Pof F/ power curve question

[winchman]

Any ideas what the correct answer is? The more i thought about it with the power curve the more i doubted the answer.....

'If an aircrafts best range speed is 60 knots indicated, and it is flying with a 20 knot tail wind, what would be the aircrafts best range speed? (Or words to that effect).

60 kts, 40kts or something else???

[BackPacker]

Gut feeling would say remove half the tailwind. So that would lead to 50 knots indicated.

But for the absolute correct response you've got to know the exact speed/fuel consumption curve of the engine/propellor/airframe. Because 50 knots indicated may, for all you know, be right above Vs and thus very wasteful.

The speed that doesn't change with wind is the best endurance speed since that speed is simply the speed of the lowest drag. But best range speed...:ugh:

[Choxolate]

Winchman
Any ideas what the correct answer is? The more i thought about it with the power curve the more i doubted the answer.....

'If an aircrafts best range speed is 60 knots indicated, and it is flying with a 20 knot tail wind, what would be the aircrafts best range speed? (Or words to that effect).

60 kts, 40kts or something else??? I am not sure if I am completely stupid but if the best "range speed" (presumably airspeed at which maximum distance would be achieved in still air) is 60 knots indicated - why would this be any different with a 20 knot tail wind (or in fact any tail wind come to that).

I must be missing something here.

[Justiciar]

Best range airspeed is the lowest point on the Thrust/Drag against airspeed graph. On the power required against airspeed graph it is represented by a tangent to the curve (ie a straight line from zero touching the curve!). However you look at it it is unrelated to the tail wind or headwind. With a tail wind the range will of course be greater, but 60 kts IAS will still be the best range air speed.

Of course many factors will alter the power required, such as altitude and weight, but that is not what you are being asked in the question!

[Midland Transport]

The answer is 60knts as the question relates only to indicated airspeed.

[BEagle]

Just think of the converse!

If best range speed in still-air is 60 KIAS, it will obviously need to be higher if the aircraft is flying into a 60 kt wind. Or the aeroplane will go nowhere.

So, conversely, it'll be lower if the aircraft is flying with a tail wind.

K.I.S.S

[John Farley]

BEagle is right of course.

If the questioner is asking what speed should you fly to go as far a possible on a given bag of fuel then it will be less that 60 kt.

But is he asking that?

That is the question!

JF

[mikehallam]

The most economical airspeed is '0' mph/kt.

Then you'll have unlimited range !

[asyncio]

If I understand it correctly, then I think you draw a tangent on the power vs airspeed curve in the same way as you normally calculate best range.
But rather than drawing the line from the origin, you draw it from -20kt.

Which would give a lower airspeed, and conversely a higher airspeed for a headwind from +20kt on the speed axis.

[Justiciar]

If the questioner is asking what speed should you fly to go as far a possible on a given bag of fuel then it will be less that 60 kt.

John: I must be loosing it - please explain. At above or below 60 kts your range in still air will be less? Therefore, with a tail wind your range will still be less above or below 60 kts, but obviously more than still air range at whatever speed you are flying!

With a headwind I accept things become more complicated - headwind offset by greater speed but offset by reduced still air range.

[sycamore]

Since the wind has no effect on the Power or Drag curves the answer is 60 kts.(theoretically).
Practically, if you have a tailwind,of a strength greater than the difference between Range ,and Endurance speed,you are better off flying at Endurance speed; any headwind will increase your time/reduce your range.....

[asyncio]

OK, after fiddling around with various ways of doing this, I think I've come up with a way of explaining what I said above.

I'll use, v = airspeed, w = windspeed, t = time, d = distance, p = power.

Starting with the obvious t = d/v
Now power is related to fuel flow, so the time we have availble is proportional to fuel/power. So t = 1/p for one 'unit' of fuel

Putting them together gives d/v = 1/p, which becomes d = v/p
So for maximum d, we have to maximise v/p, or minimise p/v.
i.e. the usual tangent on the power/velocity graph.

Similarly, if we have a wind then t = d/(v+w)
So if we do the same as above we get, d/(v+w) = 1/p
then d = (v+w)/p

So we have to minimise p/(v+w), or in other words, you have to draw a tangent from the graph to -w on the speed axis.

I hope that's right, or I've completely misunderstood it as well:bored:

[ShyTorque]

Good explanation plus pilot friendly explanatory graph given here:

Airplane aerodynamics and performance - Google Books (http://books.google.co.uk/books?id=bSq-cEf0EWsC&pg=PA523&lpg=PA523&dq=best+range+speed&source=bl&ots=iDOtxPQovN&sig=sSxaiU40ZORXifNf4W4Red4RRds&hl=en&ei=jpmVSqTNAd6gjAfsrIT0DQ&sa=X&oi=book_result&ct=result&resnum=5#v=onepage&q=best%20range%20speed&f=false)

[BEagle]

asyncio - yes, you're absolutely correct.

Draw the tangent from the relevant windspeed on the x-axis. Clearly, the wind-corrected range speed cannot be less than endurance speed unless there is an infinite tail wind.

