1. Exploiting Weather Conditions for Minimizing Transportation Energy1
By Michael Servatius2
University of Notre Dame, Department of Mechanical Engineering
Fall 2014
1 In part supported by NSF Grant 1239224
2 Advised by Peter Bauer
2. Servatius 2
Table of Contents
I. Abstract—Page 3
II. Introduction—Pages 3-5
a. Motivation and Process—Pages 3-4
b. Prior Research and Resources—Page 4
c. Nomenclature and Notation—Pages 4-5
III. Results—Pages 5-17
a. Constant Drive Speed—Pages 5-16
i. Theoretical Straight Line Distance Energy Evaluation—Pages 5-6
ii. Comparing Energies of Different Routes Across the U.S.A—Pages 6-9
iii. Comparing Energies of the Same Route on Different Days—Pages 9-12
iv. Theoretical Map Showing Winds Necessary to Save Energy—Pages 12-16
b. Changing Driving Speed—Pages 16-17
IV. Conclusion—Pages 17-21
a. What We Learned—Pages 17-18
b. Future Work—Pages 19-21
i. Continued Research—Pages 18-19
ii. Implementation—Page 20-21
c. Significance—Pages 21-22
V. References—Page 23
VI. Appendix—Page 23-47
3. Servatius 3
I. Abstract
The main objective of the work done this semester was to determine the effects (and their
magnitude) of weather on transportation energy. While this work can be applied to anything
from snow on the ground to humidity in the air, we focused on the effects that wind conditions
have on energy consumption. This work can be useful for any drivers, but the simulations were
all done with a truck in mind. Universities and research companies should highly consider
looking further into the influence of weather on energy intake, as our findings show that it can
have a major impact on saving energy, and thus money, if the weather conditions are considered
appropriately.
II. Introduction
a. Motivation and Process
The motivation behind this work was to explore something that could be very important
to energy and cost savings in the transportation industry, yet has very little research done already
on it. The first thing that we studied was the energy difference between different routes from one
point to another. We found that in some cases, it may be worthwhile to travel a slightly longer
distance in order to save some energy. This is done by taking advantage of wind conditions. In
other words, avoiding headwinds and trying to drive with tailwinds can make a big difference in
energy use.
Next, experiments were done to compare energy consumption on different days. Real
time wind conditions were tested on a relatively calm day, and then on a very windy day. The
energy uses were very different. This work brings the question of whether delaying or pushing
up transportation could be beneficial. For instance, a company may be able to save a good deal
of energy, and therefore money, if they chose to travel on a day with tailwinds rather than a calm
4. Servatius 4
day or a day with headwinds. Of course, this type of decision can only be applied in very unique
circumstances, but sometimes the little things can make a big difference.
The studies involving the testing of different routes and changing travel day were both
done at constant speed, so our next experiment dealt with altering the speed based on the wind
conditions. Overall, we found that changing speeds based on winds and keeping the relative wind
speed the same throughout a drive can have significant impacts on energy. We only touched the
surface of this idea, however, and there is much more that can, and should, be explored in terms
of changing speeds based on weather.
b. Prior Researchand Resources
There has been very little research done involving weather and its impact on
transportation energy. Hopefully, people see the possibilities that can come with maximizing
energy use based on weather and the topic is explored further in the future. In terms of our work,
the starting point was [1]. The equations and theory in this text was the backbone of the research,
as the energy equations were used along with wind conditions to prove that weather can have a
major impact on energy. Furthermore, we looked a little bit into systems that update routes based
on traffic conditions to explore if this could eventually become a reality with wind and other
weather conditions.
