Why cruise at the (L/D)max velocity

[sligo565]

Hi fellas,

Just a quick question, why do you want to fly as near as possible to the (L/D)max speed? is it to do with efficiency etc.

Would i better having a velocity equal to that of the cruise velocity or some other parameter??

[Texas Buzzard]

Hi fellas,

Just a quick question, why do you want to fly as near as possible to the (L/D)max speed? is it to do with efficiency etc.

Would i better having a velocity equal to that of the cruise velocity or some other parameter??
.................................................. .......................

Flying near the L/D optimum should provide a higher speed (To cover ground when searching for lift) & at the same time help maintain your altitude - is one way of saying it. There are other ways to say it.

[ciurpita]

i didn't think the airspeed at best L/D is necessarily high. for a given airfoil, doesn't it depend a lot on wing loading (i.e. wing area and aircraft wieght?

if your in sink, your going to fly higher than best L/D, and if your in lift, your might fly slower in order to fly a tighter circle with less bank. and aren't flaps used to adjust the best L/D to the desired airspeed?

[macboffin]

The speed for best L/D is not fast ; it is likely to be only about fifteen per cent faster than stall speed, although the l/D speed will depend on flap position if they are used.
As to the best flying speed ; what type of aircraft, powered or glider? Flying for best top speed, best duration, best range?
How long is a piece of string?

[creyes123]

L/D is the ratio of the lift being generated by the wings to the total drag being produced by the airframe. Think of it as an efficiency factor for the airframe. This factor of course varies as the airspeed varies. When there is zero wind, the best L/D speed is the speed to fly for best power-off range. That last sentence was a mouthfull - did it make sense?

My free online calculator (www.RCAdvisor.com (http://www.RCAdvisor.com)) includes an L/D ratio chart. I also display the lift and drag values separately, which might help in understanding the concepts.

[JamieL]

I'll use gliders as an example to answer the question as to why a person would want to fly at max L/D:

If the flight conditions require maximum range given the current height of a glider, then you want to be flying at best L/D (lift to drag ratio) to acheive this. To undersand why, think of it in terms of energy principals. All energy that the glider loses to drag must be, in effect, replaced by the glider's loss of potential energy (height) in order to maintain constant velocity. It follows that the best lift to drag ratio will allow for the longest range.

As far as powered aricraft would be concerned, the energy lost to drag is replaced by energy from the engine. Best L/D means least work needed from the engine.

If you are thinking about gliders, then it is a good idea to note the difference between best L/D (best glide ratio) and minimum sink. From what I've noticed, these are obtained at different speeds, with minimum sink being slightly slower than best L/D. Using gliders as a reference again, minimum sink is used when thermalling or trying to stay up as long as possible without lift while best L/D is used when ranging and searching for thermals, or getting back to the field from downwind. Well... best glide ratio actually varies quite a bit from best L/D when wind is involved, but that's another beast.

[mnowell129]

Max L/D (Cl/Cd max) speeds covers the most ground with the least lost altitude, max range as has been described. Min sink (max (Cl^(3/2))/Cd) provides maximum duration (lowest sink rate). In a sailplane you generally want to hunt for thermals at max L/D thus covering more search area, and thermal at min sink to get the most altitude from the thermal. Getting home while downwind can and will take a speed higher than max L/D, because max L/D may not give you the maximum distance over the ground into a headwind.

[BMatthews]

For general sportflying where you have a big fan on the front it's not really an issue and in fact it would be difficult what with all the turns and maneuvers to actually fly at the best L/D point.

For RC gliders it becomes far more important to get close to the best L/D for covering ground to search out lift. Similarly on severly power limited UAV's such as a solar powered UAV flying at the best L/D becomes highly important so that the craft covers the most ground with the least amount of power.

On the other hand if you were doing a UAV where loiter time is primary then flying at the lowest sink rate speed and using just enough power to cancel out the descent would be the way to go.

It all just depends on your goals and some pragmatic reality in how and where the craft will be flying in terms of how many maneuvers and how severe they are.

[yuri_base]

why do you want to fly as near as possible to the (L/D)max speed? is it to do with efficiency etc.

