Progressive Automotive X PRIZE

X PRIZE Education at Solar Decathlon and NC Museum of Life and Science

Education Outreach for the Progressive Insurance Automotive X PRIZE continued in September and October, 2011 at the  U.S.Department of Energy's Solar Decathlon held in the National Mall's West Potomac Park in Washington, D.C. Nineteen collegiate teams from around the world  competed to determine which group had created the most efficient solar powered home. Competition categories included Architecture, Energy Balance, Affordability, Engineering, and Market Appeal.

Though quite a few of the competition days were solar-challenged, the demonstration homes performed well, and visitors lined up for a chance to inspect the innovative design and construction inside and out.
   

 

 The Under The Hood - Drive Change Today activity cart was very popular with the energy-efficiency-minded Solar Decathlon visitors.  The activities in the cart are designed to provide a hands-on introduction to principles of energy use, by-products of energy consumption, and conservation. 

Mixing  vinegar and baking soda provides an immediate Carbon Dioxide reaction...

 

 

 

 

 ...while yeast and water take longer to work together to create the same effect.

 

 

 

 

The aerodynamic properties of cars of different shapes and sizes were compared on test tracks. With hair dryers creating wind resistance, it was clear that boxy designs and luggage racks can drastically reduce energy efficiency.





A favorite activity was the battery circuit station, where the challenge was to complete an energy circuit utilizing a battery, wires and tape, in order to light a small bulb.  The more batteries, the brighter the light, until the tiny lights blow from the energy supplied by about 6 to 7 D batteries.

 

  

 

 

 

 

 

The principles how of interlocking gears work to control speed and direction of movement were explored by many visitors to the booth as well.

At the NC Museum of Life and Science in Durham, a week of Progressive Insurance Automotive X PRIZE education events and activities were held in the museum's hands-on investigation lab space.  

   Museum visitors learned that under-inflated tires and dirty air filters are two enemies of energy efficiency.

 

 

 

Visitors used a high-magnification camera and display screen to compare clean and dirty filters and learned how a dirty air filter slows the intake of air needed for efficient burning of fuel. 

 

  The challenge of designing and constructing paper  luggage racks and testing their effect on a car's aerodynamics was also a popular activity using the museum's high tech spring loaded tester track.

 

Aptera: After the X PRIZE

On a recent trip to southern California, I had the opportunity to visit the new Aptera headquarters in Carlsbad and discuss the effect the Progressive Insurance Automotive X PRIZE had on the development of the 2e, one full year after the completion of the prize.

The new 100k square foot facility in Carlsbad houses the corporate offices and serves as the Aptera engineering and technology center. The facility has ample open space to work on the continued development of the 2e, as well as the 2nd vehicle in the Aptera portfolio, currently in the design phase.

Though the team is busy working on the design and development of both vehicles, the timing of the production launch is still to be determined. The work continues as the company seeks funding to fully equip a facility to house their manufacturing operation. The team has applied to the Department of Energy (DOE) Advanced Technology Vehicles Manufacturing (ATVM) Loan Program, and is still working with the DOE to complete the process. According to Paul Wilbur, CEO, the loan program “provides the kind of funding necessary for manufacturing facilitization.” It is a very rigorous and diligent process, but one that was aided by the team’s participation in the Progressive Insurance Automotive X PRIZE. “The fact that the 2e had been in the X PRIZE and at Argonne National Labs for testing, helped us validate our technical claims in the application,” stated Wilbur.

When asked about the effect of the Progressive Insurance Automotive X PRIZE on Aptera as a company and on the vehicle, Tom Reichenbach, VP and Chief Engineer, and driver of the 2e throughout the competition was quick to state that “it was worth the trip.” Reichenbach believes that the “engagement and discipline required to be in a competition like the X PRIZE is fundamental to the growth of a company.” Paul Wilbur remarked that Aptera “walked in with twenty-five engineers, each independently thinking about how the vehicle should perform, but quickly became aligned with a single purpose and were galvanized to trust and accept Tom as their leader.” Wilbur believes that “competition is healthy for start-up businesses.” The Progressive Insurance Automotive X PRIZE has helped Aptera create a sense of “team” that has made them “ready to take on any challenge.”