c. Nomenclature and Notation
As suggested earlier, the energy equation from Ehsani et al was the main driving point
behind the work done. The energy equation a can be manipulated slightly to include wind
conditions, and coding this equation based on different routes was much of the work done. The
equation is as follows:
𝐸 = ∆𝑥(𝑚𝑔𝑓𝑟 + 0.5𝐶 𝑑 𝐴𝜌𝑣2
)
5. Servatius 5
where E is the energy, ∆𝑥 is the change in distance, m is the mass of the vehicle, g is the
gravitational constant, 𝑓𝑟 is the rolling resistance coefficient, 𝐶 𝑑 is the air drag coefficient, A is
the frontal area of the vehicle, 𝜌 is the density of air, and v is the velocity of the vehicle. In the
majority of our tests, the velocity was held constant at about 55 mph (~24.58 m/s). In all the
tests, the rolling resistance was held at 0.01, the air drag at 0.8, the mass at 10000 kg, the frontal
area at 10 m2, and the density of air at 1.2 kg/m3. The change in distance must be in meters for
the units to remain consistent and then all energies were converted to kWhr. The wind conditions
were taken into account by altering the velocity term. To do this, we also had to segment the
distance based on where the winds were, often creating multiple energy calculations and then
summing them to get the total energy across the entire distance being studied.
III. Results
a. Constant Driving Speed
i. Theoretical Straight Line Distance Energy Evaluation [a]
The first step in our research was to transfer the energy equation into MATLAB and
ensure that the code was running properly. We did this on a small scale and used a theoretical
drive. This meant that we did not use real roads and just considered a straight-line path. After
confirming that the code was working by showing that with zero wind the energy consumption
was equal to that solved for by hand, we were able to take the winds into account. Because the
simulation was theoretical, we could control the winds. We chose to create 4 cases: no wind, all
tail winds, all head winds, and alternating tail and head winds.
To truly show that the wind could in fact make a difference in energy use for a truck, we
chose to use large winds for this first simulation. The distance traveled was chosen to be 96.2
miles (154818.9 m), the distance between South Bend and Chicago with wind speeds of 20 mph
6. Servatius 6
(8.94 m/s). The result showed that tailwinds could make a big difference in energy use when
compared to both a no-wind case and a test with only headwinds. The energy with no wind was
166.86 kWh, with tailwinds was 92.64 kWh, with headwinds was 274.08 kWh, and finally with
alternating winds was 183.36 kWh. The fact that the alternating case used more energy than the
no wind case (by about 9.9%) also shows that the negative effect of headwinds is greater than the
positive effect on energy of tailwinds. Thus, if choosing a driving route, the most important thing
in terms of energy use is to avoid headwinds.
ii. Comparing Energies of Different Routes Across the U.S.A [b]
The next simulation involved testing how wind changes energy use in a real scenario. To
do this, we chose three different routes from Phoenix to Chicago. One route was the direct route
suggested by [2], while the other two routes were chosen based on the wind conditions on
September 30th. The three routes are shown in Figures 1-3, and the wind conditions in Figure 4.
The wind maps found online at [3] allowed for easy calculation of wind magnitude and direction
across the country and this data was integrated into our code.
7. Servatius 7
Figure 1. Phoenix to OKC to Omaha to Chicago
Figure 2. Phoenix to Salt Lake City to Chicago
8. Servatius 8
Figure 3. Phoenix to Chicago Direct
Figure 4. Wind Conditions on September 30, 2014
In this particular case, the most direct route (Figure 3) is the smartest route in terms of time,
9. Servatius 9
distance and energy consumption. This route from Phoenix to Chicago spanned a distance of
1802 miles (2900038 m) and used 3013.6 kWh of energy. The route from Phoenix to OKC to
Omaha to Chicago of 1931 miles (3107643 m) used 3100 kWh while the route from Phoenix to
Salt Lake City to Chicago of 2051 miles (3300765 m) used 3436.7 kWh.
Although the most direct route also is the most energy efficient, going from Phoenix to
OKC to Omaha to Chicago utilizes the winds more than any other route. This shows that the
wind does make a significant impact, as the distance traveled is 7.16% more than the direct
route, but only 2.87% more energy is used. The main takeaway from this simulation is that the
wind does have a substantial impact on energy, but it may only apply in particular cases. In this
case, it makes the most sense to take the most direct route. If the winds were a bit stronger,
however, it is very feasible that the longer route shown in Figure 1 could save some energy over
the direct route.
