Best Range Speed-vs- Best Flight Endurance & Maximum Range

[Greg2041]

Hi People,

I am hoping to sit the PPL Flight Planning & Performance exam this Friday and so far it has all gone very well.

BUT, I can't get my head around the difference between best range speed and best flight endurance - also maximum range.

In really simple language can someone explain the difference?

Many thanks

Greg

[BackPacker]

Best endurance is simply the longest time aloft. You're just hanging there with the minimum power to stay airborne somehow, but you're not going anywhere. Useful in a holding pattern, when waiting for ground fog at your destination to clear, or until your destination opens for instance.

Best range is the speed is the speed where you cover the most amount of ground for the least amount of fuel.

Best endurance speed is a given speed, and is not dependent on the wind. (Unless the wind is so strong that you're being blown away from the holding pattern when flying at best endurance speed.)

Best range is dependent on the amount of head/tailwind you have. If you have a headwind you've got to speed up a little, if you have a tailwind, you can slow down a little to obtain best range. The exact correction is dependent on the exact performance curve of the aircraft. In the POH you will normally find the best range speed, assuming nil wind. As a rule of the thumb, when you have a headwind, increase that speed by half the headwind. If you have a tailwind, decrease that speed by half the tailwind.

[Ezedai]

Hi,

Best range speed is the speed to fly at (in a static atmosphere, ie. no wind or lift/sink) if you want to go as far as the plane is capable given the fuel onboard.

Best endurance speed is the speed to fly at if you want to stay airborne for as long as possible and don't care about range. If you try and fly as far as you can at best endurance speed you will fly for longer than at best range but not get as far.

It's sort of like the difference between best rate of climb and best climb angle; it depends on what you want to do.

Mark

[Keith.Williams.]

ENDURANCE
Endurance is a measure of the amount of time that an aeroplane can fly using a given amount of fuel. So maximising the endurance means making each unit of fuel last as long as possible. This means that we must burn the fuel as slowly as possible. This is achieved by flying the aeroplane at the airspeed at which fuel flow is minimum.

In piston engine aeroplanes fuel flow is proportional to power required. So for maximum endurance we must fly at the speed at which the power required is minimum. This speed is the Velocity Minimum Power Vmp. The Power required curve looks a bit like a Nike Tick and Vmp occurs at the bottom of the curve.

RANGE
Range is a measure of how far we can fly using a given amount of fuel. To maximise our range it is not enough to simply burn the fuel slowly. We must achieve the maximum number of miles per unit of fuel used.

Airspeed is how fast we are covering the miles. Fuel flow is how fast we are using the fuel. So to achieve maximum flight range we must achieve the maximum ratio of Airspeed to the fuel flow.

In piston engine aeroplanes fuel flow is proportional to power required. So the speed for maximum range is that at which the ratio of Airspeed to Fuel Flow is greatest. This is achieved at the Velocity Minimum Drag Vmd. The Drag Curve looks a bit like a bucket shape. Vmd occurs at the bottom of the drag curve. But in the PPL exam they show you a power required curve. Vmd occurs where a tangent from the origin touches the power-required curve.


BUT FOR PPL EXAM PURPOSES
1. When the ratio of airspeed to power is a maximum, the ratio of power to airspeed is minimum. So it can be said that the maximum range speed is the airspeed at which the power/airspeed ratio is least.

2. Because most aircraft are designed to cruise at speeds considerably higher than Vmd, the speed at which range is a maximum is in reality often higher than Vmd.

[Greg2041]

That's great and easily understandable. The books seem to make things so complicated.

With thanks

Greg

[Greg2041]

You've created a very useful PPL Software Q&A package Keith. I heartily recommend it.

Greg

[IO540]

Vmd occurs where a tangent from the origin touches the power-required curve.

Doesn't that assume engine efficiency being constant?

Traditionally, the best range speed is equal to Vbg (best glide speed) but this assumes constant engine efficiency, AIUI. In practice, Vbr (best range speed) occurs at a slightly higher power setting.

But you need to be careful. The exam questions are written assuming you have studied the right books - not necessarily for the most accurate knowledge.

[Keith.Williams.]

Quote:
Vmd occurs where a tangent from the origin touches the power-required curve.

Doesn't that assume engine efficiency being constant?

No it doesn't. It simply asssumes that Power Required = Drag x TAS.

It has nothing to do with the engine efficiency.

But variations in engine efficiency will affect the speed at which maximum range is achieved. I hinted at this in my explanation, but because I wanted to keep it simple, I did not go into it in detail.

The problem for the PPL student is that most of the questions on range and endurance ignore variations in engine efficiency, but one question does not. So for most of the question it is "Vmp for max endurance" and "Vmd (at the tangent to the power required curve) for best range." But for one it is "best range speed is slightly higher than Vmd."