Yes, efficiency, and the reason is really simple. When you fly level, lift L is equal to weight W, and thrust T is equal to drag D:

W/L = 1
T = D = D*1 = D*(W/L) = W/(L/D)

So, the thrust required for level flight is simply weight divided by L/D, and is minimal when L/D is maxed out.

[vintage1]

Yes, efficiency, and the reason is really simple. When you fly level, lift L is equal to weight W, and thrust T is equal to drag D:

W/L = 1
T = D = D*1 = D*(W/L) = W/(L/D)

So, the thrust required for level flight is simply weight divided by L/D, and is minimal when L/D is maxed out.

However power used is speed x drag, and therefire this may not represent minimum power to stay aloft, or minimum sink rate in the glide. Slower speed with higher drag may actually be slightly better.

It probably represents the furthest you can glide from a given altitude, or the least energy to cover distance under power (in still air) though.

A headwind may make a mockery of it however.

[mnowell129]

However power used is speed x drag, and therefire this may not represent minimum power to stay aloft, or minimum sink rate in the glide. Slower speed with higher drag may actually be slightly better.

It probably represents the furthest you can glide from a given altitude, or the least energy to cover distance under power (in still air) though.

A headwind may make a mockery of it however.
Minimum power to stay aloft (or maximum duration) occurs at max
(Cl ^ 1.5)/Cd (alternately max sqrt((cl^3)/(Cd^2))). This is minimum sink rate/max duration/minimum power to fly. Max duration (air)speed is the same regardless of the wind. Max range (or best distance from altitude) occurs when Cl/Cd is maximum (in still air). However, the airspeed required to get back upwind may be much higher than max Cl/Cd. For example if the aircraft's max Cl/Cd airspeed matches the windspeed you make zero ground progress. In this case you have to fly much faster than max Cl/Cd but you make progress upwind.

[yuri_base]

However power used is speed x drag, and therefire this may not represent minimum power to stay aloft, or minimum sink rate in the glide. Slower speed with higher drag may actually be slightly better.

Not necessarily.

Counterexamples:

- engine is running at full power, but the airplane is grounded. There's no speed, there's no drag, and speed*drag = 0.

- rocket engine. Its thrust is mass burnt every second times propellant gas speed, and more or less constant. As the speed of the rocket is increasing, so is speed*thrust, but the engine is not becoming more and more powerful.

I think the confusion about power always being equal to force times speed comes from our mental concentration of one part of the system ("useful part", for example, an airplane or a rocket) and forgetting the other parts of the whole system into account. The power produced by an engine is not spent 100% on propelling the "useful part", but "useless parts" as well. :)

"engine is running at full power, but the airplane is grounded" - here all of the engine's power goes into accelerating the mass of air (which then slows down and eventually produces heat).

"rocket engine with constant thrust" - here the engine's energy produced by chemicals every second goes into increasing the kinetic energy of the rocket and increasing OR decreasing the kinetic energy of the propellant (if the rocket is now moving at a higher speed than the gas exit speed, the gas is decelerating).

So, the actual answer to the question "Why cruise at the (L/D)max velocity" is: "it depends".

If engine's thrust is independent of aircraft speed (like rocket engines), then there are two other options: consume as little fuel per second or per mile. If it's per second, cruise at the speed of minimum drag, which is when L/D is max. If it's per mile, a little bit higher speed may be advantageous if the drag does not increase as much as the time to travel between A and B decreases.

If engine's thrust depends on aircraft speed (like props), then again, the answer depends on engine's characteristic. Just like fuel efficiency of cars: although the total friction is minimal at, say, 5mph, it does not mean that driving 500 miles at 5mph will be most efficient. :)

Max L/D speed is simply a good estimate of maximum efficiency speed, a theoretical number, but should be good enough for practical purposes. (and for educational ones)

Yuri

[Brandano]

Yuri, you are muddling the waters. Mnowell was talking about equilibrium states, and your rocket example isn't such a state. It will be if you somehow fix the mass of the rocket and consider it only once it has reached a constant speed. As for the aircraft parked with the engine running, that doesn't really fit my definition of "flight". Otherwise every aircraft should be considered a VTOL.

