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I am looking in buying one of these budget (I am on tight budget) kits:

  1. Chain driven kit cost $100
  2. front wheel hub kit cost $100

My bike is multi gear and where I live there are some challenging steep hills, not all of them paved.

Which kit would perform better?

Stealth and sound are not relevant issues for me.

BTW the chain driven (cranked?) one does not connect to the bike gear system, so it does not use advantage of changing gears.

I couldn't find any info about the chain one.

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    Did you miss a digit from your pricing? Anything at $100 of any currency will be fairly useless. Even the lowest-price hill topper kit is $500 US to start, and goes up as you add/improve batteries. – Criggie Jul 9 '16 at 0:06
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For hill climbing without the ability to change the gear the motor is in you're going to have to pick a lower gear than it was designed with, somehow, and accept that it won't help much on the flat.

The "chain driven" kit you're looking at will only work while you're pedalling, as it requires you to keep the chain tight against the motor sprocket. Despite the bike being shown with gears, the motor will only work in one gear, otherwise the chain won't hit the sprocket on the motor. If you're lucky you will be able to choose the gear, and you can choose a fairly low one to go up hills in. If you're even more lucky the other gears will still be usable without the motor.I suggest you ask the seller those questions before buying. They say:

This kit is designed for normal bike, not for the bike that can shift gears. However, you can install the kit on the left hand side if your bike is 18speed/24speed

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Note that that kit does not come with a battery or charger.

The hub motor kits normally are easier to install, especially if they come built in to a wheel already (I suggest you do this, the extra shipping is usually cheaper than the cost of getting a wheel built). Since the hub motor is already set up to drive the wheel, you don't have to adjust anything that's got a lot of force or power going through it, so it's less critical that you get it exactly right. With a hub motor you only have to get the anti-rotation setup fixed properly. The usual problems are getting the wiring to work - cheap kits will almost always work, for a while, in the workshop. Getting them to work reliably in all weather while riding the bike can be a challenge. It will help if you're willing to solder connectors in place, and you should definitely plan on buying an extra hundred cable ties to hold everything onto the bike.

I think your budget is optimistic. Normally when you find a product that's much cheaper than the competition it's because it's junk. Either it's going to fail much sooner, it doesn't work as well, or it's missing key things you assume are required. In this case I think you'll find that it's both unreliable and less than you expect - the motor will be less powerful and the battery smaller (it will go less distance per charge). It will all fall apart within a few months.

Make sure that you have a reasonable workshop and a collection of bike brackets and stuff that you can use to assemble and install the kit. Those kits either come with a huge bag of brackets and bits that you won't use for your bike because they come with every bracket you might need for any bike, or they come with one set of parts and inevitably you need a different set. Cheap kits will always be the latter type, so you will need to put their brackets in a vice and hammer/bend them to fit your bike. Or add a stack of washers and use longer bolts to get the thing to sit right. You many also end up needing to add more bracing. With the kit you're looking at, note that they mention "spot weld the sprocket"... you will also need a welder.

I have a friend who has spent a lot of time on this, and eventually built a business around importing electric bike kits and bikes from China and Taiwan. His experience has been that since he's legally required to offer a minimum one year warranty, he has to use kits that cost him at least $500 and realistically more like $1000 (because people look at the "100 watts for 30 minutes" kit you get for $500 and don't see the point).

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The cheap ones will not climb hills well. They have 1000 watt cheap ones (about $250). With all of them wattage = power to climb. 250 watt won't make it up steep hills. I like the Bfang 1000 watter. It replaces your crank about $500 add another $500 for lithium batteries. That one has the advantage of having gears. Lead acid batteries have very limited range. Hilly areas drain them fast. So does high speeds.

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I've learned the hard way that mid drives are better than hub motors for going up hills. We used to live on a dirt road that was a mile uphill, and after a few months, the hub motor died from too much strain even though it was 500 watts (hardly the lowest power e-bike). If you are planning on using your bike a lot, and going up hills quite a bit, I would highly recommend a chain drive, (or mid drive; they are the same.) as they give you more torque going up hills. If you don't go up crazy hills every day, the hub motors will work just as well as a chain drive. There will be minor differences about how they ride, which are totally up to you and how you like your bike to ride. Here is an extensive pro and con list about each type. I will say that it is MUCH easier to convert a bike to hub drive than it is to convert to mid-drive.

Buying: If you do decide to go for a hub motor, Bionx has some great conversion kits that can be relatively inexpensive. Also, another great hub motor is the Omni Wheel by Evelo, which is great for a conversion, however it is front wheel drive, and I have found that you experience speed wobble when you ride fast (around 30 mph). If you choose a mid-drive, Bosch makes really great mid-drive motors.

Overall, have fun, do a lot of research, and be cautious of overly cheap motors that will burn out on you within the first few months.

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