SOLAR IMPULSE - LESSON - MODELS (ENG)

1/15

MODELS AND MAPS “Scale that!”

For a flight such as the one by Solar Impulse to be possible, it has to be planned down to the tiniest detail.

This worksheet will help you understand how pilots keep track of where they are when they are flying. You will also get to know the maps and units that are commonly used in aviation.

Project: EPFL | dgeo | Solar Impulse

Writing: Angélique Durussel

Graphic design: Anne-Sylvie Borter, Repro – EPFL Print Center

Project follow-up: Yolande Berga

2/15 MODELS AND MAPS

HOW DO PILOTS KNOW WHERE THEY ARE WHEN FLYING?

Bertrand Piccard and André Borschberg, the adventurous pilots of Solar Impulse, and the entire ground crew have to know exactly where they are at all times. Not only is it essential that they know their po-sition while flying, they also have to know the exact location of where they would like to land! To plan their flights and keep track of their exact position, they rely on up-to-date maps and new technologies (GPS). The cockpit of the Solar Impulse HB-SIA plane is depicted below.

ALTITUDE

In the world of aviation, altitude is measured in feet. As its name indicates, the unit is based on the length of a human foot, or about 30 centimeters. In 1959, a foot was defined to be exactly 30.48 cm; before then, the length of one foot varied from country to country. The symbol for feet is ft, although you might come across pi for pied (French for foot). In some English-speaking countries that do not use the met-ric system, feet are still used to measure distances.

Omega Instrument (custom designed for Solar Impulse): informs the pilot on the bank angle of the plane. In commercial aircraft, an alarm goes off between 30° and 35°. In the case of Solar Impulse, it is set at 5°, as the plane can stall at 10°, potentially causing it to crash. Diodes indicate the bank angle as well.

Power Management Com-puter (PMC): indicates the status of the batteries, the motors, and the solar pan-els. Among other things, it checks for overheating. The smaller screen provides the same information and takes over if the PMC crashes.

Artificial horizon: indicates the position of the plane relative to the horizon. There are two, in case one stops working. Both include a compass.

Engine malfunction lights. There are four, one for each motor.

GPS

Air Speed Indicator

Transponder: emits radio signals that communicate with the control towers to provide the plane’s position when it is in controlled airspace.

The International System of Units (SI-units) has seven base units:the meter, the kilogram, the second, the ampere, the kelvin, the mole and the candela, which quantify indepen-dent physical quantities.

The United States, Myanmar, Liberia and the UK (in certain fields) use units that are not based on SI-units.

MODELS AND MAPS 3/15

LATITUDE AND LONGITUDE

GPSs provide information on the latitude and the longitude of the receiver.

Latitude and longitude are expressed in degrees. Degrees are a sexagesimal unit: like hours, they are divided into 60 equal units. A degree [°] can be written out as a decimal number, or it can be written out as degrees, minutes, and seconds. 1degree (1°) = 60 minutes (60’) = 3600 seconds (3600’’)

On the surface of the earth, one angular minute of latitude corresponds to one nautical mile, a dis-tance we will convert into kilometers in an exercise. This unit of length is used in aviation and on sea.

Be careful not to confuse nautical miles with miles (or terrestrial miles) used in English, which corre-spond to 1.609 km.

The longitude specifies the east-west position of a point on the earth’s surface. All points with the same longitude form a circle that is perpendicular to the equator. These circles are referred to as “meridians.” The zero-meridian runs through the Greenwich, England and is referred to as the Greenwich Meridian.

Longitudes range from 0° to 180° east or west.

The Lausanne airdrome is located at 46.545° north, which can also be written 46° 32’ 42.98’’ (read 46 degrees, 32 minutes and 42.98 seconds).

The Lausanne airdrome is located at 6.617° east, which can also be written 6° 37’ 00’’ (read 6 degrees and 37 minutes).

