Lets design an electric bicycle.
Our bicycle will have a number of components:
- the bike
- an electric motor, linked to the wheels somehow
- battery pack to provide power
- motor controller to regulate how much power goes to the motor
- Charger
Where do we start? We will start by calculating how much energy is needed to propel the bicycle. From there, we will know how much power we need to feed our motor. This will define requirements for our battery pack, which will help us design a battery pack. Because battery cell voltages and sizes are fairly standard, we’ll find that certain voltage motors will decrease the number of batteries we need. They will work better with our battery pack (this makes choosing the motor easier!). Our controller can then be chosen. We need to find one that can link our battery pack to the motor. With all this put together, choosing a charger mostly involves finding a suitably sized quality charger on the market.
Power Required to Propel Our Vehicle
The Power Output (Po) required by our vehicle is made up of four componenets:
- Power to overcome aerodynamic drag
- Power to overcome road drag
- Power to overcome inertia (when accelerating)
- Power to overcome gravity (when going uphill)
Go read this link, because it covers each part of the equation: link. I really like that page because it actually says what each term means! Can you believe it? If this revolutionary idea made its way into textbooks, maybe people would enjoy science, rather than feeling left behind… but anyway… Here’s another link that’s more theoretical but has a useful picture, and the beginning of this explains power and torque.
Note that the v3 term in the aerodynamic part of the equation grows much faster than any other term as velocity increases. This is why it is so important to have an aerodynamic vehicle. There are two main parts to the drag portion of the formula– coefficient of drag, which describes how aerodynamic the surface of our vehicle is, and frontal area. A Hummer, which has a drag coefficient half as great as a brick wall and a frontal area larger than most other cars, will get terrible mileage because at higher speeds it needs to output a lot of energy to overcome aerodynamic drag (at low speeds, it is heavy and the inertial term is large!). Compare the hummer to a jet airplane to understand the coefficient of drag. The jet is sleek and has nothing jutting out abruptly. Everything is smooth.
Now realize that we will actually need to input more power into this system. Why? Because we lose some energy in the drivetrain, some in the controller, and mostly, a chunk in motor efficiency. A survey of motor data sheets shows that motor efficiency falls between 70% and ~95%, with DC brushed motors being least efficient, brushless DC motors slightly more efficient, and 3 phase AC motors most efficient, though this is a vast simplification (small AC motors can be as inefficient as brushed DC motors). Controllers are roughly ~95% efficient, losing some energy as heat in the transistors that deliver power from the batteries to the motor. Drivetrains vary greatly. A simple chain drive is 98% efficient when clean and well maintained (Bicycle Science, 3rd ed, and one other source available online), whereas an automobile automatic transmission, because it has so many moving parts, can be quite a bit less. There are many other classifications of motors and some other technologies, but they are out of the scope of this work.
Batteries
Now with that worked out, lets talk about batteries.
Let me cover a little theory about batteries first. Batteries store energy. They are rated by their voltage (in volts) and capacity (in amp hours). Motor power is rated in watts, which is Volts x Amps. Note that the motor rating has no time component- there are no volt hours or amp hours in the equation. If you have a 12 volt battery that is rated at 10 Amp hours, it stores 120 Watt hours of energy. Hypothetically we could use 120 Watts of power from this battery for one hour, or 60 watts for two hours. It’s actually not this simple, but I’ll cover that later.
Now, you will probably be unable to find one battery that has both the right voltage and capacity to meet the needs of the vehicle. Luckily, we can link batteries together in two different configurations: series and parallel.
In a series connection, the negative terminal of one battery is connected to the positive terminal of another. The bike motor is then attached to the remaining terminals. In series, voltage adds. Two 12v 10ah batteries become a 24v 10ah battery.
In a parallel connection, the positive terminals are linked together and the negative terminals are linked together. The bike motor can be attached to either battery. In parallel, the capacity adds. Two 12v 10ah batteries become a 12v 20ah battery.
There is a short hand notation for the series-parallel arrangement. A 2p2s pack has 2 sets of batteries in parallel. Each set of batteries is made up of two cells in series. Some people write the shorthand backwards, i.e, 2s2p.
There are a number of battery chemistries out there, but Lead Acid, NiMH and NiCd, and Lithium Ion are the most popular. Lithium Ion describes several similar chemistries. For example there are lithium iron and lithium cobalt chemistries.
Lead acid batteries are used in today’s cars to start batteries, but they are heavy and do not store much energy. They also do not have long shelf life (how long they can be stored before they won’t charge) and cycle lives (the number of times they can be charged and discharged before they wont charge to more than than some percentage of their original capacity). They are, however, relatively cheap. You can find 6 volt, 12 volt, and 24 volt batteries at automotive stores.
NiMH batteries were used in production electric vehicles in the 90s. They have long life spans if not discharged too quickly or too ‘deeply.’ They are more expensive than lead acid batteries, and very expensive except in small sizes (like AA cells, C cells, etc) for numerous reasons, including a patent on ‘large format’ batteries. This means you have to link many batteries in series and parallel to get the desired voltage and capacity. The one difficulty there is that NiMH batteries don’t charge well in parallel. It works, but they need to be balanced periodically. This might be more effort than some people are willing to take.
Nickel Cadmium batteries are used in power tools and watches. They are similar to Nickel Metal Hydride batteries, but contain toxic cadmium. They’re getting a little harder to find these days, so the price for a cell varies widely.
