mach number and weight

[Shabez]

At an aircraft weight of 70,000lb your aerodynamic ceiling in 1g level flight will be:
A) FL440
B) FL390
C) FL320
D) FL420

ans is fl 420 ....why and how...i dont get it

[flite idol]

Was there a chart or graph?

[wiggy]

Sorry, I'm with flite, at the moment there's insufficient information, there must have been something else.

What's the source of your question?

[hetfield]

At an aircraft weight of 70,000lb Captains age will be:
A) 44 years
B) 39 years
C) 32 years
D) 42 years


;)

[Shabez]

ITs a part of the JAA curriculum

..its even on ths website

Principles of Flight Theory Test Question Bank - 081-02-02 Normal shockwaves - Question 986 (http://www.dauntless-soft.com/products/GroundSchoolATPL/TestBanks/Principles_of_Flight/081-02-02_Normal_shockwaves/Q986.asp)

[wiggy]

The link takes me to an isolated example question with no context. It looks to me as if it's possible it's one of a sequence of several about the same aircraft and without the other information that has been provided earlier in the "paper" it's impossible to answer.


Anyhow at a second glance it looks like flite was right ;) take a closer look at the fine print at the bottom of the linked page:

If this question refers to a chart or figure (as some do), please accept our apologies - figures are not available online

I think you need to download the full package to get all the information needed.

[keith williams]

The real question includes a Manoeuvre Capability (Buffet Boundary) Diagram.

The diagram provided in the question includes a worked example which makes it all self-explanatory.

Get the diagram and you will be able to answer the question.

[CaptNK_AIRBUS]

Why does Indicated Mach No. reduce if weight reduces, even if Flight Level is the same. I tried hard to find out the reason. No good.
N

[Intruder]

Simple version is that for max range you fly a constant angle of attack in cruise. As weight goes down, airspeed/Mach goes down to provide less lift at that angle of attack.

[hawk37]

Intruder, you say "for max range you fly a constant angle of attack in cruise".

Could you re think that one? Did you perhaps mean max endurance? (And even then, I'm not sure that is true given compressibility). From what I remember, the angle of attack for max range decreases as weight decreases.

Of course....I could be wrong

[Capn Bloggs]

Intruder, you say "for max range you fly a constant angle of attack in cruise".

Could you re think that one? Did you perhaps mean max endurance? (And even then, I'm not sure that is true given compressibility). From what I remember, the angle of attack for max range decreases as weight decreases.
Lonewolf is correct; best L/D (max range) occurs only at one AoA. As the weight reduces, so the speed for that AoA reduces (as of course does the Endurance speed), but the actual AoA for max range remains the same.

Have a look at page 178 of "The Mechanics of Flight", by A C Kermode.

[HazelNuts39]

Due to compressibility effects, max L/D and corresponding AoA change with Mach as shown below for a large jet transport:
http://i.imgur.com/voyi5.gif?1

[Capn Bloggs]

HN39, interesting, but the question is how the speed/AoA varies with change in weight.

I think the "max L/D" term on your chart should be "L/D". There is only one point of "max L/D", which looks to be about 0.5 Mach, at 5.5° AoA. Not knowing what the altitude is for that chart, I would have thought that that AoA is far too high to be best range speed ie best L/D.

[hawk37]

Hazelnuts, I too would be very interested in further info on this graph. What altitude would that be for? I can't think it is in the 30's, as a speed of circa mach .5 for max L/D seems a bit slow for a typically airliner at that altitude.
I note the Y axis, L/D is proportional to 1/D since L is constant for level cruise. this graph then is the inverse of the thrust required curve we typically see.
However, it includes the compressibility effects, is this why it is such a different shape?

Hawk

[hawk37]

Capn Bloggs says "best L/D (max range) occurs only at one AoA."

We should be careful here, and distinguish between jets and non jets. I don't believe best L/D is max range for a jet. Similarly, for a jet, max range is not at a constant aoa, as weight changes. The thread makes no specific distinction between jets and non jets until Hazelnuts refers to "large jet transport"

[HazelNuts39]

I think the "max L/D" term on your chart should be "L/D". Depending on weight and altitude, there is a point of maximum L/D for each Mach number. The point at M=0.5 and AoA=4.5 corresponds to a certain weight/delta(*), where delta is the ambient pressure ratio. Consequently the altitude varies with weight, such that ambient pressure varies proportionally to weight.

