zaterdag 8 november 2014

The Earth is not flat, and it is certainly not round!

One year ago my friend went on a journey on the 'Oosterschelde', he sailed from New Zealand to the Falkland Islands crossing the South Pacific and rounded Cape Horn. Together with other sailing enthusiasts, he endured the elements of the ocean and enjoyed the many exciting times he had onboard. As you may have read in my previous post, I gave him a GPS receiver for an experiment I wanted to do. He placed it on board in good view of the sky and turned it on. Despite several reception losses (storms or other effects), the data clearly shows the path of the journey.

They started in Auckland, New Zealand, where they departed on the 30th of October 2013, to set sail to Chatham Island. This small island is governed by New Zealand and is closely situated to the International Date Line. Lets say the day starts on Chatham Island. After a small visit on the interesting island, the 'Oosterschelde' and its travelers started the long crossing of the South Pacific. The crossing went without any large problems, despite the large storms, which made life onboard the 'driemaster' a bit more difficult. However, after many days Cape Horn was insight, which meant a few more days of sailing and my friend would arrive at the Falkland Islands. He could look back at a great adventure! And I had my data for the experiment. 

As I explained (here), the Earth is not flat, but it is also not round. Due to the rotation of the Earth and the fact that it can deform, the shape of the Earth is more elliptic. The poles are pressed inward and the equatorial areas are bulging outwards. So the Earth looks a bit like a volleybal after somebody has sat on it for a while. But this is not the complete story. 

The Earth has mountains and trenches, bulges and holes, which affect the gravity field and the geoid. Inside the Earth there is not a homogenous mass distribution, due to plate motion, mantle convection, post-glacial rebound and effects we don't even know. These mass anomalies are responsible for a 'potato' shaped geoid (see Figure in previous post). The oceans of the Earth follow this 'potato' shape and is what we call level (waterpass in dutch). This sea level height is defined by us as 0 meter height. This enables us to say that Mount Everest is the highest mountain on Earth, despite the fact that the top of Mount Chimborazo is further away from the center of the Earth. It becomes even weirder, when I tell people that 0 meter height can vary over almost 200 meter depending on your location. So I wanted to show this with an experiment and gave my friend a GPS receiver.

The GPS receiver should show 0 meter height (or in our case 4 meter, because the GPS receiver was attached on the deck of the ship), during the complete journey of the Oosterschelde, because it was sailing at sea level, right? This is what it observed:
Sea level height with respect to the WGS84 ellipsoid. Red line is the EGM2006 model of the geoid. Blue dots are measurements of the GARMIN GPSmap 60 CSx during the voyage of the Oosterschelde.
During the complete trip the clipper and his onboard travellers made a vertical motion of around 60 meters. I know there were storms, but I did not hear of that kind of waves. Also this would give high-frequency motion, and that is not what we see. This 60 meter drop happened in 20 days, before they went up 40 meters again. This proves that the Earth is not flat, and certainly not round ;). I know it is not the maximum 200 meters drop, but than you have to sail from the center of Indonesia towards 2000 km south of India. If somebody out there is planning of doing this, please take a GPS receiver onboard and send me the data!!! 

zaterdag 25 oktober 2014

The start of construction of the TUDelft satellite tracking station: DopTrack

Monday 20 October 2014, we started the construction of DopTrack, a satellite tracking station on top of the tallest faculty of Delft University of Technology for students to use in satellite orbit determination. I will try to report on our findings of building it in this blogpost. We are in the process of setting up a dedicated website, but for now you have to do my blog ;)

Project DopTrack
As a master student, I followed several courses on orbit determination and satellite data analyses in the Astrodynamics & Space Missions group. During this time, I also observed the design and launch of two cube-sats of the space system engineering group. I was inspired by what students and university staff could accomplish. Come on, they launched two satellites in space. SPACE!!! However, after launch and succes of the missions the satellites were left alone. It would be cool to combine the use of these satellites and the knowledge from satellite data analyses courses. So I decided, when I became a PhD candidate, to construct a space operations practical that allows bachelor and master students to get hands-on experience with satellite operations and orbit determination. The idea for DopTrack was born!

I found another researcher and a bachelor student mad enough to help me in my adventure. Together, we started to design the tracking station and wrote a proposal for some budget to buy equipment. Because both professors saw this project as a good opportunity to improve cooperation between the groups, the proposal was accepted and we could start ordering equipment.

And before we knew it, the week of construction was showing up in our agenda.

Day 1: Installation of UHF antenna and ground equipment
Monday the weather enabled us to work on the roof. The weather forecast of the rest of the week looked quite bad, with a fall storm coming our way. So, we decided to install all the equipment on the roof and make it waterproof. This meant to check the already installed VHF antenna, placing the (bit smaller) UHF antenna and GPS antennas. we need the GPS antenna for our clock, such that the radio, SDR and computer all have similar frequency stability. We saw in the manual that the clock also calculates the position of the antenna (that is what normal GPS receivers do), so we placed the GPS antenna in between the two radio antennas. The sight was spectacular:

Antenna set-up (from left to right): omni-UHF, GPS, and omni-VHF antennas
Down below, we had managed to place an old network-server cabinet (it was very heavy, and there is no elevator between the 21ste and 22nd level!) for our electronic equipment. We ordered rack mounts for our radio and SDR, while the GPS receiver clock was already in rack mount geometry. After putting the rack mounts together, we placed the equipment in the cabinet. The computer, we have now, is not yet a server rack mount one, but we are trying to get this in the coming months. For now we use a common desktop. It looks like this:

Cabinet set-up with SDR, GPS clock, radio, and computer (top to bottom)
All in all, a good day, but fall was coming!