The effects of the winds are further demonstrated by comparing the energy consumptions
of all the routes with and without wind. Without wind, the direct route shown in Figure 3 used
3125.6 kWh of energy, or 3.7% more energy than with the wind included. Next, the route from
Phoenix to Salt Lake City to Chicago used 3557.5 kWh, or 3.5% more energy than with the wind
included. Finally, the route from Phoenix to OKC to Omaha to Chicago used 3349.3 kWh of
energy, or a whopping 8% more than with the wind included. Overall, including the wind in
energy calculations gives a more realistic picture of the energy being consumed by the truck, and
if used correctly, this can save a lot of energy.
iii. Comparing Energies of the Same Route on Different Days [c]
Given our previous experiment, it is easy to see that going a slightly further distance
could potentially be beneficial is winds are accounted for properly. So going a different route to
10. Servatius 10
save energy was a possibility, and the next step was to ask if going a different time or even day
could save money. Thus, we used the same wind conditions from September 30th found in Figure
4 and compared them to the winds on October 6th. We chose a path from New Orleans to
Columbus (as shown in Figure 6), as the winds were very large in this direction on October 6th as
shown in Figure 5. The September 30th winds were relatively calm in this direction, so the aim of
this test was to show that delaying or pushing up travel has the potential to save a good amount
of energy, again only if the winds are used properly.
Figure 5. Wind Conditions on October 6, 2014
11. Servatius 11
Figure 6. New Orleans to Columbus
The results of this experiment demonstrated the importance of winds in energy
calculations for two main reasons. The first, as hinted at earlier, deals with comparing winds on
separate occasions. With no wind, the trip from New Orleans to Columbus used 1575.5 kWh of
energy. With the calm winds on September 30th, 1569.3 kWh of energy were used. Finally, with
strong tailwinds on October 6th, 1180.5 kWh of energy were used. This is a 25.1% decrease in
energy consumption from no wind to the conditions on October 6th and a 24.8% decrease from
September 30th. These savings in energy could save a lot of money. In this case, the winds are a
week apart, so a company may not be able to delay a trip for that long. It is certainly worth
looking into the wind conditions on several days when planning a trip, however, as it could save
a lot of energy to travel when there are advantageous winds.
12. Servatius 12
The second demonstration of the large impact the winds have on energy is comparing the
trip from New Orleans to Columbus and vice versa on both September 30th and October 6th. On
the first date, the energy used from New Orleans to Columbus was 1569.3 kWh while it was
1582.2 in the opposite direction. On October 6th, the energy consumed was 1180.5 kWh going
north to Columbus and 2053.2 kWh going from Columbus to New Orleans. The calm winds on
the final day of September had relatively little affect on energy, while the large winds (ranging
from 3.5-5.5 m/s) on October 6th had a huge influence depending on whether the truck travels
with or against the wind. Just to further illustrate this point, with calm winds on September 30th,
the energy changed less than 1% depending on the direction of travel. On the other hand, the
energy changed 42.5% depending on the direction of travel with strong winds on October 6th.
iv. Theoretical Map Showing Winds Necessary to Save Energy [d1]-[d3]
While these studies done on the U.S. roadways are extremely useful in showing the impact of
weather on energy use, it can be a bit difficult to visualize the winds along with the roadways.
Therefore, we decided to return to a theoretical case. The main idea was to create a wind map
and vary the conditions how we pleased, and then have an animated line show a path moving
through the wind map. There is no way to show the animation in this report, so the maps are
shown after the truck’s route has been finished. The first theoretical test is found in Figure 7,
with winds varying between 0-18 mph (0-8 m/s). Three routes were tested and all begin in the
bottom left of the figure and end in the top right. The first was a test case, taking the most direct
route (diagonally) with no headwinds or tailwinds. The second route (to the right and then up)
went around the outside with only winds that would save energy. Finally, the third route (up and
the to the right) went around the outside with only winds that would lose energy. Much like we
13. Servatius 13
did earlier, the main goal was to determine whether going a further distance could actually save
energy due to strong tailwinds.
