFi systems have multiple antennas. This is used, usually during reception, to pick the one with the highest signal (and discard the others, you CAN'T combine them at RF). When transmitting, normally one will be used (transmitting on all causes a phased array to be formed making a directional signal - not usually desired.) Such an arrangement makes the router less susceptible to the vagaries of multipath reflections.
A rule of thumb for in-building operation is to take the open-air range quoted by the maker and divide by a factor of between 3 and 10. What the factor is for your building depends on building materials and building contents.
By the way most makers won't tell you that the range is open-air, nor the fiddle factors. It makes for bad PR.
And there's another reason why the wireless LAN frequencies are free to use: they have lousy performance. At 2.4 GHz the path loss (which gets higher with frequency) is terrible, there are lots of interferers (microwave ovens, Zigbee, Bluetooth, DECT phones, wireless doorbells, baby monitors, headsets, the list goes on and on). So poor performance from Wifi is normal at all times, and when you put the equipment close to the ground / floor it should be expected to get worse.
The reason could depend on the shape or type of the antenna(e), where it is, and what surrounds it.
In general, a simple vertical antenna has a roughly toroidal coverage area. That is, its signal tends to stay within a few degrees of the plane perpendicular to the antenna. It depends on how the antenna is mounted or grounded, and on where it's situated relative to Earth ground, metal objects, and obstructions, all of which will attenuate the signal.
The distance that toroidal pattern reaches is proportional to the inverse square law, the power output, the radio frequency, and a handful of other factors. But as the angle to the horizontal plane increases, so does the attenuation.
The ideal place to put a wireless router is away from any metal objects, and well off the floor.
Without photographs of your room and a detailed survey, there is no way to know for sure, however based on the fact that you have observed this behaviour, I would say that obviously yes it is possible!
Wireless networking / WIFI works by reflecting electromagnetic waves across surfaces (up to a point), therefore the aerials may be at the bottom of the router and you may be creating an effect similar to a Faraday cage by placing it on the ground where by no signals are "getting out".
One quick test is to place the router up side down.
However, again, by the fact you have seen it happen, of course that is what is happening.
This depends entirely on the router. Modern routers with multiple antennas can even shape their coverage dynamically.
If the router has a movable antenna, it could help to try different positions, or if not, to try different (rotational) positions of the router itself. All of this can influence the coverage.
