This may be common knowledge, but that sort of thing isn't always so common. I've heard people say that a headwind isn't a big deal*, since it will be in your favor on the return trip.
Imagine a trip of 100NM each way. Your true airspeed is 100KTAS and there is a 99KT tailwind. It takes you ~0.5 hours going, but on the reverse you make only 1KT on the ground. The whole trip takes ~100.5 hours.
QED
For some algebra, I came up with this expression:
Total Time = (2*D/TAS)*(1/[1-k^2])
Where D is the distance between points, TAS is true airspeed, and k is the headwind component divided by TAS.
So, when k=0 (no wind), total time is just 2*D/TAS, which is simply the distance divided by your TAS.
Feel free to check my work.
*Approximately, it isn't a big deal. Your trip time will increase by only about 10% when the headwind component is about 30% of TAS, but the effect starts to rise rapidly at about 50% of TAS.
Imagine a trip of 100NM each way. Your true airspeed is 100KTAS and there is a 99KT tailwind. It takes you ~0.5 hours going, but on the reverse you make only 1KT on the ground. The whole trip takes ~100.5 hours.
QED
For some algebra, I came up with this expression:
Total Time = (2*D/TAS)*(1/[1-k^2])
Where D is the distance between points, TAS is true airspeed, and k is the headwind component divided by TAS.
So, when k=0 (no wind), total time is just 2*D/TAS, which is simply the distance divided by your TAS.
Feel free to check my work.
*Approximately, it isn't a big deal. Your trip time will increase by only about 10% when the headwind component is about 30% of TAS, but the effect starts to rise rapidly at about 50% of TAS.
