Best Turn of a Paraglider in a Thermal

   In this webpage you find 2 Java Applets at the bottom that simulate  turning a Paraglider in Thermal to get the best lift.

  The Java based package can be accessed from  http://sourceforge.net/projects/t3d2 or from http://t3d2.sourceforge.net/  or from here .

   If the Applets do not work then you are missing a Java  1.4 Runtime environment.

  The wing data is xml based  .

Here are some screen shots from the applet.

I am comparing an Effect 38  with a Boomerang 2.
Effect is red, Boomerang is blue.
In a 3m/s max peak thermal with a 80 m radius , the Effect can thermal slightly tighter and can therefore climb better.
The numbers on the tips of the lines correspond to the speed at the wing tips. The length of the line is roughly the projected wing span.
The inclination of the line indicates the bank angle.
The thermal strength is 10 times exaggerated compared to the radius.
Only the best toggle combination to obtain a certain radius gets displayed.
There are many more combinations of toggle settings, but they all result in a worse climb of the glider.
 

In a 2 m/s max thermal with a 40m radius an Effect can just make it.
 
 
 

If it is a very small but strong thermal then the Effect got a big advantage.

But in a weak and wide thermal the Boomerang 2 got an advantage in the thermal and will get away.

In a nutshell, a lower performace glider can outthermal a high performance glider in certain thermal conditions.
By making use of  the lower stall and trim speed one can reduce the radius and get more into the core with the stronger lift.
 

This jJava applet tries to compare and simulate two paragliders turning in a thermal.

The 2 figures at the end of each line indicate the speed of the wing tips.
How much toggle is applied.
And the code tries to find the best speed combination to make optimal use of the thermal
The Java Applet should be below this line. If not then you might need the JAVA runtime environment. Or a JAVA enabled Web Browser.

Using a different thermal crossection, more punchy, dust devil type like....

Some background info

The thermal is a math degree 3 parabola .

 The turn radius of the glider is determined by the 2 toggle speeds for the inner and outer wing.

  vi , inner wing speed

  vo, outer wing speed

 speeds can go from stallspeed to trim speed

  projected wing span is s

 turn radius is r

  inner speed vi is at radius - (s / 2)
  outer speed vo  is at radius + (s /2)

 center speed v = ( vi + vo ) /2

  vi  / (r-s/2) = vo / (r+s/2)

  vo*r - vo*s/2 = vi*r + vi*s/2

    r*(vo-vi) = (vi+vo)*s/2

    radius r = (s/2) * (vi+vo) / (vo-vi)

 The centrifugal acceleratione while turning is

  z  = v*v / r

  while the usual weight stays pointing down with g = 9.81 m/ss

 You bank angle is tan a = z/g

 The sink of the glider is determined by using the center speed v
 and applying it on the polar definition of the glider.
 But this sink would apply for straight and level flight.

  The adjusted sink = sink / cos a , with a the bank angle

 The total lift or sink of the glider in the thermal is then defined as

   total = lift by thermal + adjusted sink

    with lift by thermal a positibe value
  and adjusted sink a negative value in m/s

 The code iterates through vi and vo from stall speed to trim speed

  The polar is defined from minimum sink to maximum speed
  Which is not 100 percent correct for this approach here.
  The part of the polar from stall speed to minimum sink is missing.
  If the center speed is below  minimum sink speed I set it to minimum sink.

Want to  run the Applet on your computer and add your glider data

Download the best jar file

One can use zip or jar  to unzip the best.jar file.

Then modify the wingdata.xml file and add your glider data to it.

The wingdata.xml file format

  PolarCount can be 3 or 4 or 5 for the amount of polare points

The first point has to be the minimum sink point. Where the polare tangent is horizontal.

The next points have to points on the polare as the speed increases.

The last point is the top speed on the polare.

A point is defined by the speed in km/h   and a sinkvalue im m/s
 

Run the code on your computer in Java

Java 1.4 has to be installed

To run the code on your computer,  get the best.jar file .

In a Command Window,  jar -xvf best.jar 

And use    java appletcode/Best/BestTurnApplet_1.class  to bring up the code on your computer.

How to add your own Wing Data Information into the wingdata.xml file.

Polar data info you find at
http://www.para2000.org/wings/index.html

The code has also been integrated with T3D2

http://sourceforge.net/projects/t3d2

http://t3d2.sourceforge.net/