Drone battle: Parrot ANAFI vs DJI Mavic

Last month (June 2018), Parrot announced the release of its new drone ANAFI. ANAFI is a small and foldable drone in the same concept as the DJI Mavic and is planned to be a direct competitor for the DJI Mavic. ANAFI is already on sale (since July 2018), and some drone enthusiasts are curious about its capabilities and the comparison ANAFI vs Mavic. 5 points were considered.
  • Camera
  • Portability
  • Flight ttime
  • Price
  • Additional features

After commenting in several photography forums, we can conclude that ANAFI is better than Mavic for the following reasons:
Although both drones sport a Sony CMOS camera sensor for photo and video, while Anafi employs a superior 1/2.4” sensor that shoots 21MP (5,344 x 4,016) (Mavic Air uses a 1/2.3” sensor capable of 12MP 4,056 x 3,040). 
Comparing lenses, the ANAFI has a superior aperture (F2.4 vs F2.8) and can hit faster shutter speeds (1/10000s vs 1/8000s). This may be an important advantage for surveying applications because it would allow for higher resolution images and higher elevation flights; thus, higher elevation flight means more area covered in less flying time. 
Besides, Parrot implemented a dynamic new lossless digital zoom. This allows you magnify up to 2.8x without a reduction in image or video quality, making it easier to get details without having to get so close.
Yet another camera advantage is that ANAFI's camera is not embedded in the frame. ANAFI's camera sits by itself allowing 180 degrees of vertical movement.
ANAFI also has an advantage in video because it allows filming in 4K Cinema mode (4,096 x 2,160), which would be a great advantage in filming. Nevertheless, there is one video filming capability in favor of Mavic. Mavic films 120 FPS compared to the 24 FPS of ANAFI.
Image. ANAFI 360 degree camera

In this point I would call it a draw. Although Mavic is shorter, it is a little wider. This led to some confusion arguing that ANAFI is smaller. However, comparing the total size of ANAFI (244mm * 66mm * 63.5mm) with the total size of Mavic (168mm * 83mm *49mm), we see that Mavic is much smaller (Mavic = 683256 mm3; ANAFI = 1022604 mm3). This appears to be point for Mavic. However, ANAFI's 320 g are much lighter than Mavic's 430 g. Therefore, we call this point a 1-1 draw.
Image. Folding ANAFI
Flight time
This may also be considered a draw. ANAFI allows for 25 min flight. Although this is longer time than the Mavi Air, it is quite shorter that the Mavic Pro 27 min (point for Mavic). However, the tests showed that ANAFI has better stability. ANAFI resists winds up to 68 km/h, while Mavic (and any DJI drone) is limited to winds up to 55 km/h (point for ANAFI). Thus, this point is also a draw.
This one is a point for ANAFI. ANAFI costs only 699 $ in Amazon, which is almost half the price of Mavic Pro (1300 $). Moreover, ANAFI is even cheaper than Mavic Air's 800 $.  
Additional features
Several blogs argue that obstacle avoidance would be an advantage of Mavic. However, I do not believe so because of 2 reasons:
  • Flight planning. As a drone user, you should always plan your flight (actually I would change the should for MUST plan the flight). Flying without flight plan is like traveling without a destination. Thus, potential obstacles can be avoided prior the flight.
  • Flight regulations. Flight regulations forbid to flight drones over crowded areas. Thus, you should not be worried about crashing into a home or a person because you are not supposed to fly over houses or persons.

As we are talking about regulations, I would like to mention that several NATO countries (North Atlantic Treaty Organization) issued concerns (and in some cases bans) over DJI products. This would be a point for ANAFI (French industry). Thus, let's call it a draw.
An additional feature that may result in a point for Mavic, is that third party applications have not included updates to control ANAFI yet. Nevertheless, they already answered that upgrades including ANAFI compatibility will be issued soon.
Final result
As we can see in the following table, ANAFI wins 2-0. We can make an analogy with the current world cup, and we can consider each feature as a game. Thus, after 5 games we have 3 draws and 2 ANAFI victories
ANAFI overcomes Mavic in the features that made Mavic so popular. ANAFI is lighter, has longer flying time, better camera and is cheaper.
Image. Comparisson ANAFI vs Mavic

Physics of bicycle kick (scissors kick) in football soccer

In soccer, the bicycle kick has provided viewers moments of breathtaking spectacle that seem virtuosic in scope. The novelty of such moments is underscored by the rarity with which players have performed this complex skill during national or international tournaments. The rarity of these occurrences is both a product of perceptions that it is a high-risk, low return skill and by the fact that there is a dearth of scientific research on the biomechanics of the technique.