Launching a New Car Company is No Small Feat

Bringing a new vehicle to market is a complicated and expensive process, even for established car companies. It’s not unusual to spend hundreds of millions of dollars to do it. So it’s no wonder companies like Honda, Ford and GM tend to stick with the tried and true -- and the profitable. Even those that went out on a limb, like Toyota with its Prius hybrid, lost a lot of money before eventually turning a profit for what many skeptics once dubbed a risky experiment. Similarly, whether GM’s Chevy Volt or Nissan's Leaf will be popular and profitable is today a question for debate.

 

Indeed, start-up companies -- such as any one of the finalist teams in the Progressive Insurance Automotive X PRIZE -- face an even steeper challenge, largely because of massive up-front capital costs. Cars not only have to be engineered, they have to be built, and part costs are a major barrier to profitability in low volumes. Even more expensive, however, are the machines used to put all those parts together. Auto-related news stories often feature one class of tooling machines common to the auto industry -- hulking robots that precisely lift, position and weld frames, doors and windows together on the factory assembly line to make a car.

 

Unfortunately, it costs far more per vehicle to produce a limited run of vehicles than it is to produce at high volumes. The limiting factor is that there are few ways to start small and cheap, and then scale up as demand increases. To use a simple example, if an aspiring automaker has to spend $10 million to produce 10 vehicles, then each vehicle has to bear $1 million of that cost, before adding any margin for profit. 

 

Clearly, to make a business case to investors, startup car companies must prove that sufficient demand exists to assure their investors will get their money back, plus a bit more. That means selling enough cars to make up the cost of the parts, labor, and excruciatingly expensive tooling.

 

Tesla Motors has taken heat from skeptics and admirers alike for selling its groundbreaking electric roadster for $109,000, a price far out of reach for most consumers. While hardly a car for the masses, it well illustrates the difficulty automotive start-ups face. Even with the successful sale of over 1,000 roadsters, Tesla nevertheless required a substantial government-backed loan to produce its next generation all-electric Model S sedan. Even with the loan, Tesla estimates the Model S will cost consumers more than $50,000, and that’s with a $7,500 federal subsidy.

 

Indeed, when innovation moves at a snail’s pace in the auto industry, it should come as no surprise that Tesla was the first American automotive IPO in more than 50 years.

 

It is my sincere hope that other automotive IPOs will follow. Certainly, the winners and finalists in the Progressive Insurance Automotive X PRIZE have proved that attractive and safe vehicles can get 100 MPGe, and I truly believe Americans are ready for such an automotive revolution. While the journey to this point has just begun for many of these teams, I look forward to the day when consumers have a wide range of truly ground-breaking energy efficient models to choose from.

 

The Origins of the Progressive Insurance Automotive X PRIZE -- And Its Impact

This is a guest posting by Felix Kramer, Founder of the California Cars Initiative (CalCars.org)

Five years ago, when the Automotive X Prize was just an idea, gas prices were seesawing, and people were fed up with paying a billion dollars a day for foreign oil.  We're still addicted to oil -- but thanks in large part to the X Prize, we can see a way out.

Back then, the famed Hypercar spinoff from Rocky Mountain Institute had previewed a future of lightweight, aerodynamic, safe autos. And everyone who'd looked at ways to reduce greenhouse gases knew the answer had to include getting our vehicles off fossil fuels. It was time for cars to take a quantum leap.

Meanwhile, promising cars like the GM EV1 and Toyota RAV4 EV were history. But the death of the electric car turned out to be just the end of one chapter. In 2004, CalCars.org showed how to convert hybrids to plug in, plastering five-foot wide signs proclaiming "100+MPG" on the sides of our Prius retrofits. And Tesla raised money to build a sexy sportscar that would beat almost anything on the road. We could see a future of optimized vehicles running on cleaner, cheaper, domestic electricity.

The Automotive X Prize launched in 2006-07 with ambitions to inspire the public and spark innovation to change the auto industry. Getting the competition right wasn't easy for its dedicated, creative staff:

• When "100 MPG" came up against vehicles powered by different fuels, experts developed "MPGe" for apples-to-apples comparisons of electricity with petroleum and renewable biofuels.
• Faced with public expectations for glitzy track races, planners who knew drivers most need a fuel-miser for 25-mile-a-day commutes worked out new tests. They enlisted the U.S. Department of Energy's National Labs to validate the performance of innovative solutions.
• With hopes that some great idea would emerge from a quirky corner, they split the Prize into mainstream and alternative paths.
• And, knowing that imaginative, unique solutions also had to find their ways to millions of drivers, they made competitors show their designs could be safe, affordably mass-produced, and sold for a profit.

