Flying Car Road
Higher, Faster and Easier!
Introduction to IIE
Group : Rocinante
이종호, 유선욱, 차민철, 신은섭, 이현주
Table of Contents
1.
Abstract summary
2.
Introduction
3.
A.
Goal of the project
B.
Flying cars
C.
Models during brainstorming
D.
Feedbacks
Main sections
A.
Section1
i.
Basic structure of the model and reason why this model
ii.
Detailed model view
B.
4.
5.
Section2
i.
Detail explanation of the model
ii.
Probability of an accident
iii.
Latency time
iv.
Cornering speed
Conclusions
A.
Efficiency in the crossroad
B.
Comparing a real case between flying car system and nowadays system
References
Abstract Summary
In the near future there are going to be flying cars in the air. Our project is about which
road system will have the most optimized traffic flow when there is flying cars running on the
road. Minimizes the expected latency time caused by traffic jam, and makes the car able to
go to the arrival point with only one change of direction. We evaluated several models, which
came out from brainstorming, in probability and statistical methods to find which model is
the most appropriate one.
Introduction
Maybe everyone would have imagined of a flying car at least once in a lifetime. The
interests on flying cars are well expressed in movies. A movie called ‘The Fifth Element’ which
was released in 1997, handles with a flying car flying between the skyscrapers, and in ‘Harry
Potter’ series Harry gets on a flying car. Not only in movies but also in books, advertisements,
games, etc are paying attention on flying cars. These days this kind of ‘magical’ flying car is
being researched from many places and even several models of flying cars are introduced.
Also, in Kyungsangnam-Do, South Korea there has been a flying car contest. Lots of airplane,
automobile related venture corporations are concentrating on R&D of flying cars.
As mentioned the future where flying cars are flying around the sky is not far. However,
are we ready to accept that kind of technology? The answer is that we are not ready for the
new era. If there are tons of cars in the air it will be lots of mess. So, we have to be prepared
for the flying cars. For example, the road system has to be a lot different from now.
So in this project we are going to propose a road system model for the upcoming future
and analyze the system using industrial engineering methods.
Goal of the project
We have some conditions about the future when the flying cars are common. Firstly, we
wanted to reduce the traffic lights, which are playing an important role in today’s traffic.
Flying cars are above the ground, it means they are not on the same plane with the sidewalk
where people move. Traffic lights are necessary because there should be cross movement
between roads and sidewalks, however as they are not on the same plane it became needless.
Removing the traffic lights gives a lot of reduce in traffic jams. Secondly, thinking in common
sense a crash in the air would cause a lot more damage, so we tried to reduce the possibility
of crashing to zero. Lastly, we tried to make the turn optimized so that even there are lots of
traffic in the air, by the optimized turn we can make the traffic flow efficient. Also, without
optimized turn there would be more crashes and there would be more unexpected crash
occasions. Ultimately, when the entire road system is established the system will show you
that it is organized, safe, and fast to use flying cars.
Flying cars
In Wikipedia flying car is defined as ‘Flying car, or roadable aircraft, is an automobile that
can legally travel on roads and take off, fly, and land as an aircraft.’1 Being based on this
definition we made some restrictions about flying cars. Flying cars in the future will just look
like these day cars, but as they travel by flying there would be some technological
development. Flying cars can move upwards and downwards, and can make change in their
altitude anywhere, anytime they want. All cars have navigating system so they could travel
with fixed velocity and maintain certain distance between cars. Flying cars will have a brake
system using reverse propel mechanism. All of these technologies are used in modern cars,
although there are very few, so we can assume that these will be commonly used in the
future.
1
Flying cars, Wikipedia, ‘http://www.wikipedia.org/flyingcars
Models during brainstorming
First one was a model which resembles the double helix structure of DNA.
[Figure 1]2
What we thought was to connect the 4 main roads to the structure seen in [Figure 1], so
one helix has the direction of going up and another helix going down, so that the cars can
make all kinds of direction changes. However, this model has problem that in the case of
entering and exiting the structure there will be lots of congestion.
Second one is external circular route on each block.
[Figure 2]
[Figure 3]
2
