Max Range vs Max Endurance

[LA931]

Hi all. I'm new to this forum. I am a pilot and am tired of the "you don't need to know that to fly the plane" that I always get when I ask these type of questions.
To my question:
According to the books, a propeller-driven airplane will attain its maximum range speed at the least drag speed (Max L/D). That makes perfect sense.
Now, if I want to fly the max endurance speed I should fly the proper speed so that the fuel consumption is the lowest. I would assume that lowest fuel consumption is going to give me the lowest thrust that is still capable of maintaining level flight. Naturally that would be achieved at the least drag speed, just like for max range (no wind). So the two speeds would be the same. That makes sense to me. But the books say something different.

The books say that fuel consumption depends on engine power instead of engine thrust. But power equals thrust times velocity (P = T.V). So the faster the airplane moves, the higher the power. If we see a curve of power vs speed we can see that the minimum power is attained at a slightly lower speed than that for max range. That is the max endurance speed according to every book I've read.
But I don't understand why they say that fuel consumption depends on power instead of thrust.
If the airplane is standing still with max rpm, the power is zero because speed is zero, but we still have thrust and of course the fuel flow is going to be high. So fuel consumption depends on thrust, not power.

Any clarification will be greatly appreciated.

LA

 

[crysta1c1ear]

The books say that fuel consumption depends on engine power ....

I think the key word there is 'engine' - engine power.

If the airplane is standing still with max rpm, the power is zero because speed is zero, but we still have thrust and of course the fuel flow is going to be high.

If you fasten a plane, so that it goes nowhere, then you are doing no work on the plane, so the power is zero, but that isn't engine power. The way you expained it engine power is high as the fast spinning propeller pushes masses of air from infront of the plane to behind it. The engine is doing work on that air.

But power equals thrust times velocity (P = T.V). So the faster the airplane moves, the higher the power.

No. Suppose you have a 200 hp engine and give it full throttle. It produces 200 hp. As the plane accelerates, it doesn't become 300 hp. Have you mentally assumed fixed thrust?

 

[crysta1c1ear]

It's a shame I can't scrub a few sentences on that last post. I have been drinking!

Naturally that would be achieved at the least drag speed, just like for max range (no wind).

If you are just trying to stay in the air as long as possible, then you aren't trying to get anywhere and can be happy to trade speed for lift. A bit more drag will slow you down for the same engine power, but if you get lift in return great.

Hmmm. I may well wake up with a hangover tomorrow and regret posting!

 

[Compositepro]

Max Endurance = minimum gal./hr while still being able to fly. (max. hours per gallon).

Max. range = minimum gal. per ground mile

Gal./hr. will be proportional to engine power.

Gal./ mile will be high at low speed and at high speed.

 

[berkshire]

I think the thing being missed here, is the point on a polar curve for the airplane called minimum sink which occurs at a lower speed than max L/D usually right before the stall. power settings to achieve min sink are much lower than max L/D. hence longer endurance, it should be noted it will not be the longest range. But if you have to hang around over a spot this is what you need.
B.E.

 

[Sparweb]

There comes a point where flying the aircraft any slower requires *more* power, not less. That's "slow flight", and you are on the backside of the power curve. Stay that way too long in an aircraft, and you risk your own backside, too.

L/D max is a point where the lift over drag ratio is optimized, but that's not the same thing as "max range" in a powered aircraft.

Gliders: Max range will be achieved at max L/D.
Max endurance will be achieved at max (L/D)[sup]3/2[/sup]

Powered aircraft: The breguet (sp?) formulas combine the ratios I quoted above and the engine fuel consumption rate. You must consider all 4 forces on the aircraft to compute either the range or the endurance (thrust, drag, lift, weight) in these formulas. To gain a useful amount of accuracy, you must even figure in the effect of lightening the aircraft as you burn off fuel...

