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Understand Bike Gears, and Avoid Mistakes on your Electric Bikes
Scientific American found that bicycles are the most efficient form of locomotion for any species on this planet. A key feature of a bike is its gears.
Gears let the rider pedal at their optimal rate regardless of whether they are racing on the flat or climbing a steep hill.
Adding an electric motor to a bike affects the way the gears work, leading to disappointment when not handled correctly by ebike manufacturers.
The article:

brings you up to speed on how gears work,

explains how an electric motor impacts the gears, and
How do gears work?
This is what bicycles looked like before gears.
The front wheel is so large because, without gears, one rotation of the pedals results in only one rotation of the wheel. To achieve any speed ... to magnify up the effectiveness of pedaling, the wheel needs to be large so that the bike travels a considerable distance with each rotation of the pedals.
Gears allowed bikes to have smaller wheels because gears multiply effort.
A typical bike might have a a gear with 53 teeth at the front, connected to the pedals. What this means is that one rotation of the pedals pulls the chain forward 53 steps – one chain link for each tooth.
The larger the front gear, the more teeth it has, the more chain that is pulled forward with each rotation of the pedals. The smaller the front gear, the less chain that is pulled forward.
A typical bike might have a gear with 12 teeth on the back. This means that each time the chain is pulled forward 12 steps, the rear wheel makes one full revolution.
The larger the rear gear, the less that gear moves with each step forward of the chain, and hence the less that the rear wheel rotates.
All of this can be measured. With these two gears (53 teeth and 12 teeth), one rotation of the pedals results in 4.4 revolutions of the rear wheel … because 53 divided by12 equals 4.4.
Because the effort put into the pedals is being multiplied by over 4 times, the size of the wheel can be reduced accordingly.
Why do people change gears while cycling?
If you are going downhill, it is easier to propel the bike forward. So, when going downhill you might want to multiply the effect of your effort over 4x by using the largest gear at the front and the smallest gear at the back.
Climbing up hill, on the other hand, requires more effort. To make the pedaling easier, you change gears. You might use the smallest gear on the front (39 teeth) and the largest gear in the back (25 teeth).
A full rotation of the pedals will pull the chain forward 39 steps (because the front gear has 39 teeth). Each time the chain moves forward 25 steps, the rear wheel is rotated (because the rear gear has 25 teeth). Therefore, one rotation of the pedals results in 1.6 revolutions of the rear wheel … because 39 divided by 25 equals 1.6.
Because one rotation of the pedals carries you forward less distance, it is easier to pedal.
What are the “best” gears?
There are 3 things to think about when looking at the gears on bicycles.
First, the highest gear ratio.
In the above (realistic) example, when going downhill or trying to go fast on the flat, you might want one rotation of the pedals to turn the rear wheel 4.4 times.
An Olympic cyclist will pedal faster than weekend cyclists, and they might use a 4.75 gear ratio – this being 57 teeth on the front gear and 12 teeth on the rear wheel.
Second, the lowest gear ratio.
In the above example, when climbing hills, you might want one rotation of the pedals to turn the rear wheel 1.6 times.
A serious mountain biker might want to downshift on a steep hill to a 0.66 gear ratio – this being 24 teeth on the front gear and 36 teeth on the rear wheel.
Third, gear ratio range.
This is the ratio between the highest and lowest gears  usually expressed as a percentage. An amazing bike that is capable of both being raced in an Olympic cycling race (4.75 revolutions per pedal) and also used to climb the steep offroad hill (0.66 revolutions per pedal) would have a nearimpossible gear ratio range of 720%  this being 4.75 divided by 0.66.
Not only is this gear ratio range impractical, but you would want entirely different bikes for Olympic track racing and professional mountain climbing. So, you are unlikely to find a gear set with a 720% gear ratio range.
But 575% is available.
As a point of reference, a typical bike might have a range of 280%. In the above example, the highest gears rotated the rear wheel 4.4 times, whereas the lowest gear rotated it 1.6 times. When you divide 4.4 by 1.6 you get 2.75 or around 275%.
How are electric bikes different?
There is a separate article discussing the difference between middrive and rear hub electric motors. Briefly, the relevant difference is as follows:
Middrive motors only have a single gear at the front, reducing your gear options – reducing your highest gear ratio, increasing your lowest gear ratio, and reducing your overall gear ratio range.
However, a middrive motor adds power to the chain … and thus uses and benefits from the rear gears.
Rear hub motors are independent of the gears. So, you have the same gear ratio range as before, but these gears only affect the power you put in with your pedaling.
The motor itself has no gear options and thus can struggle at both ends … climbing hills and going fast on the flat.
What are the Common Problems?
We recommend getting an electric bike with a middrive motor.
The most common issue that arises is that the manufacturer does not compensate for the lack of front gear options.
First, they may use a standard rear gear cassette. This means that the gear ratio range is reduced from (say) 280% to 200%.
The Lectro Townmaster is an good example of this problem.
This bike is available for only £1199. However, it only has:

a 200% gear ratio range (as there is no front gear and the rear gear ranges from 14 to 28 teeth).