DNA structure image, ‘http://www.chemguide.co.uk/organicprops/aminoacids/dna1.html’
[Figure2] and [Figure 3] show the model. The arrows in [Figure 2] mean the circulating
direction on each route. After circulating those routes cars can enter to each block like shown
in [Figure 3]. We assumed that there could be extremely high speed on the circulating routes
so that cars can reduce time. However, this model had problem with detailed movement
inside the blocks and there is lots of collision possibility when changing the routes and it will
cause lots of traffic jam. In [Figure 2] you can see that between the arrows there is lots of
overlap and this means lots of crash.
Thirdly, it is a model which we presented in the second presentation which has a fourdirection rotary. Four-direction rotary has a double layer structure and based on one rotary
the car can make direction changes to four directions.
[Figure 4]
[Figure 5]
Shown in [Figure 4] and [Figure 5] it has a rotary on first floor and can make direction
changes by exiting to the second floor. Placing reversely on the adjacent crossroad all cars
can make direction changes and can go straight. There were problems with this model
because, to go straight in this kind of road the driver had to make curved movement in each
rotary. It makes lots of inefficiency so we had to abandon this model.
Feedbacks
During our discussion and 1st, 2nd presentations we had lots of other opinions and
comments from other groups. It helped a lot in developing our project.
First was about entering the road in the first time. Lots of students were curious in our
model how it is possible to enter the road. So, we made some empty space in both sides of
the road so that they can enter or exit through that road and move vertically in that place. To
reduce chaos in side roads we restricted that the cars only can only use the right side of the
road of they were moving.
Second, as the flying car is also ‘flying’ how it will be if we use the road of ‘flying’
airplanes.
[Figure 6]3
[Figure 6] is a figure about the airways near South Korea. As you can see there are lots
of restricted areas in the air, so the airway is very limited. It is not appropriate for a way of
cars as there are very many cars and they have to be able to move every direction.
Third, there was a question why we put a restriction in the altitude. If there is no
restriction in the altitude, to make the traffic flow fluent the cars have to move to the upper
side of all buildings. Moving to the top of the building takes a lot of time and it means
inefficiency. So we made a restriction in the z-axis, altitude, as only four floors in the air.
3
이진숙 외 3명(2011), ‘항공교통흐름의 효율화 방안 연구’, 핚국항공경영학회
Lastly, the question was if the car can fly it means that there is lots of technology
development, than wouldn’t there be development in buildings also. However, as I said in the
goal part, we are concentrating on automobiles and road systems, and we are assuming that
the technology level is similar.
Considering these feedbacks and the peculiarity of our subject, we had to make a model
before optimizing and calculating the efficiency of the road system.
Main Section
Section1
Basic structure of the model and reason why this model
4
During our discussion we decided [Figure
7] as the most optimized model. Now we will
discuss why this model is the most efficient,
optimized one. Above all the city which we are
going to apply this model is a through planned
city so all of there blocks is a square like [Figure
8] which is a picture of Manhattan, New York.
Also
the
size
of
the
square
[Figure 7]
reference
Manhattan’s size which is about 140m. When we
use squared-block city model to go to a place
only one direction change is needed. This mean
a tremendeous reduce in traveling time.
This model has 4 stories, and each story
has different direction of movement. The
height difference between each story is 3m. As
you can see in [Figure 9] each story has a
different direction of arrows. If the first floor is
going to east than second floor will be south,
[Figure 8]
third will be west, and fourth will be north. If
each story has different direction the use of
centerline will be zero, and the driver does not
have to be aware of the opposite side car. This
will lower the probability of accidents.
Also, this
[Figure 9]
4
Satellite picture of Manhattan, New York, US, http://www.wikimapia.com
kind of system is beneficial for the turns. A turn and entrance between one story difference
roads is very natural, it is like a right turn in our crossroads. Later we are going to calculate
how much time it takes to make a one story difference turn. Other occasions are making a
two stories difference turn, which mean a U-turn, and a three stories difference turn, cases of
going from first floor to fourth floor or from fourth floor to first floor. In these cases as cars
