48 volt 10AH versus 36 volt 12 AH LiFePo battery considerations

[GeorgiaBiker]

Yesterday I ordered a 700c Magic Pie 3 front motor kit for my Trek 7300 Alpha bicycle. I live in a rural area of South Georgia (USA). I have to traverse 3-4 miles of dirt roads before I get to the pavement. When it hasn't rained for a while the dirt roads begin accumulating sand and I am hoping the front wheel drive will help me traverse these hazards as I have come close to overturning a few times.

I have a question about batteries. I am considering purchasing one of the Lithium Iron polymer batteries to go with the Magic Pie 3, either the 36 volt 12 AH, or the 48 volt 10 AH.

I am not interested in high speed, as I don't anticipate cruising much above 20 MPH no matter which battery I purchase. My main consideration is distance. Could you tell me what distance I could expect comparatively between the two batteries? (Note the key word is "comparatively." I realize actual distance is affected by many factors such as the weight of the bike and rider, road resistance, wind resistance, terrain, average speed, etc..) I live in South Georgia, and its about as flat as Kansas here, so I have only small hills to climb.

I am guessing that the main advantage of the 48 volt is that it provides more power, resulting in more torque and higher top speeds with better hill climbing capacity. With top speed and hill climbing not being issues for me, is there any other factor that would recommend the 48 volt battery over the 36 volt?

I have seen that most electric motors gauge overall efficiency by AH/distance. Perhaps there is a thread on the forum you could point me to that discusses the comparative performance of these two batteries with the Magic Pie 3. Seeing that the 36 volt battery has an overall higher amp/hour rating, is it correct to assume it would take me further than the 48 volt 10 AH battery if I were traveling at the same speed?

Thanks for any assistance you can give me here.

[Bikemad]

Hi andto the forum.

The total energy stored in a battery is more commonly compared in watt-hours (Wh), which is calculated by multiplying a battery's average discharge voltage by its Ah rating.

In order to keep things nice and simple I will simply use the stated nominal battery voltage to provide a reasonable comparison:

36V x 12Ah = 432Wh
48V x 10Ah = 480Wh

According to my calculations, the 48V battery has approx 11% more energy available than the 36V battery, so it should therefore deliver a longer range than the 36V battery, but only if ridden at the same speed.

If you were to ride at full throttle, the 48V battery would have to expend its stored energy much quicker, and the range would be noticeably reduced as more energy would be needed (consumed) to produce the faster acceleration, and also to overcome the additional aerodynamic and rolling drag caused by the increased speed.

The relationship between power and speed is quite complicated to calculate (even on a perfectly level road) due to differences in coefficient of friction, frontal surface areas and the density of the air, the wind speed and direction etc., but it is generally accepted that doubling your speed requires eight times the power.



Even though it requires eight times the power to double the speed, it would only require four times the amount of energy to cover the same distance as it would complete the same journey in half the time!

So, if a bike needs 250 watts to maintain a steady 20mph on a level road, it would therefore need to consume around 500 watts to maintain 25mph on the same stretch of level road.

Conversely, it should only require 31.25 watts of power to maintain a steady 10mph along the same road.

Alan
 

[GeorgiaBiker]

Thanks Alan, I appreciate the explanation! I did end up ordering the 48 volt battery from Golden Motors Canada. I had not noticed previously that they offer a 15 AH battery in a bike rack bag. I am quite confident that the 15 AH battery will take me the distances I need to go, so that is what I ordered. I am not too thrilled about the weight of the batteries. With all the added weight, I feel like I will be driving a tank down the road. However, having a powered bike that is heavy, is better than having no power.