Analysis of Katanka’s Amoanimaa EV
On the 12th of August this year, I posted what was initially meant to be my thought process around analyzing the feasibility of Kantanka’s new EV which took Ghana by storm. It almost sounded the dawn of a new era in this part of the world, but before we would dance to the tune of this sound, we had to make sure that it harmonized with the practical lives of the everyday Ghanaian. I was overwhelmed by the response, and it was a massive revelation to me personally that it was of interest to many Ghanaians.
Indeed, in the ideal world, it makes absolute sense to embrace the transition to Electric Vehicles over combustion vehicles. They are far more efficient (80% — 90% compared to 35–45% for combustion engines), they drastically reduce emissions because they are powered by electricity, and for the performance lovers, electric motors (specifically, the commonly used three-phase, four pole induction motors) are able to produce near maximum torque from 0 rpm (revolutions per minute) which is amazing for drag races. Also, the efficiency is multiplied by the fact that they barely need a transmission. Having gears is very good for finding the right torque and speed balance, but they introduce efficiency losses via friction and heat into the system. Since electric vehicles barely have any of that, they can really show off how efficient they are. Nevertheless, all these advantages are not enough to drive EV adoption in Africa or anywhere in the world for that matter. They might make sense environmentally, but an extra stride has to be made for them to make sense practically. To make this happen, these are the things that have to be taken into consideration:
- Battery Technology
- Aerodynamics
- Performance parameters
Battery Technology
Battery technology is the major maker and breaker of Electric Vehicles. There are different types of batteries and the most important parameters of batteries to take note of are the following:
- Battery Capacity — This is a measure of how much energy can be stored in the battery. Electric energy is measured in Wh (watt-hours) or Ah (amp-hours). In electric cars, it is usually measured in Wh or kWh(kilowatt hours). The higher the battery capacity, the more energy is available and thus the farther the car can travel.
- Discharge rate — The discharge rate of the battery talks about how much current can be discharged at every point in time by the battery. The more current that can be discharged, the more power that is made available for the motor to use, meaning the faster the car becomes or the more the car gets the ability to carry heavier loads. Discharge rate is measured in a value called ‘C’. When a battery is rated 1C it means it can discharge 1 x the value of the battery capacity.
- Energy density — This refers to how much energy can be stored in relation to either mass or volume. It is measured in watts/kg or watts/m3. Energy density is very crucial because the higher the energy density, the more energy you get out of a smaller battery meaning you can save more weight or space which is excellent for getting your electric vehicle to travel both farther and faster.
- Depth of Discharge (DoD)- This refers to the optimum amount of a battery’s capacity you can use before recharging to increase the longevity of the battery. It is measured as a percentage of the total battery capacity.
- Charge rate — This refers to how much current can be ‘injected’ into the battery during charging without damaging the battery. This is very important for determining how fast the battery will charge.
There are different types of batteries. This is due to their chemistry (the type of chemicals used for their anode and cathodes). Back to our Chemistry, we know that redox reactions lead to release of electrons which give us energy. The elements that comprise of the chemicals used in the batteries also have different properties as per what we see from the Periodic Table. This affects the overall performance characteristics of the battery. For the sake of this post, we are only going to focus on rechargeable batteries. Some of the most popular of these batteries are:
- Lead-Acid batteries (Usually used for car batteries and small scale solar systems.
- Lithium Ion (Usually used for power banks, electric vehicles, rechargeable batteries for laptops, and some toys)
- Lithium Polymer (Usually used for toys, tiny electronic devices, laptops, phones, drones and other RC vehicles)
- Nickel Metal Hydride (Usually used for toys, tiny electronic devices, drones and other RC vehicles)
The most popular batteries used for electric vehicles are lithium ions because they have very high energy densities and have really good discharge rates and impressive depth of discharges. However, all these advantages are offset by their high costs. Around the world, there are efforts to try to reduce the cost of Lithium ion batteries using economies of scale so that electric cars will make more sense. However, Kantanka motors took a bold step to use lead-acid batteries. It is understandable due to its relatively lower cost. But will it be enough to spark an EV adoption in Ghana? Let’s find out.
Disclaimer: Prepare for some back-to-school physics lessons. Not to worry though — you will love it!