have to move 6m and 9m each to make a turn, so it is very dangerous. So we applied the
concept of P-turn in these cases. Thinking simply, it could be thought that this is a very
inefficient and inconvenience model. However, thinking in the total system, other case’s time
of turn is visibly reduced so the average time will drop in a big gap than these day’s traffic
system. Considering other parts like safety and efficiency of the system, using this kind of Pturn system is not a loss in the view of the total system.
We set the number of lanes for each direction as 2, and to each direction there is two
spare roads to there both sides. The width of the car is 3.5m, and this value is from
considering the present road width of a highway in South Korea. To enter the spare road they
only can turn to the right from the main road. This restriction is for to avoid chaos in the
spare roads. Using the spare roads, drivers can park their car or fuel or etc.
Detailed model view
The detailed shape of our model appears in [Figure 10], [Figure 11], and [Figure 12]:
[Figure 10]
[Figure 11]
[Figure 12]
Section2
Detail explanation of the model
In our model we chose the length and breadth of the block as (37.5 + 140 + 37.5)m.
140m is from an architectural fact that a person can walk 140m without realizing that he or
she is walking, i.e. walking without any thoughts. In fact, also the width of Manhattan’s block
is also 140m. 37.5m is from turns. We will explain later but to make a turn it takes 60m in a
one fourth circle, and it means the circle has a half radius of 37.5m.
The width of each lane is 3.5m. As a road has 4 lanes, 2 lanes from main road and 2
lanes from spare roads, the total width is 14m. The reason we decided the number of lanes
at the main road as 2 is because if there is 2 lanes the problem with changing lanes becomes
much easier and it will eventually lower the accident rate. Also, even though setting the
number of lanes as 2 the traffic system can digest a large number of traffic without traffic
jam.
Explanation of the corner part
[Figure 13]
Generally, with 4~5 percent of slope, the car can move without reduce in speed. 5
percent of slope means moving 100m in the plane means 5m increase in height. So paying
attention on this fact we can calculate the length of the corner. The height difference
between stories is 3m so to go up 3m we need to go 60m. It becomes like [Figure 14],[Figure
15].
[Figure 14]
[Figure 15]
Actually, it is 60m when it is on a plane so it is larger when it is in the space. However,
relatively the height is not that big to the length, so we can approximate as 60m. (In fact, if
we calculate it we get 60.07m) When making the curve we use a one fourth circle. The
reason is that tangent of a circle is always 90 degree, so after passing the corner it has the
smoothest connection to the straight road. As the one fourth of a circle is 60m, half of the
radius is 37.5m. This is well described in [Figure 14].
Probability of an accident
When the driver enters the corner course, if the driver pays caution then there will never
be an accident. However, when exiting the corner course, and entering the straight course
will be a problem. So, we had some calculation on the probability of accident in the second
case.
In high school there is a math question like: Two people promised to meet between 1pm
and 2pm. The person who comes first will wait for 15minutes. What is the probability of the
two meet each other?
[Figure 16]
Using [Figure 16] we can solve this problem in an easy way. Calculating (colored are) /
(total area) is the probability we are trying to get. This kind of thing is called geometric
probability. We can use this method to get what we want, the probability of an accident.
[Figure 17]
Safety distance (m) = v * 0.3 + v ^ 2 / 100 (definition)
a : time required when speed in straight road is v1, and the driver maintains safety
distance = (safety distance) / (speed) = (v1 * 0.3 + v1 ^ 2 /100) (v1 * 1000 / 3600)
= 1.08 + 0.036 * v1
b : time required to go 5m straight, when speed in straight road is v1
= 5 / (v1 * 1000 / 3600) = 18 / v1
c : time required when speed in corner road is v2, and the driver maintains safety
distance = (safety distance) / (speed) = (v2 * 0.3 + v2 ^ 2 / 100) (v1 * 1000 /3600)
= 1.08 + 0.036 * v2
d : time required to go 5m in corner, when speed in corner road is v2
= 5 / (v2 * 1000 / 3600) = 18 / v2
Calculating the accident possibility with these variables, we get
P = [a * c – {(a – b) ^ 2} / 2 – {(c – d) ^ 2} / 2] / (a * c)
The graph of P is like [Figure 18]:
[Figure 18]
We set the speed v1 as 80km/h so we get a = 39.6 and b = 0.225. With these values we
can get a 2D graph like [Figure 19]
[Figure 19]5
The graph in [Figure 19] shows that when v1 is 80km/h and the cornering speed v2 is
over 70km/h the probability decreases as v2 increases. Increasing or decreasing speed in the
