Noob Moped Conversion...

Skip the outrunner motor, especially if you are a beginner.. I have followed some threads of what it took to get those to work as an EV motor, and it was almost absurd. It is totally not designed for that application.

Your best bet is to talk to someone at a place like Electric Motorsports who specialize in these types of conversions. Do it right the first time. Let them design and sell you a kit where the parts will all work together.

http://www.electricmotorsport.com/

That particular bike looks like a candidate for a powerful rear hub motor, custom built onto a stock wheel. You may want to check with Doug at EV tech to see what moped sized hubs he can get his hands on at this point. You need to call him, as his web site really needs an overhaul and shows nearly none of what he has available.

http://www.texaselectricbikes.com/

45 MPH speed plus 20 mile range will take way more battery than you have listed.

Also, haven't heard many good reviews on that battery source you mention. Actually have read some really bad ones. Most of the moderate sized LIFEPO4 batteries don't have the continuous or peak output needed to run a heavier bike, especially when hills come your way.

I am by no means trying to discourage you from the fun of trying to convert that bike to electric, but I have done several small EV projects and know what is involved in doing it successfully. The speed and range you are looking to get will require some serious batteries. You mentioned in your other post you are on a budget. You can't really build an electric moped that can do even 40 MPH and have a 20 mile range without a significant budget for batteries. That's pretty much why very few people are doing this yet.
Lead acid is always a short term, heavy, less expensive option than Lithium, but it will make the bike handle and brake like a pig, and the performance will go down part way into the discharge.

This seller below has good feedback and makes some higher AH packs.

First you need to find a hub motor and controller that can power the bike, find out how high of a voltage you can safely run with then, and then research the batteries. I would think 30 AH would be minimum, with 40ah being better, and you may need a 72 volt system if you want some speed. That is going to be an expensive conversion. Another option is to accept a more sedate 25 MPH top end but with good torque and range, and go with as strong of a 48V set up you can find. going 45 on that little bike is pushing it in my opinion anyway. In California , 30 MPH is max speed for any moped.

http://cgi.ebay.com/LiFePO4-48v-40ah-BATTERY-FOR-ELECTRIC-SCOTTER-E-BIKE_W0QQitemZ170327465626QQihZ007QQcategoryZ11332QQssPageNa...

Link to an older post on similar lines.

http://visforvoltage.org/forum/6069-what-best-48-volt-rear-hub-set-35-mph-bike

If these could be adapted, they would have the power to move that bike to a high speed and make it climb well. i am not sure if the hub would fit your frame without major modification, as they are more designed for a normal bicycle..

http://www.electricrider.com/crystalyte/phoenix.htm

Check out this user's blog: http://visforvoltage.org/blog/nasukaren - not a Puch Maxi - but very similar. She used a motor intended for an RC plane and got good results. I don't recommend you use a hub-motor from EMS because they don't have them in the right size. You could try a bicycle hub motor but they might be a bit underpowered.

Good luck and have fun!

"She used a motor intended for an RC plane and got good results"

I just looked at her site and she just burned up something again.

That person has had so many problems with that set up. That out rigger motor is powerful, but the corresponding electronics to make it work in an EV application is a serious engineering project and would be a monumental undertaking for anyone, especially a beginner.

I bet one of the bigger Phoenix motors with a 40 amp 72 V controller would move that moped along no problem. I am just not sure how you'd mount the hub to the bike, drop out size, etc.

My friend used to make movie sets one and he worked on a Dr Suess flick in which they made an E powered scoot. It used a HD marine battery thar was heavier then hell.
It ran all day long on a charge with plenty of power.

I am also planning a E-Ped both a conversion and another one of my own seaign from scratch. I will used SLA batteries on mine. It should go about 20 plus on a charge based on what my local dealer has told me and with a Crystalyte Cruiser. Braking and not power will be your main challenge with the heavier batteries from what two local shops have told me.