# Sizing your Battery Pack



## b.koen (Mar 9, 2008)

*Re: Sizing a battery pack*

mattW

added a couple of commas, hope you don't mind, just thought it helped for clarity. nice article, wish i had something similar awhile back, should be helpful

b.k


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## Cymen (May 11, 2008)

*Re: The Four Steps To Sizing a battery pack*

That was quite helpful but it was odd how steps 1-3 were a straight forward calculation and then step 4 is not. Is that because step 4 depends so much on the chosen battery?

My calculations looked like this for a theoretical 80 mile range with a motorcycle (using some numbers from the example calculation):



> Step 1 (Top speed):
> 
> 72v / 12 = 6 batteries
> 70-100 Wh/mile
> ...


As mentioned, this is theoretical. 660 pounds of batteries on a motorcycle frame seems a bit much but I'll keep reading. I can see how battery technology is the #1 concern. My commute is 37 miles one way .


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## mattW (Sep 14, 2007)

*Re: The Four Steps To Sizing a battery pack*

motorcycle range is pretty limited by the size and weight restrictions. I am going with a 72V 60Ah lithium pack and am hoping to get 50 miles (80km)


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## jsmith20 (Aug 1, 2008)

I'm new here so forgive me.

Step 3. says 

" When sizing the battery pack we need to make sure that the batteries we choose have an Amp-hour rating of 187 or better to achieve our range of 40 miles."

Does this mean that each battery in your pack should have an Amp-hour rating of 187 or does this mean that your total pack should have an Amp-hour Rating of 187? 

Also, can you explain batteries in strings, I noticed if I use the calculator on EVconvert.com and I have a 144v system if I have 2 strings my range goes up.

Does this mean that I need 2 strings of 72v or 2 strings of 144v?

Also, I plan on using the Odyssey PC1500 (specs found -->) for my conversion. Am I supposed to be looking at the 20hr rate ah http://odysseybatteries.com/batteries.htm

Obviously I'm new and I'm trying to figure out my batteries before I go off and drop a load of money on them

Thanks for the help,

James


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## TomA (Mar 26, 2009)

Alternative Rule Of Thumb for LiFeP04 batteries:

It seems, based on the rather scant available data, that the new Lithium Iron Phosphate prismatic cells have a rough energy equivalent in gasoline:

8kWh of LiFeP04 cells = 1 gallon of gasoline

This is not an actual energy comparison, but a practical guideline number to compare ICEV and BEV efficiencies. Its really useful, because in most cases, the fuel efficiency of an ICE powered glider is known- if your Honda got 30mpg before converting, and you didn't add 800lbs to it in the process, then it probably will take 8kWh of Lithium pack capacity to go 30 miles. An interesting, simple and useful conversion tool. Remember to calculate _usable_ pack capacity, which in most cases is really 80% of the actual pack capacity as usable capacity (above whatever your DOD cutoff is.) 

Not a precise calculation here, but its pretty accurate, and very useful in sizing these packs, particularly where you know how much fuel the car used as a fossil fuel burner. It also kind of elegantly self-adjusts for driving conditions and style- if you got only 20mpg driving your Honda before the conversion, don't expect to get more than 20 miles from it per 8kWh of usable pack as a LiFePO4 EV. 

If nothing else, its a nice way to triangulate your other range and speed calculations with battery capacity.

Does not apply to other battery chemistries...

TomA


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## dmac257 (Jun 30, 2010)

I have read and re-read your explaination. Just want to know if your calculations are all based on the top speed. Range would be a function of how fast you are discharging the batteries. If you only do one moderate acceleration .. and only do 45mph .. the range should be a lot higher than if you are doing frequent quick starts and higher speeds, right? If you have a car capable of 0-100 in 12seconds .. but you dont really drive that way.. how do you adjust the calculations for the "normal" way you drive?


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## Franky.EV (Feb 27, 2010)

Have a look at http://www.diyelectriccar.com/forums/showthread.php/yes-another-ev-calculator-45278.html dmac257.

What you've said is correct, and the it's easy to understand with a graph.

In this calculator, the left part gives you what's required to move the car at the selected speed, and how far you can go if you stay at that speed.

The right part is how fast you accelerate if you use full power.

I also manage the gearbox, and take into account shift time. If you want to stay simple, you can use, a reduction gear instead of a gearbox.

