Increasing jet aircraft range.

[deefer dog]

Can you experts please advise. The aircraft i fly quotes LRC at M0 .74. When i look at the AFM I note that, as one might expect, the TAS is reduced as weight decreases...so too does the Mach.

I have two questions.

1. If i want to extract as much in terms of range from the aircraft, and assuming still air, would I benefit by flying slower than published? (And by this I mean reducing towards the best L/D speed as indicated in the speed tape) ?

2. When flying into wind, by how much should I increase my IAS or Mach no? Is there a rule of thumb?

3. When flying in tailwind, by how much should I reduce?

In all cases to get max range...not endurance.

Many thanks.

[bfisk]

For Boeing... Set cost index to 0 and fly ECON speed.

[Intruder]

Rule of thumb I've used is increase TAS by 40% of headwind, decrease by 40% of tailwind. Min speed is max endurance. Max speed is where the knee in the fuel flow / TAS curve is (you will likely have to estimate it).

[autoflight]

Years ago I generated data for B727-200 levels for best range for various head/tail winds and weights at M.80. At lower levels I used the recommended IAS. That was a huge job with interesting results and it was mainly used on Sydney - Perth runs. TAS and fuel flow changes related to different levels was the best way to adjust for wind gradients Thirty years ago the traffic was sparse enough to not need more complex calculations for speed changes at a fixed level.
Rules of thumb for wind gradients turned out to be a poor substitute for a lot of better preparation.

[deefer dog]

Thanks for the replies.

Here is my difficulty in understanding. The LRC schedules call for speeds which are always in excess of green dot speed, so are always faster than the speed for best L/D.

Why would this be.....or have I completely missunderstood all previous teaching that max range IS achieved at best L/D speed?

[Old Smokey]

Defer dog,

Maximum range cruise categorically is well above max L/D ratio speed. This speed (with very Minor adjustment) is more representative of Max Endurance / Best angle of climb / Minimum rate and angle of descent during OEI DRIFT-down.

Max range cruise occurs on the conventional drag curve at the point of tangency to the curve drawn from the 0/0 origin. In head and tail wind conditions, the 0/0 origin moves left/right in direct relationship to tailwind/headwind (in that order). Whilst on the subject, don't let any jerk convince you that MRC is at or below Mcrit, it's always above at normal operating levels, but EAS defined below the CAS/Mach changeover level.

[toffeez]

Old Smokey

Phew, glad you replied. Posts 6 & 7 were a bit scary for me. Still are.

[HazelNuts39]

Max endurance and max range

See earlier discussion here

[Linktrained]

For the 707, Boeing published Optimum Altitude data, which showed that as the aircraft's weight decreased with fuel burn-off, the Optimum Altitude increased. This would mean that the Opt. Alt. increased by about 1000 ft./hour. (Of course this would be restricted by other factors in practice.)

[framer]

Here is my difficulty in understanding. The LRC schedules call for speeds which are always in excess of green dot speed, so are always faster than the speed for best L/D.

I think I can help you overcome your difficulty in understanding. Go to your FCOM and look up the definition of "green dot speed", then determine if green dot is relevant to your calculations, or a red herring. I would do it but my aircraft no longer has a green dot so I don't have the books.

[Kefuddle]

have I completely missunderstood all previous teaching that max range IS achieved at best L/D speed?

Indeed, for a jet yes, but your understanding is correct for a prop. As Old Smokey says, for a jet max range is generally faster than l/d speed. I would add that min drag reduces towards l/d with altitude (at max service ceiling they are just about coincident). L/d speed is pretty much the same as clean speed (or flap maneuvering speed with flap). L/d speed is best endurance speed and what you want to fly in a hold.

However, it would seem to me that If really desperate to save fuel, then use l/d speed for descent.

Rule of thumb I've used is increase TAS by 40% of headwind, decrease by 40% of tailwind. Min speed is max endurance. Max speed is where the knee in the fuel flow / TAS curve is (you will likely have to estimate it).