Day 2: Constructing cables and stormy weather
A big storm had arrived in Holland and at the top floor of this building we could feel this. Worried for the antennas on the roof, we checked their status with a remote video camera pointed towards the antennas. Luckily, everything was fine, we had installed them properly! Despite the horizontal rain fall:

See the movie with HD settings, otherwise it is difficult to see. During this stormy weather, we continued the construction of the set-up. This meant making a lot of cables and soldering the connections. I levelled my soldering skills a lot ;).

Day 3: Making more cables and connecting to the radio
The next day, even more soldering of cable connectors. We also checked if it was possible to remotely operate the radio. And after some internet coding and scripting, we were able to remotely turn the radio on and off again (this is especially useful for trouble shooting, somehow this is important for engineers). 

To be even more in control of the electronic devices, we had installed a power switch, which made it possible for us to remotely turn the power on/off of 8 different devices. This worked and gave use nerdy feelings, when we were turning on/off equipment with our laptop (a bit like the first episode of "The Big Bang Theory"). 

Day 4: Setting up local network and finishing installation of equipment

Finally, all the different cables were made and we could hook up the different components. The radio to the antennas and SDR, and the GPS clock to all the other equipment. In between the antenna and radio we had to put a splitter-board. We ordered antenna splitters, because the antennas would also be used by other setups in the ground station. The initial setup looks a bit like this (we still need to fix it to the wall):

Antenna splitter panels for the VHF, UHF, and S-band antennas
In front of the splitters we placed bias-T amplification, which puts power in the cables to the antennas. This results in less loss in the long (25 meter) cables that run on the floor of the roof. After hooking it all up, we wanted to see if things worked.

First recording of a satellite was a fact!!! You can clearly hear that this signal is moving due to the continuous shifting of the frequency (the tone of the signal constantly changes). A good result of day four.

Day 5: Getting the SDR and GPS clock working

Friday was the last planned day for work on the ground station. This was mainly trying to get remote acces to all the different equipment components. Hours of reading operating manuals, setting up connections from the router/computer to the different ports of the equipment and testing the remote connection on a different laptop. This will we be doing for some more days, but we got connection to the radio and GPS clock:

Remote connection to the GPS clock is established
The GPS clock is up and running and locked to several GPS satellites. The hardware is installed and now we need to fix all the software, before we can test the tracking capabilities of our station. And hopefully we get figures like this:

The Doppler curves in the radio frequency domain of the Delfi-C3 and Delfi-n3Xt (courtesy of Nils von Storch, operator Delfi ground station)
In the end, we will convert this to actual information about the satellite's velocity and position. When you, as a student, are interested in working with this equipment for your master thesis, please send us an email (doptrack[at] Furthermore, this facility will be used in the new Space minor of the Aerospace Engineering faculty of the TUDelft. From a student idea made to an actual education application. 

zaterdag 11 oktober 2014

My first estimates of the gravity field of the Rosetta comet, 67P/Churyumov-Gerasimenko

Last week, I saw a very incredible photo compilation. The Rosetta ESA satellite is currently orbiting a comet in outer space. Onboard is a camera, that is constantly taking pictures of the object. On thursday 2 October, the ESA Rosetta blog showed active geysers, shooting water of the comet out into space. What we learned as a kid, we can now see with our own eyes (well via the camera lens, a high-data space downlink, and a remarkable team in the ESA Operations & Science). Active geysers on a COMET!!!!!! Amazing.

After re-finding myself from being blown away by amazement, I continued browsing this blog. There, I found that they had build a 3D model of the comet and you (as an internet user) could download it to built your own comet. Totally awesome, unfortunately, I do not have a 3D printer. Nevertheless, I downloaded the files from the blogpost (see here). You can download .wrl and .obj files. Clicking on the .obj file, opened the comet in Adobe Photoshop. Look at that, I could rotate and play with my own comet:
This is what you see when opening the .obj file
After rotating the comet for several minutes, my nerdy brain started to pinch me: "Dude, if we had the coordinates of the surface, we could do some awesome stuff!". So I looked at the .wrl file with TextEdit (or Notepad) and found the following code.

#VRML V2.0 utf8

# Generated by VCGLIB, (C)Copyright 1999-2001 VCG, IEI-CNR

NavigationInfo {
type [ "EXAMINE", "ANY" ]
Transform {
  scale 1 1 1
  translation 0 0 0
      geometry IndexedFaceSet
        creaseAngle .5
        solid FALSE
        coord Coordinate
            -0.393756 0.401856 0.442509, -0.163294 0.491935 -0.000659, -0.515386 -0.259898 -0.343331, -0.277434 -0.260428 0.279815, 
            -0.55193 0.159748 0.155219, 0.091377 -0.282348 -0.211614, -0.792302 -0.192477 -0.092299, 0.785257 0.323246 -0.017733, 
            -0.093053 0.512756 -0.20542, 0.83051 0.3069 -0.045469, 0.795553 0.336202 0.063932, 0.168434 0.640004 -0.350024, 
            0.241654 -0.381833 0.019116, 0.200554 -0.206936 -0.422803, -0.215483 -0.128884 0.356076, -0.41427 -0.434269 -0.193254, 
            -0.687416 -0.006455 0.036488, 0.920413 0.222731 0.137458, -0.511265 -0.217672 -0.356012, 0.835122 0.2753 -0.114706, 
            0.724787 -0.241446 -0.305928, -0.574952 0.063756 -0.033269, 0.509054 -0.535483 -0.079728, -0.070761 0.50456 0.425794, ...