Figure 7. Theoretical 10 x 10 Map (Varying Wind Conditions) [d1]
Much like before, the effects of the wind were very noticeable, but it was the best choice
to follow the most direct route. The direct route spanned almost 88 miles (141,421 m) and used
152.4 kWh. The route designed to best utilize the winds spanned 124 miles (200,000 m) and
used 170.7 kWh. Lastly, the course that went against the winds also covered 124 miles (200,000
m) but used 263.1 kWh of energy. While covering the same distance, the two routes that
traversed the outside of the theoretical map had a 54% difference in energy use. This percentage
14. Servatius 14
can be solely attributed to the wind conditions. Furthermore, the long route that utilized positive
winds traveled 41% further than the direct route, but only used 12% more energy.
Given the results from our first theoretical test, we decided to increase the wind
conditions in the same size theoretical map. This test is depicted in Figure 8, and the winds
varied between 0-40 mph (0-18 m/s)3. Again, there are 3 routes—a direct diagonal route, an
efficient route around the outside, and an inefficient route around the outside.
Figure 8. Theoretical 10 x 10 Map (Varying High Wind Conditions) [d2]
In this case, the weather made a huge difference, which was expected given the large
magnitude of the winds. The efficient route along the edge of the map ended up being the
3 Consult the appendix to see the wind conditions in detail
15. Servatius 15
smartest route to take, proving that the winds can make it advantageous to take a longer route in
order to save energy. This path, which covered 124 miles, used only 101.5 kWh of energy. The
direct route used 152.4 kWh of energy across 88 miles, and finally the inefficient route used a
massive 397.9 kWh.
These numbers need to be considered carefully given the large winds tested. Rarely are
there 40 mph winds, so we decided to run one more simulation on our theoretical map in order to
determine what winds would make the long and direct paths have equal energy consumption.
This data would allow us to know exactly which wind conditions need to be present in order to
save energy going the long way. In order to simplify the map, we removed all winds that were
not along the route and kept the winds the same along the route. As shown in Figure 9, the direct
route has no wind. After calculating the average winds required on the long route to utilize the
same amount of energy as the direct one, we found that the average wind conditions must be
equal to 12.1 mph (5.412 m/s). With these winds, the energy used over the 124-mile road was
152.4 kWh. The 88-mile direct course also used 152.4 kWh.
Like stated before, the difference between the routes in terms of distance was about 41 %,
but the energy difference was less than .0008 %. The reason that this model is so important is
that 12 mph winds are very realistic, and we traveled more than 40% further with the same
energy considerations. This can make a huge difference if considered over all drives, as there are
likely many cases that a relatively direct route (only go slightly out of the way), but also save
some energy. If studied and implemented correctly, this could save a lot of energy for truck
companies in the long run.
16. Servatius 16
Figure 9. Theoretical 10 x 10 Map (Constant Wind Conditions) [d3]
b. Changing Driving Speed [e]
After determining that the wind can provide energy returns while traveling at a constant
speed, the next step in our work was to investigate whether altering the speed of the truck based
on the wind conditions would change the energy considerations. The main idea in this simulation
was to slow down the truck when headwinds were present and speed up when tailwinds were
present. Our thinking in this was that we would take advantage of winds that help lower energy
consumption (tailwinds) and minimize the negative energy effects of the headwinds.
We decided to run two tests across the same path, one with constant truck speed and one
that would alter the speed based on the winds as described above. We took a 20-hour drive and
17. Servatius 17
broke it down into 10 different wind segments. We altered the speed of the truck so that the
relative air speed would remain constant. In other words, if a 5 m/s tailwind were present, the
truck would speed up 5 m/s. If a 5 m/s headwind existed, the truck would slow down 5 m/s.
Overall, over our 20 hours, the wind speeds averaged out to zero so that we could compare the
results to a test case with a constant drive speed and still have the 20-hour time period for both
cases. The winds varied between 0-33.5 mph (0-15 m/s), however, 9 of the 10 wind conditions
were 22 mph (10 m/s) or less.
It was found that keeping relative air speed constant by changing truck speeds saved
energy compared to the test case of driving at a constant speed. Both tests were done over 20
hours, and the truck with changing speed resulted in 1367.6 kWh of energy. If we did not alter
the speed of the truck and remained at a constant 56 mph (25 m/s), the energy use was 1814
kWh. This is a 32.6% difference in energy use, a huge savings when considering the time
traveled is identical. While the winds considered were relatively high, they were large for both
headwinds and tailwinds, so it was not a highly favorable path for the constant case. This
demonstrates that if we were to apply some of our previous work with rerouting based on winds
along with altering the speed of the truck, we could save a great deal of energy.