As we reach the end of this historic competition, we all wonder who will win. But it's never been more true that "the journey is the reward." Competitors that didn't make it all the way have gained significant visibility, investments, and partnerships. Some may become successful manufacturers. Others will see their teams, intellectual property, and visions acquired by larger companies. Many will celebrate their victories.

And the Prize's impact extends far beyond the competition. X Prize raising the MPG bar certainly encouraged Congress to increase fuel efficiency standards. As we debate what new car stickers should say about efficiency and emissions, a new coalition is urging a goal of 60 MPG by 2025. The DOE has funded development of an advanced U.S. battery industry and lent carmakers billions to retool for green automotive jobs. States and companies have added their incentive programs to the federal $7,500 tax credits for new plug-in cars. Engineering students have been inspired to find jobs in a reviving auto industry. High schoolers have seen how cars can be cool and clean.

And automakers? They've been watching closely and making industry-changing decisions. In 2006, I became the world's first consumer owner of a plug-in hybrid. Now, before the end of this X Prize year, my family hopes to replace that PHEV conversion with a Chevy Volt that we can drive everywhere. And we'll trade our reliable Toyota Camry Hybrid for a Nissan LEAF's daily drives with no gasoline. The cars are coming: the U.S. is on track for a million mass-produced plug-in cars by 2015!

What's next? How about a follow-on prize? As the high-MPG cars arrive, it's clear it will take decades before they'll make up a large enough fraction of our country's 250 million vehicles to have much impact on fossil fuel use. Visionaries like Andy Grove are urging us to retrofit tens of millions of pickup trucks, SUVs, vans, and buses. Like the Home Star building retrofits we're now accelerating, national gas guzzler conversions could create green jobs in communities everywhere. So CalCars hopes for a Drive Star competition -- from X Prize, DOE, or another sponsor -- to spark "The Big Fix," creating a global industry to upgrade many of the world's 900 million vehicles.

X Prize began with the Ansari X Prize for space flight. As the X Prize Foundation broadens, with prizes in genomics, lunar exploration, and ocean oil cleanup, it's never been clearer that humanity and our planet face immense challenges. We used to say "the sky's the limit." Now that we recognize we need to save that one sky ASAP, we look to future competitions for inspiration, ideas, and a global rescue.

The Competition Isn’t Over Yet: Why Validation Matters

With the on-track stages behind us and the results of those on-track stages prominently available on the Progressive Insurance Automotive X PRIZE website, one might think the winners of this $10M competition are a foregone conclusion. Well, here are a few reasons why you should think again. 

The winners must pass the Validation Stage, during which they must achieve an efficiency result on the dynamometer high enough to ensure that, when averaged 50/50 with the on-track results, it equals 100 MPGe or better. A dynamometer, or "dyno" for short, is a device that allows engineers to test a vehicle by simulating the loads associated with driving without actually moving (basically, a treadmill for cars - think of the recent Lexus super car commercial that revs its engine until it shatters a wine glass).

Though two teams advancing to Validation are alone in their respective classes, Edison2 (Mainstream Class) and X-Tracer (Alternative Tandem Class), they each must still meet some very difficult requirements on the chassis dynamometer. If you recall, competition officials ruled that Edison2 was not at fault for the incidents at Coast Down that damaged the engines of both of their Mainstream Class entries. Consequently, officials granted Edison2 a waiver from Validation testing at Argonne National Lab as the cost and timetable for repair and calibration of the engines was not feasible. However, because Roush had conducted dynamometer testing on the Edison2 vehicles that were fielded at Knockout and Finals, officials have agreed to review these third party results to determine whether they can be accepted in lieu of testing at Argonne. Tune in to the Award Ceremony on September 16 to learn how the officials ultimately ruled.

That leaves the Alternative Class. To verify the on-track results from Michigan International Speedway, vehicles must repeat efficiency, range, and emissions testing – not an easy feat on the dyno where vehicles can’t benefit from air cooling at speed. In addition, they must survive an entirely new test for gradeability, also known as a simulated hill climb. To do so, they must maintain a minimum 55 mph speed on a simulated 4 percent grade (incline) continuously for 15 minutes. They must also surmount fuel economy, range, and greenhouse gas and pollutant emissions tests.

All vehicles must meet strict EPA emissions standards and achieve an on-road life cycle greenhouse gas emissions level of 200 equivalent grams of CO₂ per mile or less. This is also known as a wells-to-wheels (WTW) calculation that accounts for the upstream pollution associated with extraction, transportation, storage, and distribution of the energy that drives the wheels. Vehicles that don’t achieve these requirements during Validation Testing will not be eligible for the Grand Prize. 