After the line "point" , a lot of numbers were printed, sets of three numbers separated by comma. These must be coordinates (x, y, z). They were normalised because the value of the numbers were between -1 and 1. So, I wrote a little code to separate these numbers and obtain three vectors, with the x, y, and z coordinates. To check if these were the surface-data points, I made a scatter plot.

The point cloud of the comet
Yes!!! I had obtained a data set of the surface of the Rosetta Comet (I call it the Rosetta comet, because its real name is very long (see title)). Now we could do some cool stuff. In previous blogposts, it might have become clear that I am a gravity scientist. My job is to look at objects (usually planets) and say something about their gravity field. In the beginning of my PhD research I had written software that is able to transform geometries + densities into gravity potential fields. I wanted to see if my software was able to generate a Rosetta comet gravity field. I already had the geometry of the object and an estimate of the density could be found on the ESA blog (do not use the English wikipedia page, because they think it is made out of material that is more than twice as light as water [400 kg/m^3], or they made a typo!), 4000 kg/m^3, which is typical for a stoney/ice comet. 

However, when I continued I run into a few problems. The .wrl file was normalised, so I needed to find a scale factor. On the blog I found a volume (25 km^3) that was given and using that value, I found that the scale value must be around 2500 m. Another issue was related to my software, which made me reorientate the origin of the comet (its one of those boring details, but if you really want to know, make a comment to this post). I translated the origin with the following values:

x = x - 0.2;
z = z + 0.25;

These modifications are a bit "sticky finger" work, but in the small time I had, I could not find better values and I really wanted to write this blog (maybe if I have some more time, or information). But now my software was able to make a gravity field model, assuming that the comet had a homogenous density distribution, which is not the case, but a good first estimate. Hopefully, after 12 November more information about that will be available (They are going to land a robot on the comet!!!!). Putting the geometry and density in my software, enabled me to make a model of the gravitational attraction of the comet.

The gravitational attraction in the radial direction at an altitude of 500 m above the highest point of the comet (in my reference frame), which is located around -120 degree longitude and +40 degree latitude.
I calculated the radial attraction (mGal is 1/100000 m/s^2, so very small) at 500 meters altitude above the comets highest point (in my reference frame). On Earth the radial gravity is dominant and doesn't vary that much, because of its spheroid shape, but here you even got negative radial gravity field, which is quite fascinating, or I am doing something wrong. Doubting my quick computing skills, I also plotted the magnitude of the total gravity vector.

Magnitude of the gravity vector felt at 500 m altitude.
Luckily there was no negative gravity, but in the southern area of the comet the gravity was quite low. At close distance the gravity field of a comet fluctuates very rapidly. You have to stop thinking in Earth or planet terms. To fly a satellite in this kind of environment is very tricky. I wish the Operations team at ESA a lot of success and hopefully they have a better representation of the gravity field (in a better reference frame) than I have.

zaterdag 23 augustus 2014

The tale of the two tides

Last week, I was sitting on the beach looking at the "Oosterscheldekering", one of the largest engineering constructions on Earth. It was designed to protect Zeeland from flooding during large storms and extreme high tides. As a boy I was always remembered of the power of the water (my complete family is from the island Schouwen-Duiveland, where the storm of 1953 hit hard). It gave me a sense of aw and pride, that engineers designed and build these large constructions. Maybe even, it gave me motivation to go into engineering.

As I was admiring the view, I was thinking about tides and their cause. One of the most common questions about tides is: Why are there two high (and low) tides a day? If tides are caused by the Moon, due to its gravitational attraction, there should only be one tide a day, because the Earth rotates only ones a day, right? The answer to this problem is: Correct Frame of Reference!

Since we, humans, know the Earth is round, we tend to place our point of origin in the center of the Earth. We can stand on the surface of the Earth, because gravity is pulling us (and sea water) towards this center of mass. This is why you do not fall off at the other side of the globe (yes even in Australia, everything falls down, I tested this myself!). This same force, together with the angular momentum of the Moon, keeps the Moon rotating around the Earth.

The Moon also has its own gravitational attraction, pulling other mass particles towards it, even our own Earth. If we look at a mass particle at an arbitrary location around the Earth, it experiences several forces. The gravitational attraction of the Earth is counteracted by the normal forces of the surface (me) or centrifugal force due to rotating motion (our mass particle). Another force is the gravitational attraction of the Moon (red arrow). However, both the Earth and the particle feel this force. This is where the correct frame of reference is coming into play.

The Earth is pulled a little bit, which means that the center of mass shifts a little bit towards the direction of the Moon. But as I told you, we like to think that our point of origin is at the center of the Earth. We live on the Earth, that is our frame of reference, that is how we experience tides.  Therefore, we (mathematically) have to correct for this by adding a resulting force (green arrow) to the Earth and any other mass particle (you, sea water, or our mass particle in an arbitrary location), same in magnitude as the gravitational attraction of the Moon exerting on the Earth, but in the opposite direction. This correction sets us back in the reference frame that we like, Earth centered.