[mnowell129]

When flying, min sink rate represents the minimum power to fly for the aircraft, it doesn't address the relative efficiency of the engine at that speed. Max Cl/Cd, or max range is the max efficiency for the aircraft, that is the farthest distance for the least power. It also does not consider engine efficiency.
Here comes the great compromise. You have to decide what you are building and pick the engine and flight condition to match. If you design an airplane that needs to loiter on station like some kind of RPV then you probably will want to pick or gear your engine/prop to be a peak efficiency at the min power flight speed. If you are designing something to go out and back then you want engines/props/gearing to match the max Cl/Cd.I'll bet that Maynard Hill knew the difference.
It's quite easy to put the wrong engine combo on for the mission and get terrible efficiency, poor climb, whatever.
The whole point of variable camber on sailplanes is to create a min power/max lift geometry for launch and thermal, and max Cl/Cd condition for thermal hunting.
Airliners are another great example. The engines are very inefficient at low altitude and all kinds of flaps/slats, etc are used to get climbout and slow landing speeds, but the things are designed to fly at constant speed in flight configuration at an altitude and speed where the engines are most efficient.

[yuri_base]

mnowell129, I agree with your excellent explanation.

Since the original question was more theoretical in nature, let us assume that we have an ideal engine that has thrust T independent of speed, and that fuel consumption is directly proportional to thrust (rocket engine is a good example).

1. If we want to fly for maximum time, thrust must be minimum, and that is at max L/D.

2. If we want to fly for maximum distance, we need to maximize speed/thrust (since time is proportional to 1/fuel consumption, or 1/T). So we're maximizing V/D ratio (since drag = thrust in level flight). Since in level flight D = W/sqrt(1 + (L/D)^2), and L/D = Vx/Vy, we're maximizing V*sqrt(1 + (Vx/Vy)^2), or (Vx^2 + Vy^2)/Vy function. Where the maximum of this function is, depends on plane's polar characteristic Vy = f(Vx).

[mnowell129]

1. If we want to fly for maximum time, thrust must be minimum, and that is at max L/D.

I disagree. Maximum time is at the min sink rate or
where ((L^1.5) / D) is maximum (power factor is minimum), not L/D is maximum.
This derivation is commonly available, Martin Simons does a good job with it.

2. If we want to fly for maximum distance, we need to maximize speed/thrust (since time is proportional to 1/fuel consumption, or 1/T). So we're maximizing V/D ratio (since drag = thrust in level flight). Since in level flight D = W/sqrt(1 + (L/D)^2), and L/D = Vx/Vy, we're maximizing V*sqrt(1 + (Vx/Vy)^2), or (Vx^2 + Vy^2)/Vy function. Where the maximum of this function is, depends on plane's polar characteristic Vy = f(Vx).
I disagree again. Maximum distance occurs at max L/D, which is roughly by definition the farthest you can fly for the least amount of power.

[vintage1]

I'm with Mnowell on this.

Best L/D gives flattest glide, but not lowest rate of sink. A little bit of up elevator nets you a slower plane that stays up longer, by and large.

The calculatio of optimum criuse sped is very dependent on windsped.

With a strong tail wind, you would slow the plane down somewhat to get lowest sink rate and let the wind get you there. With a headwind you may ned to go somewhat above best L/D airspeed wise.

I seem to remeber analogue computers being used on WWII style aircraft for these sorts of purposes.

[biber]

There were analogue computers for full size gliding too, that are quite easy to be built by yourself.
They still are able to serve educational purposes very well.

biber

[MCarlton]

Surely it depends on whether you want to stay aloft for the longest time or the furthest distance for a given amount of fuel (or height if gliding)?

Hence in cross country, most of the time you would opt for flying as near to max LD as possible but in a pure duration situation, you'd stick to minimum sink?

In my limited experience of full size flying, it was always a case of choosing a throttle setting that would get you to the point you needed to be at, in the shortest time, whilst retaining a sufficient fuel reserve for safety.

