This topic split from "Adjusting calculated take-off roll for slope." -1SeventyZ
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Ha, I loved the formula with the exponent that was described as the "exponent that gives the best results"!

This wind / slope problem reminds me of another wind problem I've always thought about. One time I was puttering along over Hell's Canyon, and I looked at the Seven Devils next to me and it looked like I wasn't even moving. I checked my airspeed, it was 90 kts, and I checked my ground speed on the gps and it was 40 kts. I was enroute to McCall, and while I initially had a little over an hour reserve, I thought there was a good chance I would run it dry before I ever got there if I was only making 40 kts on the ground. I thought it through, then decided that I was in a constriction of the valley that was catching a lot of wind and forcing it through a small area resulting in a locally higher wind speed. I decided to give it full throttle to get past the narrow spot to see if the wind abated. If it did, I would continue to McCall, if not I would head back to Grangeville for some more of the blessed av juice. About five minutes later, the headwind reduced to 30 kts, and so I continued on to McCall, landing with about a half-hour reserve and only a mild cramp in my puckered sphincter.

Since that day I've always wondered about fuel efficiency and headwinds. According to my POH, the more you pull the throttle back, the higher the miles per gallon. However, that obviously can't be true in a strong headwind. If you're flying into a 100 kt headwind at 100 kt airspeed, you just stay in one place until you run out of fuel. If you give it a little more throttle you actually make some headway before you run out of fuel, so it's obviously more fuel efficient to open the throttle more in a headwind.

And that leads to my question: How *much* should you increase your fuel burn in a headwind to achieve maximum miles per gallon?

And that leads to my question: How *much* should you increase your fuel burn in a headwind to achieve maximum miles per gallon?

kevbert

Thats a very interesting question. I'd like to know more about this so I'll bite and all youall can correct me.

Increase the throttle a lot in a head wind for maximum miles per gallon. My reasoning is it's like the trick question "How much fuel is needed to make a round trip when there is a constant speed wind giving you a tail wind going and head wind coming back?" You can't just use the no wind fuel required answer because you are in the head wind longer than you are in the tail wind. So, seems logical like you found out to spend as little time as possible in the head wind. There's probably a point near full throttle where you run in to diminishing returns though. How's that?

This has moved from uphill to head winds but running out of gas before you get to where your going is how they found out about the jet stream, they lost a lot of planes when they just flew with a stopwatch IFR and really high.
I'm kind of remembering a book I read once???
GT

At a certain RPM, at a certain fuel mixture, at a certain barometer, you are going to burn so much fuel /hr. ....ground speed be damned. Watched a friend of mine fly his Cub backwards...figure his burn/mile? The harder you run the engine, the more fuel you'll burn. More headwind, the fewer miles/gal..simple math. If you want to go faster..with or without a head wind, the higher RPM and the fuel burn/hr goes up. If you are like me, it seems I most times have a head wind. I once traveled from Wisconsin to SNY with a 225 Bonanza, I was in a 118hp Citabria. He left me in his dust and arrived at SNY 2 hrs ahead of me. When we calculated fuel used it was with .2 of a gal for the distance, I had a lower burn/hr but it took me longer to get there. The end result, he traveled faster, burned more fuel/hr, but we both used the same fuel for the trip...about 17mile/gal.
HC

I was always told on a round trip with a strong tailwind/headwind, to power way back on the tailwind leg and on the return leg push the power up. No matter what I try I still use more fuel on a trip with a strong wind than one with a little wind.

hicountry wrote:At a certain RPM, at a certain fuel mixture, at a certain barometer, you are going to burn so much fuel /hr. ....ground speed be damned. Watched a friend of mine fly his Cub backwards...figure his burn/mile? The harder you run the engine, the more fuel you'll burn. More headwind, the fewer miles/gal..simple math. If you want to go faster..with or without a head wind, the higher RPM and the fuel burn/hr goes up. If you are like me, it seems I most times have a head wind. I once traveled from Wisconsin to SNY with a 225 Bonanza, I was in a 118hp Citabria. He left me in his dust and arrived at SNY 2 hrs ahead of me. When we calculated fuel used it was with .2 of a gal for the distance, I had a lower burn/hr but it took me longer to get there. The end result, he traveled faster, burned more fuel/hr, but we both used the same fuel for the trip...about 17mile/gal.
HC

That's interesting, I didn't think the gas mileage of a Citabria was anywhere near the Bo. The Bo has better mileage than the 182, 180, 185 and Cubs. Do you recall what the 65% and 75% cruise speeds and fuel flows are for a Citabria?