First of all, we have to pull up the characteristics of the lead-acid batteries. To do this, I looked up standard manufacturer specs for lead-acid batteries from this site:
The best one I could find was the last one which produces 12V with a capacity of 100Ah and a volume of 343 x 172 x 213 mm with a mass of 33kg. To get the capacity in Wh, we multiply it the capacity in Ah by the battery’s nominal voltage, like this:
12V * 100Ah = 1200Wh = 1.2kWh.
This is for one battery. To get more power, you can either set it up in parallel or series. Setting the battery up in series gets you more voltage but same capacity and discharge rate while setting it up in parallel gets you the same voltage but more discharge rate and capacity. So If we set up 3 of these batteries in series we will get 1.2kWh but 36V (12*3V). If we set it up in parallel we get 12V but 3.6kWh (3*1.2kWh). Not only that. lead-acid batteries have a discharge rate of about 1C. This means that the max current we can draw from this battery at any time is 100A for one battery and 300A for three batteries in parallel. Power = Voltage x Current
Therefore the max power we can get is 1.2kW for a single battery and 3.6kW for three batteries in parallel or series. However, batteries are usually set up in parallel because before the energy gets to the motors, it is taken through an inverter. The inverter converts the DC (direct current) from the batteries to 3-phase AC (alternating current) like the ones we use in our homes. In this case, it is quite advisable to set up the batteries in parallel for maximum capacity and maximum current discharge as this will give more range to the electric vehicle. Thus at maximum power for three batteries, we get 3.6kW. To convert that to the horsepower available to the motor, we divide that by about 740. That gets us about 4.8 horsepower without accounting for battery discharge efficiency, inverter efficiency and motor efficiency which will reduce the horsepower to the wheels. Note that the motor horsepower is different from the battery horsepower. The motor can produce higher horsepower but is effectively limited by the amount of power coming from the battery.
Aerodynamics
The aerodynamics of the car is very important. Because air is a fluid, it possesses some amount of viscosity which generates resistance against objects moving through it, which we usually refer to as air resistance. Engineers call it aerodynamic drag. Aerodynamic drag is usually measured with a value called Cd which means drag coefficient. This is a non-dimensional value which tells how easily a body will cut through the air or will experience little resistance. The lower the value, the more aerodynamic the body, or in this case, the car will be. The Cd, along with other parameters are used to calculate the Drag Force acting against the car. Drag force is given by :
To be able to calculate the drag force, I assumed that the Kantanka Amoanimaa EV had a drag coefficient of 0.344 (which is the same as that of a Daewoo Matiz since they are of a very similar form factor). But as Melinawo (Twitter Handle: @meli_nawo) pointed out, it would be better to rather use an empirical technique which involves analyzing the airflow around the planform of the vehicle to determine the drag coefficient of the vehicle. I stuck with this value because several cars of the at same form factor have an average drag coefficient of around 0.32 to 0.36. I also estimated the frontal or cross-sectional area by multiplying the track-width of the vehicle (Daewoo Matiz) by its height minus some heuristic value leading to 1.5m2 . Melinawo also criticized this technique and would be better to get the actual dimension of the frontal area either from a CAD (Computer Aided Design) file or from some specification sheet. I however stuck to this because of the information available to me. However, I see this as a fair assessment of the vehicle. As and when I can get more accurate specifications of the vehicle, I can make a more accurate analysis.
In order to find the drag force, I also assumed a constant velocity of 60km/h. For electric vehicles, they usually use a constant velocity of 60mph which is about 100km/h. However, I felt 60km/h was cool as an average speed of town driving in Accra. Any other opinion is welcome and as Melinawo also pointed out (again! Wow, this guy was just giving back-to-back feedback), it would be great to analyze it at varying speeds, because the nature of the air changes (laminar to turbulent) as speed changes and can lead to a sharp increase in drag. Please keep in mind that I also laid out this process so that you guys can make your own analyses using different parameters of your choosing and further draw more insights. The assumed density of air was also 1.225kg/m3. The drag force on the vehicle at 60km/h will be:
60km/h = 16.67m/s
Fd = (1/2)*0.344*1.225*(16.67)² = 58.55N
Performance Parameters
From the information we have gathered so far, we can now calculate things like range, endurance (running time) and the optimum balance between range and performance for the electric vehicle. I don’t know how many lead-acid batteries Kantanka decided to use, so I just made a spreadsheet of the number of batteries and their resultant performances. These are the calculations I made:
Initial car weight = 650kg
Depth of Discharge = 70% — Evans Addo (twitter handle: @EvansAddoK) pointed out that the standard depth of discharge for lead-acid batteries was typically 50%. This is true, however from some graph I pulled up from academia.edu, 70% was not too bad a difference from 50%:
Speed: Constant 60km/h
To calculate power consumed by the vehicle, the formula is:
Power = Force x Velocity
We can also use Power = Torque x Wheel radius x wheel angular velocity. However, for simplicity we are just going to stick with the first one.
