We will be in Peru visiting Machu Pichu (altitude 7,972 ft or 2,430 m). Then we'll go down to the jungle (essentially sea level) for 4 days and then to Cuzco (altitude 11,152 feet or 3,399 meters). Will it take less time to re-acclimatize? Will we have to "start again?"
I am not a Dr but it seems to me the body would declimitize as fast as acclimatise. So you would lose 4 days of acclimatisation.
For example we have seen well acclimatized people arrive in La Paz, then take a trip down to the Pampas & Jungle in Rurrenabaque, which is around 300 meters, then return wanting to climb a mountain but find they are struggling to be at the altitude of La Paz.
Something to note though, and a mistake some people make, is that you have to make sure yout don't go to lower altitudes during this acclimitization period as you will start to declimitize as your blood cell count readjusts back to its previous levels.
Wiki defines Acclimatisation as:
The process in which an individual organism adjusts to a change in its environment (such as a change in altitude, temperature, humidity, etc), allowing it to maintain performance across a range of environmental conditions.
Now, I take that since you asked this question you are already aware of what Acclimatization is, but "start again?" asks for above definition.
Based on your itinerary, which will commence at Machu Pichu (altitude 7,972 ft or 2,430 m), its usually safer to spend some time acclimatising before getting at 7972 ft altitude. I am assuming that you have already planned for it.
Considering the next higher altitude you are planning to get to, I'd strongly recommend getting fully-acclimated to 7972 ft, spend a night around that altitude if possible.
You'll naturally feel way better in the jungle once you descend. Now if you are planning to stay in the jungle (essentially sea level) for 4 days as you say, you don't entirely loose the acclimatisation that you have already attained, but with certain precautions. Avoid Alcohol consumption, avoid any medication for headache, hydrate properly, keep doing something rather than laying lazy. With this you'll actually let your body recover from whats lost (or craved for) at higher altitude.
- Avoid alcohol consumption
- Keep hydrating yourself
- Go easy on diet, don't hog all that you see. (This actually happens to me when I descend from a higher altitude trek)
- Avoid headache and other pills for no reason. If there is discomfort, seek attention, be open to the fact that further plans to climb higher may go for a toss based on professional advice
- Balance adequate sleep/rest and exercise in your schedule
Will it take less time to re-acclimatise?
It ideally should, but its highly based on the routine that you follow.
Will we have to "start again?"
No, unless you spend a very long time sitting idle with no routine and random diet.
I've seen and followed a pattern of load-ferrying up the higher camps, purely for acclimatisation purpose. When you spend a night at altitude, the best thing that your body will get at lower altitude is the quality sleep.
For example, a schedule for acclimatisation for a high-altitude climb would be similar to this:
- Day 0: Reach Base camp (Which is higher than where you normally live), spend a couple of days: camping, packing stuff.
- Day 2: Hike up the mountain to another camp, dump some stuff that you've carried and that will be required for further stages of expedition, and Return to Base Camp.
- Day 3: Hike up the mountain with almost no load, pick-up stuff that was dumped at camp 1, load it all the way to camp 2 and return to camp 1 for sleep-over.
- Day 4: Descend to Base camp, rest.
- Day 5: Carry a heavier load this time to Camp 1, assume that you aren't descending to base camp till the end of expedition, unless necessary. Stay at camp 1.
- Day 6: Carry load to Camp 2 and sleep-over at camp 2.
- Day 7: Carry load to camp 3 / Summit camp and return to camp 1 for sleep.
- Day 8: Ascend to camp 3 / Summit camp and sleep.
- Day 9: Descend to camp 1 and stay there for 2 days.
- Day 10: Recovery
- Day 11: Recovery
- Day 12: Ascend to summit camp / camp 3, and sleep.
- Attempt Summit.
The reason I shared this itinerary, because it involves a lot of time spent at lower altitude for recovery after having gained a considerably higher altitude and being fully acclimatised. I have known people who followed this (or similar) itinerary and with no problems whatsoever managed to get to the top of a 7075 m (or 23211 ft) high bad-ass mountain, with a base camp set to about 4,800 m.
Update: I've stayed my life at sea level (Mumbai), and I've hiked up to world's highest village connected by a motorable road (Komik, at 15k ft), starting at about 7k ft (Pooh village), then came to a town at 6.5k ft and stayed there for a week and then travelled to a place at 11k ft in a day by road, and then went up a mountain top at 20k feet with no problems whatsoever.
On your itinerary -- sea level, Machu Picchu, low altitude, Cuzco -- you do not have to start from scratch in acclimatization after four days at low altitude, but you are far from acclimatized to Cuzco, even if you were fully acclimatized to Machu Picchu.
The acclimatization you attained going to Machu Picchu will help, but over 11,000 feet is very different from under 8,000 feet and, in fact, not everyone will acclimatize to 11,000 feet, especially if they have only a few days.
If you go to Cuzco first, and become well acclimatized to Cuzco, you may have no trouble going to Machu Picchu after four days at low altitude. The reverse is not true: i.e., Cuzco requires further acclimatization -- This article gives a survey of the problems you may encounter, and some steps to take, not all of which I recommend.
In particular, the advice to take Tylenol or another pain killer for headache is bad advice. Painkillers could mask the onset of High Altitude Cerebral Edema, which is life-threatening. Cuzco is low for HACE, but HACE is not unknown at that altitude.
The best advice is to allow at least two days to travel from the jungle to Cuzco, and follow all the usual advice about keeping well hydrated, cutting out alcohol completely, and not getting overtired. Diamox has apparently helped people in certain specific situations, but this is a prescription drug and should be taken only on the advice of your doctor. Don't take other people's word, even if it has helped them, and don't get any from friends.
The stress on your body will be the same, and it will take about the same time again to acclimatize, as others already explained.
I wanted to add some other information: different people react very different to quick height gains, and not everybody has an issue.
We went (only last month) from Lima directly to Lake Titicaca (>3800m), without acclimatization (in a plane). None of our group had any issues, and we were able to walk for hours, some of it uphill, in Puno (well, huffing and puffing, sure, but no other issues).
From local guides I was told that only about 20-30% of people coming to Puno have headaches and other lighter issues, and about 1 in 20 gets really sick (yes, we also saw some people vomitting on the street and rolling in pain).
I am not recommending to ignore the elevation issues; but understand the risk, and don't overreact.
P.S. funny when the pilot says 'Please take your seat, we are now beginning our final ascend to Juliaca airport'...