the highest gear ratio of 3.3 this being 42 teeth at the front, 14 at the back; and

the lowest gear ratio of 1.6 (this being 42 teeth at the front, 28 at the back).
The lowest gear ratio is an acceptable 1.6, meaning that it can climb hills. However, given that it is a heavy bike, without power assistance you would find this a challenge. (And, because this bike uses a rear hub motor and not a middrive, the bike itself will find hills to be a challenge as well.)
The highest gear ratio is a shocking 3.3, meaning that once you get up to any speed, you the rider will be contributing nothing. The electric motor will be doing 100% of the work.
One result is that when the ebike achieves its maximum speed (15.5 mph) there is no way to go any faster. The effect is called "spinning out". You (the rider) have to pedal at an impossibly fast rate.
Perhaps fortunately, the Townmaster uses a rear hub motor, meaning that it does not "assist" you. Instead, your pedaling merely acts to indicate how fast you want to go.
Second, even if they use a better rear gear cassette, they may bias the range towards the low gears.
The Haibike Trekking 4 Lowstep is a good example of this problem.
This bike is available for £2,449. It has:

a respectable 327% gear ratio range (the rear gear has from 11 to 36 teeth);

an impressive 1.1 low gear ratio (38 teeth on the front, 36 on the rear); but

a disappointing 3.5 high gear ratio (38 and 11).
So, despite this bike having a better gear ratio range than a traditional bike, the bias towards low gears means that you will "spin out" if you try to cycle beyond 15.5 mph (when power assistant stops).
Some people might argue that this is a trekking bike meant for offroad use and thus the bias towards the low gears is justified. This argument may have some merit; however, many reviewers do suggest bike like this for city commuters.
Note: Haibike no longer produces the sDuro Trekking 4.0. Other than electric mountain bikes, this is their lowest price electric bike.
What is the solution?
The solution is in three parts.
First, look for an electric bike with a decent gear ratio range (i.e. at least 300%). As mentioned above a 280% gear ratio range is fairly standard for traditional bikes. Electric bikes are heavier and therefore need the low gear ratio to be slightly lowest than normal (1.6).
How to do this? Ask for the number of teeth of the largest gear and the smallest gear on the back. Divide the larger number by the smaller number.
Second, consider if you will be riding up steep hills. If you will only be riding on the flat, then the standard 1.6 lowest gear ratio is fine. Modest hills, then go for around 1.3. Steep hills, then go for around 1.0 For comparison, the best mountain bikes go down to 0.66.
How to do this? Ask for the number of teeth on the front gear and on the largest rear gear. Divide the front gear number by the rear gear number.
Third, consider whether you like going fast and are happy to pedal to get the bike above 15.5 mph. If you are then the highest gear ratio must be over 4.0. Remember that a traditional bike is around 4.4 and the best racing bikes are around 4.75.
Note: To be completely clear, the smaller the wheel, the higher the ratio required.
How to do this? Ask for the number of teeth on the front gear and on the smallest rear gear. Divide the front gear number by the rear gear number.
Good Example: Riese & Muller Charger3
There are different configurations of the Riese & Muller Charger3, all of which are good examples of electric bikes that get their gears right.
The Touring HS version has a front gear with 48 teeth. The rear cassette has 11 gears ranging from 11 to 46 teeth.

The gear ratio range is 418%.

The highest gear ratio is 4.2.

The lowest gear ratio is 1.04.
The Vario version uses different technology (a continuously variable internal gear hub).

The gear ratio range is 380%.

The highest gear ratio is 4.6.

The lowest gear ratio is 1.2
CONCLUSION
Gears are what make bikes such an efficient form of transportation.
When you come to a hill, you downshift to make the hill easier. A good bike has a low gear ratio that is low enough for the hills you are likely to encounter.
If you ride only on the flat a ratio of 1.6to1 is fine. Modest hills 1.3. Steep hills 1.0. Professional mountain bikes can shift down to 0.66.
When you want speed on the flat, you upshift so that each pedal stroke takes the bike further. The high gear ratio is what allows you to go fast while not pedalling fast.
UK law says that the motor of an electric bike must stop providing assistance above 15.5mph. If you may want to pedal to go faster than 15.5mph then you need a highest gear ratio of at least 4.0to1.
A traditional bike is 4.4to1 ratio. An Olympic racing bike is 4.75 but these bike include many other features for speed, and Olympic cyclists pedal much faster than a casual cyclist is able to.
Note: Wheel size is also a factor here as one rotation of a larger week takes the bike further than one rotation of a smaller wheel.
Middrive motors add power to the chain and thus take advantage of the gears. In contrast, hub motors do not. The gears only benefit the power that the rider is providing. This is a main reason why we recommend middrive motors instead of hub motors. Further reasons are given in a separate article.