Today is Good Friday and here in Bermuda is all about codfish cakes, hot cross buns and flying homemade traditional Bermudian kites.  It was a great SW breeze, sunny and low humidity today, possibly the most perfect day to fly kites!  Mine didn't go so well though, flew for a bit and then the spindle I was holding broke into two and got out of my hands.  I chased the remaining bit as the kite soared away before it got stuck in an oleander hedge.  The kite lost control and crashed in the neighbour's garden.  Sadly they were away and have three really scary dogs,  who savaged the kite!  Oh well....  next year we will go to the beach to fly it instead.  So, no photos of the kite.  Bermudians take a huge amount of pride in kite making and there are a lifetime of tips and tricks to learn.  They are quite fiddly to make and require some patience.  My friend Hannah is an artist and produced the kite of a lizard that is shown below for the Ag Show last week.  Today she was making a sandcastle version of a baby T-Rex being hatched from an easter egg at Horseshoe Bay.

Anyway, after my disastrous excursion into paper aviation, I sat and watched others being far more successful and thought about how kites actually fly......

Once the kite is airborne there are four forces acting on it:  weight, drag, lift and the tension of the string.  The lift force is the most important and the one that holds the kite aloft.  Lift is generated when air flows over the surface of the kite as it is held at an angle to the wind.  This angle is critical and is known as the 'angle of attack'.  If the angle is too shallow, there is not much lift generated and the kite falls.  If the angle is too steep, the air flow is disrupted by the kite and the kite stalls and falls down.   So, being able to control this angle is critical to a successful kite.   The higher the kite is, the stronger the wind speed and the greater the lift.

The angle of attack is controlled by:

• Placement of the bridle (called 'de loop' by Bermudians).  The measurements of these are very precise.  The one from the middle must be as long as the top curved section, the two that come from the ends of the curved section must go to an inch below the centre of the kite sticks.  If these are incorrect, the angle of attack won't be within flight range.  
• The angle and tension of the kite string - must be forwards and downwards!  Which is why it is so important to pull downwards a bit on the line as the kite is being thrown upwards when it is being launched.
• The drag and weight of the kite - which is significantly affected by the length and weight of the tail - usually lengths of bed sheets that have been torn up and knotted together.   Note that the centre of mass of the kite is moved backwards from the geometric centre by the mass of the tail. 

Without the tail, the kite would be unstable and jitter around all over the place.   The idea is that the centre of drag lies behind the pivot point (loop) so that the kite maintains a head-to-wind attitude.  The curved section at the top (where Hannah's lizard head is), aids the airflow over the kite and produces a more natural aerofoil than would be obtained from a flatter kite section.

Hummers - these are strips of tissue that are mounted on strings from the headstick to the top of the curved section.  They are free to vibrate and produce a loud noise.  Hannah's hummers are white with black spots on them. If made from stiff paper (grocery bags) or plastic they can be very loud and extremely annoying!  

One year, some inventive people from St David's tried to launch a huge kite made from 12' lengths of 2" x 4" timber.  Unfortunately, despite being dragged by a pick-up truck, it was not successful.  The reason was obvious to me as a physicist, unless it was blowing a gale the lift generated would not exceed the weight of the kite until the kite was very high and the angle of attack from a 'normal' style launch would be too steep and the kite would stall.  Possibly if they had chosen a really windy day and mounted the kite at a shallow angle on top of the pick-up truck with a securely mounted spool for the line, and then they drove fast down a road straight into the wind - unspooling the line as the kite gained lift - they may have been successful!

It has been a very exciting time in astrophysics this week, with the first ever image of a black hole published across the news.  Here is a link to the BBC Science article.   So I thought that it would be a good exercise to do some AP-style physics on some of the data that has been published.  I have simplified things a bit as I don't know how to do calculations on rotating black holes and general relativity!

Size
The article states that the diameter of the event horizon is 40 billion km and its mass has been determined to be some 6.5 billion solar masses.  The mass could be calculated from the orbital speed (determined by the Doppler Effect) of the matter that forms the accretion disk surrounding the black hole, but no data on that is given in the article.  So, turning to classical physics, the event horizon is the radius where the escape velocity is equal to the speed of light.  The escape velocity is calculated from the law of conservation of energy.

A quick bit of algebra gives us:

which gives a diameter of 38.5 billion km, which is very close to that quoted in the article!

Interferometry

Essentially the limit of what we can see is determined by Rayleigh's Criterion (see AP-2 Unit 15), where the objects in question must diffract through the aperture of the telescope by less than their separation.  The variables that affect this are the diameter of the aperture through which diffraction occurs (the opening at the business end of a telescope), the subtended angle of the object, which depends on its size and distance from us, and finally, the wavelength of light observed.  The article does not specify the wavelength, but says that it is the high frequency end of radio.  Assuming that this value is 0.1 m, lets use the Rayleigh Criterion to determine the maximum size of the black hole that can resolved at the stated distance of 55 million light years using the EHT array shown above.

The Rayleigh Criterion for a circular aperture is:
​

As these are incredibly small angles the sine and tangent of the angle will be the same.

where O = diameter of the black hole, A = distance from the Earth and d = diameter of the telescope.  Remembering that a light year is the distance traveled by light in one Earth year. 

which is in the microwave to infrared region of the EM spectrum.  Although I am sure that the effects of red shift due to both the expansion of the universe and the intense gravitational field of the black hole would have a significant effect on this calculation!

So, why would the black hole be a) so large and b) rotating?  The large part is easiest to understand, as the gravitational field is so strong matter would be drawn into the black hole, increasing its mass.  As its mass increases, the event horizon would expand further outwards and the gravitational field strength would further increase, creating a positive feedback cycle.  Eventually one could imagine that the black hole at the centre of that galaxy eventually consuming the entire galaxy.  Scary thought.  It may be possible to orbit a black hole, but the friction due to other incoming matter would probably cause the orbit to be unstable and quickly decay.  It is observed that stars rotate or spin.  It seems that the angular momentum of the star and its planets remains constant during stellar and planetary formation, therefore as the star's core collapses further to form a black hole, its angular velocity would increase.  Here, of course, we have another problem with classical physics.  As the black hole shrinks to a zero radius at its singularity (we think), then it angular velocity would tend towards infinity, which is certainly greater than the speed of light....  ah.....

Much has been reported about the fact that the team leader of this impressive international project is female.  What is astonishing is that this should be surprising!?  I know of at least two Bermudian females that have studied or are studying astrophysics at university.   Girls can be every bit as geeky as boys ya know.