Wheelchair battery life calculation
Pretty much every calculation involving batteries is an approximation. Battery life depends on a ton of factors (battery chemistry, temperature, load profile, battery age, self-discharge effects, other effects such as gas build-up).


  [...] the website lists the run time for all different models as 1.5 hr so clearly this information isn't correct!


The vendor is probably designing to meet "at least 1.5 hours" with some extra margin, and making some (hopefully safe) assumptions about usage and whatnot. For example they probably don't presume that the motor is continuously running at max speed for the entire 1.5 hour period.


  I understand more Ah are better but I'm not sure if more W would mean more run time (because bigger is better) or more W would actually decrease the run time because it's drawing more power in a shorter amount of time?


The second one. I presume that first number (Watts) is specifying how much power the motor has (and, in turn, how much power the motor draws from the battery). A 350 W motor would draw 9.7 amps at 36 V. A 500 W motor would draw 13.9 amps at 36 V. (These are all peak numbers, I presume the motor is variable-speed and variable-power.) So the math becomes pretty simple: a motor drawing 9.7 amps would deplete an 8.8 Ah battery in 0.91 hours or about 54 minutes, if the motor were continually running 100%.

Again, if your use case is a little more benign -- i.e. if you actually slow down and/or stop once in a while -- then the actual battery life should be longer.


  the Chinese ones I've found are literally 10% of the price... I just don't want to find I make it to the corner shop then haven't got enough battery to get home and that's why they're much cheaper (but all that's affordable to me).


Yeah unfortunately that's a very valid concern. Most Chinese components I've worked with are pretty good, but there are some bad apples as well. Your best bet is to see if you can find anyone who has experience with those batteries; unfortunately I'm not that person.