Equator

angular value of the latitude of Lausanne

Lausanne

distance ≈ 2792,7nautical miles for a 46,545° angle at the center of the sphere

46.545°

All of the points on this circle have the same latitude as Lausanne

All of the points on this circle have the same longitude as Lausanne

anglular value of the longitude of Lausanne

Lausanne

6.617°

GreenwichMeridian = 0°

The latitude specifies the position of a point on the earth’s surface rel-ative to the equator. All points with the same latitude form a circle that runs parallel to the equator, which is why latitudes are also sometimes referred to as parallels.

Latitudes range from 0° to 90° north and south.


MAPS

Today, thanks to satellites that communicate with receivers in our mobile phones, cars, planes, and boats, we are used to always knowing exactly where we are. Because of that, we no longer rely as heavily on printed maps, despite the fact that mankind spent over 2000 years improving their accuracy.

In the early 15th century, the great discovers such as Christopher Columbus and Magellan only had access to rudimentary, incomplete maps. Their voyages contributed enormously in improving world maps.

The picture to the right shows a representation of the world according to Mercator (end of the 16th century), offering navigators a true description of the boundaries of the landmasses.

As early as the 2nd century AD, Ptolemy compiled the world’s geographical knowledge. To each known point, he attributed coordinates based on a grid that spanned the globe.

The picture to the left shows a map from the 15th century of the world as described by Ptolemy’s writings.

The intersection between the latitude and longitude lines defines the position on the globe.

Example : 30° N 60° E

Latitude 60° N

Latitude 30° N

Longitude 60° O

Longitude 30° O

Longitude 60° E

Greenwich Meridian

Longitude 30° E

Equator

Latitude 30° S

The town of Greenwich (near London)


The first balloon pilots and aviators to see the earth from the sky also contributed to these im-provements. Photography became a fantastic tool for cartographers.

Later on, the Apollo missions and then satellites helped achieve major leaps forward. The picture on the left shows a photograph of Earth taken during the Apollo 17 mission.

Mathematicians at the service of geography!

Rulers were always interested in mapping their territories – be it to serve the military or to improve transportation routes. To do so, they called on the great mathematical minds of the their times. Thales was one of the earliest to represent his region as maps. Over the following centuries, maps became more and more accurate thanks to improvements in pro-portionality, trigonometry, and other mathematical tools.

Léonard Euler (1707- 1783), a great Swiss mathematician and physicist, also had a go at improving maps under a mandate of the Russian tsars. Although we remember Euler for his mathematical contributions (trigo-nometry, algebra, calculus, number theory, his work on solids, and more), we should also recognize him for his cartography of the entire Russian Empire, which he carried out with French astronomer Delisle. And he didn’t limit himself to the earth; he even managed to calculate the trajec-tories of comets! The Swiss ten-franc bills used from 1976 to 2000 pay tribute to his achievements.


The only printed maps that the pilots of Solar Impulse take on board with them are detailed airport approach charts.

The map on the right is an airport approach chart for Paris.

Flight simulators that compute and provide simulations of the environment to pilots could be considered to be maps, at a scale of 1: 1.

These simulators play an important role in pilot training. They give the pilots an opportunity to learn how to overcome prob-lems they could face during a flight, and that without putting their lives at risk (because the training takes place on a com-puter).

SCALES

For a map to be usable, you have to the ratio between the distances depicted on the map and the distances in reality. Of course all proportions are conserved in order for the reproduc-tion to be true to the model. The ratio between the map and reality is referred as the “scale.”

There are many ways to express the scale of a map. The most common one is to annotate the map with a fraction (1: 25,000 or 1/25,000). The fractions give the correspondence between the distance between two points on the ground and the distance measured on the map. On a map with a scale of 1: 25,000, 1 cm on the map corresponds to 25,000 cm (or 0.25 km) in reality.

True False

On a map drawn to scale, the proportions are always conserved

4 cm on a map with a scale of 1: 25,000 represent 100 m on the ground

A diagram always depicts objects as being smaller than they are in reality

If 1 cm on a map represents 0.02 cm in reality, the scale of the map is 50 : 1

Quiz

Sometimes the scale is also specified in words (e.g. 1 cm represents 2 km in reality) or lines representing distances in reality, as shown below:

2.5 km

250 cm 500 m


Solar Impulse has a wingspan of 63 meters. Once on land, the plane is vulnerable; a gust of wind can be enough to knock it over. That is why it has to be stored in a hangar for protec-tion. During missions, the logistics team has to make sure that large enough hangars are available. A mobile hangar was even built to protect the plane when there were are no other options.

