Speed vs Efficiency

Using physics to travel smarter.

Sep 11, 2024

Nobody likes waste. That is, spending something and getting nothing. Efficiency is a ratio of how much of something we get out compared to how much of something we put in. The inputs and output quantities used depend on what we're evaluating.

Efficiency = Output ÷ Input

For cars, it's how many miles of driving we get per gallon of gasoline burned. For dehumidifiers, it's how many liters of water we get per kilowatt-hour of electricity. For solar panels, it's how much electricity we get from the available energy in photons coming from the sun.

Everything we humans want to do is governed by physical laws that determine efficiency. The first step in optimizing efficiency is understanding the physics of what we want to do. We will focus specifically on transportation—moving from one place to another—and, more specifically, how speed affects efficiency.

Automobiles

Cars, trucks, and buses experience many losses when they convert fuel into motion. Internal combustion engine-based powertrains in automobiles only convert about 20-25% of the energy in the gasoline or diesel they burn into motion. The other 75-80% is lost to heat and friction (which is ultimately converted to heat). Electric powertrains are much more efficient, converting 85-90% of their electrical energy into motion, and only 10-15% is lost to heat.

Whether gas or electric, all automobiles experience the same fundamental forces as they travel down the road. We will look at how speed affects these forces and what the implications are. On a flat road and at a constant velocity, all forces on the car will be balanced. Note that velocity is just speed in a direction.

Gravity pulls the car downwards against the road. The road exerts a normal force on the car upwards equal in magnitude to the gravitational force. The force of gravity is equal to the mass of the car multiplied by the acceleration due to gravity, "g" (9.81 m/s2), and the normal force is the same but in the opposite direction. Neither of these forces are dependent on speed, nor do they act to slow the car down since they act perpendicular to the car's direction of motion.

The two forces acting in the direction opposite to the direction of travel are drag (air resistance) and rolling resistance. The force the car's engine or motor needs to apply is equal to the combined rolling resistance and drag. The greater the force the engine or motor needs to apply, the greater the energy consumption.

But that does not necessarily mean that minimizing engine force maximizes fuel efficiency because the engine burns fuel just to stay running. Minimizing engine force by minimizing drag and rolling resistance would mean that the car is not moving, so efficiency in terms of miles per gallon would be zero. The car needs to be moving to have an efficiency greater than zero. Theoretically, if there were no drag or rolling resistance, the faster a car traveled, the greater the efficiency since a tiny force applied by the engine or motor would keep accelerating the car infinitely.

This doesn't happen in the real world because of drag and rolling resistance, which are critical for understanding how to maximize automobile efficiency.

Rolling Resistance

Rolling resistance = rolling coefficient x weight

or,

Frr = c W

The rolling coefficients for air-filled tires on dry roads can be estimated as:

c = 0.005 + (1 / p) (0.01 + 0.0095 (v / 100)^2)

where

c = rolling coefficient

p = tire pressure (bar)

v = velocity (km/h)

We can see that rolling resistance is proportional to the square of velocity.

If we take a standard car weighing 4000 lbs, having 42 psi in the tires, and traveling 60 mph, we get a force of rolling resistance of 116 Newtons.

Drag

Fd = 0.5 cd ρ v^2 A

where

Fd = drag force (N)

cd = drag coefficient

ρ = density of fluid (1.2 kg/m3 for air at NTP)

v = velocity (m/s)

A = characteristic frontal area of the body (m2)

We can see that drag is also proportional to the square of velocity.

If we take that same standard car with a frontal area of 2.5 square meters, a drag coefficient of 0.3, and traveling 60 mph, we get a drag force of 324 Newtons. Notice that the drag force is almost triple the rolling resistance.

Other Losses

Rolling resistance and drag aren't the forces that rob energy from an automobile. In internal combustion engine (ICE) vehicles, powertrain losses occur when fuel is burned in the engine, and that force is transferred to the wheels. For our calculations below, we will generously assume an ICE powertrain efficiency of 25%.

EVs also experience powertrain losses when energy is discharged from the battery and used to drive the electric motors. We'll assume an EV powertrain efficiency of 85%.

Automobiles also require energy just to keep them running/on. ICE vehicles can require 0.5 to 1.5 gallons of fuel per hour just to idle without moving. Below we're using 1 gal/hr for a pickup truck. Although EV's require much less energy to be on and idle, they still require some to power displays, internal computers and controllers, lights, etc. Below we're using 1.2 kW for an EV's baseline power demand without moving.