This correction introduces an additional force on our mass particle (and on you and sea water, you get the point). With elementary vector addition (black striped lines), we obtain the true tide force (black arrow) that the particle experienced, as seen in the reference frame we live in, Earth centered. Theoretically we can do this for any particle, so also for the sea water on the surface of the Earth. The following sea level curve (which should be an ellipsoid, but my paint skills are not excellent) is observed due to the attraction of the Moon:

As you can see there are two bulges, instead of one. Lets take a better look at both locations. At location 1 (closest to the Moon) the gravitational attraction of the Moon is slightly larger than that at the center of the Earth. Gravitational attraction looses strength quite fast with distance (this is a good thing, otherwise black holes would be devastating and walking on the Moon, even more difficult). This means that the resulting tidal force is towards the Moon, as we all expected. Location 2 is experiencing the opposite, the gravitational attraction at the center of the Earth is larger than the force exerted on the sea water. This results in a tidal force, similar in magnitude as location 1, but in opposite direction, away from the Moon. However, Living on the surface of the Earth (as we all do), both tidal forces look similar, so therefore we experience two tides a day. 

Of course, the complete problem is much more elaborated and complex, but than you have to follow courses like Planetary Sciences, Astrodynamics or even Satellite Orbit Determination. Or post a comment on this blog and I will try to see if I can explain some more.

donderdag 14 augustus 2014

Gravity Expeditions at Sea: Promotion movie

Several blogpost are about this historic project I am working on. We, together with people of the library of the TUDelft, are describing the work and voyages of one of the most adventurous scientist and professor of my university, Professor Vening Meinesz. In the beginning of previous century, professor Vening Meinesz measured Earth's gravity field onboard several submarines of the Dutch Navy. Me, being a geoscientist with experience in gravity field modelling, was asked to explain his work and relate it to Solid Earth Science. Diving into his work and stories, I became very enthusiastic and motivated for the project.

We are in the middle of the project and are asking people to help us in any way they can. For this purpose (and because we live in a media-type world), we have made a promotional video. And I wanted to share this first version of the film. Please be aware! You will see me talking science :). If you like the movie and the project, please share it among your friends. Maybe we find somebody, that can help us in our quest:

dinsdag 5 augustus 2014

The Waddensea Experiment: combining sailing and science

Last week, I read in the papers that the Danish part of the Waddenzee is also put on the World Heritage List. This means that the complete Waddenzee (Dutch, German and Danish) is a protected nature site. Me, as a strong admirer of this region, makes this news happy and content! It also gave me new inspiration for a blogpost. In this blogpost I will look at an experiment that I did on the Waddenzee. At the end I will prove that the Earth is round (or more precisely, not flat).

The Waddensea is an area north of Holland, north-west of Germany and west of Denmark. when inspecting any atlas or google Earth, you can spot a row of islands from west to north-east. In between these islands and the mainland is the Waddensea, with all its beauty! 

The Waddensea is the area between the mainland and the small islands. The Dutch, German and Danish part can be seen.
Special about this region is the large influence of Earth's tides on the landscape and nature, the Waddensea is a very shallow sea. At high tide, the area is completely covered with water, but at low tide, large parts of the area become dry. This creates a very special eco-system thriving with life, see Wiki (The English page is quite short, but if you can read Dutch go to that page for more information). I know the Waddensea mostly onboard a "platbodem", or flat-bottom sailing boat. This is the best way of visiting this area and really get to experience the nature, people and water. Speciality of this ship is that at low-tide it can rest on the ocean floor, without tipping over. You just have to wait 6 hours, before continuing your journey.

We made the trip with the platbodem "de Overwinning".
Onboard one of these voyages I did my first GPS and navigation experiments. I just got my Garmin GPS receiver and I wanted to play with it. So, during a trip between two islands (from Ameland to Vlieland) I turned on the Garmin receiver and recorded the data. It was quite a nice trip, because at the end the wind started to increase and the captain put out all his sails to maximise the speed. We will see this later in the data. The track we sailed is shown in the next figure:

During this voyage, I challenged the "schipper" (captain) to go as fast as possible, because he was all the time bragging about the speed of his vessel. So, he put on all the sails he got and we flew over the water. I experienced this at the front of the ship, where I was responsible for the Fok. The speed and excitement is felt best at this location. The GPS receiver was turned on and recorded the whole trip, also the velocity of the ship.

Recorded velocity of the ship
As you can see, our averaged velocity was 6 knots, but at a certain point we touched the 11 knots (set-up of the many sails). We couldn't maintain this velocity, because our destination port was close. However, the trip was a good test-run for my GPS receiver. That night, enjoying a proper "schippersbitter" (sailing booze), I post-processed the data. One of my goals was to see how accurate the velocity was that was given by the GPS receiver. To find out, I used the more frequent position measurements, which I numerically differentiated. As we have learned in high school and again on university, the derivative of position/path/length/voyage is velocity. This is what I obtained:

First try at computing the velocity of the ship. Blue line is the recorded velocity. Red line is the computed velocity.
What was this about? My computed velocity was much higher then the GPS receiver presented. What did I do wrong? Because of a storm, we could not sail out. We had to stay in the harbour, which gave me time to explore the island (Vlieland, the second island from the west, see figure 1 and 3) and to clear my head. While enjoying the scenery of violent waves and stormy weather, I found my bug/error/stupidity. After getting back to the ship, grabbing a hot coffee to heat up, I jumped behind my computer and changed my code. "The Earth is round!", I stated. "Yes", said the captain, "it will be like that for some years, they say!".

