Absolutely not. At most they help strengthen the diaphragm, at the worst, they do nothing and limit your workout capacity. They make it harder to breathe but the air you're still breathing has exactly the same ppO2 as the atmosphere you're in.
By elevation training what are you asking about? How to get fit so when you get to altitude you minimize risk of AMS? If so then I hate to break it to you, but there is nothing "specific" you can do outside of somehow finding a hypoxic tent to work out in or living at altitude. The general approach to fitness for the mountains is a combination of strength and conditioning. The go to textbook for this is Training for the New Alpinism.
There is a mountain, literally Olympic training programs, predicated on zones 1-3 training of which walking is in. It’s just often called something different. Many “walkers” train by hiking or similar activity obviously the distances are probably far longer than 3 miles but there is no shortage of recent fitness literature discussing the benefits of zones 1-3 training over higher intensity zone training.
Training for new alpine ski, is one of several books that discusses this, cardiovascular and metabolic implications, study citations and Olympic athlete programs including failed athletes who tried to shortcut with more higher intensity exercise routines like HIIT and crossfit.
https://www.amazon.com/Training-New-Alpinism-Climber-Athlete/dp/193834023X
Anyways I have often said this and continue to say. Walking is one of the healthiest things you can do and it absolutely can have huge metabolic and cardiovascular benefits.
Functional fitness stuff. Gym Jones, cross fit, Mountain tactical institute.
Note the difference between activities and lifestyle. Push ups and sit ups aren’t a lifestyle but elite level fitness is. With a lifestyle, your world is structured around what you are doing. It’s where you spend your time, money and effort. Become a member of a cross fit gym. Tell them what you are trying to do. Become apart of the community. Let them help to hold you accountable. On weekends test yourself in the mountains. What you can’t afford, do it yourself. Make dumbbells out of old pipe and cement, score weight he’s on Craigslist, watch YouTube videos if you can’t afford a gym membership. Don’t have mountains, move. Or find the biggest hills you have. Run and lift every day. This is how you fill your extra time. Find a buddy who wants to train too.
Be a student of what you are doing. This book has a ton of insight into functional mountain based fitness: Training for the New Alpinism: A Manual for the Climber as Athlete https://www.amazon.com/dp/193834023X/ref=cm_sw_r_cp_api_i_S0WHFb7WKN90K
Do yoga. It will help to injury proof.
Consider getting this book: Training for he New Alpinism House discusses training for mountaineering and climbing. He goes into detail about how different types of training affect your aerobic ability, etc. He also lays out how to structure your training plans. Some of it is geared towards climbing, but for the most part its been a great resource for training for hiking/backpacking. I highly recommend picking up a copy and a heart rate monitor.
You have time to buy Training for the New Alpinism and follow its training guidelines. Besides being a great training manual, it's full of inspiring (and scary) photos and stories. It's considered the standard text on the subject.
Get yourself a copy of Training for the New Alpinism, though its mainly directed at Alpine Climbers the theory and exercises are certainly applicable to trekking especially at altitude.
Have you checked out Steve House's Training for the New Alpinism? It's focused specifically on mountaineering, but can definitely be applied to any long days in the mountains. There are some good workouts in there that you might find helpful.
http://www.amazon.com/Training-New-Alpinism-Climber-Athlete/dp/193834023X
Training for the New Alpinism is the standard text for mountain fitness. The authors even have advice for people stuck in the flatlands.
What worked for me, a 37yo male: a weighted pullup program outlined in Training for the New Alpinism.
8 weeks, weighted pullups twice a week, 2 to 4 sets, at or near 1rm. So 1 to 3 reps per set, 2 to 4 sets.
At the start I could do 8 good ones and after 8 weeks I could do 14. When I started my 1rm was with 13 extra pounds, and at the end I did 3 reps with 40 pounds.
Not a mind-blowing improvement over eight weeks, but consider that I was only doing pullups twice a week, and between 4 and 9 reps per workout. The lack of high reps really saves wear and tear on your shoulders and elbows, especially if you have any history of injury or tennis/golf elbow.
Check out Training For The New Alpinism and Training For The Uphill Athlete. I've been reading TFTNA and it has a lot of good information on how to periodize your lifting and aerobic training, along with recommendations for specific workouts.
My advice is that most of us are climbing to live, not living to climb.
Steve Bechtel and Charlie Manganiello of ClimbStrong both advocate cutting down on cardio to truly hit your climbing peak, both of them ski and run, and have put plenty of thought into progressing while being a multi-sport athlete.
It also depends on your current goals. Trying to cut weight? eating right and engaging in some mild cardio can help. Trying to climb long trad routes and be a mountaineer? Buddy there's a whole massive debate about how to become the most insane cardio machine possible.
You should do the thing you feel is most rewarding. I tend to cycle in and out of climbing-heavy and running-heavy periods of my life because they both make me happy. Am I the strongest at either that I could be? Definitely not.
In addition to powerlifting/strongman, I'm also an avid hiker. In prepping for a backpacking trip coming up, I've been reading a lot from "uphill athlete" and "training for the new alpinism" (one of the authors is on the uphill athlete site). Another endurance coah, Phil Maffetone is very similar. They are all big fans of long slow cardio based around a measurement of aerobic threshold.
Basically, they argue that's how you improve your aerobic system and that most of us exercise at too high of an intensity. I've not done it long enough to notice big improvements myself, but I can't deny it's also healthy, so that's a perk.
I started thinking about it b/c I could keep up with my wife hiking, albeit with a heart rate that was in the 150's while hers was in the 120's. I was strong, I could move weight quickly, I could push myself hard, etc., but boy was my heart rate up there.
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*edit: +1 on seeing a doc to make sure there's not an underlying condition
For something a bit more specific, you might check out Training for the New Aplinism - Steve House is always a good read. Sold all over the UK.
I was subscribed to Fit For Trips for a while and they have good content on how to train without hills/mountain readily available. Check out the training section of their blog: https://fitfortrips.com/training/
Also, if you see yourself pursuing the activity beyond your initial trip I would recommend getting Training for New Alpinism by Steve House and Scott Johnston. Super good manual on how to train for big objectives with a first principles approach. Link to the book here for your reference: https://www.amazon.com/Training-New-Alpinism-Climber-Athlete/dp/193834023X
Personally, like some have mentioned, I like long periods of low intensity cardio - Stairmaster, jogging.
Check out Training for the New Alpinism
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https://www.amazon.com/Training-New-Alpinism-Climber-Athlete/dp/193834023X
I've seen "Training for the New Aplinism" referred to as the gold standard for training several times by people that spend lots of time on mountains.
Training for the New Alpinism by Steve House and Scott Johnston