The Challenges of Going Faster

What if we want to go faster than the small Autonomous Vehicles you just saw?

Power losses due to Air Resistance and Rolling Resistance are major challenges. Weight creates additional challenges with speed, as do safety and comfort.

Before getting into the details, here are the key points:

• Air Resistance grows rapidly with speed, and dominates losses at high speed
• Tesla achieves the lowest Air Resistance Coefficient of any regular production car, equal to the Shanghai Maglev train
• Air Resistance grows linearly with frontal area, and more slowly with length, so long vehicles can be more efficient than fat ones, which is part of the reason for long trains
• For light vehicles, like bicycles, with smooth surfaces, like wooden tracks, we can achieve Rolling Resistance at least an order of magnitude better than conventional cars and roads
• Air Resistance grows linearly with air density, so for very fast travel, it is desirable to create a partial vacuum, like Elon Musk’s Hyperloop.

The bottom line for us is that to go fast efficiently we can design long, streamlined vehicles to run on the optimized surfaces in our A-Ways.

Now at this point you’re probably envisioning trains where you have to wait to get on, then search for a seat, and stop at lots of intermediate stations before finally getting to your station, or worse yet the train doesn’t even stop at your preferred station. You will see in subsequent posts that we can do much better than that with Continuous Convoys and En Route Sequencing.

Let’s start by looking at the power required to overcome losses. Power to overcome Air Resistance grows as the cube of the speed, so it becomes the dominant power requirement at high speeds. Power to overcome Rolling Resistance grows linearly with speed, so this is more of a challenge at lower speeds, and varies strongly with type of tires and road surface.  

The graph below is based on the design parameters of the Tesla, as best I can determine.

At the risk of getting too technical for some readers, we’ll look in some detail at comparisons of Air Resistance for different designs, and Rolling Resistance for different wheels and surfaces. You can skip to the next section if you like.

The Coefficient of drag is a measure of how easily an object slips through the air – Tesla has the lowest of any regular production automobile, at 0.24. Power required to overcome Air Resistance losses is the product: ½ (density of air) x (speed)³ x (Frontal area of the Vehicle) x (Coefficient of Drag). The density of air at sea level and 15° C is 1.225 (kg/m³). The frontal area of the Tesla is 0.58 m²:

P_d = ½ ρ S³ A C_d

Note for the dolphin that the density of water is 800 times higher than air, and the dolphin can’t go that fast. The density of air at 40,000 feet is only 3% that at sea level, fortunately, because the plane is going very fast.

(http://www.engineeringtoolbox.com/drag-coefficient-d_627.html accessed 11/19/15)

Object	Drag Coefficient
Dolphin	0.0036
Subsonic Transport Aircraft	0.012
Tesla & Shanghai Maglev	0.24
Bird	0.4
Tractor Trailer Truck	0.96
Person standing	1.3
Motorcycle and rider	1.8
Passenger Train	1.8

The Coefficient of Rolling Resistance is a measure of how Weight contributes to the force to push an object – The Tesla weighs about 4600 pounds. The Power required to overcome Rolling Resistance is characterized by  (Speed) x (Weight of the Vehicle) x (Coefficient of Rolling Resistance):

P_r = S W C_r

Interestingly, Bicycle Tires on a Wooden Track are as good as, or better than the steel wheels and tracks of Railroads. That suggests we can achieve low Rolling Resistance for our Vehicles with optimized wheels and A-Way surfaces. Rolling Resistance varies by a factor of 8 depending on the road surface. Using Bicycles on a Wooden Track as an option for our light vehicles, we can do better by a factor of 10 to 30 over conventional car tires and road surfaces.

Wheels	Rolling Resistance Coefficient
Railroad Steel Wheels On Steel Rails	0.001 - 0.002
Bicycle Tire On Wooden Track	0.001
Bicycle Tire On Concrete	0.002
Bicycle Tire On Asphalt Road	0.004
Bicycle Tire On Rough Paved Road	0.008
Low Resistance Tubeless Tires	0.002 - 0.005
Ordinary Car Tires On Concrete	0.01 - 0.015
Car Tires On Tar Or Asphalt	0.03

Weight is an issue not only for increasing Rolling Resistance, but for acceleration. The energy stored in a moving Vehicle is proportional to the Mass of the Vehicle and the square of the speed:

E_S = ½ M S²

At high speeds, that’s a lot of energy stored, and in case of a crash the energy has to go somewhere. That’s why cars have the crumple zones, air bags, heavy frames, heavy brakes, and many other features. And since the energy grows as the square of the speed, you can see why even going a bit faster is a lot more dangerous. That’s partly why our designs include so many features to prevent crashes before they can happen.

Otherwise, this energy of motion is only a major issue if you are trying to go very fast, or if you start and stop a lot. Fortunately, it is possible to get most of that stored energy back when decelerating through regenerative braking. You will see how our techniques are particularly efficient at this recovery.  Of course, we can’t recover the losses from Air Resistance and Rolling Resistance because they go to heating the vehicle and the environment.

Another issue with higher speeds is other accelerations. For example, a “small” bump or “slight” turn may be barely noticeable at low speed but can be significant, or even disastrous at higher speeds. So the higher the speed, the flatter, smoother, and straighter the A-Way surface needs to be. You can “bank the curves” so you are pressed into your seat rather than thrown sideways, but the proper banking depends on the speed. 

One of the criticisms of trying to use existing highway right-of-ways for high speed transportation, like the Hyperloop, is that they have lots of hills and curves, which aren’t a problem at 65 mph, but are bothersome at 120 mph, and disastrous at 300 mph.

When we get to more detail on A-Way design, you will see how we work with all these issues.

In the next post we’ll look at vehicles for higher speeds.