I miscalculated the length of our voyage by using math for a flat Earth. I told my software that latitude was y and longitude was x, before calculating the length between two points by the following equation:

s = sqrt{(x2-x1)^2 + (y2-y1)^2}]

Which is correct on a flat surface, but not on the round Earth. Luckily, I was following a course on spherical geometry, which enabled me to calculate the distance between two points on a spherical surface.

s = 111.317*rad2deg(acos(cos(lat(2))*cos(lat(1)) + sin(lat(2))*sin(lat(1))*cos(lon(2)-lon(1))))

(Its less complicated than it looks). Inserting this relation in my code, for the previous one would give me the correct result.

The correct computed velocity in red overlies the recorded velocity in blue.
You can clearly see that the computed velocity has a higher time resolution, due to the high resolution in position recordings. Nevertheless, I found that the presented velocity of the Garmin receiver was as accurate as the position estimates. But more important, I rediscovered that the Earth is round and will be for many years to come (because, a "schipper" never lies).

zaterdag 5 juli 2014

Onboard a submarine

Last week, I could cross something from my bucket list. As the title already hints at, I was onboard a submarine. Ok, the submarine was not submersed in the ocean, it wasn't even in the water, but it was a real submarine, the Hr. Ms. Tonijn ("Tuna"). You can visit this submarine in Den Helder at the museum of the Dutch Navy. However, our project group (Vening Meinesz, I wrote about this) and I were guided by one of the officers that had served on board the Hr. Ms. Tonijn, who gave us an incredible tour inside the submarine.

The Hr. Ms. Tonijn was in service between 1966 and 1991 for the Dutch Navy, so it is a more modern version than the Hr. Ms. K18, but some technical details, as we will see, are almost similar. This three cylinder submarine was designed by ir. M. F. Gunning with the top cylinder, being the living quarters and visitable in the museum. The bottom two cylinders contained the massive diesel and electric motors, as well as the chemical battery compartment for the electric motors.

The Hr. Ms. Tonijn from above made suitable and safe for the visitors of the museum.
So, me being 2 meters tall, I thought to be very claustrophobic inside the submarine. However inside, I found it very cool and amazing. Ok, at some areas it was cramp and I got almost stuck, but overall I felt very good onboard the submarine. I might have spoken differently, if it was 100 meters underwater. Everything had its place and rules and the captain had a chair!

Captain's hut with his own chair (roughly 2x2 meters)
But as an engineer, I was mostly fascinated by all the technology onboard. The communications hut, the navigation hut, torpedo area and the control center. The heart of the ship is in the control center, where the ship is being sailed by several men. From here, the entire ship is commanded. It is also the place where the periscope is situated.

One of the periscopes of the Hr. Ms. Tonijn
Just like in the movies, it had two handle bars and could rotate around. Furthermore, this was one of the few places onboard that I could stand upright and move freely a little bit. So, me feeling like a little boy in a Lego shop, I tried out the periscope and..........IT WORKED!!!!!

The North Sea from inside the submarine
I felt like a real Captain Nemo and maybe also a Prof. Vening Meinesz onboard this incredible piece of technology. Solely designed to operate for many days under the Earth's oceans. I even pressed the button to launch Torpedo no. 7. (Un)fortunately it was not armed, so I did not shoot the German caravan that was passing by, traveling to the ferry of Den Helder. Before this act of bravery (or stupidity), our guide was telling us that the diving mechanism was almost similar to that of the K18. The levers and bars that controlled the ballast tanks for diving were designed and constructed in the docks of Fijernoord, which was also responsible for building the K18. So, by looking at these mechanism, I could go back onboard the K18, which I had studied and read about so much.

The diving mechanisms of the Hr. Ms. Tonijn were similar to those of the 35 year older K18. 
So, all in all a very impressive visit, where I learned a lot (yes, also that submarines do not dive to 5 km depths *blush*, see comment). I have grown aw and respect for the men onboard these incredible machines. Their companionship and seamanship is one of the best that you can find on the oceans of the Earth. But you have to be, if you eat and sleep in quarters like this.

Eating and sleeping quarters of the crew of the Hr. Ms. Tonijn
For me it was a great day full of little boys stories and wishes-come-true. It gave me motivation to continue my work on Prof. Vening Meinesz and his voyage onboard the K18. It gave me the strength to carry the K18 and its stories and bring it to the public, because those stories are fantastic!

Me holding the K18!
PS: Please also take a look at this website:, which is about the search for the only lost and missing Dutch submarine the Hr. Ms. O13.

vrijdag 16 mei 2014

Gravity Art: "The Face of the Earth viewed by a Gravity Scientist"

Last week I visited a conference which had the theme: "The Face of the Earth". At the conference were very inspiring talks and interesting scientists. It gave me new inspiration for my blog and my PhD research. It also gave me artistic creativity. So enjoy my art work titled: "The Face of the Earth viewed by a gravity scientist!" (click on figures to enlarge)

The figure represents the free air anomaly of the Earth. This anomaly is the deviation of the gravity signal from the main ellipsoidal signal (the 9.81 m/s^2 you learned in high school). The colors represent the magnitude of the deviation. So more mass is red and blue means less mass then the main signal (green is zero). But you don't want to talk numbers, you want to enjoy the colors, because that is art all about. The above picture is of course the old continent Africa. You can clearly see some nice features in the gravity field. In the middle of Africa (Congo) is a large blue area, showing the location of the Congo Basin and the old craton beneath it. Also you see the characteristic gravity signal of mid oceanic ridges, where the dynamic mantle pushes material up, creating a gravity high (reddish/orange). Furthermore, the large collision zone between Africa and Eurasia is viewed as large red band of mountainous land. Finally, the subduction zone near Indonesia is seen as a very thin ribbon of blue and red. What else can you see?