[Deeday]

Another way to look at it: with a strong tailwind, you are better off floating around in the air for as long as you can (= flying close to the best endurance speed) and let the wind carry you along. :ok:

[IO540]

The best range IAS, Vbr, does depend on the wind.

Loads has been written on this topic ( Prof. Rogers (http://www.nar-associates.com/technical-flying/technical_flying.html) etc) but basically the way this works is that if you have a tailwind, you need to fly slightly slower than Vbr in order to take maximum advantage of the tailwind, and if you have a headwind then you need to fly slightly faster than Vbr in order to spend less time in the headwind.

The exact amounts of "slower or faster" depend on the combined gradients of the engine's specific fuel consumption v. power curve and the L/D curve. This Q cannot be answered because neither we, nor I suspect the OP, have any idea what this is.

For any normal gliding aircraft, the best range speed is theoretically equal to Vbg - the best glide speed. Obvious really ;) And every aircraft is a glider. An engine merely gives you the option of a positive rate of climb.

For a powered aircraft, this doesn't quite work because it assumes engine efficiency is constant over the power setting, which is obviously not going to be the case because the pumping and friction losses are largely constant so - assuming LOP operation - low power settings will be less efficient and thus Vbr will be higher than Vbg. On my TB20 Vbg is ~ 95kt but Vbr is about 110kt (still very slow!).

It is possible that if you have a 20kt tailwind you need to fly 10kt slower but there is no such rule; this would be a pure coincidence. I actually very much doubt it would be that much because if Vbg was say 60kt (IMHO pretty slow but possible) then 50kt will yield a pretty large AoA. I'd say the IAS adjustment will be a few kt at most for a talwind. But it could be a lot more for a strong headwind because one can so rapidly reach a situation where one is going literally nowhere and looking at the limiting case of say Vbr being 60kt and the headwind being 59kt, it is obvious that full power will be the optimal power setting regardless of efficiency. But as I say this is type specific.

[hatzflyer]

In reality a flight at 60 knots with a 20 knot tailwind is likely to be most uncomefortable and not something I would want to do anyway, unless of course you are very high where the wind is likely to be smoother.
But then you have other variables entered into the equation,engine leaning at height gives a better range in theory, and wind speed usually increases with height, so you would pick up more tailwind the higher you go,but burn fuel getting higher thereby decreasing the range.

So the information gained from this little excersize is about as much use to the average pilot as knowing the average inside leg measurement of a camel!:ok:

[mm_flynn]

But the principles discussed are just as applicable to more normal speed 'extended range' flying.

because almost all pilots normally operate at WAY above Vbr, if you are trying to stretch your range you should

1 - In a tailwind slowdown (potentially by the whole tailwind component) as you will still arrive in a reasonable time, but with a much lower fuel burn.

2 - In a headwind you should NOT speed up, because you are already operating way faster than Vbg still air, and unless you have a tremendous headwind, you are also going faster than Vbr adjusted for the headwind component. With a piston aircraft facing a significant headwind, you are almost always better off giving up the TAS of altitude for a lower headwind (which normally this means decend) if you want to maximise range.


At a constant power setting your range is pretty much independant of the altitude at which you are operating (assuming no wind)

[IO540]

a flight at 60 knots with a 20 knot tailwind is likely to be most uncomefortable and not something I would want to do anyway

How? a plane is not aware of the wind. It flies within its own frame of reference, which is always still air. "Wind" is a separate frame of reference: the whole chunk of air moving over the earth's surface.

you are almost always better off giving up the TAS of altitude for a lower headwind (which normally this means decend)

I agree.

At a constant power setting your range is pretty much independant of the altitude at which you are operating (assuming no wind)

So long as you are LOP the whole time :)

[worrab]

So the information gained from this little excersize is about as much use to the average pilot as knowing the average inside leg measurement of a camel!http://images.ibsrv.net/ibsrv/res/src:www.pprune.org/get/images/smilies/thumbs.gif
... I suppose it may have helped Capt Biggles...(IIRC there's a question like this in The Confuser and perhaps therefore in one of the Aeroplane-Technical papers)

[hatzflyer]

So if a plane always flies in still air, how come I have still got the bruises on my shoulders from the straps on my shoulders fron a recnt flight across France where my head was hitting the canopy.
Or did I just imagine it?:confused:

[mm_flynn]

So if a plane always flies in still air, how come I have still got the bruises on my shoulders from the straps on my shoulders fron a recnt flight across France where my head was hitting the canopy.
Or did I just imagine it?:confused:World of difference between the horizontal component of airflow (i.e. the wind) and the local vertical component (bumps). I have been beaten around the sky on a calm day (very hot so lots of vertical airflow but in a high pressure system so little horizontal) and had a ride smooth as glass with 80 knots on the nose at FL100.

[IO540]

That was due to turbulence, which is a different thing. Turbulence can be caused by air flowing over terrain below. Here (http://www.aviationexplorer.com/av_info_pics/turbulence.jpg) is a nice picture. This is not related to whether the airflow is a tailwind or a headwind relative to the aircraft.