The bonanza had an electric adjustable prop..I have no idea how much maniflod preasure he had...but I do know he was not babying it. I had a fixed pitch and was running 2500-2600 rpm. The total burn for the trip really surprised me. I have flown several other cross countrys with slower and faster planes and the total fuel consumption is very close...especially if we fly at the same air speed and lean in a similar matter. This may not be true for other combinations ( Large heavy planes vs slow light airplanes) or types of engines.
As far a takeoff roll.....I think (unless it is very steep uphill or downhill) the air density, surface, direction and angle of wind, and skill of the pilot have more to do with the takeoff roll that just the incline.
HC

I had a 182 for 7 years and at top of the green I would indicate 135 mph in the summer and about 140 mph in the winter and that would be burning 12.5-13 gph. In the Bo, I have the 520 at 285 HP, I can run 45% power LOP and be indicating 5-10 mph more than the 182 but be burning 8.5 gph, thus saving at least 4 gph. That's how i normally fly around the local area. Or I can haul ass and indicate 180-190 MPH burning 15 gph. Either way better gas mileage than a 182. We have family in the MSP area. One time I flew nonstop in the 182, 4.4 and 55 gallons. In the Bo the trip was 3.7 and 50 gallons. Both flown at WOT and max cruise RPM. If I reduce airspeed to whatever the 182 indicates I use tremendously less gas, for the above trip it would be about 20 gallons less. But there's no way I'm going that far that slow for no good reason.

Bonanza Man wrote:I had a 182 for 7 years and at top of the green I would indicate 135 mph in the summer and about 140 mph in the winter and that would be burning 12.5-13 gph. In the Bo, I have the 520 at 285 HP, I can run 45% power LOP and be indicating 5-10 mph more than the 182 but be burning 8.5 gph, thus saving at least 4 gph. That's how i normally fly around the local area. Or I can haul ass and indicate 180-190 MPH burning 15 gph. Either way better gas mileage than a 182. We have family in the MSP area. One time I flew nonstop in the 182, 4.4 and 55 gallons. In the Bo the trip was 3.7 and 50 gallons. Both flown at WOT and max cruise RPM. If I reduce airspeed to whatever the 182 indicates I use tremendously less gas, for the above trip it would be about 20 gallons less. But there's no way I'm going that far that slow for no good reason.

Man, that is one slow 182 you had. All the ones that I have flown did an honest 135-140 knots, or 155-160 mph.
Was it an early one with the longer gear legs?

I had a 67 182K with no wheel pants and 8.00's on the mains and a 6.00 nosewheel as well as VG's. It trued out at 127-130 kts.

tcj wrote:

And that leads to my question: How *much* should you increase your fuel burn in a headwind to achieve maximum miles per gallon?

kevbert

Thats a very interesting question. I'd like to know more about this so I'll bite and all youall can correct me.

Increase the throttle a lot in a head wind for maximum miles per gallon. My reasoning is it's like the trick question "How much fuel is needed to make a round trip when there is a constant speed wind giving you a tail wind going and head wind coming back?" You can't just use the no wind fuel required answer because you are in the head wind longer than you are in the tail wind. So, seems logical like you found out to spend as little time as possible in the head wind. There's probably a point near full throttle where you run in to diminishing returns though. How's that?

The fuel burn vs airspeed curve is a parabolic curve. As long as the airplane is flown over the relatively flat portion of the curve fuel consumption is not greatly affected by flying faster than the max range airspeed. But as you say, as you increase horsepower there is a point where there are increasingly diminishing returns and then probably negative returns. On the other hand decreasing your speed allows for the wind to have a longer effect on your airplane's ground speed because your trip is longer.

Mathematically, I would think that marginally increasing your speed over what your "normal" cruise speed would be is the most efficient operation in a headwind. What is "marginal"? Well, you would have to calculate where the flat portion of the curve exists for your conditions and then set your speed to the fast end of the flat portion Could there ever be a rule of thumb? Don't know. I would think that if you normally putter along at 45-65% power in cruise like I do, increasing your TAS in a headwind by a few knots is more efficient than doing nothing or pulling power back even more. But increase power too much and you will fall down the backside of the curve. Need more slide rules and better instrumentation in the panel than I currently possess to get any better than that.

once&futr_alaskaflyer wrote:

Mathematically, I would think that marginally increasing your speed over what your "normal" cruise speed would be is the most efficient operation in a headwind. What is "marginal"? Well, you would have to calculate where the flat portion of the curve exists for your conditions and then set your speed to the fast end of the flat portion Could there ever be a rule of thumb? Don't know. I would think that if you normally putter along at 45-65% power in cruise like I do, increasing your TAS in a headwind by a few knots is more efficient than doing nothing or pulling power back even more. But increase power too much and you will fall down the backside of the curve. Need more slide rules and better instrumentation in the panel than I currently possess to get any better than that.

I just now looked in "Stick and Rudder" to see if there is anything about this. there is and I think the author agrees with your take on it.

"How to stretch your fuel against a wind"
"...If you are trying to to make your tankful of fuel take you as far as possible, and you have a head wind, it does pay to add a few miles per hour...The calculations by which you mind find the exactly right air speed are exceedingly intricate...But, if you work it out you will find that wind influences the Speed of Best Distance very much less than you might think..."

once&futr_alaskaflyer wrote:

tcj wrote:

And that leads to my question: How *much* should you increase your fuel burn in a headwind to achieve maximum miles per gallon?

kevbert

Thats a very interesting question. I'd like to know more about this so I'll bite and all youall can correct me.