Another one I made for my Auntie Down Under:

She wanted to see more colors so I played a little with the colormap. Can you see cool details? For Example, I noticed small red/white blobs just offshore the west coast of Australia. Those are marine volcanos, which I did not know they existed (but now I found them on Google maps). Furthermore, I filtered the effect of mantle convection and deep density anomalies to get a better view on the crustal structures.

Can you see the differences (colormap is the same)?

Let me know what area of Earth you would like to see Gravity Artified, and I will see what I can do!

zaterdag 10 mei 2014

Gravity shows the shape of Earth (I need your help!)

I need your help! A few posts ago, I tried to measure the shape of the Earth using my acceleration chips in my macbook. After a quick sensitivity analyses I found out that the precision of the chips was not sufficient to do this exercise. However, I really want to see if I can measure the curvature of the Earth by looking at its gravity field. So instead of high-tech measurements with my macbook, I want to see if a low-tech solution (a string pendulum) is more accurate.

The basic physics behind a pendulum measurement. The relationship between the period (T) of the pendulum and its length (l) and the local gravity (g) is (yes, high school again):

Well, this is not entirely correct, but for this experiment (keep the amplitude low!!!) it is good enough (take a look here to get a better relationship). So, to measure the local gravity (g) we need to know the length of the pendulum (half-measure!!!) and the period of the pendulum.

So, what is my set-up? A piece of string with a weight of some sort attached to the end, such that it can move freely. Also I have a half-measure to measure the length of the string. For the experts out there, a temperature and air pressure measure instrument, which could be handy to determine the drag of the pendulum.

Schematic of the pendulum experiment obtained from Wikipedia
As we all learned in high school, the amount of mass does not influence the period of a pendulum. However, it does influence the amount of loss due to drag (ballistic coefficient, see my blogpost), so use a weight with substantial mass. I use a mass around 5 kg. Finally, some sort of stopwatch or clock!

Oh, and know at which latitude you do the experiment (as accurate as possible). Find the latitude on a map, GPS device or use Google Earth. We want to see the relation between gravity and latitude!

Lets start the experiment!

  1. Measure the length of the pendulum (rotation point to center of mass of the weight). Do this every measurement, because this could change due to temperature differences. This measurement must be done with a precision of 4 digits. So for a string of 1 meter, the absolute length must be know within a mm.
  2. (This one is for the experts!) Look at the temperature and pressure instruments. Write them down.
  3. Let your pendulum swing! Don't start with a too large angle (losses are strongest), but also not to small (difficult to measure period accurately). Lets say, 5-10 degrees.
  4. Start the stopwatch when the pendulum has no velocity, so at one of its highest points. This is much easier to time exactly, then when the pendulum is moving very fast (in the middle of the swing). Let the pendulum swing 50 times (or 10, however this will not give enough precision in your time measurement) and divide the measure period by 50 (or 10). This reduces the timing error and makes the measurement more precise.
  5. Calculate the measured gravity and repeat this experiment several times (calculate the mean and standard deviation).

My results are listed below:

Latitude: N 51 deg 59' 04.2'' ±0.2''
Height: 7 ±5m

Measurement 1: 9.8155 m/s^2
Measurement 2: 9.8012 m/s^2
Measurement 3: 9.8212 m/s^2
Measurement 4: 9.8126 m/s^2
Measurement 5: 9.8254 m/s^2
Measurement 6: 9.8083 m/s^2

Final gravity measurement: 9.814 ± 0.0087 m/s^2 (one standard deviation)

Now It is up to you! Can you do the same and send me your measurements? Lets see if we can get a global coverage (at all latitude) and try to measure the shape of the Earth!

Good luck!

woensdag 16 april 2014

Listening to the sound of satellites

Last week, components of the TUDelft satellite tracking station were delivered. This includes a radio, amplifiers, Software Defined Radio (SDR), a GPS-based clock and other cool electronics. We are now planning the integration of all the components in the existing ground station, which is used for the data downlink and command uplink of the Delfi-C3 and Delfi-n3Xt (both student designed and built satellites currently orbiting Earth). But how does this tracking (you speak of) works?

It starts with capturing and recording the communications signal of the satellite, which is transmitted continuously (if the Sun shines on the solar cells to produce energy). This is where all the fancy and complicated electronics play a role. (However, I am not an expert in this, so I will only explain the physics behind it). The high frequency (145.870 MHz) electromagnetic signal is down-converted to a signal that can be made digital, such that a computer can process it. First we put the signal through a Fourier Analyses to see its frequency spectrum (The pictures I showed many times on this blog):

So, here we see a part (zoom in) of the frequency spectrum of the recorded signal. The colors represent the amount of energy (sort of) of the signal at a particular frequency (x-axis) at a certain time (seconds after start of recording). What you can see is the characteristic Doppler-curve or S-curve. Due to the Doppler effect (just like sound of a passing ambulance), the recorded frequency of the signal is received higher than transmitted by the satellite when the satellite is flying towards you. The opposite happens when the satellite is flying away from you. The received frequency of the satellite is smaller than is transmitted by the satellite. So if the satellite was not moving with respect to you, you would see vertical straight lines in the figure above. 