You can modify any blue text parameter in the spreadsheet.
You can also modify the gearbox, motor, batteries tables to fit you needs.


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## kothapalli (Jan 7, 2011)

Assumed Gross weight of vehicle = 1500 kg
Desired top speed = 30 Km/h
Desired Range = 100 Km 
Coefficient of rolling friction (μr) = 0.015
Density of air at 20° C = 1.2 kg/m3
Acceleration due to gravity (g) = 9.8 m/s
Voltage of the electric system = 48V



Force of rolling friction Froll = μr n
= 0.015*1500*9.8
= 220.5 N

Air resistance force (at 30 Km/h) Fair = ½ CdAρv^2
= ½ *0.5*1.8*1.2*8.34^2
= 37.56 N

Power required to maintain the constant speed of 30 Km/h
= (Froll + Fair) v
= (220.5 + 37.56)*8.34
= 2152.22 W

Time taken by the vehicle to cover the desired range at 30 Km/h
= 100 / 30
= 3.34 hrs

Current consumed to generate a constant power of 2152.22 W (IDC)
= 2152.22 / 48
= 44.84 Amps

K-factor for 3.34 hours of back up = 4
Depth of discharge of batteries = 80%
Depth of discharge Factor = 1.25
Temperature deviation of battery performance = 10%
Temperature factor = 1.1
Design Margin = 10%
Design Factor = 1.1

Final Ah rating = IDC*K-factor*Discharge factor*T-factor*Design Margin
= 44.84*4*1.25*1.1*1.1
= *271.282 Ah*


The requirement is either 8 X 6V or 4 X 12V batteries with a capacity of 280 Ah or more.

Is my calculation correct? or did i put too much power for the requirement? Please help me, as i think this capacity batteries are not available (costly) and if i want to make one by connecting batteries in series, it will be too heavy. I'm very new to this. I started working on this only a week back. 

The subscript and superscript thingy is showing up there.
for your clarification,

Cd = coefficient of drag = 0.5
A= cross section area = 1.8 m2
v = velocity in m/s = 8.34
rho = density of air = 1.2


Thank you,
Uday


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## HyperactiveSloth (Jun 19, 2011)

Does the calculated amp/hour rating of the pack mean _each_ battery must have that rating, or the the _total_ of the batteries in the pack must equal that?

I have a hard time imagining a lead-acid battery pack with 187ah rating per battery.


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## GizmoEV (Nov 28, 2009)

The amp-hour (not amp/hour) rating of a battery is independent of its voltage. Current (amps) is a rate at which electrons pass a given point over a given time period. (See http://en.wikipedia.org/wiki/Ampere for more detail.) The voltage at which this happens doesn't matter. If a battery is 100% efficient then the Ah it has will be the same regardless of how much current is pulled out of it. For example, if our fictitious 100% efficient battery is a 100Ah battery then it could be drained in 1 hour if we pull 100A of current out of it or it could be drained in 2 hours if we only pulled 50A out of it. An amp-hour is derived from the current (A) multiplied by the time interval. With the 100Ah battery it doesn't matter what current is pulled or how long it is pulled as long as the product of the two add up to 100Ah.

Now suppose there are two of these perfect batteries, each a 100Ah battery but one is a 5V battery and the other is a 10V battery. The amount of *energy* stored in each battery is quite different but the Ah capacity is the same. In both cases if we pull 20A out of each it would take 5 hours to drain each one. But that 20A current will be at 5V for one battery and 10V for the other. (Remember we are talking about a perfect 100% efficient battery so the voltage doesn't sag.) Power = Volts * Amps so the power out of the 5V battery is 5V * 20A = 100VA or 100 Watts. The power out of the 10V battery is 10V * 20A = 200W. Similarly the energy stored in each battery is 5V * 100Ah = 500Watt-hours and 10V * 100Ah = 1000Wh = 1kWh.



> Does the calculated amp/hour rating of the pack mean _each_ battery must have that rating, or the the _total_ of the batteries in the pack must equal that?


The answer to your question is *YES*. Both the pack and each battery has the *same* Ah rating but the energy stored in each battery is naturally less than the amount of energy of the whole pack.

