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Maxpowerhome
28th May 2004, 03:24
Just a quick question,


Max range is defined as a speed, for a given weight and alt, that max fuel milage is obtained.

How is range increased when flying into a headwind?

Tinstaafl
28th May 2004, 04:05
By flying slightly faster.


Note that the original, no headwind range won't be regained. Flying a bit faster in the headwind regains a little bit of the lost range.

More accurately:

Best range speed can be found from the power required graph. Draw a straight line from the origin to just brush past the power req'd curve. The airspeed at which the two lines touch is the best range speed.

For a headwind the best range speed can be found by moving the origin along the X axis the same amount as the headwind component (X axis scale is airspeed). The effect is to subtract the headwind component to give a 'shorter' speed scalar.

For a tailwind move the origin in the opposite direction.

If you've done it correctly you will see the speed increase with a headwind component and decrease with a tailwind.

Maxpowerhome
28th May 2004, 04:29
Thanks, i understand that now. I was trying to make sense of it in Davies book. :cool:

VH-ELP
28th May 2004, 07:16
If flying at 100 kts TAS into a 100kt headwind, you would have to increase TAS to go anywhere (ie increase range) is how I explain it to my students.

Genghis the Engineer
28th May 2004, 09:47
The maths is fairly straightforward, but generally requires a bit of background information.

- You should have somewhere a table or graph comparing cruise speed and fuel consumption (power should be in there somewhere as well).

- You can convert that into a table or graph of airspeed against "specific air range" - this can have virtually any units you want, but personally I usually use something like nm/litre.

- Now in still air, the actual range per given fuel is (TAS * SAR * fuel available)

- But in, say, a 10kn headwind, it'll be ( [TAS - 10] * SAR * fuel available), or in a 30kn tailwind it'll be ( [TAS + 30] * SAR * fuel available ).

- What you'd then do is plot a series of graphs (all on one scale, this is called a "carpet plot") of range (or range per fixed amount of fuel).

Either there will be a maximum on each curve, which is the speed for best range in a given condition, OR it'll be a continuous positive or negative slope - in which case the aircraft should be flown as fast or as slow as other conditions permit (like stall, Vh, turbulence, Vno, etc.).


Now in best Blue Peter fashion, "here's one I prepared earlier". I was writing the POH for a 2-seat SEP monoplane (the type is irrelevant), I started with three graphs which showed cruise speed (in kph - funny foreign units) against engine speed, another which showed fuel consumption against RPM, and finally one which compared IAS to CAS (which is TAS at ISA S/L condition). From that I constructed the following table:-

IAS, kph TAS, kph TAS, kn RPM kg/hr Litres/hr Litres/nm
120 98 52.8808 4000 2.88 4 0.075641821
140 122 65.8312 4250 3.96 5.5 0.083547011
160 143 77.1628 4600 5.904 8.2 0.106268824
180 166 89.5736 4850 7.776 10.8 0.12057124
200 190 102.524 5200 9.072 12.6 0.122898053
220 235 126.806 5600 12.96 18 0.141949119


I could then using the formula I've described, take the TAS and Litres/hr figures and produce this, which is a table of nm/10 litres:-

TAS, kn Litres/hr -20kn -10kn Still +10kn +20kn
52.8808 4 82.202 107.202 132.202 157.202 182.202
65.8312 5.5 83.32945455 101.5112727 119.6930909 137.8749091 156.0567273
77.1628 9.5 60.17136842 70.69768421 81.224 91.75031579 102.2766316
89.5736 10.8 64.42 73.67925926 82.93851852 92.19777778 101.457037
102.524 12.6 65.4952381 73.43174603 81.36825397 89.3047619 97.24126984
126.806 18 59.33666667 64.89222222 70.44777778 76.00333333 81.55888889

This then allowed me to produce the following carpet plot (speed has gone back to IAS again, it has to)


http://static.photobox.co.uk/public/images/70/29/8857029.s.jpg

As you can see, it shows that in, say a 20 knot headwind, the best range speed is about 97 knots IAS, where I'll get about 62 nm for each 10 litres of fuel. On the other hand with any tailwind, I should fly this aircraft as slowly as my patience will allow and there isn't actually a best range speed downwind (this is unusual, but not unique).

G

N.B. If anybody knows a better way of showing tables in Pprunevision, please let me know.

(Edited 31 May following excellent advice on use of proportional fonts below, although it only helped a bit).

Genghis the Engineer
28th May 2004, 16:36
Postscript.

What you can also do with a graph like that, is take the speeds at which the maxima occur (in this case 97 knots for a 20kn headwind), about 67 knots for a 10 kn headwind and probably around 45 knots for still air, and plot two more graphs from those.

- Best range speed against head or tailwind component.
- Range (or range per fixed fuel quantity) against head or tailwind component.

Which can be useful for some aircraft types - sort of thing I used to do e.g. for a military patrol aircraft like the Nimrod, or just for emergency "how the hell am I going to get home" procedures.

G

Young Paul
31st May 2004, 21:05
Genghis:

Using courier will
(generally)
allow you to
line characters
up under
one another.


Use of only 3 sig figures might also help readability.

Genghis the Engineer
31st May 2004, 23:43
Good point, I confess to cutting and pasting directly from Excel, which was perhaps a little lazy on my part so far as sig-figs were concerned, but using a non-proportional font is a very good idea.

G