First, let’s review a few know properties. In the particular example calculated last month it was determined that the pibal would rise at 444 feet per minute. Second, you will need to know that one mile per hour is equal to 88 feet per minute. Third, it will be necessary to calculate the angle of climb of the pibal at each interval of time, say one minute.
By determining the angle of climb (see figure 1) you will be able to enter the information into a spreadsheet problem to determine wind speed. Okay, now for the math.
Solve for distance traveled by balloon in one minute
First, find the distance the balloon traveled (see figure 2):
b = 444/tanc = 444/.563 = 787 feet
Then convert to miles per hour (MPH):
(787 ft/min)/(88 ft/min) = 8.9 MPH
In English, “h” is the rate of ascent you computed in last months article. “C” is the angle you measure as the pibal drifts up and away from you when you let it go. The last and most important calculation is “D”. This is the distance the pibal traveled across the ground as the wind blew it away. This distance, divided by 88, gives you the ground speed of the pibal in MPH.
I can tell by the grin on your face you are enjoying this, so we will continue with a spreadsheet which will show angles from 9 to 48 . The accompanying chart will allow you to make a quick decision whether to drag out the bag or pop a cold one!
Spreadsheet calculations
Now some balloon math. We will try to print a chart using the calculations from
above. Hopefully without even asking a second opinion from the crew, even a pilot can
raise that swollen head and say with some authority, “It’s too windy today for a safe
flight!”.
One assumption made here is that you have access to a computer and know how to generate a spreadsheet. Now, for those of you left, let’s get on with the show.
In column “A”, enter number from 9 to 48. In column “B” next to the number “9”,
enter the magic formula:
=(444/tan(A4*(3.14/180)))/88
The “444” number needs to be the pibal rate of ascent you computed from the first article. Your number will probably be different. Cell “A4” is actually “9” which you entered. (To define this more precisely it is the cell number of the A column that corresponds to your B column cell. For each B column calculation the A_ will change.)
The 3.14/180 converts the angle into radians, the unit of measure required for computers (a calculator automatically does this for us nimnodes).
After entering this info, you should get 31.9 MPH in the cell “B4”. If all goes well, copy this formula into the other cells and paste them in any order you so desire. If you have problems with the computer, don’t waste your time debugging—contact the nearest twelve year old.
Graduate work
There you have it. A handy way to calculate wind speed as the pibal speeds away
from you. If you are still with us here’s a homework challenge. As the pibal tracks away
from you record not only the angle it has risen from the ground but also the azimuth
that it is tracking at regular intervals, say every 15 to 30 seconds. Record both of these
numbers. Using information that can be found in Mapping Your Way to the
Target, Balloon Life July, 1991, you can built a computer spreadsheet program
that will give you winds aloft, heading and speed, just like the information that the
competition pros get from their expensive Windreaders. Good luck.