I had not heard of that one. My guess was that given that a typical drag curve is very flat at around min drag speed for a jet, I assumed that one would want to increase speed into a headwind by much more than one would want to reduce it with a tail?

[bfisk]

A common misunderstanding is that LRC gives you max range. It gives you exactly what is says - long range - but not max range.


-Max endurance speed is whatever you get with the lowest fuel flow. It is not affected by wind. On the Speed/Drag curve, this is the lowest point.

-Max range speed is defined by the lowest fuel flow pr. ground distance covered, thus it is dependent on wind. Assuming no wind, then on the Speed/Drag curve, this is the tangent with the lowest angle.

-Long range cruise speed is slightly higher than max range speed, and is a tradeoff, that gives you a (relatively) big speed increase for a (relatively) small range penalty. On the Speed/Drag curve, this will be a bit further up-and-to-the right from the max range; you will see that although the drag increases, the speed also increases by nearly the same amount.



(image courtesy of the internet)

[framer]

Thanks for that graph.

I use the Cost Index to give me an approximation of VMR in the 737 but I am aware that it is taking account of the wind while in EcON mode so isn't exactly right.
1/From VMR can I work backwards to get VMD in IAS?
2/ Is VMD purely a function of weight and therefore the same IAS at FL380 or 2000ft for a given weight?

[deefer dog]

Thanks again, Now I think I'm starting to get a clear picture.

So, in essence, what some of you are saying (in a jet) is this:: Best L/D speed for a given weight would give max range, but because the engines may not work as efficiently at this lowish speed, a better mileage per pound of fuel is obtained at a speed somewhat above that of best L/D. Is that it?

What I didn't understand was the post by toffeez. What did you find so scary about my post 6, which, after all, was only another question? Was it that I asked a stupid question?

[HazelNuts39]

Originally Posted by framer

Is VMD purely a function of weight and therefore the same IAS at FL380 or 2000ft for a given weight?

No, at FL380 VMD would be higher due to Mach effect on L/D.

Originally Posted by deefer dog

Best L/D speed for a given weight would give max range, but because the engines may not work as efficiently at this lowish speed, a better mileage per pound of fuel is obtained at a speed somewhat above that of best L/D. Is that it?

No it isn't. Best L/D speed VMD is the speed V for minimum drag D.
VMR is the speed for minimum D/V.
For a parabolic drag polar in still air VMR is equal to VMD times the 4th-power root of 3.
If it assumed that engine efficiency (thrust specific fuel consumption) is constant, then VMD is the speed for max endurance and VMR is the speed for maximum range.

[bfisk]

I use the Cost Index to give me an approximation of VMR in the 737 but I am aware that it is taking account of the wind while in EcON mode so isn't exactly right.

Well, it is actually right, because Vmr (max range) is dependent on wind.

On the 737:
For Vmd (min drag, best endurance), use HOLD page to get holding speed. This is close to Vmd.
For Vmr (max range), set cost index to 0 and fly ECON CRZ.
For Vlrc (long rang cruise), use LRC CRZ. (cost index has no influence).

(For info, LRC is equivalent to ECON speed at cost index around 35-ish. Ie, if you fly at a low cost index, say 15 or 20, going from ECON to LRC will actually decrease your range slightly)

[framer]

Hazelnuts, any idea where I could read up about Mach effect? A google search brings up medical info.
Bfisk, thanks for that.

[deefer dog]

HazelNuts, thanks for informative answers. Could you please explain what 4th power root of 3 means.

An example would help. What is the 4th power root of 3 if the starting number was, say, 10?

Thank you.

[deefer dog]

And a question to bfisk, please.

I read elsewhere the numbers 1.32 and 1.37 as in your diagram. Can i therefore assume that in a jet, VMR is always VMD x 1.32?

Thanks

[HazelNuts39]

Could you please explain what 4th power root of 3 means.

If you have a calculator that produces the square root of the number entered, enter 3, take the square root and you get 1.732 ... . Take the square root of that result and you get the fourth-power root of 3 which is 1,316... .