IV. Conclusion
a. What We Learned
The goal of our work was to determine if weather has an impact on energy consumption
in transportation. More specifically, we wanted to explore the effects of wind on a truck. After
doing a myriad of simulations, it is clear that wind does in fact have a noticeable impact on
energy. Asking and exploring three main questions helped determined this.
18. Servatius 18
The first was to determine whether taking alternative routes could help save energy. We
looked at going from one place to another via different path both across the country and
theoretically and showed that, if exploited properly, the wind can help save a substantial amount
of energy. The extent of energy savings depends on the strength and direction of the winds, of
course. It is up to the user, most likely a truck company, to determine if the savings along one
route are worthwhile as opposed to another route.
Second, we looked at wind conditions along the same route on multiple occasions to
decide if changing travel time could provide energy savings significant enough to change travel
plans. Based on our comparison of winds on September 30th to October 6th along the path from
New Orleans to Columbus, we showed that considering wind conditions when planning travel
has the potential to save a notable amount of energy. In this case, the difference between the two
days was about 25%. Now this difference was a week apart, but these conditions could be
present days apart or even hours apart under the right circumstances. Because of this, universities
and research companies should seriously consider researching more into planning travel based on
the winds, as it can go a long way in saving money.
Finally, the last question involved changing the speed of the truck, something we had not
explored in any previous simulation. We decided to keep the relative wind speed the same and
this led to noticeable results, saving 32.6% energy over a 20-hour drive with reasonably high
wind speeds. It would have been interesting to continue to explore changing speeds, whether
keeping the relative wind speed constant or not, but unfortunately we ran out of time before the
semester’s end.
19. Servatius 19
b. Future Work
i. Continued Research
Because there has been very little work done on this subject to date, there are many
directions to take this research in. First, there are numerous more studies that can be done
involving the wind. More specifically, we did not do a great deal of work changing speeds so
there is a lot more that can be done in this domain. Furthermore, if the areas we studied were
combined, this would likely lead to some astounding results. For instance, if a truck company
were to consider taking a different route to avoid headwinds and take advantage of tailwinds
while also keeping relative wind speed constant by changing the truck’s speed, this would likely
lead to major energy savings.
In addition to the effects of wind, there are many other weather conditions that would
certainly change the energy considerations. For example, having wet road conditions due to rain,
slush, snow, or ice would alter the rolling contact coefficient and thus modify the energy
calculations. Furthermore, there are weather conditions such as humidity that may or may not
have any influence on energy, but must be studied further in order to know for sure. And aside
from weather, we also did not include any acceleration effects or traffic patterns. In a realistic
situation, the truck would not be driving at a constant rate the entire time of travel, so that must
be taken into account when considering our results. If traffic and weather were integrated
together in a simulation, this would help give a more realistic answer as to how energy can be
saved.
Additionally, this study was done with the mass, frontal area, and air drag coefficient of a
medium-sized truck, so further research can be done to determine if the wind has the same effect
on a sedan, crossover, motorcycle, or any form of transportation. It is very viable that the wind
20. Servatius 20
has an effect on all forms of outdoor transportation and we simply need to determine how great
an impact that is in order to decide whether it is worth taking advantage of.
Finally, some of the research not previously mentioned was to calculate the percentage of
the energy consumption that can be attributed to rolling resistance, and that attributed to air drag.
It was found that the rolling resistance accounted for 25.26% of the energy, and the air drag
74.74%. This data suggests that the wind conditions are even more important than we believed
before, as the air drag component of energy makes up almost three-fourths of the total energy. It
would be interesting to see how much these percentages change based on altering the coefficients
of air drag and rolling resistance, and it would not be tough a study to pursue further.
ii. Implementation
This research is interesting, but it is useless unless it is implemented correctly. As we
have shown, the wind has a visible effect on energy use. Therefore, it would be beneficial for
universities and companies to at least look into further research and determine whether rerouting,
preplanning travel, or other considerations based on wind are a realistic possibility to apply to
truck businesses or even an average driver.