That's about all I can do without quoting the textbooks. If you need more, I recommend Anderson's Introduction to Flight (though there are plenty more)

First link on Google to "breguet formula":

http://web.mit.edu/16.unified/

http://www/FALL/thermodynamics/notes/node98.html

Steven Fahey, CET

 

[LA931]

Crysta1C1ear, I totally agree with you with the fact that if we use airplane speed to calculate power, then that isn't engine power. I don't understand why the books use airplane speed instead of using prop angular speed or something.

To make things simpler, I'm going to take the engine out of the question and reformulate my question to what berkshire said:

Why is it that the minimum sink speed is lower than the minimum drag speed? I would expect to get max time in the air if Lift is a max and drag a minimum ( at L/D max speed).

 

[tbuelna]

If you accept that an aircraft powered by a high-bypass-ratio turbofan engine is technically "propellor driven", then airspeed, air density, air temperature and engine speed all can have a significant effect on specific fuel consumption. And the lowest practical engine operating speed definitely does not produce the lowest overall SFC. Generally, turbine engines are most efficient at whatever condition yields the highest pressure ratio. And that's typically somewhere near the max speed & power setting.

With recip piston engines, min. SFC will usually be whatever the minimum speed the engine is capable of running at with a WOT condition. Part throttle operation is seriously detrimental to fuel efficiency.

 

[thruthefence]

Seems like I read that during the war, Charles Lindbergh was working as a tech rep for Lockheed, and was in the pacific theater advising air crews as to how to stretch their endurance; the technique was to pull the props back to the minimum rpm stop, and add manifold pressure until the engine was on the verge of detonation.

 

[manyhelicopterman]

The simplest way to get maximum range data is to use fuel flow (and not power). Especially for turbine engines, which become more fuel efficient at higher power settings.
And the maximum range airspeed is for maximum air range, not ground distance. Factoring in headwinds and tailwinds slightly complicates the matter.
Sort of like equal time point is a distance calculation, and point of no return is a time calculation…

 

[swearingen]

I disagree. The simplest way to get maximum ENDURANCE is to use fuel flow - it doesn't matter how fast you're going, as long as you're still flying. To calculate max range, you plot your air speed divided by your fuel flow and find the peak. Of course, this is where the aircraft will fall from the sky, so some safety factor is warranted.

To equate this to boating (where a clearer difference between the two can be seen), if you just idle in the boat, you'll get max endurance. However, you must be going fast enough to get the boat on plane to achieve max range. This burns much more fuel and you will not travel as long a time, but you will travel a much greater distance.

I think it is understood that external factors such as head or tail winds are not considered when giving the base range. Obviously your range will be decreased or increased accordingly. This is analagous to boating upstream or downstream in a river.



If you "heard" it on the internet, it's guilty until proven innocent. - DCS

 

[crysta1c1ear]

Why is it that the minimum sink speed is lower than the minimum drag speed? I would expect to get max time in the air if Lift is a max and drag a minimum ( at L/D max speed).

To stay in the air for the longest possible time, you don't care what drag is. If you can get more lift great, even if it is at the expense of drag. If the plane rises, cut the power a bit. If you can adjust a control to give more lift, cut the power a bit more. When finally you have optimised everything so that you have as much lift as possible for as little fuel use as possible: voila, job done. Drag could be horrible and the plane flying slowly, but drag doesn't matter.

The last sentence in the quote reads to me as if you are expecting some settings of the flight controls to simultaneously give maximum lift and minimum drag.

Hold your hand out of a car window and you'll feel that if it's horizontal it'll have low lift and low drag, and if it's at an angle, eg 30° then it will have higher lift and higher drag. By the time your hand gets to 90°, you'll have lots of drag, but the lift will have gone again.

=

Imagine for example varying the angle of a wing to maximise lift. Graphs reach a maximum where they are flat at the top, so small changes in wing angle (plus or minus) will not greatly affect lift. But changing the angle will affect drag: a smaller angle of attack will give less drag. So the lift to drag ratio can be improved: you can have about the same lift for less drag.

So maximum lift and optimised L/D are not the same.

 

[thruthefence]

Load the aircraft aft CG, less induced drag, better performance, at the expense of stability.