cornering section would be a burden for the drivers. So, it would be better if v 1 equals v2. By
other condition v2, the cornering speed cannot exceed 90km/h; I will explain the reason later.
5
WolframAlpha Calculator, ‘http://www.wolframalpha.com’
So for both reasons the speed in straight roads and speed in corner section should be
80km/h.
Putting v1 = v2 = 80km/h into the P formula we get c = 3.96 and d = 0.225, and finally
we get P = 0.11.
Latency time
P = 0.11 means if there is 100 cars entering the straight road then 11 of them will crash.
It is a terribly dangerous system. However, thinking with an active mind, it means that we
have to modify the vehicle’s speed to avoid accident only 11 times among 100. To avoid
accident the driver will decrease speed a little and then speed up to match 80km/h.
Considering the zero back (time required to accelerate from 0km/h to 100km/h) is about 1.8
seconds (regarding Bugatti Veyron) the speeding down and speeding up will take maximum
2 seconds. The latency time of 11 times among 100 is 2 seconds and the other 89 times will
be 0 seconds. So, the average latency time is 2 * 0.11 = 0.22 seconds, only 0.22 seconds. It
will not harm the traffic fluency, so there will be no harm or inefficiency in the system. In
other words, there is no reason to reject this model.
Cornering speed
We want to explain if speed 80km/h in the corner section is appropriate. As the flying
car is more similar to airplane than cars, we wanted to find the answer from the airplane case.
[Figure 20]6
[Figure 20] shows that to do a normal turning, centrifugal force and the horizontal
component of lift force should equal. Normal turning means an airplane doing a turn with
enough stability. Formula about [Figure 20] mentions that there is a relationship between
angle of circulating, air speed and turning radius. It could be expressed as R = V ^ 2 / g +
6
교통안전공단, ‘초 경량 비행 장치 가이드’
tanθ. R is turing radius, V is air speed, g is gravitational acceleration, and θ is angle of
circulating. If angle is too big the airplane will lose stability and give a burden to the body, so
the air department is restricting the angle as maximum 60 degrees. Applying to our model R
is 37.5m, θ as 60 degrees, and as g is 9.8m/s2, we can get that V is maximum 90.826km/h.
We cannot fly with the risk of exceeding the restricted angle, so we took 80km/h for the
circulating speed.
Conclusion
Efficiency in the crossroad
출발
1
2
3
4
평균
1
1.7초
2.9초
X
37.3초
14초
2
2.9초
1.7초
2.9초
X
2.5초
3
X
2.9초
1.7초
2.9초
2.5초
4
37.3초
X
2.9초
1.7초
14초
평균
14초
2.5초
2.5초
13.4초
8.3초
도착
[Table 1]
In this part we will examine the
efficiency in the crossroads. [Table 1] is
expressing how much time it takes to
make a turn each case. U-turnning is a
special, and unoftenly used case so we
excluded in our calculation, placing X
in the table. Going straight, case of 1-1,
2-2, 3-3, and 4-4, takes time 37.5m /
80km/h = 1.7seconds. Making a turn
between one story difference is 60m /
80km/h + 0.22seconds = 2.9seconds.
Lastly making a turn for three stories diffence, case 1-4 and 4-1, is (140m * 4 + 37.5m * 2) /
80km/h + 2.9seconds * 3 giving 37.3 seconds. Making the average of all cases gives us 8.3
seconds. It means averagely it takes 8.3 seconds to make a turn. In our real life when we
want to make a left turn, in maximum it takes more than 1 minute. So we can know that this
is a very efficient system.
Comparing a real case between flying car system and nowadays system
The best way to show the efficiency of our model is caculating the time required based
on a real case. In case of going to Seoul station from Yonsei University it takes 4.87km.
[Figure 21]7
[Figure 21] shows that it takes 4.87km and it takes 11minutes to go, and the map shows
that it needs approximately one turn. Calculating this case with our model 4.87km means
passing 27blocks. The time needed to pass 27 blocks, assuming that we make one turn (we
said that with one turn we can go anywhere), is {75m + (140m + 37.5m) * 27} / 80km/h + 8.3
seconds. This formula gives us 3.8minutes. Even though considering the time to enter the
road we can know that this model has a much more shorter, which is less than half, time
required. By this we can explain that the model we made is much more efficient than
nowadays model.
References

Flying cars, Wikipedia, ‘http://www.wikipedia.org/flyingcars

DNA structure image, ‘http://www.chemguide.co.uk/organicprops/aminoacids/dna1.html’

이진숙 외 3명(2011), ‘항공교통흐름의 효율화 방안 연구’, 핚국항공경영학회

Satellite picture of Manhattan, New York, US, http://www.wikimapia.com

WolframAlpha Calculator, ‘http://www.wolframalpha.com’

교통안전공단, ‘초 경량 비행 장치 가이드’

Naver Maps, ‘http://maps.naver.com’

하늘을 나는 자동차, ‘http://crazycar.kr/50125725245’

경상남도 신비차 경연대회, ‘http://peakhill.blog.me/140139940515’

하늘을 날아다니는 자동차,
‘http://www.aric.or.kr/trend/tendency/content.asp?idx=6&search=&k_s=0&k_e=0&k_so=0
&page=9&e_mail=’
7
Naver Maps, ‘http://maps.naver.com’