The most logical thing to determine rerouting would be to set up a system similar to those
that are already in place to give the most efficient traffic routes. If a GPS system were improved
to show not only roads and traffic, but also energy based on weather conditions this would allow
a customer to make decisions about which route to take based on the value they place on time
and energy. Because heavy traffic wastes a lot of energy, it is likely that in many cases the
shortest travel route in terms of time would also be the most efficient in terms of energy.
Furthermore, there are a few different ways to employ our new knowledge that keeping
the relative wind speed constant can help save energy. First, is by simply making people more
21. Servatius 21
aware to check the winds and drive accordingly. This is a nuisance, however, and the vast
majority of people would be unlikely to change their habits. Instead, having digital speed limit
signs that adapt based on the wind conditions would help change people’s habits. For example, if
strong tailwinds were present, the speed limit would be increased. If strong headwinds existed,
the speed limit would be dropped. This would help save energy and money for all drivers
whether they know of the effects of the wind or not. Another solution might be to have cars that
drive themselves and adjust speed based on the wind. This is not that far fetched considering cars
have and continue to be developed that drive unmanned, and sensors measuring the wind are
very prevalent.
b. Significance
As mentioned before, the goal of this work was to determine if manipulating
transportation based on winds could save energy. While energy saving is extremely important
and a growing concern, at the end of the day, the significance of this work revolves around
money. Some of the ideas discussed in the previous section have the potential to be very
lucrative business ideas. If a GPS system could update traffic and weather, it would provide
insights that truck companies and regular drivers alike could utilize to make quick decisions
about saving both time and energy (and thus money).
Next, average people owning cars and trucks that drive themselves is extremely likely to
occur in the future, so being able to program them to adjust their speed based on the wind would
help save a huge amount of energy and money. As we showed, keeping the relative wind speed
constant by changing truck speed can save a significant amount of energy for one truck, but
imagine the possibilities if this were programmed into cars and trucks on a larger scale.
22. Servatius 22
Very few businesses will get involved in a project that they do not eventually see
becoming profitable, so for research to be truly significant, there must be business opportunities.
That is what makes this work so meaningful, as it has the possibility of helping to save a great
deal of energy if studied and implemented further, while also allowing businesses to profit by
developing the software and bringing it to market. We have only uncovered the very tip of the
iceberg, and we need to continue to research this field as there is great opportunity to not only do
good for the world by saving energy, but also develop something extremely useful and
profitable.
23. Servatius 23
V. References
[1] Ehsani, Mehrdad. Modern Electric, Hybrid Electric, and Fuel Cell Vehicles: Fundamentals,
Theory, and Design. Boca Raton: CRC, 2005. Print.
[2] "MapQuest Maps - Driving Directions - Map." MapQuest Maps - Driving Directions - Map.
N.p., n.d. Web. 03 Dec. 2014. <http://www.mapquest.com/>.
[3] "Wind Map." Wind Map. N.p., n.d. Web. 04 Dec. 2014. <http://hint.fm/wind/>.
VI. Appendix
[a]
%% Michael Servatius
% 9/26/14
clear all
clc
%% Parameters
Cd=0.8; % air drag coefficient
m=10000; % mass= 10,000kg
ar=10; % area= 10 m^2
fr=0.01; % rolling resistance coefficient
rho=1.2; % density of air
g=9.8; % 9.8m/s
v=24.58; % 24.58 m/s = 55 mph
deltax=154818.9;%96.2 miles (Chi to South Bend)
deltax10=deltax/10;
%% Wind at 20 mph (32 km/h) in alternating directions
c1=cosd(0); % angle of wind speed
c2=cosd(180);
c3=cosd(0);
c4=cosd(180);
c5=cosd(0);
c6=cosd(180);
c7=cosd(0);
c8=cosd(180);
c9=cosd(0);
c10=cosd(180);
vwind1=8.94; % wind speed (ignoring direction)
vwind2=8.94; % angle takes care of direction
vwind3=8.94;
vwind4=8.94;
vwind5=8.94;
vwind6=8.94;