Lithium Ion cells are even more expensive than NiMH, but a cell comparable to a AA NiMH has 3x the voltage of a NiMH cell. I will explain why this is important later. Lithium Ion cells suffer from one other problem– like lead acid cells, they degrade over time. The degredation depends on how hard the cells are used and the environmental conditions under which they are stored and used. Heat is bad, and laptop cells lose about 20% of their capacity per year. Tesla Motor’s water cooled Lithium Ion battery pack is projected to lose 30% capacity over five years. A lithium ion pack needs to be sized appropriately to account for this loss of capacity. Lithium Ion cells hold a lot of promise because of their widespread use in electronics. Many industries would greatly appreciate better lithium ion batteries. Oh, and they charge in parallel just fine. One additional note: the cases of ‘exploding’ lithium cells has to do with ‘abuse’ of the cells. When a battery starts failing, it becomes less a source of energy than a resistor. A resistor with current flowing through it heats up. Lithium cells generally do not like heat, it’s one of those environmental factors that decreases their life span. So when one possibly flakey cell starts to go bad, and a battery pack has no safety measures to shut down if excessively heated, that cell heats up, which heats up the other cells around it, which start to fail too, until a cell gets so hot that it ruptures. Simply adding a thermal cutoff prevents this situation from escalating.
Now that we’ve covered all that, let’s get onto the one nasty detail. Discharge current is measured in amps. Discharge rate is measured as a multiplier of the battery capacity (a number followed by the letter ‘C’). What does that mean? The 10ah battery from above, if discharged at 10 amps, is being discharged at a 1C rate. If it’s being discharged at 20 amps, then the discharge rate is 2C. This also applies for charging. A battery can be charged at 0.5C rate, or 2C, whatever.
Supposedly, an ideal 10 amp hour battery should also be able to provide 1 amp of current for 10 hours, or 10 amps for 1 hour. No. hours x Amps = Capacity then, right? But this is actually an approximation. Real life batteries are not ideal, and their useful capacity decreases with increasing discharge rate.
A German scientist named Peukert in the late 19th century devised an equation to express the actual capacity of a battery based on the discharge rate. You can read about it on Wikipedia. There’s a Peukert number for batteries. This number is an exponent in Peukert’s equation and it describes how far batteries deviate from this ideal when discharged. Go ahead and look up the data sheet for a NiMH AA cell. The manufacturer will state the capacity, and then an ‘apparent’ capacity when discharged at a certain rate. This apparent capacity is always lower. What this means is that when you work your batteries hard, they will discharge faster than you’d think. To minimize this problem, you can add more capacity to the system, use batteries that have a better Peukert number, or increase the voltage of the system. The latter works because remember power = voltage x current. If you keep the power requirement the same but raise the voltage, the amount of current you need drops– so for the same battery, the discharge rate is lower.
Lead acid batteries perform very poorly when discharged quickly. NiMH and NiCd allow higher discharge rates, but they are still not too great. Lithium Ion cells have the best Peukert number and can endure very high discharge rates. Expensive lithium polymer cells do even better.
The consequence of all this is that to make lead acid battery packs, you have to build in a lot of spare capacity. Since the cells are so heavy, this adds additional weight, which requires additional power to move, which means you need more power from the batteries, which means more batteries… the problem escalates.
NiMH and Lithium Ion cells are considerably lighter. Lithium ion cells, however, have almost 3x as much voltage per cell as NiMH. This means you need less of them overall if you build the pack right. However, they also cost more than 3x as much as NiMH cells.
To figure out which batteries to use, we need to consider the following factors:
- Cost per Amp hour
- highest practical system voltage
- Cost/difficulty to charge
- We can then determine a suitable pack size and its cost
One easy solution to the NiMH parallel charging problem is to charge each series set of cells with a separate charger. If our pack uses 20 cells in parallel, then we would need 20 chargers, which would be too expensive. If we use only four cells in parallel, having four chargers would probably be practical.
It’s tempting to increase the voltage up, up, and away because then Peukert’s Law has less effect. However, practically, 500V would be great, but we’ll never find a bicycle motor or a controller that uses 500v. Common motor ratings are 24v, 36v, and 48v. Some motors can be run over their rating, up to about 72v. So you’ll want to head for higher voltages, but make sure to weigh the cost of these components. If a 24V motor and controller costs $40, and a 48v costs $300, yes, you will have some savings by going to 48v, but could you get the same benefit by spending less than $250 on more batteries?
Controller
The most popular brand of controllers are manufactured by Crystalite. I believe these cost roughly $150. From what I have seen on the bike forums, these do NOT survive going up to 72v. To reach those voltages, you have to open the controller up and replace the transistors (MOSFETs) with models that can survive such voltages.
Kollmorgen 300W to 400W motors have a built in controller, but they must absolutely not exceed 24v.
Another consideration is whether the controller allows regenerative braking. This is when you let off the throttle and apply the brake– the motor is run ‘backwards’ and generates energy which it pumps back into the batteries. One other much simpler variation of this braking scheme does not charge the batteries (as this can be complicated) and instead dumps the energy into a coil of wire. The coil of wire resists the flow of energy, and heats up. In either case, you end up having a brake that doesn’t need to have pads adjusted or maintained. You can always make your own braking setup with a coil of wire, a permanent magnet motor controller, and a relay. The motor controller is wired up backwards– taking its input from the motor, and outputting to the coil of wire. The relay is necessary so that the braking controller and motor controller aren’t on at the same time.
Chargers
I haven’t quite gotten here yet.
Mind you, I did ride the recumbent bicycle a good deal without electric power!