Combustion Engine Vehicle Efficiency

Below are graphs showing the rolling resistance and drag forces on a typical 1/2 ton ICE pickup truck at different speeds, followed by the energy usage in watt-hours per mile that this translates to, and the data table for the graphs. (click to enlarge)

We can see that the faster the truck goes, the less energy per mile is used for the baseline energy demand for the engine. However, the energy required to overcome the rolling resistance and drag forces increases with the square of speed. The result is that ICE vehicles are inefficient at both very low and very high speeds. These graphs show energy consumption per mile, which is the inverse of efficiency. This data shows that a pickup truck will be most efficient around 40 mph. In reality the optimal speed for a pickup is likely slightly faster, since engine efficiency increases slightly under moderate torque loads.

Vehicles that are more aerodynamic, like sedans and sports cars, will have a faster speed at which optimal efficiency is reached. Less aerodynamic vehicles, such as trucks and SUVs, will be most efficient at slower speeds since aerodynamic drag is more of a factor. ICE sedans are most efficient around 55 mph, and ICE trucks and SUVs are most efficient around 45 mph. These theoretical calculations align well with real-world data from Oak Ridge National Laboratory.

EV Efficiency

Below are graphs showing the rolling resistance and drag forces on an electric sedan, a Tesla Model 3, at different speeds, followed by the energy usage in watt-hours per mile that this translates to, and the data table for the graphs. (click to enlarge)

We can see that the drag force on the Tesla Model 3 is much lower than the truck since it's smaller and more aerodynamic. This means that the Model 3 will be less impacted by drag at higher speeds. However, since the baseline energy demand for the car is so low, drag is still the most important factor determining the speed of optimal efficiency. The speed of optimal efficiency for EVs is much lower than ICE vehicles because they don't experience large baseline engine losses.

Efficiency at different speeds has significant implications for the range of EVs. Below, the range of a Model 3 is plotted against driving speed.

If the car were driven at 70 mph, the range would only be 267 miles. But at 25 mph, the range would be 476 miles.

To minimize the reduction in efficiency and range from drag, especially at high speeds, we need to design vehicles to be more aerodynamic.

The need for improved aerodynamics is highlighted by the switch to EVs since we don't have the inherent inefficiencies of ICE powertrains masking the drag effect.

Aircraft

The forces acting on aircraft are similar to the ones acting on automobiles, except the normal force isn't provided by the ground, so some of the aircraft engines' energy is required to create a lift force to keep it aloft.

The dynamics of aircraft are more complex than those of automobiles, so we won't attempt to model them here. But the key point is that drag is still proportional to velocity squared. As an aircraft approaches its maximum speed, drag increases rapidly, decreasing efficiency.

Using Physics to Rethink Travel

We've seen that drag is the predominant force that steals energy anytime we move a vehicle through a fluid such as air since drag is proportional to velocity squared. So, to maximize the efficiency of travel and use less energy overall, we can simply slow down.

But our culture is obsessed with getting places fast. We view our daily commutes and flights for business or vacation as necessary evils to be minimized by driving or flying faster. But this leads to more energy for our trips, pollution, and negative environmental consequences.

What if we redesigned travel so the journey was entertaining or productive, allowing us to use less energy by going slower?

Instead of driving 70 mph on the highway, we could have a slow vehicle route or lane for vehicles that go 40 mph with the help of autonomous driving. This would free up the passengers to read books, watch documentaries, or have a mobile office on wheels. And this slower speed would be safer since kinetic energy is proportional to velocity squared, and kinetic energy is what injures or kills people in accidents.

Or, instead of taking a commercial flight at 500 mph, we could take a train that does 80 mph but has the luxury of office spaces, movie theatres, and fine dining experiences. It would take longer to reach your destination, but you could accomplish a lot and have a wonderful experience. Think of it as a land-based cruise ship. The money saved on fuel can be used to make a luxurious travel experience.

Conclusion

Drag is the predominant force that kills efficiency, and it increases rapidly with speed. If you want to save energy, decrease pollution, and save money—drive slower on the highway. The speed of optimal efficiency for an ICE vehicle is 45-55 mph. For an EV, it's around 25 mph. We can save a lot of energy as a civilization and avoid pollution by rethinking travel and slowing down.

How else can we improve automobile efficiency?
How would you feel about taking a slower form of travel that's more luxurious, entertaining, and productive?
What could this look like?