Now comes the beauty of the physics! When we measure this frequency change, we can get information about the velocity of the satellite and its trajectory. Maybe you know it from your high-school physics book:

The difference in observed frequency (f) with respect to the transmitted frequency (f0) is the transmitted frequency multiplied with the ratio of the relative velocity (v) and the speed of the signal (c, which is the speed of light). The relative velocity is the change in distance in time between the transmitter and the receiver. In our case is the satellite transmitting and we are receiving. So in theory by measuring the received frequency and knowing the transmitted frequency (which we not exactly know) we can deduce the relative velocity of the satellite with respect to the ground station. We like to call this observable the range-rate.

Some of my students did this exercise using the signal of the Delfi-C3 that we recorded. With some assumptions on the transmitted frequency and neglecting atmospheric refraction, the following range-rate profile of the pass was obtained:

They used two different assumptions for the transmitted frequency (blue and red), but that is not what I want to show you. Look at the y-axis, the relative velocity is plus/minus 6 km/s. So at the beginning of the pass the satellite is flying with 6 km/s towards the ground station (lets assume the ground station is not moving). Then at around 460 seconds after the start of the recording the relative velocity between the satellite and the station is 0 m/s. This is exactly the Time when the satellite is at Closest Approach (TCA) or just above you. From then on the satellite will fly away from you. This change in relative velocity is not because the satellite slows down, stops, and speeds up. No, the velocity of the satellite is constant (well almost, but lets not go into the details). 

The change in relative velocity is because the satellite's location also changes. The following cartoon illustrates this.
What we measure is a component of the velocity of the satellite, the component towards us. At the horizon (when we start hearing the satellite), this component is largest due to the geometry of the setup. During the first part of the flight of the satellite this component becomes less (not well drawn in my cartoon, I am sorry for this), because the angle between the velocity direction  and the relative velocity component decreases. Just overhead, this angle is 0 degrees, which means that the velocity component in the direction of the satellite is zero. Also at this moment you are receiving the transmitted frequency of the satellite. The signal experiences no Doppler shift (This was assumption one of the students (blue)). However after this point, the relative velocity increases again, resulting in a change of received frequency. 

So by listening to the sound of satellites, you can predict its orbit and velocity. But how you transform range-rate observations into orbit determinations is a science in it self. I will need more than a few blogs to teach you this.

zondag 30 maart 2014

Propagating trajectories

It is many weeks since my last blog post, my humble apologies! I was very engaged with my work. I was teaching students the wonders of Planetary Sciences, which is a difficult task, because 80 percent of them just wants to build satellites (damn you engineerings, wanting to built stuff). However I do not complain because this year's group is really participating and some of the students even want to do some science (mate).

In one of their last assignments they had to work with ballistic trajectories (calculating planetary geysers and volcanic exit velocities). This particular subject gave me inspiration for a new blog post, so there you go. Ballistic trajectories always interested the minds of many young boys (and might a say girls) and I have a great story about it, but I was always hesitant to write it in my blog. Some would say (me being one of them) that guns are bad (but can be modeled very well with ballistic trajectory theory)! Still my fascination for modeling and science wins this internal discussion.

What is the ballistic trajectory assumption? It is a way to model objects that are kicked, thrown, blasted and shot into the air. For example a stone, arrow, bullet or cannonball (Oh, I am re-living knights and dragons, which I played when I was a boy). Lets say you want to know at what angle you should hold your bow and arrow (gun or cannon) to shoot the farthest. What is your maximum reach! Very handy to know, so that you can shoot your enemy knights. In the movies (I saw a lot of cowboy, king Arthur and Roman age movies) they always state that you want to shoot the farthest, the angle of bow and arrow should be 30 degrees. Lets check that with the ballistic trajectory assumption.

When shooting an arrow in our model world it is only affected by gravitational attraction of the ground. On Earth this acceleration is around 9.8 m/s^2 (depending a little bit where you are on a Earth). It is pulling the object (in our case the arrow) back to the ground. However, this is delayed because we give the arrow a certain initial speed at a certain angle, when we release the bow. This will give the arrow a parabolic flight path.

The exit velocity in this case was 100 m/s and the exit angle was 45 degrees. This results in a parabolic flight of the arrow.
Depending on the angle, the arrow flies high or low and will drop to the ground far away or close by. The trajectory of the arrow is characterized with the following equation:

Here is s the location of the arrow, v is the velocity of the arrow and a is the acceleration of the arrow. Both s0 and v0 are the location and velocity at the beginning. In 2D space this relationship is a vector equation with two dimensions, x and y. So s is a vector which states the location of the arrow in x and y dimensions. The acceleration on the arrow is only the gravitational attraction, ay = -g. This relation can be solved when we have an estimate for the exit velocity and the angle of the bow and arrow. Because the exit velocity is fixed (depending on the strength of your bow, or how much gunpowder you use), essentially we have to solve this equation for maximum distance depending on the angle. Or, in other words, the longer the arrow stays in the air, the further it travels. So (using the abc-formule):

Solving this results that the maximum distance with a bow and arrow (or any other trajectory producing device) is 45 degrees. Hmmm, this is not the same as in the movies! Are the movies incorrect? Of course not!

We miss an essential parameter, namely air-drag. The arrow is flying through an atmosphere which slows the arrow down. So we have to model this as well and here is where the propagator comes into play. The introduction of drag makes the problem that much complex that it cannot easily be solved analytically. Therefore, a numerical propagator is used to solve the problem. What is a propagator and how can we solve the problem with drag.

There are many different propagators: Runge-Kutta, Adams-Bashford (see my previous post), and many others. But to explain the principle we use the most simple one called the Euler propagator (after the famous mathematician Euler).