A lot of pilots think that a plane flies somehow "sideways" when there is a crosswind, for example. One pilot swore blindly his plane vibrated more if flying in a crosswind. It's a favourite old topic - always raises a little smile. I have even met an instructor who believed this.

[hatzflyer]

But the whole point is that you are more likely to encounter turbulance on a windy day.
Plus when the wind componant is 30% of the cruise speed the effect is much more noticeable.
I have always found it more comfortable flying into wind on a turbulent day, rather than tailwind. Hard to define but the plane just feels "happier" .

[IO540]

Plus when the wind componant is 30% of the cruise speed the effect is much more noticeable.

I would say the contrary. The faster you fly in turbulence, the harder the bumps are. Also, one needs to fly below Va if the turbulence is significant (whatever that means).

I have always found it more comfortable flying into wind on a turbulent day, rather than tailwind. Hard to define but the plane just feels "happier" .That may be subjective. Can anyone come up with a technical explanation? Relative to the aircraft trajectory, turbulence is mostly a vertical air movement.

[hatzflyer]

It may be pure conjecture but if the plane is going to pitch up, it always appears to pitch up tail first(ie nose down) as if the turbulence is coming from the rear.
As I say, it may just be me, but I know I am much happier in a headwind if its turbulent.
I take your point about the " hardness" of the bumps.
Coming over the channel on the day mentioned above, I was well throttled back to stay well clear of the yellow arc but we were still covering the ground at over 200mph on what would normally almost be decent power!

[mm_flynn]

In general if the windspeed is 30% of cruise, I would expect more turbulance down low than at 20% (i.e. 50 knots rather than 30 knots). However, I have never noticed that bumps on a 30 kt day are worse when I slow down. The physics say the particularly hard bumps should be softer at a slow speed (because the wings stall a bit and you can't get as high a G load).

However, in my flying, I am most likely to be slow at less than 1500 ft (fitting into circuit traffic) and fast at altitude, which means it is typically rougher when I am slow than fast - but this is down to altitude not speed.

None of this has anything to do with the practicality of flying at best range speed and how this changes with head/tail wind.

your preference for headwind may be that it gives more time to think and therefore you have less pressure. With 60knots of wind I find it easier (other than the frustration) to have it on the nose as everything that relates to the ground happens at half speed relative to the wind from behind.

----
A further thought, the main cause of turbulence will be a change in local vertical airflow - and this will happen over a certain distance. The faster you are going over the ground the higher the frequency of these reversal (you should have more g reversals per second). this may be perceived as less comfortable or being more beaten up (head bashes per minute goes up but the total number of head bashes remains constant)

[Andy_RR]

http://i93.photobucket.com/albums/l79/Andrew_E_Rabbitt/Misc/DragCurve.gif

[IO540]

Andy; I think that diagram is still missing the engine efficiency variation factor.

And this does matter because one is burning fuel to do this.

[Andy_RR]

IO540, if you're going to make it that complicated, then you'll need to specify whether its FP or CSU, since you can maintain quasi-constant BSFC with a CSU, but it will degrade more rapidly when reducing power with a FP propellor.

edit: actually, I don't think it will make any difference to my badly drawn graph, since the only thing that will change is the shape of the drag power curve (OK, you'll need to re-label that as SHP to be strictly correct). I think the curve will only change subtlely - not enough to make my diagram any more inaccurate.

The main point is to demonstrate the effect of a tailwind (in this case), where GS > TAS

[ShyTorque]

Aircraft have inertia.

If a "headwind with updraught" gust hits the aircraft, it will momentarily give an increase in IAS and in lift, which will tend to amplify the updraught effect because the wings will generate an addition to the upwards "bump".

If the same aircraft is travelling downwind, the same gust will be "tailwind with updraught". The reduction in IAS will decrease the lift, which will offset the "updraught" and give a lesser "bump" effect.

Obviously, this is one case where our oft mentioned "aircraft on a conveyor belt" might be an easier ride....until it takes off, of course.

[IO540]

ST - I agree, but is there evidence that turbulence has a significant horizontal component?

[ShyTorque]

I've never heard otherwise - surely on finals the horizontal variations in IAS are known as "windshear" - larger aircraft being more affected by it due to their larger inertia.

As moving air, like other gases, likes to form a vortex, an aircraft passing through one is likely to experience both horizontal and vertical components.

[IO540]

Wind shear is not turbulence. WS is just the natural variation of wind speed with height, and yes a plane with more inertia (or a longer engine spool up time) will be more affected because it won't be able to maintain a constant IAS.

[ShyTorque]

I think our opinions will continue to differ in that respect.

[IO540]

OK, there are umpteen types of turbulence but I was thinking of the kind referred to higher up, which was caused by wind passing over terrain, and causing a bumpy ride for a plane flying at say 1000-2000ft AGL.

It would suprise me if there was a significant small-scale horizontal airflow speed variation in the above case. But plenty of vertical movement.