For lead acid batteries they have a significant internal resistance so the higher the current drawn from them the fewer Ah you can get out of them. For example, I helped the local community college convert a Mazda Pickup and the battery pack is made up of 24 Trojan T-105 batteries. These have a 225 Ah rating at the 20 hour rate meaning if you draw a current of 11.2A it will take 20 hours to drain the battery. If the current is 37A, however, it will only take 5 hours to drain the battery it will only deliver 185Ah. Increasing the current to 75A will drain the battery in 115 minutes (1.917hr) so it will only deliver 143.75Ah. Since lead acid shouldn't be drained beyond 80% there are really only 115Ah available to drive with. As you can see if you take half of the 20hr amp-hour rating of a lead acid battery and use it as the capacity available to drive an EV you will be reasonably close to what you get.

From my experience and many others with LiFePO4 cells the Ah rating of the battery is really close to the same as long as the currents are not extreme so for all practical purposes if a LiFePO4 cell is a 100Ah cell you have all of it available but should only use 80% or less to prolong the cell and not kill it by a full discharge.

Hope that helps.


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## HyperactiveSloth (Jun 19, 2011)

Hmmm, thanks, that answers my question.  Now I'm only confused by the fact that I've checked quite a few lead-acids and about the strongest I've found is an Optima Yellow Top with only 55ah. According to this that would be nearly useless. Back to the drawing board.


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## Ravishankar (Jan 26, 2009)

kothapalli said:


> Assumed Gross weight of vehicle = 1500 kg
> Desired top speed = 30 Km/h
> Desired Range = 100 Km
> Coefficient of rolling friction (μr) = 0.015
> ...


You might convert thus into a MATLAB script


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## Vince Stanley (Oct 1, 2008)

In the conclusion section it talks abour 800 Amps peak that come out of a 187Ah battery pack. Can this be calculated?


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## GizmoEV (Nov 28, 2009)

Vince Stanley said:


> In the conclusion section it talks abour 800 Amps peak that come out of a 187Ah battery pack. Can this be calculated?


Can what be calculated?


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## Vince Stanley (Oct 1, 2008)

GizmoEV said:


> Can what be calculated?


 
How do we know that a battery pack with 120V and 187Ah pack can produce 800A. How do we get to the 800 Amp value? Do we know from experience that a pack this size makes 800A or is there an math equation.

Does a 144V and 187Ah pack to behave the same as a 120V and 187Ah pack? I think the 144V would be higher peak amperage but I don't know where to start.


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## GizmoEV (Nov 28, 2009)

Vince Stanley said:


> How do we know that a battery pack with 120V and 187Ah pack can produce 800A. How do we get to the 800 Amp value?


Experience of someone mostly. For example my batteries are rated to 3C continuous. This means I can pull three times the Ah capacity value in Amps and remain in spec. Testing has shown that they can put out much more than this. I set my pack up to be a 200Ah pack so 3C would be 600A. Someone once tested one of these 100Ah cells with a dead short and got something like 2500A. I know Jack Rickard of EVTV has seen 1000A from a 180Ah pack so it stands to reason that 800A out of a 187Ah pack would be quite feasible. Note that the voltage of the pack is largely irrelevant.

800A out of a 187Ah pack is only 4.3C which is a relatively low current for the pack. CALB cells are rated to 4C continuous and something like 10C pulse even though they can do more.


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## Vince Stanley (Oct 1, 2008)

GizmoEV said:


> Experience of someone mostly. For example my batteries are rated to 3C continuous. This means I can pull three times the Ah capacity value in Amps and remain in spec. Testing has shown that they can put out much more than this. I set my pack up to be a 200Ah pack so 3C would be 600A. Someone once tested one of these 100Ah cells with a dead short and got something like 2500A. I know Jack Rickard of EVTV has seen 1000A from a 180Ah pack so it stands to reason that 800A out of a 187Ah pack would be quite feasible. Note that the voltage of the pack is largely irrelevant.
> 
> 800A out of a 187Ah pack is only 4.3C which is a relatively low current for the pack. CALB cells are rated to 4C continuous and something like 10C pulse even though they can do more.


 
Thanks, that helps. Summing up so I understand; Capacity rate dictates controller size to an extent.

The Gizmo is impressive, excellent work.

Vince


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## GizmoEV (Nov 28, 2009)

Vince Stanley said:


> Thanks, that helps. Summing up so I understand; Capacity rate dictates controller size to an extent.


