Electric Land Speed Simulations

I am slowly but surely converting an old Porsche 911 to electric power. I have run my gas car on the Salt Flats ( http://www.saltflats.com ), and went 133 mph after 1 mile with a pretty good headwind. It was great fun! I also want to run my electric car on the Salt Flats once it is done.

The Salt Flats are sometimes called "The Great White Dyno," meaning they are the actual proving grounds that have confounded many calculations! Simulations need to be taken with a grain of salt, or in the case of land speed racing, tons and tons of salt. Simulations can, however, provide good insights, and are fun to do for nerds like myself.

One of the first steps was to figure out how much horsepower it would take to propel a Porsche 911 at high speeds. Luckily, I was able to find a FAQ on the Porsche 911 that listed top speed vs. horsepower for many years. Here is a plot:

I believe these to be flywheel horsepower numbers. From this plot it looks like it requires around 150 to 200 horsepower to push a Porsche 911 130 to 140 mph. Now, why choose 130 to 140 mph? There are multiple reasons. If you can go 130 to 140 mph in 1 mile, you can get into the 130 club with the Utah Salt Flats Racing Association (USFRA), http://www.saltflats.com . It sounds easy, but many cars don't make it. Also, to my knowledge, the fastest a street legal electric conversion has gone on the Salt Flats is 133 mph, done by a Ford Taurus named "Silent Thunder." It would be fun to go, say, 135 mph in a street legal vehicle and have the bragging rights of having the world's fastest street legal electric conversion. I'm not sure I'll be able to go that fast, but it'll be fun to try.

A couple of people astutely pointed out to me the graph looks too linear, and that power should scale as P ~ v^3. This plot is not for one car, but for many years and models of Porsche 911. The newer, more powerful cars also tend to be more aerodynamic, so the power graph does not jump up as fast as you might expect. For my simulation, I used the graph to anchor a single point, and then calculated P ~ v^3, F ~ v^2.

I won't put a bunch of math or computer code on this page (maybe someday on another web page). Here are the assumptions I made for my simulations:
  • 1977 Porsche 911
  • 275 flywheel horsepower to go 155 mph
  • Traction limited to 0.7 g acceleration (the Salt is a bit slippery compared to pavement)
    * A member of a land speed racing list told me the best acceleration anyone can get on the Salt is 0.61 g, many thanks for that information. In the future I'll use 0.5 g.
  • Lithium -- 179 kW (about 240 flywheel horsepower), lightweight lithium A123 batteries, 2300 pounds vehicle weight
  • Lead 2 min -- 1100 pounds of Hawker batteries, run at the 2 minute rate for 179 kW, 3200 pounds vehicle weight
  • Lead 5 min -- 1100 pounds of Hawker batteries, run at the 5 minute rate for 129 kW, 3200 pounds vehicle weight
  • Lead 5 min heavy -- 1500 pounds of Hawker batteries, run at the 5 minute rate for 172 kW, 3700 pounds vehicle weight
  • Lithium 2x -- 358 kW (about 480 flywheel horsepower), lightweight lithium A123 batteries, 2700 pounds vehicle weight
The first results show distance vs. time:

Distance vs. time is useful to see how long we need to run the batteries for a run. USFRA times every mile of the run. It takes about 30 to 40 seconds to hit the first mile, 50 to 70 seconds to hit the 2nd mile, and 70 to 100 seconds to hit the 3rd mile. Note the "Lead 2 min" line ends early, as the batteries are flat after just 2 minutes at that rate. The 130 club is just one mile, the 150 club is 2 miles, and a 3rd mile would be for an all out record effort. I think more than three miles would be too stressful, and not as fast, for lead acid batteries. Lithium batteries could keep going faster for subsequent miles.

Land speed racing is a bit different than many other autosports. Often the fastest time wins a race. For land speed racing, it is the fastest speed. This chart shows the speeds for all the cases as a function of distance, and is the most crucial chart for measuring land speed performance.

The kinks in the graph are due to shifting. When I ran my gasoline car, I could actually feel the wind resistance slow the car when I shifted from 4th to 5th at about 120 mph -- it felt like I hit the brakes for a moment. Note all the cases hit about 90% of top speed at the one mile mark, and are very close to top speed at the 2 mile mark (caution, I would not extrapolate these results to streamliners or cars with alot of power). The "Lead 2 min" looks like it might be competitive with Lithium -- but I think that is optimistic. In reality the battery will sag as the run progresses. I think the safer numbers are the "Lead 5 min" lines. Lithium 2x really flies! However, this much power would require twice as many lithium batteries (very expensive), and two or even three electric motors to handle the power (also complicated and more cost).

Racing generally doesn't consider time to speed (although car magazines do). These results were already there from the simulation and are included for fun.

Again, you can see the kinks due to the car slowing during shifting. The slowing gets worse with higher speed, due to greater wind resistance. Note the slope for the Lithium 2x case is close to the same for the 1st four gears! It might actually be faster to start out in 4th gear, and save the time spent shifting! Electric motors have so much starting torque this is actually feasible. Many electric drag racers ( http://www.nedra.com ) actually run just one gear. This would make the 0 to 60 mph about 4 seconds for lithium batteries. Indeed, the Tesla http://www.teslamotors.com and the Tzero http://www.acpropulsion.com/ are electric cars with lithium batteries that can accelerate this fast, on about 200 kW of power, with just 1 gear for the 0 to 60 sprint.

Go to http://www.ExplodingDinosaurs.com to see more of my stuff on electric racing.