For the five teams in the Alternative Side-by-Side Class, placement was determined by the Combined Performance & Efficiency Test, the last event conducted at the Finals Stage. Given that Team Li-ion achieved 171.4 MPGe in on-track testing, they do not appear to be in danger of falling short of the fuel economy mark. However, should they fail any component of testing on the dyno, including the simulated hill climb, they would fail to pass the Validation Stage. In that event, eligibility for the prize would fall to the next team in the placement order, in this case RaceAbout.

Validation Stage testing is no slam dunk. Teams must not only pass these very strenuous challenges, they must achieve 100 MPGe or better when averaged 50/50 with on-track results to claim the prize.

The bottom line: No one will know for sure until the winners are revealed at the final Award Ceremony on September 16^th. So stay tuned!

Coast Down Testing at Chrysler’s Proving Grounds Complete: Teams Advance to Validation Stage at Argonne National Lab

With the close of the on-track stages barely 12 hours behind them, teams spent the better portion of Wednesday, July 28^th loading and transporting their vehicles from Michigan International Speedway to Chrysler’s Proving Grounds in Chelsea, a short distance away.  Since then, all vehicles that advanced to the Validation Stage (the last and final hurdle toward the $10 million purse) were put through a Coast Down exercise, which involved test engineers accelerating each vehicle up to approximately 70mph on a 2.25 mile long, level paved roadway and then “coasting” them in neutral until they come to a stop, unassisted by brakes.

The exercise provides a few key metrics that are required for Validation Testing on the chassis dynamometers at Argonne National Lab facilities located just outside Chicago:

· First is aerodynamic resistance, a factor of the vehicle’s shape and footprint that determines how much air the vehicle has to push out of the way as it moves. The more resistance, the more energy has to be expended.

· Second is rolling resistance, a factor of tire design that determines how much energy the vehicle has to use to overcome the resistance caused by the friction between the tires and the road.

· Third is mechanical resistance, a factor of the vehicle’s powertrain and how much energy the vehicle has to use to overcome internal friction to drive the wheels.

Day 1 of Coast Down weather proved less than ideal, so Chrysler test engineers made the best of it by rigging up the vehicles with the needed instrumentation and training Chrysler’s professional drivers to handle the vehicles. Thankfully, the weather on Day 2 proved ideal, and teams RaceAbout Association, Li-Ion Motors, ZAP, and Aptera wrapped up under sunny skies and little wind without incident. All four vehicles were shipped off early the following morning on a hauler to arrive at Argonne National Lab for Validation testing.

Also on the morning of Day 3, Edison2, TW4XP, and X-Tracer hit the proving grounds for their turn through Coast Down. On the straight-away of the test track, Edison2’s Mainstream Class entries, vehicle numbers 97 and 98, were fielded. In both cases, as third party test drivers accelerated the vehicles to speed, a mechanical over-rev condition resulted in engine failures and the tests had to be aborted.

The fact that the Edison2 vehicles employ sequential transmissions may have contributed to the unintended downshift and subsequent mechanical over-rev condition that damaged the engines. In a typical racing configuration, the driver pulls rearword on the shift lever to shift up through the gears. This is opposite the convention used by many US automakers in their semi-automatic transmissions (like Chrysler's AutoStick), where manual upshifting is executed by pushing forward, away from the driver. Further, given that this is a competition vehicle, the automated software that would normally override an unintended downshift at speed or at high RPM is not yet perfected.

Chrysler’s test engineers, working with Oliver Kuttner and Ron Mathis of Edison2, were able to quite literally push their way through this particular setback, however. With the engines of both Edison2 vehicles out of commission, Chrysler, with Kuttner piloting the competition vehicle and Mathis behind the wheel of one of their trucks, put their assist vehicles to work, pushing one of the identical Edison2 vehicles to a speed sufficient to acquire the needed measurements.  

Coast Down data was ultimately obtained for the Edison2 vehicles, and the tests were completed successfully.  Both X-Tracer and TW4XP successfully completed Coast Down as well.

And so the week ended not without incident, but with a bit of determination and resourcefulness. All of the finalist vehicles have safely arrived at Argonne’s facilities for Validation.  Testing began Tuesday, August 3rd, and will continue throughout the month of August.