Many controllers have settings to limit, among other things, battery current. For example, you could have a 1000A controller but limit battery current to 500A. The controller could still send 1000A to the motor but at a voltage lower than your battery voltage. To make it easy assume you have a 200V battery that doesn't sag in voltage. 200V * 500A = 100,000W or 100kW. At the motor it could see 100V * 1000A = 100,000W or 100kW also. This is ignoring losses in the system.

You don't want to size a controller smaller merely because your battery pack isn't capable of (or you don't want to push it) putting out the max current the controller can. Most of the time the battery current will be below the motor current, especially when you have a pack voltage higher than what the motor is set to take and you have the controller limit motor voltage. The Warp9 is rated to 170V, IIRC. If you have a 200V pack and have the controller limit the motor voltage, the motor current will always be above the battery current.



> The Gizmo is impressive, excellent work.


Thank you. I've put quite a few upgrades in it since I bought it in 2006. It has been a fun, and useful, learning experience.


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## !George (Jun 9, 2009)

Fixed three typos that I found.


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## EVEngineeer (Apr 11, 2012)

I hope someone can answer me. If I get a Warp 9 motor with a 2006-present Honda Civic + all the other components for the EV, I would also buy LiFePO4 from either Thundersky, GBS, or CALB. I also know that I would need to get 45-55 3.2v batteries. I know it would cost over 10k, but i don't care about the cost. I just want to know the figures. The only thing that I don't know is how much ah is required. I have compared other vehicles on the evalbum and noticed that to get approximately 100 range at 30mph and 70 range at 55mph with somewhat less aerodynamic vehicles than the civic they had about 50 3.2v 100ah batteries. I would like to do a little better than that. I would like to get about 75 miles range at 65-70mph. For a little more efficiency I would put on racing hubcaps aka moon wheel hub caps. I would also like to have 80% DoD or better, maybe someone could explain my options. I saw somewhere that 70% DoD could be 3000 cycles instead of the 80% with 2000 cycles. I'd rather spend a little more to get much more life than to have to spend a lot more in a shorter time period to replace them all. So I guess the 75 miles range at 65-70mph with 80% DoD or better would actually end up being closer to 100 miles range. If I need to answer any questions let me know. Thank you.


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## adeyo (Jun 6, 2012)

I'm not trying to bury the previous post. Please don't look over EVengineers question above, but when that is dealt with, please advise.

Can anyone tell me, i have a motor that unfortunately is very high voltage (230/460 AC motor with 135/67.8 amp rating...60HP continuous). With an inverter, what voltage do i need my batteries at and what batteries do you think are best suited for that high voltage? 


(if EVEngineers batteries are 3.2 volt 100amp hour, wouldn't i be need 100 in series just to get close to my operating range? Is there anyway to use my motor and get the voltage i need with any type of battery??)

Sent from my PG86100 using Tapatalk 2


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## TomA (Mar 26, 2009)

EVEngineer, there's a very good rough number emerging from the growing fleet of LiFePO4 vehicles: The cars are using about 1 Wh per mile per 10lbs of curb weight- regardless of drive system. Some cars do a little better, some a little worse, and of course YMMV, but its a workable number. Here's how it would work with example numbers in your case:

Let's say your Civic weighs 2700lbs. Let's also say you strip 350 lbs of ICE gear out of it. Then you put back 250lbs of EV drive components and battery boxes, and 550lbs of cells. (45 180Ah prismatic cells.) That's a curb weight of 3150lbs. Using the good rough number, the car will use about 315Wh per mile.

The 45x180Ah pack has about 26kWh in it, about 20,750wH of which is usable to 80% DoD. Dividing that by 315Wh/mi, you can expect the car to have a usable range of about 66 miles on that pack. To get to 75 miles, you're going to need more batteries and more weight. 

Adding 5 more cells at about 60lbs puts the car over 3200lbs, and you'd have a 28.8kWh (23kWh usable to 80%DoD) pack that you'd be using at 320Wh/mile, so you could expect to go 72 miles on it. Another 5 cells for a total of 55 (now you have over 675lbs of batteries in the car!) brings the pack up to 31.7kWh (25.3kWh usable) and the car up to 3275lbs. At 328Wh/mi that pack should take you about 77 miles.

Of course, these are not precise calculations, nor are the curb weights actual, just all based on assumptions about your car, but it does give you a good measure of estimation. Weigh up your stuff and run your own numbers. You can improve efficiency (lower you Wh/mi consumption) with tire upgrades and pressures, aero mods and driving style, but I wouldn't count on all being worth more than 5%-10% if you really need the range.

