I have a Trek Dual Sport 3 Gen 5 hybrid bike. I want to understand how to optimize the stem length and height. Is there some guideline? More than just trial and error? Especially since changing stem length required spending money to buy and try different stems.

I bought the Trek bike 4 months ago. My original goal was recreation. I find the fit is fine for weekend rides.

But now I also commute to work 1 or 2 days per week. My commute is 14 miles one-way. It is great route along the bay. The downside is that there is no cover, so I have to deal with wind. On some days, it can be up to 12-15 mph headwind, which really kills my conditioning (or lack of) and commute time. And I noticed the bike fit and position can make a big difference. When I bend my upper body (and belly button) forward and down, I can generate more power in my pedal strokes; plus I'm in more aerodynamic position for the headwind.

What I read is that fit sequence is:
1. Saddle height. I have this dialed in.
2. Saddle offset. It is more difficult as it is not as black and white as saddle height, but I think I got this reasonably optimized.
3. Stem length or handlebar reach.
4. Stem height or handlebar height.

On the hybrid bike, I find my reach is too short. My upper arm and torso do not make 90 deg angle. Is this 90 deg angle applicable to drop bars or flat handlebar also? And when I bend over more in strong headwind, my arms are dropping straight down. I feel that longer stem length might work better.

Current specs and measurement:
* I'm 5'9" (177cm). My inseams are 31.5" (80cm). I have shorter legs, but relatively longer torso and arms.
* My Trek Dual Sport 3 Gen 5 is large (L) frame.
* Stem length is 80mm at 7 deg angle.
* Stack is 62.4cm; reach is 39.1cm; ratio is 1.60.
* Handlebar to head tube is 10.1cm in height (y) and 4.9 cm in horizontal distance (x). So effective stack including handlebar is 72.5cm; reach is 44cm; ratio is 1.65.
* Handlebar is 4.4cm higher than the saddle. Handlebar to seat (along seat tube) is 65.1cm.

I haven't tried it yet, but I can drop the stem and increase the reach by adjusting the spacers and flipping the stem from 7 deg to -7 deg. Using trigonometry, I estimate I can drop the handlebar by 4.7cm in height and increase the reach by 1.6cm, or anywhere in between. It is not much change in reach, without going to longer stem.

Any guidelines or suggestions that I can follow to find what stem length works for me?

Hey D00M, I know those headwinds on the Bay Trail! I don't do the commute, but I did once and it was very very windy. And was 20 miles one way for me - I returned on a different route. But overall no thank you! I was on a steel road bike. Good for you that you can commute!!
To answer your question about stem length and height, there may be a formula (but I don't know it), but depends on the bike use. I think your efficient aero commute mode and recreational weekend rides may need opposite solutions...you want to be low and stretched for efficiency but more upright for fun rides. That said, I added innerbarends to my XC MTB and that is a better aero and climbing position for both road and trails. I have the SQLabs version. there are similar very inexpensive versions on Amazon. They add a dorky look to an otherwise sleek bike, but I love them! The old bar ends on 90's MTBs were added to the end of the bars, when bars were narrow. but still caused issues catching trees, etc. The newer innerbarends are inside of the grips, wherever you choose, sort of like mini road aero bars.
The other thing you can do for free and very easily is reduce the space between your headset and stem, by moving the spacers from under to over, that slightly increases the reach since the fork is at an angle.that is of course if you have spacers under your stem.And/or reverse the stem to minus 7° which will will give you a lower position, without affecting reach. It may be too much though. 80mm is fairly long for a MTB stem, but I know you have a hybrid. You could go in between and try a 90mm long stem with less or zero rise. Stems are fairly inexpensive. some bikeshops have boxes of spares/takeoffs,etc and sell cheap.

I'm so sorry you have to endure the 'Flat Bar'.
Solution - look for a nice used Road bike with a drop bar and modern shifters/brakes (stay away from anything with downtube shifters !!!!).
It's not just the drops which matter, but the fact that with your hands on the hoods or bar bends, your hands are in a natural position with the elbows inward, in line with your shoulders....
less shock thru to the shoulders and neck and adjusting your posture to more or less aero is just an easy elbow bend away...
you'll thank me for this suggestion...
Ride On
Yuri

Just follow-up:

1. Saddle height. I have this dialed in.
2. Saddle offset. I updated this. Previously, I had the seat forward. Because it felt like it opens up my hips more so I can generate more power. But I'm over-using my quads and not my hamstrings. I now set the seat setback back to nominal (seat rail markings are centered). It definitely results in more balanced muscle usage between quads and hamstrings. Not an expert, so not sure if this is final. But setback centered is definitely better than seat forward.
3. Stem length or handlebar reach. With the saddle offset changed to nominal, I find that my reach feels much better now.
4. Stem height or handlebar height. This is a trade off. Couple cm higher will be more comfortable; lower will be slightly more aerodynamic. My stem spacer is set to the highest setting currently. It is possible to lower the stem by adjusting the spacers. Something to test out in the future.

FWIW: Everyone has different comfort levels. I got rid of my drop bars for flat bars and found them more comfortable. I get a wider hand spacing (about 520 across the bars now) and my hands don't fall asleep (become numb) like they did with drop bars even with changing hand positions. I tried riding a friends flat bar bike for 30 miles and it felt great, changed one of mine to flats and did a 3-day tour on it (170 miles) and felt great. I recently changed my other dropbar bicycle to flats. I'm satisfied with 'flat bars.'

Probably the bike is just too small. Go to a bike shop and say you want to buy a bike. Get the sales person to size the bike for you, so that your arms are properly extended. Then go home and compare what you experienced to your current bike. It might be that you could find the perfect size used on Craigslist or similar, if it looks like you won't be able to adjust your current bike to that fit.

Looking at hybrid geos yesterday, the top tubes vary little in different sizes. So I doubt the short reach is caused by the size.

Wow. Really. So also a good argument to get a road bike. I'll certainly take your word for it, but WTF.

Because they are made for sitting more upright. Tall people don't need extra reach if they aren't bending forward.