Math help request ?

[Snead1]

I need math help with a spreadsheet. I want to enter 1: Wind Direction 2:
Wind speed 3: Desired track of the glider 3: Speed made good by glider in
still air.

I want to solve for 1: Glider heading 2: Speed made good of glider along
desired track.

I would appreciate any help form anyone who might have been a little more
focused in math class than I.


Bill Snead
6W

[tango4]

start off at
http://williams.best.vwh.net/avform.htm

wind triangles are what you wnat.

Ian

[Rory O'Conor]

If you find the maths complex in http://williams.best.vwh.net/avform.htm

then I suggest:

a) plenty of scrap paper and pencil
b) remember that Excel works in radians not degrees: 2 pi radians = 360
degrees
c) make sure that you fully understand sin, cos, tan (and their inverses)
d) solve some simple examples using paper and spreadsheet eg wind 10 kph at
90 degrees to course, XC speed 60 kph.

as you make the examples more difficult, draw the triangles on paper and
then create right angle triangles which will help you to solve the problem
eg wind 10 kph at 45 degrees to course headwind/tailwind.

e) if still going, try to answer your original query - may need to add
180/360 or work modulo 360 at intervals.

Now you should be able to understand the Aviation Formulary.

If you still want a challenge, try solving for varying climb rates and
varying glide rates, and an overall height change.

I have just been solving the latter equations for a 300km task to find:
i) most important is the climb rate achieved - this outweighs all other
factors
ii) the start/finish height loss is important and especially the leg on
which it is applied (best into wind)
iii) for a modern glider, winds below 10 kt are relatively benign
iv) with stronger winds some courses are better than others:
a crosswind Out/Return is better than a triangle which is better than a
with/into wind Out/Return.
v) as is already known, the glide speed is not too critical and can be too
fast.

ps: I dont fly very fast.
Rory

[Doug Hoffman]

Snead1 wrote:

> I need math help with a spreadsheet. I want to enter 1: Wind Direction 2:
> Wind speed 3: Desired track of the glider 3: Speed made good by glider in
> still air.
>
> I want to solve for 1: Glider heading 2: Speed made good of glider along
> desired track.
>
> I would appreciate any help form anyone who might have been a little more
> focused in math class than I.
>
>
> Bill Snead
> 6W
>

Here is a simple little spreadsheet setup that models the situation. I
threw it together rather quickly, so use with care. It is iterative in that
you have to try a few values to get your answer. I didn't bother to work
out the complete algebraic/trigonometric solution. That's one of the neat
things about spreadsheets. You can keep things simple and try a few
different values until you get what you want.

This is most easily viewed as a vector problem. There are 3 vectors:

1) DV is your destination vector
2) WV is your wind vector
3) CV is your course vector (or air speed/direction)

The relationship is DV - WV = CV

Type the following in the indicated cells of your spreadsheet:

A1 vector
B1 mph
C1 heading(degrees)
D1 radians
E1 x
F1 y

A2 DV
B2 110
C2 50
D2 =radians(c2)
E2 =b2*cos(d2)
F2 =b2*sin(d2)

A3 WV
B3 30
C3 280
D3 =radians(c3+180)
E3 =b3*cos(d3)
F3 =b3*sin(d3)

A4 CV
B4 =sqrt(e4*e4+f4*f4)
C4 =degrees(asin(f4/b4))
D4 <leave blank>
E4 =e2-e3
F4 =f2-f3

You input the mph and heading for the DV and WV. The output is the CV. In
this case I have supplied some made up vectors of DV = 110 mph at 50 degrees
heading, a WV of 30 mph at 280 degrees heading (wind is blowing towards the
south-east). To arrive at your destination direction at 110 mph groundspeed
you must set a course of 35.8 degrees and travel 93.6 mph indicated
airspeed. If the CV airspeed isn't what you wanted, just change the DV
ground speed until it is.

Again, this isn't *exactly* what you asked for because you have to guess at
the speed made good to destination (DV) until the correct speed made good by
glider in still air (CV) is obtained. I could do it but it would take more
time. Besides, this is simple to enter and use. Someone has surely written
a spreadsheet to directly solve as you stated. Maybe someone will send it.
Meanwhile, this will work.

Regards,

-Doug

[Snead1]

Thank for the help.

Bill

[Doug Hoffman]

Please ignore the spreadsheet formulas I posted. They suffer from 2
problems I've always had with pilotage, one being that the zero degree axis
is North (not east, as is commonly used in college math), and the other
being the aircraft vector points in the same direction as the movement of
the aircraft but the wind direction is given in terms of where the air is
moving *from*, not *to*. Regardless, I blew the calculation.

Rather than redo it, I think Tango4's suggestion of looking at the website
with the wind triangles would be better.

Most humbly embarrassed (because I really should know better!),

-Doug