The obvious conclusion from the example is that long range costs you big time. If you absolutely have to have 75 mile range, you're going to have to stuff 650+lbs of cells into the car. That will require suspension and chassis changes, and will flirt with the GVWR of the car. On a 4 door sedan, that could render your rear seats unoccupiable in some jurisdictions (in Australia, for example, they would de-rate the passenger capacity of the car if you were only a few hundred pounds under the GVWR.)

Anyway, that's how you run the numbers. YMMV, especially on stripped glider weight. Not precise calculations here, but actually very close, and a total fogbuster of blind optimism about range.

HTH,

TomA


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## GizmoEV (Nov 28, 2009)

TomA said:


> EVEngineer, there's a very good rough number emerging from the growing fleet of LiFePO4 vehicles: The cars are using about 1 Wh per mile per 10lbs of curb weight- regardless of drive system.


Tom, do you know if that average includes pickups too? I know that the number doesn't work for my Gizmo. Typically it ranges between 120-150Wh/mi but then it is quite a different shape. Curb Weight is 829lbs so about 875lbs with me in it.

It would be interesting to plot the data from the different vehicles on a graph to see if there are some general trends based on vehicle type or what happens at the extreme ends where I would guess my Gizmo would be.


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## GizmoEV (Nov 28, 2009)

EVEngineer,

Once you figure out what you need to 80%DOD you might want to consider increasing the size of the pack a little to account for the loss of capacity of the pack over time so that you still can get your desired range a few years down the road. Maybe size your pack for 70%DOD to give you a 10% buffer.


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## EVEngineeer (Apr 11, 2012)

gizmoev, yes i agree with adding more batteries, for that reason.

tomA, thanks for your help.


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## GizmoEV (Nov 28, 2009)

Also, based on my CycleAnalyst numbers 3.2V is a reasonable number for calculating Wh capacity for continuous currents in the 0.6C range. At least for my TS cells so I would think that CALB cells are a little better.


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## Robocar (Jan 6, 2013)

Wow, now I'm depressed. I was excited when I got a good deal on a motor for my old Nissan Pulsar but after reading this and checking battery prices a half decent running car is way out of my price range. I may as well just buy a golf cart to drive aroung like they do up in The Villages (retirement area in Florida).

I was hoping for 55+ mph with 40+ miles range minimum but a few thousand dollars in batteries is way out of my reach. Time for a new project.

Or I could put a couple resistors and vacuum tubes in a 2 foot box with a couple of rods sticking out and drive around with NO batteries.


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## Robocar (Jan 6, 2013)

Dang, I just missed out on 6 Trojan T-105 225ah batteries for $640 on Craigslist. That would have been a start, at least egtting the car running initially.


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## Ziggythewiz (May 16, 2010)

6 trojans...is that for the golf cart? I'd say that's a deal if they were new, but craigslist?


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## Robocar (Jan 6, 2013)

Yes. The ad said something about them being the wrong ones for the cart so when they got the right ones these had to be sold as used. Price included delivery but someone grabbed then already.


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## Robocar (Jan 6, 2013)

This might be a stupid question but has anybody tried buying a bulk load of NiCad batteries and built their own battery pack?

Just wondering,


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## Tylenol (Jun 18, 2015)

Based on a 400Wh/mile vehicle using Li-ion for 500miles range I got 2410ah at 144v At 375v you get a massive drop to 930ah. (all round up to nearest 10). Which makes me wonder why HPEVS and Thunder EV and other companies seem to only have 144v AC motors. Is 144v just a base line? Can they handle more? I have seen 300v plus controls by the same companies. Has anyone tried a 288v or higher EV? Most seem lower is that do to cost or safety? Does having more volts result in less batteries or does it work out to be roughly the same?
I should add that I multiplied the 1.05 and 1.32 variables first, then the 1.25 20%DoD offset, I figured it was better to guess a little high.
Is there any where/mile estimation calculator, something simple like vehicle weight tire size and drag coefficient?


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## rangerdev (Oct 25, 2015)

Hey guys. 

I am curious if you can buy a gauge to measure Dod? I'm doing a dirtbike conversion, so the distance I will be travelling differs from ride to ride, and will be difficult to keep track of. If I had a gauge I would keep track of where I am at and then swap out the battery pack before I put the batteries through too much abuse. Let me know if you could. Thanks!


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