For its mission in the United States, the plane had to be transported, which was a hard nut to crack for the team that had to ensure that dismantled, all of the pieces of the plane found a place on the cargo plane.

How can you make sure that the plane can be stored safely when it lands on foreign soil? What kinds of solutions can help to carry out missions and at the same time protect the result of years of work? Questions like these keep Léone-Aure Bes busy at work.

LÉONE-AURE BES, TECHNICAL LOGISTICAL COORDINATOR FOR MISSION FLIGHTS

PORTRAIT

Before the American mission in 2013, Léone-Aure was part of the team that prepared the tests of the mobile hangar, a revolutionary inflatable structure that was designed to house the plane during its jour-ney around the world. What she loves about her job is that she always has to custom-design solutions: the demands imposed by the project are so uncommon that commercial solutions simply don’t exist. Léone-Aure, who graduated from the Strasbourg Business School, is the technical coordinator for lo-gistics for the Solar Impulse mission flights. Following a six-month internship, she was hired full-time to take part in preparing the missions of the 2013 flight, but also to manage the plane’s hangar in Payerne.


ALL OF THIS IN NUMBERS…

Exercise 1

Models played an important role in the construction of Solar Impulse. Models of several prototype de-signs were made before the plane that we have before us today was built. Several full-size prototypes of the cockpit were constructed out of wood to confirm that there was space for all of the necessary instruments and that the wiring would not disturb the pilots.

This model of Solar Impulse has a wingspan of 31.6 cm, while the wingspan of the actual plane is 63.8 m.

a) What is the scale of this model?

b) How tall would a figurine representing the pilot be if it were built according to the same scale?

Exercise 2

a) Calculate the length of a nautical mile, considering that the circumference of the globe is 40,000 km.

b) The town of Eyrarbakky in Iceland lies at a latitude of 63°50’.

At the beach, you can read the following information:

«If you go straight south from this point, then you will sail over the vast ocean and not reach land until at the shores of Antarctica. This will be the ice covered Lyddan Island, by the shores of Coats Land on Greater Antarctica, at a distance of 15,329 km. Add 1,782 km in the same direc-tion, and you will stand on the actual South Pole, which is 17,111 km from here.».

What is the latitude of Lyddan in degrees and minutes?


Exercise 3

The map below represents the Solar Impulse’s European tour in 2011.

a) Considering that the scale of the map is 1: 4,500,000, calculate the distance from Brussels to Paris (as the crow flies).

b) The latitude of the Payerne airdrome is 46° 50’ 35’’ N. Convert this value into decimal degrees.

c) The longitude of the Payerne airdrome is 6° 54’ 54’’ E. Considering that Belfort is at the same longitude, determine the distance that separates the two cities given that the latitude of Belfort is 47.633° N?

Payerne

May 14, 201112 hours 59 min.

June 14, 201116 hours 5 min.

July 13, 201112 hours 31 min.


Exercise 4

The following is a plan of an Airbus A340, with a wingspan of 64.45 meters.

a) Add a dimension line to the diagram representing the wingspan of Solar Impulse, which measures 63.8 meters.

b) Also add a dimension line representing a small Cessna 170 propeller plane (4 seats) with a wingspan of 11 meters.

c) What is the ratio between the wingspans of Solar Impulse and the Cessna?

d) The same question as above for the Cessna and Solar Impulse.

wingspanof the airbus


Exercise 5

The altimeter indicates an altitude of 4,900 feet when the plane is flying at low altitudes and 28,000 feet when flying as high as it can. What is the difference in altitude in meters between both readings?

Exercise 6

- Control tower to HB-SIA* : What is your current altitude?- HB-SIA to control tower : 5,600 feet- Control tower to HB-SIA : Be careful! You have to gain altitude! Thepassyouhavetoflyoverisat2200m!