This relation states that a state of an object in the future can be determined by its previous state plus its time derivative times the amount of time between the two states. For example, when I run with constant speed (15 km/h) and I know where I am now, I can predict where I will be after one second, because of my constant running speed. You can even go a little bit more complex by using the Euler propagator to estimate your velocity, when accelerations are known.

With these two relations, the trajectory of the arrow can be computed (or propagated) with any known force model (gravity, drag, wind, rotation of the Earth, aliens shooting at it, higgs boson, ...). We only have to determine the force model, which in our case, now is gravity and air-drag.

To determine the air drag, we need some physical parameters of the arrow (ballistic coefficient!!). I found another geeky site which explains this quite well. Furthermore, I need a density profile of the Earth's atmosphere. Because we are not doing rocket science, I will estimate the density of the atmosphere by a simple exponential decaying relation (you will be surprised how many rocket scientists still using an exponential decaying density distribution). Now that we have all the physical parameters, lets shoot some arrows!

Great thing about modelling with computers is that you can do many experiments in seconds. So I used the physical parameters of a heavy thin arrow (best of the best!) and shot the arrow at angles between 0 and 90 degrees and I measured the distance they traveled. These were the results:

As you can see, around 30 degrees the arrows travelled the furthest. So you see, movies are correct when it comes to arrow trajectories.

Arrows are very nice, but does this also work with the biggest gun ever made: the Paris gun. This gun was used by the Germans to shoot at Paris (giving its name.), however they used an elevation angle (exit angle) of 55 degrees. Could they shoot even further?

Using the parameters from the wikipedia page to calculate the ballistic coefficients of the Paris Gun bullets and putting this in my program, resulted in the following plot.

Clearly, a different profile is seen with respect to the bow and arrow case. First of all, the used elevation of 55 degrees results in the largest distances achieved. Also an asymmetric profile is seen, this is mainly due to the atmosphere. The projectiles of the Paris Gun flew between 20-60 km height. At these altitudes the atmosphere is very thin, which caused the the projectile to fly even further. The 55 degrees elevation would cause the projectile to fly quickly above the thick atmosphere and travel its largest distances above the troposphere. However, at exit angles below 30 degrees, the projectile would stay in the troposphere experiencing a lot more air drag.

Again modeling proves that movies and wikipedia tell the truth!

maandag 10 februari 2014

How to stay at the boundary of our current knowledge

As a scientist, your are expected to be at the boundary of the current knowledge in your field. You should know which state-of-the-art methods are used. The newest findings should be know to you. And more importantly, you should know what is still unknown.

As a PhD candidate, you are learning to become a self-sustainable researcher. Therefore, a PhD candidate should, in the end, be at the boundary of the current knowledge of his subject and maintain that knowledge. So how do you keep up with the fast expanding frontier of knowledge in your field?

My trick to stay at the boundary of the current knowledge is to keep an eye on the most important journals in my field. You can do this even if you are not subscribed to the journals. Every journal has an RSS feed (I know this is an ancient tool, but it works so why don't use it), that gives information on the latest publications of the journal. Most of the cases, it releases the abstracts of the latest accepted articles.

Journal of Geophysical Research: RSS-feed for example 

Just look for RSS-feed on the home page of the journal.

If you link these RSS feeds to your email, you will be posted when new articles are available. A quick look in the titles and abstract texts of the new journal papers should give you an idea about the relevance of the article. So open your email to the frontier of knowledge!

PS. cool link about this subject. It keeps you humble!

donderdag 2 januari 2014

TUDelft students are awesome!

A few weeks ago the second TUDelft satellite (Delfi-n3Xt) was successfully launched into an orbit around Earth. In space, yes! This satellite was designed and built by students of my university. However, their other 5-year-old satellite (Delfi-C3) is still flying and communicating its data towards Earth. A student, a colleague and I are using this old satellite to test our idea for a new satellite-orbit determination-project. I always like to call it: "Listening to the sound of satellites" (see previous posts). 

During the launch event I was thinking that it would be cool to capture both satellites' transmission in one observation using the VHF antennas. So I ask the ground station operator (the student), if this was possible. After a few days he send me this figure:

He found a day that both satellites were visible from the TUDelft ground station. The red line is the orbit track of the Delfi-n3Xt (new one). The green cross is the location of the TUDelft ground station and its visibility area shown with the dotted yellow line. Delfi-C3 (old one) can be seen in between the red lines, shown here as green dots. Both satellites were in view of the ground station that day, which meant that they both could be recorded at the same time. 

There is, however, a small theoretical problem. Both satellites use a transmitting frequency of 145.870 MHz, so they would be plotted on top of each other in a frequency plot. Still, I asked to record both satellite's signal and this is what it looked like in frequency domain:

(Click on the figure to get an even better view.) Here both TUDelft-built satellites are observed by recording their transmitting signal and performing a Fourier transformation. Both satellites shown the characteristic S-shape due to the Doppler effect (see previous posts). The left and slightly smaller signal is the Delfi-C3, which was less powerful than the newly launched Delfi-n3Xt, shown here on the right. It can also be seen that the carrier frequency of both satellites is not the designed 145.870 MHz, because they do not overlap each other (and the vertical green line in the middle represents 145.870 MHz).

I can't stop watching this figure, because it shows student engineering at its best. Two TUDelft tandem-flying satellites in space. Next time, think again, when you want to say that students aren't capable!