The math on this page is experimental.  It is most likely correct (or close enough to get the point across) but should not be used as the only basis of design. 

                       

 

 

        Click .....here..... to go back to the main webpage

Caution : You have landed on the Math Planet.  Please don't panic.  It is only math.  It is not really real.  The contents of this page will not affect how your next hamburger will taste or how many miles per gallon your car gets.  The information on this page is rather specific and requires you to want to understand a complex aerodynamic system represented by the most basic equations of flight.  However, if you are asking yourself what a math model is.......there is little hope that this page will be of any help to you.   A math model is defined as a set of logic conditions that hope to simulate real world behavior from within the confines of mathematical manipulation.  That should be clear as mud.  Well, in any event, the formulas presented are strung together loosely to help define the flight characteristics of an aircraft on paper......long before the real thing is built or tested.  This is the starting point.  

Shown below are segments of the team's basic math model of the DragonFly Mark I aircraft :  The math model was established using printed values for the basic aeroshell shapes and performance of the aircraft.  Some "tweaks" were made to reflect input of real aircraft owners and builders that have flown this class of machine.   We tried to keep the math simple.  It is far less complex than the math model we have for our Eos Raptor, but is based upon the same core equations.  There is documentation down the left  side of most pages that may help to interpret the string of equations that run down the right side.  Hopefully, the documentation can be read and understood by a non "aero" person.   

The model is taken from an interactive program called MathCad.  The colored sections in the text are set up so that you can see what is what :

 The blue sections are general comment,

The green sections are "assumptions" and "basic input values", 

 The white sections are general math calculations. 

 The yellow sections are "computed values" from the equations. 

If you have a mono screen....well.....get into the 21th century and buy a 17" SVGA color monitor. 

There are about 30 pages of the basic math model for the Mark 1.  The difference from Mark 1 to Mark 2 are small but important.   There are about 110 pages of math model for the Eos Raptor ( along with X-Plane simulation runs, load cell, aerodynamic testing data , etc.)   

                                Click   < here >   to see section 1  of the Mark II  math model.

                                Click   < here >   to see section 2  of the Mark II  math model.

                                Click   < here >   to see section 3  of the Mark II  math model.

                                Click   < here >   to see section 4  of the Mark II  math model.

                                Click   < here >   to see section 5  of the Mark II  math model.

                                Click    < here >   to see section 6  of the Mark II  math model.

Coming some day..............the complete Mark 1 and Mark 2 math models.  We have them completely done, but..........well............we are waiting for the factory to catch up and show us the way........... 

The really great looking pressure graph shown below is from a different type of aerodynamic analysis and is not a part of our math model.   But it looks too cool.    If David L. is reading, "great job" .  How about a version for the Mark 3 ?  We are just now getting this sophisticated with our math engine and will some day have detailed pressure graphs of the multi segment airfoils to show on this page.