Battery Derating and Chemistry Comparison

This weekend, Dave K was asking me some questions about the performance of our sweet LiFePO4 battery packs for the power wheels cars. At the time I was only able to answer his questions in generalizations, so I decided to sit down and show exactly how our lithium compares to more conventional lead-acid.

We’re running a custom 32-volt pack, but we can calculate with a more convenient size and all the observations will be proportional. Conveniently, our new teal cells are designed to create a nearly drop-in replacement for an existing form factor of gel cell. This makes direct comparisons really easy. Both options are 20 Amp-hours and both have nominal 12v output, with true output being a volt or two above that. So, straight off the bat, you’ve got the same form factor and voltage, with one option weighing 14 lbs and the other option weighing 6.6 lbs. More than double the energy density.

However, there’s quite a bit more to it than that. The two battery types are rated differently and have very different internal resistance. The lead battery gets its rating at a 20-hour rate, and the lithium is designed around a 30-minute discharge. When you use either battery outside of its intended performance envelope, you wind up with something other than the nameplate rating. There’s a formula to estimate this effect, called Peukert’s Law.

Peukert’s Law uses the following equation:

Where “It” is the effective capacity of the battery, “C” is the rated capacity, “I” is the discharge current, “H” is the rated discharge time in hours, and “k” is a constant for each different battery chemistry. For lithium, k is approximately 1.01, and for gel cells it’s around 1.15.

Do the math, and you wind up with a chart like this:


Bearing in mind we race with a 40 A fuse and occasionally burn one up, the benefit of lithium batteries in this application is pretty significant. We’re still getting more or less 20 Ah out of our packs, while the equivalent lead-acid would be derated to around 11 Ah. Suddenly we have 3.7 times the capacity per pound!

Beyond all this, there’s one other effect to bear in mind – voltage sag. When you load a battery heavily, some of the power is lost to internal resistance and you wind up with a lower output voltage than nominal. I don’t have the information to calculate this, but the effect is a lot more dramatic for lead than it is for lithium. We know from KITT that even during heavy use, we maintain close to 32 volts out of our pack until it’s almost completely flat. The “equivalent” gel-cell pack would produce at least a couple volts less in use, which means less total power is delivered to the motors.

In the end, our lithium batteries are giving us more than four times the total power of an equivalent weight in lead-acid. It’s also a lot easier to charge and maintain three battery packs than the dozen or so we would need to race two cars on gel cells. Surprisingly, even total purchase cost doesn’t look all that bad: Our total cost for the two packs on Project STEVE, including shipping, is $655. By comparison, 12 of those gel cells costs $454 and they’re so heavy that particular supplier won’t even ship them (but figure at least $100 in shipping from anyone who will). The only real disadvantage is that we’re carrying a larger portion of our $500 on-track budget in batteries and have less left for the rest of the car.

I think it’s worth it.

Power Wheels Racing Progress

Progress on the new Power Wheels racing car (Code Name STEVE) continues at a good pace! We’ve completed our innovative wood torsion box frame and are starting to lay out the other components for mounting. Here’s the recap:

The overall dimensions of the cart are 4′ in length (to make good use of our raw material) by 29″ in width (to drive through the narrowest doorway in the shop). Once we’d cut the torsion box skins to this size, we set them on the bench and started laying out the wheels and controls. Here’s James working on the seating position and handlebar layout:


Next, we started working on the internal bracing grid, using construction grade 2×4 boards ripped in half. We did this instead of just buying 2x2s because the larger boards tend to be straighter, higher-quality wood. After cutting the grid boards to length, we cut half-lap joints in them so they could cross while maintaining at least a portion of the grain all the way across the chassis.




Once everything is glued up, you can start to see the merit of this design – it’s very stiff, but incredibly lightweight. I don’t have any measurements of a steel frame to compare to, but at 21 lbs this will be hard to beat. And with the frame propped up on rollers at the axle locations and Eric sitting in the driver’s seat, there was no visible deflection.



Finally, our new batteries are in. These are BatterySpace LiFePo4 20 Ah cells, approved for us by the PRS Sanctioning Body. Right out of the box, we divided the cells into two packs and set about bottom-balancing each. Basically, we wired the cells up in parallel and did a deep discharge to 2.6 volts, putting every cell at the same minimum state of charge. Then, once they’re wired back in series we charge until the first cell hits a maximum safe voltage, setting the capacity of the pack equal to the weakest single cell. This way, we can charge and discharge without needing complicated balancing or monitoring. The minimum pack voltage is 2.6 volts per cell, and in practice we’ll set our cutoff at 28 volts or more for a 10-cell pack. The maximum voltage is whatever the pack happens to be at when one cell peaks, but we’ll generally charge to around 34 volts. As it turns out, all our cells finish charging in balance to at least 10 mV, the resolution of our multimeter. Build a sturdy box to contain and protect the cells, and we’re ready to race!



Next up, we’ll be working on the axles and steering, and then we can get to mounting motors and electronics. Stop by and give us a hand!

Trebuchet Contest Results

Thanks to all who took part in our Trebuchet Contest! We had perfect weather and all involved had a great time. With nine people competing on six teams, we saw a wide variety of designs and lots of experimentation.

Each team fired three shots, which were analyzed for efficiency and for accuracy. The efficiency score is calculated as the length of the best shot divided by the mass of the counterweight – to discourage anyone from using small cars as counterweight and hurling the projectiles all the way to Dodge Street. The accuracy score is the standard deviation of the three shots. To combine these into a final score, each category was normalized to 5 points for the best team in that area, with proportionally fewer points going to every other team. As a result, the best possible score is ten points, which would only be awarded to a team winning both categories.

Rank Team Efficiency (ft/lb) Accuracy (St Dev) Score
1st Ben 8.5 0.05 9.3
2nd Dave 9.8 2.4 5.1
3rd Eric 8.9 85.2 4.5
4th Kyle and his Dad 7.9 18.3 4.0
5th Kevin 7.6 6.4 3.9
6th Don, Stephanie, and Sarah 6.2 31.2 3.2

Ben, competing with a trebuchet constructed years before and “conveniently” fitting the contest requirements, had the longest throw of the day at 214 feet, but the use of a rather large counterweight dropped his efficiency to mid-pack, though not nearly low enough to offset his astonishing repeatability and accuracy.

Dave, winner of the “Least Effort Possible” award which nobody has bothered to create, gave a spectacular performance, particularly considering that his machine was constructed and tested in under fifteen minutes.

Eric nearly forfeited the contest after some mysterious last-minute bugs, but came back with a very solid 94-foot throw. Unfortunately, with two of his three shots launching backwards, his accuracy score reminded everyone to stand well to one side of a firing trebuchet.

Kyle and his Dad arrived with the only machine too large to be assembled indoors. Installing a competitive amount of counterweight earned them a respectable score, but before and after the contest, their 50-lb maximum capacity gave the neighbors something to think about.

Kevin competed with the only machine requiring three hands to safely load, and was also the only entrant to attempt self-amputation during testing. Despite this, the device proved acceptably reliable and fired many shots without incident.

Don, Stephanie, and Sarah may have earned the lowest score, but they were also the only team to compete with no prior testing. Their trebuchet was not completed until several minutes after the start of check-in and was immediately put to the test with none of the tinkering and tweaking afforded by the other teams.

Once again, a huge thanks to everyone who took part in this contest! We know it was the most difficult challenge we’ve yet conceived, and everyone who took part worked extremely hard to make the firing line yesterday. We promise the next event will carry wider appeal – more on that in the coming weeks.