# Power consumption calculation in cadence as large

## Is there an optimal cadence on an e-bike?

Posted on Aug 14, 2018 in Tech | 13 comments

The question of the optimal e-bike cadence can also be asked like this: With more power step on the pedals with every revolution, for that less quickly turn the crank? Or pedal faster at less leg strength and produce the same power / speed?

What is more effective and better - for the body and its performance or for the e-bike motor, its effectiveness and load? On inclines, in headwinds, on tour?

Self in cycling you can observe different pedaling speeds and riding styles: Jan Ullrich preferred to ride with a little more power, but fewer revolutions per minute, Lance Armstrong with a faster step, but less power.

But what would one be ideal cadence?

It's actually quite simple:

The one in which you have to use the least physical strength at the same speed and the same route type and you have the least strain on your heart, circulation, muscles and joints.

The cadence is often underestimated by non-professionals: In addition to your effort and the choice of gear, it is the greatest adjustment screw for motor performance and battery range - and for the body load.

### Here is a little derivation of the cadence

First, some technology and numbers - I'll get to health below.

If you want to achieve the same performance with as little effort as possible, the first comes path into play: as we know from school, force x distance results in what has been achieved job (Example: pulley block). And the circular path that you cover with your foot when pedaling is longer with faster pedaling - higher cadence - per unit of time.

Put simply, when cycling, your strength begins with the fixed crank length (which is usually 17-17.5 cm) Torque together, results in an “energy per angle”, so to speak. Torque has the same physical unit as work, namely newton meters. But one says torque and not work, because the force output here does not take place continuously over the distance, but is different depending on the angle and is calculated differently mathematically. Incidentally, you can give off the greatest force at the moment when the crank is exactly horizontal and you push it downwards. In humans, this force roughly corresponds to their body weight. You give off the least amount of force when your leg moves upwards.

For thepower is now still the time included, in our case via the Turning or Angular speed of pedal movement: The power then results from the equation power = torque x angular velocity.

In other words, the angular speed of the bicycle crank is the most important variable for performance while driving - along with leg strength and the driving position - which we use for Cadence would be.

So how high is the ideal cadence to ride in the ideal area of ​​the human / machine system? You read them again and again recommendationthat the most effective “cadence”, i.e. step sequence or number of revolutions, for e-bike mid-motors 70 to 80 rpm lie.

At first, that seemed quite high to me - you can get good support from the motor on an e-bike with fewer revolutions.

### Why 70 pedal revolutions per minute and more?

E-bike newcomers have to get used to it, just as it has happened to us: Often, even 60 pedal revolutions per minute seem to be sufficient and intuitively correct. This is probably the most efficient pedaling speed even with a normal bicycle - it is said that this is where the efficiency of the muscles is greatest.

I myself now prefer to ride the Haibike SDURO HardSeven with the Yamaha PW motor at cadence between 70 and 80 revolutions. I can read the rpm - rounds per minute - on the display. More about my practical experience with cadence in the article “With the e-bike into the Priental”. This is now about motor effectiveness, body load and battery range.

### Technically, cadence is about torque, physically around the circulation and joints

The recommendation of 70-80 rpm is about that Effectiveness of the engine. Some e-bike riders feel most comfortable with 85 rpm on the trekking e-bike and 85-95 rpm on the e-MTB and measure that their battery lasts the furthest.

In relation to the motor, effective means that the power used, which is drawn from the battery, is transferred to the motor with as little loss as possible and to support physical strength. In engine technology, loss-free means above all: with as little as possible Heat development. Because an e-bike motor that converts the battery power into heat can transfer less of it to the motor and the crank. Every motor has an area in which it can develop the greatest power from the available energy.

At the automobile it's similar. There is a point on the torque curve where the best power is delivered. Example: A motor has a torque of 155 Nm at a speed of 4000 rpm. This then corresponds to an output of 64.9 kW or 83.3 PS. The combustion engine does not work below a minimum speed. It cannot start running like an electric motor. At low speed the car accelerates poorly, starting at traffic lights without a clutch or in third gear, the engine stalls because of the too low speed and the lack of torque in the torque cell. How wide or narrow that optimal speed range in the car, it depends on the engine characteristics (displacement, turbo support, valves and control ...).

It's similar with the e-bike.

### The cadence also determines the range

In a discussion in the Facebook group “E-bike + pedelecs, exchange, information, tours, and more without tuning” on our article called “E-bike motor: Which incline can my pedelec manage?”, A development engineer even went to work , effectiveness and Heat loss at the E-bike motor arithmetically to be estimated.

