I thought we should have a thread to discuss exactly how time gaps work, as the same issues have come up a few times.
WARNING: post contains math. But the worst of it involves multplying 5 by 3, so I think you guys are ready.
And I've never managed to find any kind of official explanation of all this, so what I've written here is based on common sense and watching races. If anyone has any sources (especially about the GPS system) that show that I'm being Wrong On The Internet, please let me know and I'll update the post. As if I needed to tell you that.
Let's say a break (G1) is ahead of the Peloton (P). And let's give all positions as kilometers to go to the finish, just like the TV graphics.
Here's how a time gap is calculated. When G1 passes a fixed position, say 52km to go, they start the stopwatch. When P reaches the same position 52km, they report the time on the stopwatch. This used to be done every few km by moto, it's now done continuously by GPS, but the principle is exactly the same.
It's important to realize that you can only measure a time gap when both groups have covered the same distance. So the time gap always applies to the position of the chasing group P. However, the TV graphic shows the race situation as the position of the leading group G1, with a time gap to P.
For example, if the TV graphic says [ G1 49km to go, P at 4'00" ] this really means something like:
G1 is now at 49km; P is now at 52km; G1 passed the 52km position 4 minutes ago
The time gap applies to the position of the CHASING group.
The TV graphic can be misleading, because it suggests that the time gap applies to the G1 (49km) position. But if you think about it, this can't sensibly be the case, right? That would mean making some kind of forecast about the future speed of the chasing group P between the 52km position and the 49km position. We don't know that yet, and in fact, that's exactly the unknown thing that the race is all about. Incorporating an arbitrary unstated forecast into a TV graphic that is supposed to show the current race situation wouldn't make sense. So in this example, the time gap applies to the position of the chasing group P, 52km.
The relative terrain does not affect the time gap.
A common fallacy is the idea that if the break starts going uphill, while the peloton is still going downhill, this will make the time gap shrink. This is wrong for two reasons.
(i) The time gap is measured to the position of the chasing group, because you can only measure a time gap for a distance that both groups have already completed. Any terrain ahead of the position of chasing group is not yet relevant to the time gap. When a hill becomes relevant, it will only be after both groups have gone up it, so that their times over the same terrain can be compared.
(ii) Even if we somehow made a forecast of the expected time gap at the position of the leading group, terrain affects relative speed and therefore the distance between the groups - but with similar rider effort in each group, the time gap would not be expected to change.
When do all these details matter? On mountaintop finishes.
If you remember that the time gap is always expressed at the position of the chasing group, it makes the situation easier to read at the critical point of some races. It's most important when the speed and time difference are both large, which means a long steep climb to a mountaintop finish. Here's an example where the GC guys in the chasing peloton are trying to close down a large time gap and traveling much faster than the break.
Lead rider G1 (remnant of the break) is ahead, traveling slowly, taking 3 minutes per km.
GC guys P are chasing, moving much faster, taking only 2 minutes per km.
The TV graphic says [G1 5km to go, P at 6'00"].
Since G1 takes just one minute longer per km, it seems that P cannot close a 6 minute gap in only 5km. So if they continue at the same speeds, it appears that the break should win the race.
However, it's not so simple. Remember that the time gap refers to the position of the chasing group P. It tells you how long ago G1 passed the current position of P, which is much further away from the finish than 5km.
Here's how it works out.
In the last 6 minutes, G1 has covered 2km, therefore the current position of P is 7km.
P has 7km to go, taking 2 minutes per km -- P will take 14 minutes to reach the finish.
G1 has 5km to go, taking 3 minutes per km -- G1 will take 15 minutes to reach the finish.
So in fact, the break is caught before the finish.
This explains why the GC chase often seems to overhaul the break remarkably quickly on final climbs. We sometimes assume that the lead rider just "cracked" in the last few km, when in fact it's just the misleading way that time gaps are expresssed