This magic skill has captivated fans and also the scientific community. Some studies such as Shan et al., (2015) applied 3D motion capture and numerical simulations to better analyze and understand this movement. 

In this post we will summarize the physics processes involved in bicycle kick (or scissor kick) taking as example the famous kick from Pele, the greatest player of all times. This movement of less than 1 second will always amaze soccer fans and physics fans.

The movement can be described in three phases:

1. The jumping: Pelé places himself back to the intended direction of the kicked ball and to jump, his center of gravity (CG), defined as a point where the resultant of all the weight forces can be considered acting upon, projects a little behind of his impulse foot. This allows him to gain rotational momentum when he applies force on the ground that passes within a certain distance from the CG to jump like in a back somersault. 

2. The scissors: Once completely in the air, Pelé, in astonishing synchrony with the ball trajectory, elevates the leg which is going to hit the ball and moves the other leg in the opposite direction; like the movement of a scissors, as can be seen by the angles between the thigh and the trunk for each leg shown in Fig.1c. While the movement is performed, the head is kept in a very stable posture because he must gaze at the ball. To facilitate the rotational movement of the kicking leg at the beginning, he bends the knee of this leg, approximating his limbs to the hip, and fully extends this leg just before the kick to hit the ball as high as possible, like the divers do to rotate faster during a dive. The physical property being altered is called the rotational inertia, the property of a body to resist change in its state of angular movement. The rotational inertia is calculated as the product between the body mass and the squared distance from the body to the center of rotation. Decreasing the distances of each segment to the hip joint decreases the total rotational inertia of the lower limb. In the air, the arms stabilize the body position: the arms are kept away from the trunk in the frontal plane to intentionally increase the body’s rotational inertia in the longitudinal direction to diminish any rotational perturbation in this direction, like a circus acrobat walking on a rope with a balancing beam in the hands.

3. The ball striking: The leg, at high speed, intercepts the ball above the height of a standing person, and changes its movement. Then, for a moment (see the video), it seems as if his body stops in the air and only the legs rotate around the hip. This phenomenon is due to the movement of other segments of the body that move faster than the trunk: although the entire body CG is in a parabolic trajectory, as predicted by the classical laws of motion, the trunk vertical trajectory (trunk CG) actually slows down in its apex.
Analysis of Pele's bicycle kick (Source: Demotu)

GPS basics: GPS requires at least 4 satellites

Several times I encountered people misunderstanding how GPS works and believes that GPS requires just 3 satellites. Other misunderstood concept regards how GPS works. Some people believe its triangulation. The real methodology is trilateration. In this post I will summarize how GPS works and show that it requires at least 4 satellites.

How GPS works?

GPS are based on trilateration, which is a method of determining the relative positions of objects using the geometry of triangles. GPS does not use triangulation because it does not measure angles. We can visualize this concept in the following way:
  • When a GPS connects with a satellite, the GPS device estimates the distance between the device and a satellite. This distance define the radius of one sphere. Thus, the GPS device can be located on any point of the sphere’s surface.
  • When the GPS connects to a second satellite, it defines another sphere. The intersection of those 2 spheres define a circle. The GPS can be located anywhere on the surface of that circle.
  • When the GPS connects to a third satellite, it defines another sphere. The intersection of this third sphere defines 2 potential points (in a worst case scenario it may define a line segment). Thus, 3 satellites are not enough to define one single location. The GPS requires a fourth satellite to define one single location.

Image 1. GPS trilateration (Source: Trimble)

Time is the 4th variable

Some people argue that 3 satellites are enough to define one position, because one of the mentioned 2 potential locations is a not reasonable one, or non real one. This idea could be better understood by looking at the maths. When GPS connects with three  satellites, it is possible to define three distance equation with three unknown variables  (the x, y and z coordinates of the point). As the equations are quadratic ones, sometimes  one solution may involve imaginary numbers or very far location. Thus, some people  believe that 3 satellites may be enough. However, is GPS we have a fourth variable.  This 4th variable is time.

Summarizing, GPS estimates the distance to a satellite based on the travel time of a  signal emitted from the satellite. Satellites are emitting signals at given times, and when  the GPS receives the signal it records the time when signal was received. However, the  satellite’s clocks are more accurate than the clock of the GPS device. Thus, there is a  time discrepancy that will affect the measurements and the solution. GPS solves this  problem by applying a correction factor (a 4th variable). Therefore, GPS has to solve  4 variables
  • X coordinate
  • Y coordinate
  • Z coordinate
  • C time correction factor
4 equations (4 satellite connections) are needed to solve the 4 variable.
Image 2. Set of equation solved by GPS

Note. for simplicity I used the term GPS. However, currently the new term is GNSS (Global Navigation Satellite System)