Since the Edison2 engines require costly repairs due to damage that was no fault of their own, and because the timing of these repairs presents substantial schedule challenges, competition officials have agreed to review objective third-party dynamometer results on Edison2’s vehicles to determine whether the data can be accepted in lieu of Validation Testing at Argonne National Lab. Until this determination is made, Edison2 will be granted a waiver that releases the team from the requirement to present their vehicles at Argonne for Validation Stage testing.

Again, both Edison2 vehicles remain active in the competition, and eligible for the $5 million prize purse.  Visit www.progressiveautoxprize.org to follow the progress of the remaining vehicles and track the competition.

Final Day of Finals -- Teams on the Homestretch for Multi-Million Dollar Prize Purses

The first week of Progressive Insurance Automotive X PRIZE finals brought the competitive field from 15 vehicles at the start of the week to 11 vehicles by the end of the day on Friday 7/23. After a weekend away from the track, the remaining competitors have once again taken the track for the Dynamic Safety tests today. Teams demonstrated that they could meet requirements for 0 - 60mph acceleration, 60 - 0mph braking, and accident avoidance tests. 

Two additional teams have been eliminated (preliminary) from the competition after today's events: Western Washington University and the Edison2 #95 car. The WWU Viking 45 vehicle did not pass the accident avoidance test within the 6 attempt limit (they did complete the course on attempt #9), and the Edison2 #95 car had mechanical troubles that prevented it from completing the day's tests. 

This brings us to the exciting final day of the finals event. Nine vehicles remain: 2 Edison2 vehicles in the mainstream class, 2 X-Tracer vehicles in alternative tandem, and 5 competitors in the alternative side-by-side category (Aptera, Li-ion Motors, RaceAbout, Zap, and TW4XP). Teams will compete in a timed event called the "Combined Efficiency and Performance Test", in which they will travel a minimum of 100 miles for the alternative classes and 200 miles for the mainstream class. Teams may not exceed 70mph, but the total time to complete the course and MPGe will be important factors that will be considered when determining the winning vehicle for each class. Live telemetry and a webcast of the event will take place on Tuesday, 7/27, starting at 8am EDT. Please visit http://www.progressiveautoxprize.org/live to tune in for the action, and watch for updates on Twitter, Facebook, YouTube, and Flickr!  

What it Takes to Make it to the Validation Stage

With the release of the results of efficiency testing from Week 1 of the Progressive Insurance Automotive X PRIZE, followers of the competition might be wondering why vehicles that didn't quite reach 100 MPGe on the track are moving on to Week 2 events.

As it turns out, to qualify for their share of the $10 million Grand Prize, teams must average 100 MPGe when their on-track results are combined with results from the lab. Thus, a team whose vehicle didn't quite peg 100 MPGe at the speedway could conceivably make up the difference during Validation Stage testing next month.

Given this, competition officials set the bar at 90 MPGe as the number to beat to progress to the next stage. For example, one of Edison2's entries (#97) came in at 95.6 MPGe and Western Washington University's vehicle (#45) scored 97.2 MPGe on last week's efficiency test. Presuming they pass the remaining tests, both cars will advance to the next stage.

With the on-track elements behind them, the surviving Finalists move on to coast down testing at Chrysler's Proving Grounds in Chelsea, Michigan where each vehicle will be instrumented, accelerated up to 80 mph on a flat level road course, put in neutral (or its equivalent), and quite literally coasted to a stop. Sensors record three key pieces of data: (1) Aerodynamic Resistance, (2) Rolling Resistance, and (3) Mechanical Resistance. Each is a key input to the Validation Stage testing.

Validation Stage testing will be conducted throughout August at Argonne National Lab facilities just outside Chicago. There, on-track performance will be verified on dynamometers and final eligibility for the Grand Prize will be determined. The winners will be announced at a formal awards ceremony in Washington, DC September 16.

Following the Finals of the Progressive Automotive X PRIZE

Years of hard work by staff, teams, and volunteers involved with the Progressive Insurance Automotive X PRIZE has finally culminated at the Finals Event of the competition. 12 remaining teams are putting their vehicles to the ultimate test this week, meeting minimum efficiency requirements of 100MPGe, minimum range requirements of 100 miles (alternative class) / 200 miles (mainstream class), and required safety standards.

At this point, you're probably thinking, "That sounds cool. So what's the best way to follow the Finals?" Well, here is your quick guide to following the PIAXP events happening over the next several days. 

