What determines the distance between signals?

Essentially, the minimum safe stopping distance (for a normal, non-emergency stop) for the heaviest and fastest trains operated on the line, under adverse weather conditions, like wet rail, and taking into consideration whether the track in approach to a signal is level, ascending, or descending, plus a safety margin added on. For freight railroads today, two miles is a typical distance. If it is desired to increase train speeds, either the stopping distance has to be increased, and the signal spacing increased accordingly, or additional signal indications added to provide earlier notice to an approaching train. The longer the distance between signals, the fewer trains that can be handled over a given territory. To enable an increase in the frequency of trains, the signal spacing may be shortened by adding additional indications so that a train approaching a stop signal still receives sufficient notice to come to a controlled, orderly stop. One example of this was the NYC on its lines approaching Grand Central Terminal, which had signals spaced one-half-mile apart. The resulting signal indications were as follows (the direction of movement being from bottom to top).

0.0 mile - R/R (or R/R/R) = Stop.
0.5 mile - Y/R = Approach = Proceed approaching next signal prepared to stop.
1.0 mile - Y/Y = Advance Approach = Proceed approaching second signal prepared to stop.
1.5 mile - G/Y = Advance Approach Medium = Proceed approaching second signal at 30 mph.
2.0 mile - G/G = Clear = Proceed.

The Advance Approach Medium indication was needed because 1 mile was less than a safe stopping distance. (On Metro-North today, all this has been replaced with cab signals, with wayside signals every half mile eliminated. I have heard from some engineers that this makes it much more difficult to "read the road," which an experienced engineer could do using waysides as a guide.)

In addition, there is a rule of long standing (predating the present FRA delayed-in-block rule) providing that if a train is delayed in a block it must approach the next signal prepared to stop, in case it is found necessary to "take away" an existing proceed indication in order to permit a different movement.

The location of a junction, beginning or end of a siding or main track, movable bridge, etc., will determine the location of a controlled home signal protecting movement through that point, and the placement of intermediate signals will be calculated from there.

This varies widely depending on the type of traffic on the rail line. If the rail line is a subway or similar rapid transit type of operation, generally the signals are spaced fairly close. By comparison, most class 1 and 2 railroads have signals separated by two miles or more, because some trains take that long to stop.

When I worked for BNSF, signal separation was about two miles. Sometimes other conditions made that impossible, such as the proximity of two junctions to each other and the length of sidings in that particular area. When signals were more than two miles apart, there was no Approach Medium (Flashing Yellow) indication displayed, since two miles between Approach and Stop indications is sufficient distance to bring a train to a stop, consistent with good train handling. If the Approach and Stop signals were less than two miles apart, the signal prior to the Approach would display Approach Medium, to give that extra warning to the crew that the train may need to be stopped. The signals in this area were all installed by the Northern Pacific a long time ago. It was an ABS system, so the dispatcher had no control over the signal system.

Up here on Alaska Railroad, the two miles is also fairly standard, except for some more recent CTC installations. The Approach/Approach Medium thing described above also holds true on Alaska Railroad. Interestingly, when the Whittier branch was made CTC, they just made the old distant signals the new intermediate signals, and put no new signals between them, despite the fact that the branch is over 12 miles long and and signalled across about 10.5 miles. So two of the blocks are just under two miles long each, and the one in the middle is over six miles long! That branch also has an interlocking that is just over 2.5 miles, in which there are no switches or crossings! It is a shared rail/highway tunnel, and the interlocking protects vehicle traffic using the tunnel. Being a single lane tunnel, the vehicle traffic actually drives on the tracks through the tunnel.

Anyway, that was a long winded way of saying the type of traffic using the railroad determines the distance between signals. On most railroads operating freight trains, somewhere around two miles is fairly typical. On railroads dedicated to smaller, lighter trains, distances can be shorter, although in locations where several different types of trains share the same tracks (passenger and freight, for example), the distance will usually be determined by the type of train that needs the most space to stop.

With the signal changes being required to implement PTC my carrier is respacing signals where possible to be approximately 3 miles apart. 9000 foot 15000 tons trains require space to stop - you don't operate a train under the same operating concept that you do with a automobile. Automobiles you can operate at speed on observable information in your line of sight. A train cannot be stopped in the distance of one's line of sight - so signals 'expand' the sightlines of the locomotive engineer as it pertains to other trains and/or switch positions.