One step, repeated
A number 6 frog opens one unit sideways for every six units along, and under the exact definition that is an angle of 9.527 degrees. To get two tracks 2 in apart you need 2 divided by the tangent of that angle, which is 11.92 in along the through track. Every track in the ladder costs the same 11.92 in, so five tracks is four steps and 47.67 in of board gone before the last turnout begins.
That number is the whole design problem of a small yard. On a 72 in shelf, 47.67 in of ladder leaves 24 in, and the last track has to fit its turnout lead and its bumper into that.
Which definition your frog number uses
Two conventions are in circulation. The exact one measures the frog number as the ratio of length to spread and gives an angle of two arctangents of one over twice the number. The approximate one just takes the arctangent of one over the number. For a number 6 they differ by 0.065 degrees, and on 2 in centres that is 0.08 in in the step — 11.92 in against 12.00 in.
Across four gaps that is a third of an inch, which is nothing. On an eleven gap ladder at a number 10 it is 0.55 in, and that lands exactly where the board runs out. The select is there so you can put in whichever your supplier drew to, and the page reports both angles either way so you can see what the choice is worth.
The last track is the one to look at
With the defaults, track one has 65 in of clear length and holds 10 cars of 6.5 in. Track five has 17.33 in and holds 2. The yard holds 30 cars in total, and 57 percent of the board length is clear track, with the rest going to ladder, lead and end allowance.
That spread is normal and it is why real staging yards are usually drawn with the ladder at the end you enter from, so the short tracks are the ones nearest the throat. It is also why adding a sixth track to this board is worth roughly nothing: it would start 59.6 in in, leaving 5.4 in, which does not hold a car.
The frog number trade runs the other way from instinct
A bigger frog number is a shallower angle, which everybody wants for the way it looks and the way long cars take it. It also lengthens every step. Going from a number 6 to a number 8 on these centres takes the step from 11.92 in to 15.94 in, which across four gaps is 16 in more ladder and 16 in less train. On a 72 in board that is two or three cars of capacity given up for the appearance of the turnouts.
Neither answer is right. The point is that the trade is quantified rather than argued about, and it is a different trade on a 12 ft wall than it is on a 6 ft shelf.
What this does not model
It describes the plain ladder, where each turnout sits in the through track and each diverging route curves back to parallel inside the lead you entered. Compound ladders, pinwheels, double-slip arrangements and three-way turnouts all recover some of that step length, by geometry this page does not attempt. It also assumes every car is the same length, which no yard has ever contained.
Questions people ask
How long is a yard ladder?
The spacing divided by the tangent of the frog angle, times one less than the number of tracks. A number 6 frog on 2 in centres steps 11.92 in, so a five track ladder runs 47.67 in before the last turnout starts, plus whatever straight that turnout needs after it.
What angle is a number 6 frog?
It depends which definition the drawing uses. The exact one, one unit of spread across six units of length, gives 9.527 degrees. The approximate one, the arctangent of one sixth, gives 9.462 degrees. The page shows both and lets you pick, because the two conventions are both in use and this page cannot know which your turnouts were drawn to.
How many cars fit in a staging yard?
Fewer than the board length suggests, because each track loses the ladder step ahead of it. On a 72 in board with five tracks off a number 6 ladder, the tracks hold 10, 8, 6, 4 and 2 cars of 6.5 in — 30 in total, with 57 percent of the board length left as clear track and the rest lost to ladder, lead and end allowance.
Should I use a bigger frog number in a yard?
It costs capacity. A number 8 on 2 in centres steps 15.94 in against 11.92 in for a number 6, so four gaps take 16 in more of the board and that comes straight off the trains. A shallower frog looks better and suits long cars better, and on a long wall the cost is trivial. On a short shelf it is two or three cars. The page prices the trade rather than settling it.
Does the frog number change the track centre spacing?
No. The spacing is whatever you decide to build to, and the frog number only sets how far along the through track you have to go to reach it. A shallower frog takes longer to open the same gap; it does not open a different one.