# Road Load Equation

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Simulation and calculations

The road load equation describes all the forces applied to your car: aerodynamic drag, rolling resistance, and braking. EcoModder's calculator can crunch these numbers for you for steady state driving on flat ground, if you know a few parameters such as your car's mass, CdA, and CRR. Looking through the equations behind the calculator will give you insight into what aspects of your car and driving affect your fuel economy.

**Aerodynamic drag** is given by F = ½ * Cd * A * ρ * V².

Cd*A is drag coefficient times frontal area. You can look up these values for your car in the wiki [link]. Cd describes the smoothness of the vehicle's shape, but frontal area is just as important. These variables never appear seperately from each other in the physics. Much of our work on EcoModder is an effort to improve our Cd, to move through the air while disturbing as little of it as possible.

ρ is the density of air, which is around 1.3kg/m³, but varies with temperature and barometric pressure. Your car will cut through the air better when the air is thinner, e.g. when it's hotter, or at higher elevations. Don't ignore this term.

V² is your vehicle's airspeed, SQUARED. This means that driving twice as fast means four times as much aerodynamic drag. A headwind or even a crosswind will give you an airspeed higher than the value on your speedometer. A crosswind will also increase the CdA of a car that's optimized for driving forward, such as a bus, tractor trailer, or a Prius.

Cars and bicycles generally spend the majority of their energy overcoming aerodynamic drag. You can improve your fuel economy by reducing any of the factors in the above equation: slower speeds, a more slippery shape, a narrower or shorter car, or thinner air. Note that aerodynamic drag is not affected by mass (assuming that weight of that mass doesn't deflect your suspension).

**Rolling resistance** = CRR * weight = CRR * mass * gravitational acceleration

CRR is your coefficient of rolling resistance, a property dependent on your tire and the road surface. Low rolling resistance (LRR) tires are an excellent way to reduce your CRR.

USCS people will probably use lbs for weight. The metric system makes it clear that mass is an amount of material (measurable in kg), while weight is a force due to gravity.

Note that according to this simplified model, the force of rolling resistance is the same regardless of vehicle speed, while aerodynamic drag varies with V². The amount of rolling resistance per mile depends only on your vehicle's weight and CRR. In reality, your CRR rises significantly above about 50mph, but for most cars, aerodynamic drag force completely dominates the equation at those speeds.

So, the road load equation for steady state (constant speed) driving on flat land with no wind is:

F = ½*CdA*ρ*V² + CRR*m*g.

This makes for simple math, but it really only applies to highway driving, and even then not all the time. Still, studying the steady state road load gives you insight into what parameters of your car and driving cause you to spend the most gas.