Total Force needed to move the vehicle at a constant 60km/h = Forward Force + Force needed to overcome drag force.
Forward force = Coefficient of rolling resistance*Weight of vehicle
Coefficient of rolling resistance is the coefficient of friction, mu for bodies with wheels.
Drag force is 58.55N from the previous calculations
Power = (Forward Force + Drag Forcce) x Velocity
But it doesn’t end there. I factored in the efficiencies like
motor efficiency = 95%
Inverter efficiency = 95%
Therefore,
Power = (Net Force) * Velocity * 1.05*1.05
To find the car endurance, which is the amount of time the car will be running for:
Endurance (Time) = Battery capacity/power. I factored in the Depth of Discharge so that will be
Endurance (Time) = DoD * Battery capacity/power
Range (Distance) = velocity * endurance
Then I put all of these up in a spreadsheet to find out the vehicle will perform using more batteries. This was the result:
The sweet spot for me was 9 batteries, which would give a range of about 139km when no one is sitting in it. If we factor in the weights of adults, we get a shorter range. On Kantanka’s side though, they would optimize for the economic cost of getting more batteries as well as how much space the batteries will take in the car.
What does this all mean in Real Life?
If we assume my sweet spot, it means that for a single charge, you will be able to cruise around for about 120km before the battery dies. But you will have a heavy car, and this will affect the handling of the vehicle.
Is it cheaper than running your normal Matiz?
The answer is roughly a yes. In my first analysis, I thought it would be three times cheaper than fueling a Matiz because I used the household electricity tariff of 0.369 cedis/kWh from:
but Evans Addo pointed out to me that it was infact about 0.93cedis/kWh. I verified this after I checked online again for Ghana’s Public Utilities Regulation website:
Using the same parameters I did for this tweet:
That will be 0.186 cedis/km. From the tweet, the 0.1cedis/km was just a rough mental estimation. The 0.186 here is a more accurate one. So being twice as cheap, would it be good for Uber? That depends on the cost of buying the vehicle, and the time it takes to charge — which eats up into potential money made from customers. Herein lies the problem with lead-acid batteries. They take a really long time to charge. Charging at about 17A from 0–80% and about 5A from 80 to 100%.
We know that the capacity for each battery is 100Ah. so if we charge at 17A, it will take 5.88 hours to get to 80% and an extra 4 hours to get to 100% leading to a total time of 9.88 hours to get from 0% to full battery. However, the good news is since our depth of discharge is 70%, we actually start charging from 30% so it will take
50/17A =2.9 hours to get to 80% and 4 hours to get to 100%. If we are charging 9 batteries, that will take 6.9 * 9 = 62.1 hours to fully charge all those batteries.
But do not fret!
If we have a charging infrastructure that can charge even 3 batteries at the same time, we can cut the charge time by 3 giving us 20.7 hours of charge time. That still isn’t good enough, but it’s also easy to beef up the charging infrastructure to get even up to 9 at the same time, giving us the normal 6.9 hours to charge. In this case, you can charge your car overnight, but you would have to spend more on charging infrastructure. (If Kantaka is interested, I’m actually working on a charger design that can do multiple batteries at the same time).
Is it good for long distance travel?
Not at all. It will only get you through town travelling. You can’t even do from Accra to Cape Coast on that juice. It will die on the way. But this problem is not only limited to the Kantanka EV. It’s also limited to most small EVs. Although the ones that use lithium ions will make you go much further. Maybe Cape Coast and back.
How’s the performance like?
If we are running on 9 batteries, we can get about 43 horsepower. That will give you a slower top speed than the Matiz, but it sure will give you a faster acceleration since it will be able to access all its torque at 0 rpm unlike the Matiz.
Overall Verdict
As Matt Watson of CarWow would say, Should you
- Avoid it
- Consider it
- Shortlist it
- Buy it
I would say, this car may not be as practical as a Matiz, but if you find that you can live within the means of the performance and range the car can give you and if you are passionate about saving the environment, go ahead and shortlist it. Thank you.