In commercial aviation, I am sure this is the aim too, and I'm guessing all the information regarding AUW, fuel capacity, engine efficiency, weather conditions, route conditions and the like are fed into a computerised system which will determine, calculate, adjust and advise on throttle and trim settings throughout a flight?

[creyes123]

You've got the general idea.

When in circling flight in a thermal, the base speed is minimum sink speed. You adjust it up to account for CG forces (which increase the apparent wing loading) and to have a safety margin if the air is very turbulent (stalling is very bad, specially if somebody is circling below you).

When crusing between thermals, the base speed is best L/D. You adjust it up to account for heavy sink (yikes!) or if you are expecting the next thermal to be strong (basis of speed-to-fly theory).

Carlos
www.RCAdvisor.com (http://www.RCAdvisor.com)

[Flight Engineer]

Surely it depends on whether you want to stay aloft for the longest time or the furthest distance for a given amount of fuel (or height if gliding)?

Hence in cross country, most of the time you would opt for flying as near to max LD as possible but in a pure duration situation, you'd stick to minimum sink?

In my limited experience of full size flying, it was always a case of choosing a throttle setting that would get you to the point you needed to be at, in the shortest time, whilst retaining a sufficient fuel reserve for safety.

In commercial aviation, I am sure this is the aim too, and I'm guessing all the information regarding AUW, fuel capacity, engine efficiency, weather conditions, route conditions and the like are fed into a computerised system which will determine, calculate, adjust and advise on throttle and trim settings throughout a flight?

It's all about money in commercial aviation so a cost index is used to balance fixed operating costs against fuel costs and a speed that gives the lowest overall cost is used.

But suffer an engine failure and its "drifdown speed" that you aim for and funilly enough driftdown speed is usually Cl/Cd Max.

Same is used for engine failure after take off. Once the aircraft is clear of obstacles and no lower that 400' we accelerate and clean up. The speed we accelerate to in this case is called Vfs and is Cl/Cd Max.

[yuri_base]

Here's a quick numeric example.

I'm answering the following question: An airplane with ideal engine whose thrust is independent of speed and is directly proportional to fuel consumption rate, is flying level with no wind and no thermals. What is the optimal speed to fly for a) longest time and b) longest distance, given a certain amount of fuel the weight of which is negligible compared to the weight of the aircraft?

The airplane weighs 10000N and has the following polar: at 100mph, its descent rate without engines is 10mph (L/D=10), at 121mph, its 11mph (L/D=11), and at 150mph, its 15mph (L/D=10). To produce 1N of thrust, engine spends 1 [arbitrary] unit of fuel per hour, and there are 1000 arbitrary units of fuel on board.

The thrust required for level flight is

T = W/sqrt(1 + (L/D)^2)

So:

at 100mph, T = 995N
at 121mph, T = 905N
at 150mph, T = 995N

For a), maximum time, we have:

at 100mph (L/D=10), engine is consuming 995 units of fuel per hour, so it will last 1000/995 = 1.005hr.
at 121mph (L/D=11), engine is consuming 905 units of fuel per hour, so it will last 1000/905 = 1.105hr.
at 150mph (L/D=10), engine is consuming 995 units of fuel per hour, so it will last 1000/995 = 1.005hr.

So, at the speed of maximum L/D, the airplane can fly level for the longest time.

For b), maximum distance, we have:

at 100mph (L/D=10), engine is consuming 995 units of fuel per hour, so it will last 1000/995 = 1.005hr, and airplane will fly 100mph*1.005 = 100.5mi.
at 121mph (L/D=11), engine is consuming 905 units of fuel per hour, so it will last 1000/905 = 1.105hr, and airplane will fly 121mph*1.105 = 133.7mi.
at 150mph (L/D=10), engine is consuming 995 units of fuel per hour, so it will last 1000/995 = 1.005hr, and airplane will fly 150mph*1.005 = 150.75mi.

So, the airplane can fly level for the longest distance not at the speed of max L/D, but at some higher speed. Exactly what speed, depends on exact shape of the polar curve.

