In 1903 a Russian schoolteacher named Konstantin Tsiolkovsky published the equation that still governs every trip to orbit. It says, in effect, that a rocket's worst problem is itself.
The equation is short. The change in speed a rocket can achieve equals its exhaust speed times the natural logarithm of its mass ratio: how heavy it is fully fuelled, divided by how heavy it is when the tanks run dry.
Change in speed = exhaust speed × ln(full mass ÷ empty mass)
The logarithm is the cruel part. A rocket that is two-thirds propellant, a mass ratio of 3, reaches about 1.1 times its exhaust speed. To double that, you do not need twice the fuel. You need to square the mass ratio, to 9, which means a vehicle that is nearly 90 percent propellant. Every kilogram of fuel has to be lifted by fuel burned earlier, and that fuel had to be lifted too. The cost compounds.
Rocket engineers live with this by obsessing over two things: packing as much energy into each kilogram of propellant as chemistry allows, and throwing away mass the moment it stops being useful. Stages fall off. Tanks get lighter as they empty.
Cars are not rockets. But they carry a quieter version of the same problem, and it explains a lot about why electrifying big vehicles has been so hard.
A tank that never gets lighter
A car does not have to fight gravity the way a rocket does, so its penalty for weight is gentler. It is still real. Heavier vehicles take more energy to accelerate and more to roll. Some of the braking energy comes back through regeneration, but not all of it. A common rule of thumb, from the National Research Council's review of light-vehicle fuel economy, is that cutting a vehicle's mass by 10 percent cuts the energy it uses per mile by roughly 3 to 4 percent.
That sets up a spiral. Add battery to go farther, and the extra weight raises the energy every mile takes, which calls for a little more battery, which adds a little more weight. The series converges, unlike the rocket's, but it converges on a heavier, costlier vehicle than the first estimate suggested.
And a battery has a handicap no fuel tank has. It weighs the same full as empty. A rocket sheds mass as it burns. A gasoline car gets a little lighter with every mile. A battery pack hauls its full mass on the last mile of the trip, the same as on the first.
A hundred to one
The gap starts with energy per kilogram. A gallon of gasoline holds about 33.7 kWh of chemical energy. That is the figure the EPA uses to rate electric cars in miles per gallon equivalent. At about 0.74 kg per liter, that works out to roughly 12 kWh per kilogram.
SampoVolt's modeled LFP pack for a series-hybrid SUV stores 29.25 kWh in 249 kg. That is about 0.12 kWh per kilogram, counting the whole pack, not only the cells. Before anything is burned or discharged, the fuel holds about a hundred times more energy per kilogram.
The engine gives much of that back as heat. Suppose an engine-generator turns 35 percent of the fuel's energy into electricity. That figure is an assumption, not a selected engine. The fuel still delivers about 4 kWh of electricity per kilogram. A battery that uses 85 percent of its capacity delivers about 0.1. The gap shrinks from a hundred to one to about forty to one. It does not close.
The engine is not free, either. It is a fixed weight you carry whether you use it or not. In our van study, the lightest credible 45 kW generator set with a 40-liter tank came out at about 100 kg when full. That is an estimate. A 70 kW unit for the SUV would be heavier, and its mass is not settled.
Now run the trade. That 40-liter tank holds about 30 kg of fuel, which at the same assumed efficiency becomes roughly 125 kWh of electricity. Delivering the same 125 kWh from a battery would take about 147 kWh of installed LFP at our pack's level, or around 1,250 kg. One reserve weighs about 100 kg. The other weighs more than a tonne.
"A battery weighs the same full as empty. A tank of fuel is the lightest reserve a vehicle can carry."
Why size decides
This is why the answer depends on the vehicle. The engine's fixed weight pays off only when the reserve is large. A small commuter car that rarely leaves town needs a modest pack and no generator, and a pure battery car makes good sense. A full-size pickup is a different animal.
An electric full-size pickup on the EPA's test uses about 48 kWh per 100 miles at the plug. Allow 90 percent charging efficiency, and that is about 0.43 kWh per mile out of the battery. Give it a 300-mile range with an 85 percent usable window. At our LFP pack's energy per kilogram, the pack would weigh about 1,300 kg. Denser chemistries shrink that number. They do not erase it. Towing raises the energy per mile, so the same pack goes less far.
SampoVolt's modeled pickup pack is 43.9 kWh and about 355 kg. It covers the daily miles on electricity, and a fuel tank holds the long trip, the trailer, and the day without a plug. The battery works nearly every day instead of riding along as a reserve that is rarely emptied.
The catch is power, not energy
If the answer were this simple, every truck would already be a small-battery hybrid. The obstacle is that a small pack still has to deliver the vehicle's full power.
In a series hybrid the engine never turns the wheels. The motor does, and the battery feeds it. Our SUV case assumes a 150 kW peak. Drawing 150 kW from a 29 kWh pack is a rate of about 5C, five times the pack's capacity per hour. Large flat cells cooled through their broad faces run out of thermal room near 2.7C. To deliver the same 150 kW inside the same heat limits, the conventional pack has to grow to about 56 kWh and 436 kg. It grows not because it needs the energy, but because it needs somewhere to put the heat.
So the small pack only works if it can take the rate. SampoVolt builds stacked ribbon electrodes, cooled along their edges so no electrode is far from the coolant. In our model, that holds about 5C continuously inside a 5 K temperature spread and a 45 °C peak. Those are modeled figures, not test data. The power and cycle life essay walks through the thermal numbers.
Put the pieces together. A pack that can take the rate stays small. A small pack weighs less, so each mile takes a little less energy. A light tank of fuel covers the reserve the battery would otherwise have to carry as dead weight. In our model, each kilogram of that small pack displaces about 33 gallons of fuel over its life, against about 19 for the conventionally cooled pack sized for the same peak.
What the equation does not say
Tsiolkovsky's equation is exact for rockets. The car version is a rule of thumb, and the numbers here are SampoVolt models and public reference figures, not measurements of a vehicle. No engine has been selected, no vehicle has been built, and the engine efficiency and generator mass are assumptions. Longer pack life is the design goal; it is not yet a measured result.
The lesson the two share is the one rocket engineers learned first. When a vehicle has to carry its own energy, the lightest store for the reserve wins, and anything that does not have to come along should stay behind. For a pickup or an SUV, the big battery is the thing that should stay behind. A smaller one can do the daily work, if it can take the heat.
Sources
- U.S. EPA and DOE, fueleconomy.gov. MPGe treats 33.7 kWh of electricity as equivalent to one gallon of gasoline; electric full-size pickup ratings near 48 kWh per 100 miles. https://www.fueleconomy.gov/
- National Research Council, Assessment of Fuel Economy Technologies for Light-Duty Vehicles, 2011. Rule of thumb of roughly 3 to 4 percent less energy per mile for each 10 percent less vehicle mass. https://nap.nationalacademies.org/catalog/12924
- K. E. Tsiolkovsky, "The Exploration of Cosmic Space by Means of Reaction Devices," 1903. The rocket equation.
- SampoVolt pack, generator, and fuel-displacement figures are modeled, not test data.