zssp , Congratulations on your pass.
Cron, unfortunately it cannot be done that way, because as a percentage penalty or gain, the same Wind Component has a greater effect upon time as a Headwind than when a Tailwind. Thus, the solution can not be found by taking the total distance against the total time, the TAS will always come out on the low side.
Consider a 100 Kt TAS over a 100 mile course. In nil wind, it comes out at 60 minutes both directions, so far so good, but now insert a 20 Kt Headwind outbound, which becomes 20 Kt Tailwind for the reverse direction –
100 nm at G/S 80 Kt = 75 minutes (EXACTLY)
100 nm at G/S 120 Kt = 50 minutes (EXACTLY)
Now, if we use your technique of total distance against total time, that’s –
200 nm in 125 minutes = 96 Knots – Wrong, we knew in advance that the TAS = 100 Kt.
Now, if instead we calculated the G/S in both directions, and found the mean, we would have the answer –
100 nm in 75 minutes = G/S 80
100 nm in 50 minutes = G/S 120
Mean G/S = (80 + 120) / 2 = 100 Kts – Correct!
(All of the above assumes of course, that there was no drift, because any drift will effectively increase the Headwind and decrease the Tailwind).
It’s because of this type of reasoning that we need to use a more complex formula in calculating PNRs, than simply taking half of the useable endurance to be used on the outward leg.
Regards,
Old Smokey