Increase the throttle a lot in a head wind for maximum miles per gallon. My reasoning is it's like the trick question "How much fuel is needed to make a round trip when there is a constant speed wind giving you a tail wind going and head wind coming back?" You can't just use the no wind fuel required answer because you are in the head wind longer than you are in the tail wind. So, seems logical like you found out to spend as little time as possible in the head wind. There's probably a point near full throttle where you run in to diminishing returns though. How's that?

The fuel burn vs airspeed curve is a parabolic curve. As long as the airplane is flown over the relatively flat portion of the curve fuel consumption is not greatly affected by flying faster than the max range airspeed. But as you say, as you increase horsepower there is a point where there are increasingly diminishing returns and then probably negative returns. On the other hand decreasing your speed allows for the wind to have a longer effect on your airplane's ground speed because your trip is longer.

Mathematically, I would think that marginally increasing your speed over what your "normal" cruise speed would be is the most efficient operation in a headwind. What is "marginal"? Well, you would have to calculate where the flat portion of the curve exists for your conditions and then set your speed to the fast end of the flat portion Could there ever be a rule of thumb? Don't know. I would think that if you normally putter along at 45-65% power in cruise like I do, increasing your TAS in a headwind by a few knots is more efficient than doing nothing or pulling power back even more. But increase power too much and you will fall down the backside of the curve. Need more slide rules and better instrumentation in the panel than I currently possess to get any better than that.

I'm reviving this thread because there seems to be a common misconception that "speeding up" into a headwind will increase your range.

Increasing your speed into a headwind to maximize range will ONLY work if your already starting from your best range speed, I.E. L/D max or "Best Glide". For example: that's 80 MPH (IAS) at max Gross in my 182. I don't know many who plan a XC going 80 MPH in a 182.

So, you must SLOW down in a headwind, from "normal" cruising speeds, to extend your range. If you must continue to slow even further to make your destination, you need to re-dispatch as you approach your new "best range" speed or if you will be going so slow that making an extra fuel stop(if possible) and losing an hour+/- makes sense and would be the better(faster) option in the long run.

I thought of this one time when I set the plane up for best glide into a 10 kt head wind. Best glide for my plane is 90 mph. afyter it was all over I think I should have set it up for 95 to 100 mph. I think that next time I get a chance, I will do some experimenting at Weed apt when we get on on those 25 KT days.

Tim

ROT for headwind, add half of the wind velocity to Vbg.

WSH wrote:ROT for headwind, add half of the wind velocity to Vbg.

That's a decent rule of thumb for maximizing range, providing headwinds aren't extreme. When this discussion started, I entered my cruise performance chart from my POH into excel so I could play with the numbers.

The first four columns are from my POH that applies to operation at 10000'. Last two columns are calculated for 60 mph headwind. Per the POH, numbers are miles and mph.

Code: Select all

RPM    TAS   hrs   range           60hw, gnd spd    range

2650   130   4.1   535               70             287
2600   127   4.3   555               67             288
2500   120   4.8   590               60             288
2400   115   5.4   630               55             297
2300   108   6.2   670               48             298
2200   101   7.0   720               41             287
2100    95   7.9   755               35             277


Look at the ranges for the 60 mph headwind. I can't believe how similar it is across all of the speeds!

I played with various headwinds at various altitudes, and for my plane's published numbers, using 2/3 of the headwind instead of 1/2 gives a much better match (my Vbg is 65). For "normal" headwinds (say, less than 1/3 of the cruise speed) either value is close enough.

The best ROT:
Fly with your tail pointed into the wind!

Garmin 696, get winds aloft and fly the best altitude is all I do.

Kevbert

kevbert wrote:

WSH wrote:ROT for headwind, add half of the wind velocity to Vbg.

That's a decent rule of thumb for maximizing range, providing headwinds aren't extreme. When this discussion started, I entered my cruise performance chart from my POH into excel so I could play with the numbers.

The first four columns are from my POH that applies to operation at 10000'. Last two columns are calculated for 60 mph headwind. Per the POH, numbers are miles and mph.

Code: Select all

RPM    TAS   hrs   range           60hw, gnd spd    range

2650   130   4.1   535               70             287
2600   127   4.3   555               67             288
2500   120   4.8   590               60             288
2400   115   5.4   630               55             297
2300   108   6.2   670               48             298
2200   101   7.0   720               41             287
2100    95   7.9   755               35             277


Look at the ranges for the 60 mph headwind. I can't believe how similar it is across all of the speeds!

I played with various headwinds at various altitudes, and for my plane's published numbers, using 2/3 of the headwind instead of 1/2 gives a much better match (my Vbg is 65). For "normal" headwinds (say, less than 1/3 of the cruise speed) either value is close enough.

The best ROT:
Fly with your tail pointed into the wind!

Actually my headwind ROT response was intended for Tim and what I thought was an engine out/zero thrust "gliding" scenario question.

Sorry for any confusion.

Engine out zero thrust is what it was. With a tailwind would you take off half the wind speed.

Tim

If you've got zero thrust, then headwind or tailwind doesn't mean a thing. Headwind or tailwind is relative to the ground. Your plane doesn't interact with the ground if your wheels aren't touching it. The plane's indicated airspeed is all that will matter, and the plane's Vbg is your best glide speed, whether the wind is blowing or not.