How can I estimate how fast a train that I am in is going?

Q. How can I estimate how fast a train that I am in is going?
There are several ways to get good estimates for a train's speed. Distance markers by the side of the tracks provide indications of how far the next (or previous) important station is (in kilometers) and it is straightforward to time the train for a distance of a couple of kilometers to estimate its speed.
Telephone poles or other posts by the side of the tracks often have indications such as "100/5" on them. The top number is usually the number of kilometers from some station; the lower number marks the number of posts within that kilometer section. There are usually 15 or so such poles in a kilometer. So, successive poles may be marked as follows: 79/13, 79/14, 80/0, 80/1, etc. Sometimes these indications are found on the distance posts at ground level next to the tracks. Timing the train while observing these indications can give you a good estimate of the speed. You can't always assume there are 15 poles to a kilometer, though, so estimates are better made by timing from, say, 15/2 to 16/2 or 80/1 to 79/1
Similarly, electric traction poles usually occur at regular intervals spaced at about 16 per kilometer; they too are often numbered as above, or sometimes with every other number left out: 212/5, 212/7, 212/9, etc. Taking the time from, say 70/3 to 71/3 will provide a reasonable indication of the time to traverse 1km, and you can calculate the speed from there.
Rail lengths vary, but it is also possible to time the train while counting off the clicks of the wheels across rail gaps. On BG tracks, the rails are usually 13m long. A simple rule of thumb to use is to count the number of rail joints crossed in 45 seconds; this gives the approximate speed in km/h. For instance, 70 "clickety-clacks" in 45 seconds implies a speed of about 70km/h.
On MG tracks, the rails are usually 12m long, and a similar calculation can be made. Things are trickier on narrow gauge because there are a few different lengths of rails used. Bear in mind, also, that a few BG section have double-length rails. This method is of course likely to be very inaccurate on curves, bridges, approaches to stations with many points, etc.
On welded track it is usually possible, by listening carefully, to count the number of joints passed by the faintly different sound made when the wheel passes over the weld (the spot where the weld is often has a slight concavity with the typical thermite welding technique). Only with sections where the track is flash butt welded is it truly impossible to hear the rail joints. Often wheels have flat spots which add to the noise and make it more confusing. All this makes timing by rail lengths very hard.
The most common rail length on BG sections is 13m, but some places have 26m-long rails. MG rails are usually 12m, and for NG, a commonly-seen rail length is 9m.
If all fails, time the train between stations, and look at the route-km for the stations in a timetable or other source; this will necessarily be a less accurate method as you will only get the average speed.
Using a GPS device
If you have access to a portable GPS receiver, that can be the most easy and accurate way to find the speed of a running train. You will need to place the device close to the window so it can receive the satellite signals, and 'see' as many satellites as possible. Extensive superstructures (overhead bridges, etc.) or heavily built-up areas make it difficult for the GPS unit to track the speed. And of course, it won't work inside a tunnel!
Bear in mind that the speed read by GPS is more accurate on straight and level stretches, mostly because errors creep in as the GPS unit will give you the straight-line distance travelled between two points at which the positions are recorded. Absence of gradients is especially important when only 3 satellites can be received by the unit, because GPS receivers normally need 4 satellites to measure vertical position. To even out short-term errors, it is probably best to log the GPS readings frequently (1 second intervals, perhaps) to a laptop computer. Note that receivers with extensive logging capabilities can be much more expensive.
If you are serious about measuring positions by GPS and correlating them to maps, note that civilian GPS units are guaranteed only to about 20m accuracy in horizontal coordinates and 33m vertically (95% circular error probability) by the US DoD. In practice, accuracy down to about 4m is possible under good conditions and the use of differential GPS receivers can improve on this as well.
However, you should bear in mind that the datum used for coordinates by most commercial receivers is WGS-84, but most maps produced in India use a different datum (Indian datum based on the Everest 1956 ellipsoid), and you will need coordinate transformations to go from one to the other. Keep in mind that the more sophisticated your equipment, and the more 'serious' your measurements and surveying activities, the more likely it is that you will be picked up by questioning by the railway police or other security personnel. Indian authorities tend to be quite strict and unyielding when it comes to dealing with activities of this nature. The Survey of India announced some time back (around 2001) that new official maps of India based on the WGS-84 datum would be published, in the years to come.