Pof F/ power curve question
 

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???

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:

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.

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!

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

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

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

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

Then you'll have unlimited range !

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.

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.

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.....

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:

Good explanation plus pilot friendly explanatory graph given here:

Airplane aerodynamics and performance - Google Books

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.

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:

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

Loads has been written on this topic ( Prof. Rogers 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.

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:

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)

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.

I agree.

So long as you are LOP the whole time :)

... 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)