We renumbered our local airport (LSGY) this week due to magnetic declination changes, and it reminded me of a question that I have about runway numbering.
Does anyone know why the digits of opposing runway numbers add up?
There may be a mathematical explanation, but I can’t seem to figure it out or find it.
For example:
Runway 01/19 is a bit of a special case – 0 + 1 = 1 + 9, which might mean that this is all just a coincidence. I’ve seen this explained that the 1 + 9 becomes 10, which reduces to 1 + 0.
Suppose runway is XZ and YW, then X+Y = Z+W as 10=9+1 and 18=9+9
10*X=9*X+X
10*Y=9*Y+Y
9*X+9*Y=18
The latter does not work for 01/19 
If runways numbers were in base 9 rather than base 10 life would be easier to find opposite runway
life would be easier to find opposite runway
+200 -20, or – 200 +20 still works for me
Though given enough years most reciprocals come to mind automatically 
Ibra wrote:
If runways numbers were in base 9 rather than base 10 life would be easier to find opposite runway
I wonder how many people can do base-9 calculations Anyone with some computer training can usually (eventually) figure out base-2, base-8, and base-16, depending on age and experience. …… but base-9??
I bet this belongs to so called modulus maths which I don’t know very well. But in this special case it is not very difficult to explain:
Let’s describe the lower value with xy where x represents tens (0-1) and y singles (0-9), so runway = x times 10 + y.
If the orig value ends with not-zero (like 02 07 11 19 25 etc) and you add there 9, the left digit x (tens) climbs up by 1 and the right hand digit y goes down by 1. For example 15 + 9 = 24, you understand what I mean? Adding 18 means that you add 9 two times, so the result basically is that x → (x+2) and y → (y-2), so the sum always remains the same.
The other option is that y=0 like 10 20. Then you really have to believe in modulus 10 calculation: adding 9 to the sum does not change the modulus (which actually applies to the previous case as well). For example 10 => 1+0 = 1 add 9: 19 => 1+9= 10 => 1+0= 1 and 20 => 2+0 = 2 add 9: 29 => 2+9= 11 => 1+1= 2.
Not very clear to my little brains but something like that. Well, with bigger values like 36 33 it goes backwards but still the same idea.
Years ago I did a lot of programming with 16 8 and 2 bases which were pretty easy to handle at that time. But never tried 9-base. If I remember right, in France you have had 12-base in use zillion years ago, so you even have some numbers in French still based on that? Interesting.
I wonder how many people can do base-9 calculations
In general population or pilots? base 9, NFW ! I guess base 60 & base 12 are way more useful (as they have lot of divisors, a bit like Hex16) to pilots & navigators, especially the subset who sail with Breitling watches, they know these by heart (also 1:60 = 180/Pi assumption flattens trigonometry )
Recap from PPL training = the two letter numbering of runways is the magnetic direction rounded to next tens and trowing away the last zero, so the calculations base is a modulus 18. Yes, the adding up can be just looked up in text books of number theory.