I am quoting his post here with his consent, slightly abbreviated:

Now I wanted to know how big the influence of the cadence is and have calculated a small example for this ... There are three different types of losses in machines ... The electricity heat losses are the dominant ones, so I only look at these in the example. For this I have assumed a few values ​​and calculated the difference for cadence rates of 50 1 / min and 85 1 / min.

His calculation is based on an output of 150 W, i.e. a medium support level for the e-bike motor:

Here is the link to the discussion, you have to be a member of the group to see the article and the comments.

His result:

With the low cadence of 50 rpm and medium pedal assistance / speed level (power: 150 W) they are Electricity heat losses three times as large as at 85 1 / min. The efficiency of the motor is at only 50 revolutions per minute by 24.5% lower than at 85 rev / min!

In practice are the flat stretches, slight inclines or headwind passages that you drive. Especially those tempt you to drive lazily, to pedal more slowly. For example, the e-bike pedalist may be on the road quite often with a sub-optimal effectiveness, and may be surprised about a range that is 30% less than specified ...

A calculation with 250 W (the maximum power for a Pedelec motor) still results in a difference in effectiveness of 82% to 93%. In practice: Especially on stretches where the high or turbo mode is used, if the cadence is too low, ten percent of the power is wasted on heat production.

Both on straight stretches and on inclines, in headwinds, on longer climbs - where the battery is particularly demanding - I actually get a slightly better range overall at the end of the day with a higher cadence because of the better use of power by the motor.

### Bosch range calculator correct?

In the range calculator from Bosch eBike Systems, the difference between, for example, a cadence of less than 60 rpm versus> 70 rpm is reflected with a difference of only approx. 2 km range. The range decreases again slightly in the ranges from 90 rpm. Is that really true with a difference of only 2 km? I read on the excellent website of Elektrorad-Mott that he thinks that too little:

The exact cadence rpm is unfortunately not shown on the BOSCH display. What helps is the switching recommendation, which appears as small triangles in the BOSCH display. It shows whether you are pedaling too slowly or too quickly. Many pedal too slowly, which experience has shown is reflected in the power consumption much more than the BOSCH range assistant calculates. (Source)

Some other comments on Facebook also speak from our own observation that a pedaling frequency that is too low has a more significant effect on the range. Just like the calculation shown above speaks for it. Maybe Bosch can explain this to us?

One final note on engine technology: One Upper limit not only applies to the speed (max. 25km / h), but also to the cadence from which the motor no longer delivers power: the Yamaha PW motor supports cadence of up to 100 rpm, the PW-X motor up to at 120 rpm. Motors in S-Pedelecs provide further support.

In addition to the engine technology and battery range, don't forget: That too Material load chain, pinions, gears, etc. is higher at low cadence.

Aside from the technology, there are other advantages of slightly higher cadence:

### Better blood circulation and more protection for the knee joints

At high cadence, the phases of tension are shorter, so that the blood flow within a muscle is only briefly disturbed. During a contraction, the blood vessels are compressed and the circulation of the blood is impeded. But this is important for the transport of oxygen and nutrients. The metabolic intermediates such as B. the lactate are better transported away with a good blood flow.

A higher cadence is better for the joints - the peaks are shorter and often lower. A cadence of> 75 revolutions per minute is recommended by sports medicine. Incidentally, as a patient in rehab, you will be trained to 75 rpm - this is the lower limit to keep knee loads as low as possible.

### The optimal e-bike cadence - for leisure, tours, mountains and trails

As already described in the introduction, there really is the optimal cadence: The cadence at which you have to use the least amount of force for the same performance.

Expressed in numbers and viewed from the engine, it seems to be between 70 and 90 revolutions per minute. From a human point of view, also from 75 rpm, which I take from the recommendation of rehab doctors for training that is as gentle on the joints as possible.

The overall human / motor system could therefore work most efficiently around 75 rpm.

Regardless of whether on a straight route, in a headwind, on inclines ... according to the above, this applies not only to the very sporty ones on the trail, but also to all e-bike riders from beginners to leisure and touring riders, commuters and many others E-MTB riders of every engagement.

To maintain the ideal cadence is switch hip, trendy, popular. With the many options that are now available, choosing the most suitable circuit is a different story. Just like that Responsiveness and the Character of performance development with the engines. Yamaha's PW-X, for example, responds faster than the Yamaha-PW and is therefore even better suited for starting up on steep places and obstacles. The upcoming Flyon with TQ engine (more about the Haibike FLYON) is also presenting with the new gearbox. Here too: more in this theater soon!