[biber]

It rather depends on the characteristics of your engine and propeller combo.
If you assume your combo to behave like in your example you're right.
But there are many combos possible with many different characteristics.
Your example assumes about the behaviour of a jet engine.
Propeller drives behave very different from that, so that the best mileage may be reached even at slower speed than that of the best L/D.
But if you seek an all in all best range and efficiency, you will make the plane fly at best L/D and make sure that the engine and prop are optimised for that speed.


biber

[mnowell129]

Yuri

An airplane with ideal engine whose thrust is independent of speed and is directly proportional to fuel consumption rate,

...thrust is not independent of speed... thrust being directly proportional to fuel consumption only applies at one airspeed....

The thrust required for level flight is

T = W/sqrt(1 + (L/D)^2)

So:

at 100mph, T = 995N
at 121mph, T = 905N
at 150mph, T = 995N

You have missed important points, thrust is not power and the thrust goes up with the square of velocity (it's not strictly a constant based on L/D) and fuel consumption is proportional to power, not thrust, . Power goes up as the CUBE of velocity for an aircraft, Thrust = D = Cd * 1/2 * rho * S * V * V). So the actual thrust required goes up as the square of velocity (regardless of the L/D). Power = thrust * V, so Power = Cd * 1/2 * rho * S * V * V * V, that is thrust goes up with the square of velocity, power as the cube. Fuel consumption is proportional to power of the engine, not the thrust. Even if the fuel consumption were proportional to thrust it would still go up as the square of velocity. Thus it is impossible for it to take the same amount of thrust to fly at both 100 and 150 mph.
When you properly formulate the equations based on power you will find that the max range occurs at the Max (Cl/Cd) and the max duration occurs at the Max ((Cl^1.5) / Cd)

You can't just substitute L/D for Cl/Cd because you get erroneous results like this by virtue of the V^2 terms. The problem is for level flight you have to hold L constant, thus Cl has to go down as the reciprocal of velocity squared, the Cd doesn't change that much because of the drag bucket and because profile drag goes up with velocity, essentially Cl/Cd is not linear, and especially non-linear with velocity so you can't mix square terms across nonlinear relationships.

[mnowell129]

A reasonable explanation of max duration, max range, etc.
http://www.eaa1000.av.org/technicl/perfspds/perfspds.htm

[vintage1]

A reasonable explanation of max duration, max range, etc.
http://www.eaa1000.av.org/technicl/perfspds/perfspds.htm

Excellent stuff. I hadn't appreciated the 'optimal cruise' which represents a compromie between best speed, and best fuel for the trip.. and in any kind of headwind, is probably where you pitch the airspeed.

[mnowell129]

Excellent stuff. I hadn't appreciated the 'optimal cruise' which represents a compromie between best speed, and best fuel for the trip.. and in any kind of headwind, is probably where you pitch the airspeed.
Yep, a good refresher. I had done the calculations for optimum cruise a looooong time ago and forgotten about them because they don't mean much in models. But it's the get there the fastest with the least gas strategy. Kinda reminds me of the cold weather motorcycle problem, do I speed up and freeze and get there quicker or slow down and warm up but take longer.....

[vintage1]

Yep, a good refresher. I had done the calculations for optimum cruise a looooong time ago and forgotten about them because they don't mean much in models. But it's the get there the fastest with the least gas strategy. Kinda reminds me of the cold weather motorcycle problem, do I speed up and freeze and get there quicker or slow down and warm up but take longer.....


or in my case, drive very fast, use the fear to fight te fatigue, and get to a bed quicker, or slow down and risk falling asleep at the wheel..

[jinal007]

(L/D)max or (Cl/Cd)max is the condition for minimum drag.

At this point, the parasitic drag is equal to the induced drag. i.e Cd_0 = Cd_i

Satisfying this condition will lead to flattest glide hence max range.

(Cl^1.5/Cd) is the condition for minimum required power.

At this point, the 3 X parasitic drag is equal to the induced drag. i.e 3Cd_0 = Cd_i

Satisfying this condition will lead to lowest sink rate hence max endurance.