Come Visit the Michigan International Speedway

Seeing these amazingly fuel-efficient cars in action and speaking to the teams firsthand about their vehicles is a truly unique experience -- and one that the public is invited to take part in on Friday, July 23! If you are in the area, we are pleased to invite you to the Michigan International Speedway so that you can see the Finals event, speak to the teams, and see the cars up close. Here are the details:

• Event is free!
• The Speedway will be open to the public from 10am - 4pm. 
• Use the Brooklyn Highway entrance to the Michigan International Speedway. You will then be directed to the designated parking area.
• Vehicles will be available for viewing, teams will be available for questions. Finals events will be taking place on the track. 

We hope to see you at the track!

Track the PIAXP online -- we're everywhere!

Follow the competition online by visiting the "Live" section of the website, at http://www.progressiveautoxprize.org/live. On this page you can:

• View the competition schedule and event details
• View real-time telemetry of cars on the track, including MPGe and track position
• Watch the live webcast and chat with X PRIZE/team members, or cheer on your favorite team
• View recent YouTube videos, Flickr photos, Facebok and Twitter updates

This is sure to be an action-packed week as the competition heats up and the winners of $10 Million in prize purses are determined. We hope that you'll share the excitement with us! 

The Car Equation

The physics of automotive motion is complicated, but the basics are clear from a relatively simple equation. It’s worth posting, as it illustrates some of the main challenges faced by design engineers and drivers who aim to increase fuel economy. 

So, ignoring secondary effects, here is what might be termed the fundamental equation of automotive force: 

F = mgC_rr + ½ρC_DAv² + ma + mgsin(θ)

where 

F = force required at the wheels of the vehicle
m = mass of the vehicle
C_rr = coefficient of rolling resistance between tires and road surface
ρ = density of the ambient air
C_D = 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

To increase fuel economy, engineers work to increase the efficiency of the drive train that delivers the force that’s required at the wheels. This is complicated work, and they have been at it for decades. But only recently has attention focused on the capture, storage, and re-use of kinetic energy that is normally lost when vehicles slow down. Electric hybrids are just the beginning. 

On the other side of the equation, engineers work to decrease the amount of force that’s required. From that side, you can see why they try to do three things based on variables that are primarily under their control (vs. the driver’s control): 

• reduce the vehicle mass (particularly important, since there are three terms in the force equation that are proportional to the mass, and because vehicles today are made from heavy materials) 
• reduce the rolling resistance (tires) 
• improve the aerodynamics (reduce cross section, reduce coefficient of drag)

Of course, there are economic and other tradeoffs involved. Reduce mass, but don’t give up too much safety; reduce rolling resistance, but don’t give up too much wear or grip; improve aerodynamics, but don’t give up too much comfort, convenience, and carrying capacity (and don’t make it ugly!). 

While these variables are primarily under the design engineer’s control, the driver has some control as well. If you load up the car, the mass increases. If you put stuff on the roof, the aerodynamic drag increases (likewise if you open all the windows). If you choose the wrong replacement tires or don’t keep the tires properly inflated, the rolling resistance increases. 

On the other hand, the equation shows the importance of variables that are primarily under the driver’s control: 

• acceleration - how often and how strongly you accelerate 
• speed - particularly important given that the second term is proportional to the square of your speed (drive a little faster, and there’s considerably more drag) 
• road surface – where you drive affects rolling resistance 
• hills - how often you go up them and how steep they are; (the sign of the last term becomes negative when you go back down, but you never get back all you lose going up. Although there are many variables involved - speed, cornering, braking, regeneration, etc. – at best you can recover most of the potential energy gained by climbing the hill. However, the energy spent going uphill is considerably greater than that potential energy gain since engines and drivetrains are not 100% efficient. The difference is lost forever.)

As mentioned, these variables are primarily under the driver’s control; but they are also affected by vehicle design. For example, drive trains may be most efficient at a particular speed (so driving very slowly may not yield the best fuel economy). And, obviously, you can’t accelerate or drive faster than the vehicle’s capabilities (which may be electronically limited). Similarly, unless you’re an off-roader, your choices of road surface and terrain are limited strongly by those in charge of road construction and maintenance.

Finally, note that there’s an important effect that’s beyond the scope of the equation above, namely that fuel economy is reduced by diverting energy for purposes other than forward motion – in particular for comfort and convenience features, including climate control, on-board electronics, etc. Here, the engineer is responsible for how energy-efficiency the features are, while the driver is responsible for how much they are used.

Note: post revised on 12 November, 2007; see comments; js