15% is pretty steep, and will take a lot of power. Doing it at those speeds takes a lot more power, and the total weight increases it.
If your priorities are listed in the order they are important to you, first one most important, etc., then keep in mind that "off the line torque" and "acceleration" are generated by the same things (really *are* the same), so you'll want to decide which place they take--first, or third.
If efficiency (wh/mile) is least important to you, that's good because to get quick acceleration and high speed especially with steep hills, it's not going to be a very efficient system (15-25% or more wasted power, at least, in various conditions).
If efficiency is more important to you then you might want to consider aerodynamically streamlining the bike (and your riding position), which will decrease power usage.
You can also use a middrive that you can shift gears for (just like when you pedal, and usually these actually use your pedalling gears for that reason), so you can keep the motor in the more efficient range for the conditions and speed you're trying to go. Setup the gearing and motor system so that the fastest the motor can go is your 30mph top speed or a bit more (to account for headwinds) on the lowest gear you will need to use to climb the worst-case hill with whatever power limit you have (depends on which motor, battery, controller you use).
A quick simulation with the ebikes.ca motor simulator for 15% hill at 30mph with 300lbs rider + bike/etc for a hubmotor system
Our ebike motor simulator allows you to easily simulate the different performance characteristics of different ebike setups - with a wide selection of hub motors modeled, and the ability to add custom batteries and controllers and set a wide variety of vehicle parameters you'll be able to see...
ebikes.ca
shows you need roughly a 100A-battery-current system (for some margin of higher occasional loads, like headwinds, etc). I could only get it to work with 72v, not 48v, but you might find a motor/controller/battery setup capable of those speeds at those power levels at a lower voltage and higher current.
Numbers from the simulation are listed below, but basically at 30mph on 15% slope, 72v battery, cromotor with statorade and hubsinks, it takes over 5kw from the battery, nearly 4kw at the motor, less than 75% efficiency (so a lot of waste heat, which means sustaining this will overheat the motor relatively quickly). The math in all of my notes here is rounded off for simplicity, and everything assumes worst case (because if you want a system that can reliably do a job, always set it up for worst case scenario, and then it can always do what you actually throw at it).
5200w / 72v = 72A sustained (continuous) battery current required.
172Wh/mile is very high power usage, and requires a large battery for range. Since you're only using this for about 20% hills, we'll do 0.2 x 25 miles range total at 172Wh/mile, so 0.2 x 25 = 5 miles x 172wh/mile = 860wh required for those hills, if they were all 15% and ridden at 30mph.
| Graph | Syst A |
| Wheel Torq | 93.3Nm |
| Mtr Power | 3824W |
| Load | 3830W |
| Efficiency | 73.2% |
| RPM | 391.3 rpm |
| Electrical | Syst A |
| Mtr Amps | 95.0A |
| Batt Power | 5221W |
| Batt Amps | 80.7A |
| Batt Volts | 64.7V |
| Performance | Syst A |
| Acceleration | -0.01 mph/s |
| Consumption | 171.5 Wh/mi |
| Range | 8.5 mi |
| Overheat In | 8.7 minutes |
| Final Temp | >250 °C |
Riding on the flats at 30mph is much easier and only takes about 1200w battery power, and about 1000w motor power, only eating up about 40 Wh/mi.
So for the 80% of the 25 miles you'll ride on the flats, then it'll be about 20 x 40wh/mile, or only another 800wh to get the range you want.
Rounding up the other number to 900wh, plus this 800wh, means roughly, rounded up (because you don't want only the exact amount, you always want more than you need so aging and / or poor conditions, etc don't eat into your range as much), a 2kwh battery to get the range you need. At 72v, that's 2000 / 72 = 27Ah. At 48v, that's 2000 / 48 = 42Ah.
Either way, it's a pretty big and heavy battery. Most likely it will be over 20lbs, probably closer to 30-35lbs. Volume, shape and actual weight will depend on the cell type you choose to use, and the quality of the cells (lower quality (cheaper) will mean more cells, more weight, more volume, to get the same capacity and current delivery.
Note that if you were estimating a smaller battery with less weight in your total system weight estimate, you would want to resimulate using the higher weight of the battery needed to do what you want, because that will increase power requirements to climb the hill, and also the wh/mile on the non-flat portions. Also increases accleration requirements for the same reason as the hill.
| Graph | Syst A |
| Wheel Torq | 25.7Nm |
| Mtr Power | 1043W |
| Load | 1051W |
| Efficiency | 85.8% |
| RPM | 387.8 rpm |
| Electrical | Syst A |
| Mtr Amps | 27.0A |
| Batt Power | 1215W |
| Batt Amps | 16.5A |
| Batt Volts | 73.7V |
| Performance | Syst A |
| Acceleration | -0.01 mph/s |
| Consumption | 40.3 Wh/mi |
| Range | 41 mi |
| Overheat In | never |
| Final Temp | 42 °C |
This is different from your first paragraph's requirements. Is it just a refinement of those, or something else?
I ask because how fast you need to go up a hill, and how steep the hill is, greatly affects the power needs of your system. Play with the simulator linked above to see what I mean--just use the existing simulation and change the slope and speed (drag the vertical speed line left or right) to see what guesstimated power requirements are for various numbers.
It also greatly affects the wh/mile, which tells you how big your battery has to be to give you the range you need.
You can also read the instructions on using hte simulator for middrives, and figure out how much less power you may need or how much more efficient it may be at that power level for various gearings.
For the rim, you could lace your own wheel, if you're up for learning how (this is not too difficult, but does take some practice; there are a lot of resources here and elsewhere on this if you're interested). You'll also probalby end up with a better wheel than the ones motors are usually built into (most prebuilt motor wheels use spokes too thick for the rims they have, which can cause the rims to fail from overtension or the spokes to break from undertension, or both).
