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The Governing Equation

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This is what has driven RLR's entry and what governs all other automobiles on the planet.

Understand this equation and you understand what it takes to make a vehicle fuel efficient. More to the point, if you're talking to someone who doesn't understand what this equation says then they have at most an intuitive understanding about what they're doing and at worst no clue how to make a vehicle fuel efficient. Beware the smooth talking salesmen selling snake oil. Physics doesn't care how good an idea sounds.

 Ignoring secondary effects, here is what might be termed the fundamental equation of automotive force

F = mgCrr + ½ρCDAv2 + ma + mgsin(θ)

where,

F = force required at the wheels of the vehicle
m = mass of the vehicle
Crr = coefficient of rolling resistance between tires and road surface
ρ = density of the ambient air
CD = coefficient of drag of the vehicle in the direction of travel
A = cross-sectional area of the vehicle
v = speed in the direction of travel
a = acceleration of the vehicle
g = local acceleration of gravity
θ = angle (relative to horizontal) of the road surface.

Note: Energy, or the amount of fuel or electrons or any other energy source, E, on the planet that can be used to power a vehilce must at least equal the force required at the wheels of the vehicle, F, multiplied by the speed in the direction of travel, v:

           E = Fv.                                     

The take away from the above equation is that a highly fuel efficient vehicle will have:

1. Low mass (or weight in terms of mg),

2. Low rolling resistance tires,

3. Optimized aerodynamics for low drag (or low coefficient of drag),

4. Small cross-sectional area.

Why use one of the lightest (Insight 1G will weigh approximately 2,000lb), most aerodynamic (Insight 1G has the lowest coefficient of drag of any mass produced vehicle made at 0.25), smallest frontal cross-sectional areas (Insight 1G has one of the smallest cross-sectional areas), on the lowest rolling resistance tires commercially available combined with one of the most efficient automotive engines ever produced? Because physics says so.

Now that you know how the equation of automotive force works, if you wanted to build a car that got 100 mpg what would it look like? Would your car look like the VW 1L pictured below? Funny. This car resembles an Insight....

 VW 1L

 

 

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