[BackPacker]

But variations in engine efficiency will affect the speed at which maximum range is achieved.

It's even more complex because you need to take propellor inefficiencies into account too. So:

- The power output of the engine (HP/torque vs. fuel flow) is not linear.
- The thrust output of the propellor (thrust vs. HP/torque) is not linear.
- The total drag (parasite plus induced) vs. speed curve of the airframe is not linear.
- The thrust angle of the engine at low speed is not aligned with the flight path (high AoA).

So to go from fuel flow to speed you've got to match at least three compound curves to each other. This is tough work for aerodynamicists with CFD computer models and impossible for a PPL with just an E-6B (which you're not allowed to use in that exam anyway).

So as Keith said, keep it simple. Bottom of the power required curve is max endurance, tangent of the origin to the power required curve is max range in still wind. Move the origin left/right to account for a head/tailwind. And hope that you don't get that one question that requires you to know why max range is actually a bit higher than Vmd, even in still air - the reason is the various inefficiencies in engine/propellor/airframe design, and optimization for a higher cruise speed than Vmd.

[Big Pistons Forever]

Originally Posted by BackPacker

It's even more complex because you need to take propellor inefficiencies into account too. So:

- The power output of the engine (HP/torque vs. fuel flow) is not linear.
- The thrust output of the propellor (thrust vs. HP/torque) is not linear.
- The total drag (parasite plus induced) vs. speed curve of the airframe is not linear.
- The thrust angle of the engine at low speed is not aligned with the flight path (high AoA).

So to go from fuel flow to speed you've got to match at least three compound curves to each other. This is tough work for aerodynamicists with CFD computer models and impossible for a PPL with just an E-6B (which you're not allowed to use in that exam anyway).

So as Keith said, keep it simple. Bottom of the power required curve is max endurance, tangent of the origin to the power required curve is max range in still wind. Move the origin left/right to account for a head/tailwind. And hope that you don't get that one question that requires you to know why max range is actually a bit higher than Vmd, even in still air - the reason is the various inefficiencies in engine/propellor/airframe design, and optimization for a higher cruise speed than Vmd.

The above is correct and usefull for passing the exam. The good news is the theory around determining a particular best range speed is it not something you have to worry about when you are actually flying. The best range speed will in practice never be used because it results in an impractably low cruise speed. For your typical light trainer/tourer, a more normal cruise speed in the 55 % to 60 % power range will result in only slightly reduced range but yield a usefully higher speed. Also for slow aircraft wind has as much more profound effect on actual range than the theoretical differences mentioned above because wind will always be a large percentage of the cruise speed.

[IO540]

But variations in engine efficiency will affect the speed at which maximum range is achieved

That's what I meant

The best range speed will in practice never be used because it results in an impractably low cruise speed.

That's true in low-level PPL hacking but when I go up to say 18000ft (and a lot of airways flight is done at those levels) my IAS is nothing to write home about (say 95kt).

Also, on any reasonably equipped aircraft, the best range speed is read directly off the GPS which is linked to the fuel totaliser This figure is based on the current GS and is thus already adjusted for the wind and everything else.

Last year I was researching an article on engine management and one interesting thing I picked up was that TAS and therefore the range was virtually independent of altitude, and climbs and descents - so long as the engine remained peak-EGT/LOP the whole time. And this is actually true.

Not that any of this applies to passing exams

[Pull what]

You've created a very useful PPL Software Q&A package Keith. I heartily recommend it.

Greg

Gosh Greg you learn very quickly-it just took you 40 minutes to read, understand and review Keiths PPL package and understand the above posts, you will go far, even in advertising!

[Greg2041]

Gosh Greg you learn very quickly-it just took you 40 minutes to read, understand and review Keiths PPL package

Really? Why have you assumed this? I bought the Q&A disc over a month ago. Maybe there's some humour I am missing?

Sorry if I am not supposed to recommend a good product.

[screetch]

hi i am also taking the exam this weekend and i remembered:

- best range: - best lift drag ratio (as in gliding range)
- lowest ratio of power to airspeed
- into headwind , increase airspeed to increase range
- with tailwind, lower airspeed to increase range
- fly furtherest with a given fuel load

- best endurance: - at minimum power setting and
lowest altitude
- fly longestest but slowest with a given fuel load


For best range it will be interesting to see actual figures of how much range increase when flying with a tailwind and a headwind and which one has most effect. I gather the tailwind and you are drifting and burning less fuel at the time..but this will depend on so many other figures.
Does anybody have numbers as an example?

[Greg2041]

Well thank you all. I passed the exam on Friday and got all the questions right. Your explanations certainly helped on one of the questions.

Many thanks

Greg

[glen26]

Did you find a job seven years later ?