You can't make up a headwind on the return trip

jasc15

jasc15

Pre-takeoff checklist
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Joe
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.

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True and interesting but a lot simpler if you simply make the wind speed equal to the plane speed. You get there in a hurry but never get back.
 
Graueradler said:
True and interesting but a lot simpler if you simply make the wind speed equal to the plane speed. You get there in a hurry but never get back.
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Or worse if the wind speed is greater than your airspeed.:D

José
 
Don't restrict the headwind to being at 12 o'clock relative. If the wind is at 090 relative you will have a headwind component; i.e., your ground speed will be less than your TAS. Guess what? Turn around to fly home and you still have a headwind component!

-Skip
 
Joe, that's the curve that led Dr. Melville Byington (ERAU) to publish a headwind rule-of-thoumb: For headwinds comkprising >25% of TAS, add power for 1 more kt TAS for each 2 knots TAS above >25% of TAS.

....for max economy.
 
bbchien said:
Joe, that's the curve that led Dr. Melville Byington (ERAU) to publish a headwind rule-of-thoumb: For headwinds comkprising >25% of TAS, add power for 1 more kt TAS for each 2 knots TAS above >25% of TAS.

....for max economy.
Click to expand...

Gee, thanks. Now I need to figure out the optimization problem.
 
It's pretty simple math but easy to misunderstand. The same is true in the investment world. If you gain 50% the first year, then lose 50% in the second your annual rate of return averages to 0%, right? In reality, however, you've only got 75% of what you started with.
 
You can't make up a headwind on the return trip
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Sure you can.

Sometimes.

Sometimes you can stay low to duck under the headwind in one direction and get up high to catch the tailwind in the other. The best I've done out and back in the same day was a 35kt difference. 20kt headwind at 3500 vs. 55kt tailwind at 10500.
 
bbchien said:
Joe, that's the curve that led Dr. Melville Byington (ERAU) to publish a headwind rule-of-thoumb: For headwinds comkprising >25% of TAS, add power for 1 more kt TAS for each 2 knots TAS above >25% of TAS.

....for max economy.
Click to expand...
Of course that only makes sense if you're starting from best range speed. Cruising at 65+% power usually means you're so much faster than best range that you'd need hurricane winds to make going faster more efficient.
 
timwinters said:
Sure you can.

Sometimes.

Sometimes you can stay low to duck under the headwind in one direction and get up high to catch the tailwind in the other. The best I've done out and back in the same day was a 35kt difference. 20kt headwind at 3500 vs. 55kt tailwind at 10500.
Click to expand...

That works especially well if the wind is at a significant angle to your course. With a direct headwind of any significance, dropping down to escape it often means flying below 1000 AGL and/or in some pretty bumpy air and I'd rather just accept the time penalty and stay higher in smooth air. When the wind is at a significant angle to your path, a several thousand ft altitude change can turn a headwind into a slight tailwind if you're lucky. Another trick is to plan your flight around frontal movements to get tailwinds in both directions. Sometimes that involves taking a different route in each direction to take advantage of the rotational flow around the lows and highs. There's also the constant pressure method involving a more circuitous route to minimize the flight time.
 
Just remember if your flying with a tailwind your headed for the low pressure system more than likely..

<---<^>--->
 
Graueradler said:
True and interesting but a lot simpler if you simply make the wind speed equal to the plane speed. You get there in a hurry but never get back.
Click to expand...

Very convenient if you are traveling from the frozen north to the tropical south in winter! :idea:
 
p1l0t said:
Just remember if your flying with a tailwind your headed for the low pressure system more than likely..

<---<^>--->
Click to expand...

I can say that in a paltry 500 hours I had a tailwind both ways TWICE. It was pure joy and one heck of a groundspeed.
 
It's also a truism (assuming no altitude changes to duck under the headwind or go higher to catch more of the tailwind on the return leg) that if you always had the same wind for both legs of your cross-countries, you'd have spent much more *time* flying into headwinds than enjoying tailwinds in the logbook overall.

Thus, our feeling that our memories of good tailwinds are less often than bucking headwinds.

There was a fun USENET post long long ago where someone had attempted to calculate a probability percentage for light aircraft pilots for the amount of time they'd fly into headwinds in a typical lifetime's logbook. It was full of assumptions which could have been argued, but it was a fun read.

Stuff like always taking off into the wind and the lower likelihood of flying extended legs with a tailwind because that would be flying toward low pressure and worsening weather, therefore more likely to have such a leg scrubbed versus flying generally upwind toward better weather (hey, I know he left out the turning effect of ground friction...), etc etc.

It was a fun set of assumptions and math. He came up with something around 70% of the time in a light aircraft we'd be bucking headwinds, by time.

Wish I'd have kept that posting somewhere. (It would have been on floppy disk. Heh.) It'd make great fodder for discussion even today.

He had based his numbers on his own logbook and had removed pattern work from that and he had kept a bazillion flight logs on paper with wind notes. I remember not too many folks replied since most of us don't log wind data.

Fun brain teaser though.
 
jasc15 said:
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.
Click to expand...

That's interesting.

I thought about it a while ago then completely forgot, then continued thinking that a tail wind will compensate for the headwind :mad2:. Thanks for posting.
 
I too just play the altitude game, the 15kts in my face west bound at 1500AGL isn't bad when I can go a mile or two higher and catch 30-50kts on my tail going east.
 
timwinters said:
Sure you can.

Sometimes.

Sometimes you can stay low to duck under the headwind in one direction and get up high to catch the tailwind in the other. The best I've done out and back in the same day was a 35kt difference. 20kt headwind at 3500 vs. 55kt tailwind at 10500.
Click to expand...

Exactly. Last week I flew from KMDD to KGTU with a 40-knot tail component at 7500, and later that same day I returned at 4500 with only a 15-knot head component because of the different direction of the wind. I won the game on fuel that day, because I paid attention to the winds aloft.
 
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