How often should a person on the front get off and go behind the person in the back when there is only a group of two? Every minute? Every 10 minutes? When there are several people, a paceline is quite straightforward, but I don't know what would be the equivalent with two people.
Do you both have a speedo on your bike's handlebars for reading the current velocity, (ie speedometers/head units/bike computers/) ? It can be very hard to ride on feel, so one of the better ways to pace a group is to pick a target speed that is not flat-out, and the lead should aim for that speed.
When the leader feels its time to rotate, then you gently swap places. The new lead should work to maintain the nominated speed, and not blast away from the now-tired other rider.
How long apart is this? It depends on how long each person can maintain the nominated speed while on the front, and how long you each need on the back to recover for your next pull.
If you find you're holding that speed for multiple minutes and not getting tired, then perhaps you want to raise the target a couple of km/h. Or you might be advantaged by a slight descent or a good tailwind.
Likewise if you're not getting enough shelter on the back before its your turn again, then perhaps the target speed was too high for this day, and knocking it back by 2~3 km/h would help. Some-days you just don't go as fast, its okay.
If the group were bigger, you'd have up to about 6 riders in a single paceline, where the front one gets tired and then peels off, drifting back down the line and leaving a fresh new face to take the wind. Tired rider has to kick it up again to hook onto the back end, but there will get a good wind saving.
Your two-person paceline is a bit too short for a casual drift back and recovery, but still its up to the leader to make a decision when to peel off and drop back.
Aside - more than about 6 riders and you have enough for a nice double-paceline, where the rider drifting back isn't just on their own, they're in a second line which slowly drops back and then across into the forward line. Imagine a paternoster lift slowly revolving around.
It will depend heavily on the cyclists and the ride. I assume here that both riders are equal - clearly if one needs some help they should take shorter pulls. In addition, trying to stick rigidly to timing is often unrealistic. A sudden burst of traffic from behind can lead to a much longer turn on the front, and potentially more recovery on the back. Trying to maintain the pace up a small rise in the road will take its toll on both riders, but more so the leader.
While switching places you're both in the wind, so if you switch too often you'll experience a noticeable increase in total drag. The quicker you are at getting back into your best position, the less this will matter, but it's going to take a significant fraction of a minute for most riders, so every minute is too frequent - unless you're training for this specific aspect.
On the other hand, if the rider in the wind is pulling for long enough that they start to slow down, you should probably have switched sooner. If it's a slog into a headwind, you can probably keep going until the lead rider starts to flag, but this would be suboptimal considering it as like a team time trial, where pace is more important. In the intermediate case of just having fun going fast, a pull that's long enough to feel ready for a break, and a break that's long enough to recover a bit, will make it most enjoyable. I've found this to be around 5 minutes at a time, several hours into a full day ride and going not quite flat out. Longer turns work if road conditions mean you have to back off a little.
It depends very much how far you are going and how fast you are intending to ride. If you are doing a 25 mile 2 man time trial you are probably going to be swapping every 30 seconds. On the other hand if you are riding a 200 mile challenge ride it is more likely to be 5-10 minutes.
As others have noted, the terrain and relative strength of the riders is going to play a big part. The stronger rider may take a 60-70% share on the front. On downhills the rider on the back is getting a great rest so turns may be shorter - opposite on uphills. And similar with headwind/tailwind.
And finally, pay some consideration to what type of rider you and your partner are. It is easy for a climber to go too hard on the climbs and hurt their partner, and similarly a large strong rider can hurt a light rider on the flat without realising.
If we were to think about an "optimal algorithm" for two people exchanging positions while drafting, we could consider one "event", which is the condition to exchange positions, and one "state", which is the period while one same rider is at the front.
It seems to be this is a good description for this optimal algorithm:
- The riders should exchange positions when the solo speed of the rider in the back would be larger than the solo speed of the rider in the front.
- The speed of the rider ahead should be close, but not exceed, to the speed the rider behind can keep up without being dropped.
The conditions for the event 1 would depend on the combination of each rider's strength and level of fatigue. The relative durations of each rider in state 2 would depend on the relative strength between the riders. Then, if one rider is stronger than the other, he/she would be in front for longer periods than the opposite. If the difference in strength is large (or if, for exemple, one of the bikes is not so fast), then I would expect that the duo never changes positions.
It seems to me that this makes generally inadvisable to use fixed durations or fixed speeds as criteria, unless it is a prescribed training thing.
In my experience, this works naturally for more or less experienced riders that know each other's riding style.
Also, if both are on an energetic mood, I believe it is best if the rider behind decides when to swap, by overtaking the rider ahead and jumping to the front. On the other hand, if drafting is being used as a way to conserve energy, like after being tired in a long ride, then it works best if the rider ahead "gives way" to the rider behind (which in some times can be so tired that he/she declines - been there, done that).