*RegistrationnumberoftheSolarImpulseplane

Exercise 7

The plan below is of the tow tug that is used to move Solar Impulse on the tarmac. The dimen-sions are in millimeters.

What is the scale of the plan, and what is the maximum height of the tow tug.

How many meters does the plane have to climb to clear the pass by 400 meters?

height of the tow tug


BRAINTEASER

From takeoff to landing, the Brussels-Paris flight (about 300 km) took about 15 hours. You can’t call Solar Impulse quick! In fact, using proportionalities suggests that the plane progresses at an average speed of only 20 km/h.

In reality, the plane flies much more quickly. The problem is that it has to take off and land when the sun is below the horizon. Why? When the sun is out, it heats the earth, creating turbulence that Solar Impulse is ill-quipped to handle. To avoid this, it has to take off early and land late, even if it makes it to the destination earlier, in which case it has to circle the airport until it is finally able to land.

For a Payerne-Brussels flight, Solar Impulse took off at 5:00 a.m. from Payerne and arrived in Brussels airspace at 1:00 p.m.

On the next page, you can see a diagram of the plane’s trajectory. Using the diagram and the road map that has been provided, answer the following questions:

a) What towns will the plane fly over on that day at 7:00 a.m., at 9:00 a.m., at 10:00 a.m., and at noon, considering that at 6:00 a.m. the plane is expected to be between Morteau and Le Russey, to the north-east of La Chaux-de-Fonds, on the French side of the border?

Draw the plane’s flight path on the roadmap.

b) To get a chance to see the plane with his binoculars, Jean, who lives in Metz, could drive to the vicinity of Grostenquin (east-south-east of Metz) at 9:00 a.m. and then to Saarlouis at 10:00 a.m. He has to be back at noon to have lunch with his children. Jean plans on traveling by car to be able to access strategic locations (average speed: 60 km/h). He has the plane’s flight chart to prepare his trip.

1. Will he be able to see the plane at both locations? 2. Where would you recommend him to go to see the plane? 3. At what time would he have to leave, and when would he be back?

c) What distance did the plane travel from its departure at five o’clock to its arrival in Brussels airspace at one o’clock in the afternoon? What was its average speed?

d) What distance did the plane travel from when it arrived in Brussels airspace until it landed at 8:00 p.m., considering that it continued flying at the same average speed for the remainder of the flight?

e) One person would like to be witness both takeoff and landing. Can he make it if he travels from Payerne to Brussels by car?


11:00 Luxembourg

5:00 Payerne

Bern

Switzerland

France

Germany

Belgium

13:00

12:00

10:00

9:00

7:00

6:00

Brussels


DELVING DEEPER…

On the next page are detailed plans seen from above of how the pieces of Solar Impulse will be loaded. The components of the motor and the batteries, as well as the rotors and various tools, etc. are all kept in boxes labeled as “auxiliary parts” on the plan.

a) The wings (with a total wingspan of 63.8 meters) have been disassembled into three segments. The horizontal and vertical stabilizers have been placed whole into the freight deck, along with the hull and the cockpit. Find these pieces on the plan. Look carefully at the cross sections at C and B.

b) Draw a sketch of the Solar Impulse plane as seen from above.

c) Determine the scale of the plan using the wingspan of Solar Impulse as a reference. Compare the scale that you calculated with the scale that is indicated on the plan. You will notice that they are not the same. Can you find an explanation for this?

d) Use the information on the plan to determine the width of the wings at cross section B (which cor-responds to their maximum width).

Solar Impulse was disassembled to be transported to the United States, where it flew across the country from the West to the East Coast. The plane was transported on board a cargo plane (Boeing 747), which just barely managed to land at the small Payerne airdrome.

The main internal deck holds all of the dismantled pieces of Solar Im-pulse as well as the material needed for the “Across America” mission, including the tools required to reas-semble it.


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Technology

SOLAR IMPULSE - LESSON - MODELS (ENG)