(*)For this airplane: mass/delta=392 tonnes

[Natstrackalpha]

Why does Indicated Mach No. reduce if weight reduces, even if Flight Level is the same. I tried hard to find out the reason. No good.
N If you are just flying along, as time goes on the weight of the aircraft gets less due to fuel burn. If left to it`s own devices the aircraft either increases altitude or gets faster and faster. If let to go faster and faster (apart from mach crit - another thread) then the angle of attack gets lower and lower (or you climb). Kinda good in a way but at the same time you have to trim off the tendency for lift - more lift in there somewhere = more induce drag albeit trimmed off. Best to have the aircraft at optimum ATT for the FL and the Weight and at that temp which, also affects . . .Machno.

Have I done that right? Is that the answer to your question? the objective being to go as fast as possible . . .as high as possible . . using as little fuel as possible . . .

Power plus Attitude = ?

[Capn Bloggs]

Similarly, for a jet, max range is not at a constant aoa, as weight changes.
We (Intruder and I) are not saying it does. What we're saying is that the IAS for max range changes (reduces) as the weight reduces to maintain the best L/D.

If you are just flying along, as time goes on the weight of the aircraft gets less due to fuel burn. If left to it`s own devices the aircraft either increases altitude or gets faster and faster.
Only if you don't control the speed to maintain the best L/D ratio/AoA. For example, at a constant Cost Index (say max range CI), the speed will reduce as weight reduces. Have a look at page 100 of the Airbus CI description (http://www.smartcockpit.com/data/pdfs/flightops/aerodynamics/Getting_To_Grips_With_The_Cost_Index.pdf).

The point at M=0.5 and AoA=4.5 corresponds to a certain weight/delta, where delta is the ambient pressure ratio. Consequently the altitude varies with weight, such that ambient pressure varies proportionally to weight. (For this airplane: mass/delta=392 tonnes).
Sorry, but I do not understand. If that chart is for a 392t aeroplane, I cannot believe that L/D stays constant at near stall speed (Mach 0.2) all the way through to just under MMO (Mach 0.8). The lift will obviously be constant (same altitude and weight) but the drag will vary enormously. The L/D curve cannot be almost flat.

[HazelNuts39]

If that chart is for a 392t aeroplane
You should read more carefully. I wrote:
The point at M=0.5 and AoA=4.5 corresponds to (...) mass/delta=392 tonnes

[hawk37]

Capn Bloggs; "the IAS for max range changes (reduces) as the weight reduces to maintain the best L/D"

It is dangerous to use the terms "max range" and "best L/D" in the same sentence. A jet at an IAS for max range is not at the speed for best L/D.

Generally, for a jet, flight at best L/D gives max endurance (usually close to published holding speeds) and is at or near a constant aoa.

If we want best range however, we need to fly at the speed where the ratio of TAS/FuelFlow is the greatest. This is faster than the speed for best L/D, and is not at a constant aoa.

Best L/D speed is the lowest point in the Thrust Required vs TAS graph.

Best range speed can be determined by drawing a line from the origin to the point where it tangents the Thrust Required vs TAS graph. Some assumptions of course, eg constant TSFC Thrust specific fuel consumption (lbs of thrust, per pound of fuel, per hour)

[Capn Bloggs]

You should read more carefully. I wrote:

Quote:
The point at M=0.5 and AoA=4.5 corresponds to (...) mass/delta=392 tonnes

OK, sorry. What are the details of this aeroplane then? What altitude is this chart at? What is the "delta" value? The more I look at it, the less that chart makes sense.

Could you address my comment about the drag change from 0.2 to 0.8?

[HazelNuts39]

Capn Bloggs;

The chart is not for a particular altitude. It covers all weights and altitudes.
"delta" stands for the ambient pressure at altitude expressed as a ratio to sealevel standard pressure, i.e delta=Pamb/Psls.

P.S.
The more I look at it, the less that chart makes sense.If you plotted a family of curves on the graph, each curve showing for a particular weight and altitude the variation of L/D versus Mach, then each curve would have a maximum L/D at a particular Mach. The L/D curve shown on my chart connects all these maxima, i.e. all curves for any weight or altitude would stay below the L/D curve on the chart.

[Capn Bloggs]

Hawk37,

It is dangerous to use the terms "max range" and "best L/D" in the same sentence. A jet at an IAS for max range is not at the speed for best L/D.
Point taken. Will not use L/D in jet discussion any more! ;)

Nevertheless, the answer to Capt NK Airbus' question in post 8:
Why does Indicated Mach No. reduce if weight reduces, even if Flight Level is the same. I tried hard to find out the reason. No good.

is related, is it not? As the weight reduces, the lift required reduces and so the drag for any particular speed also reduces (given we're on the front side of the drag curve) and we would normally accelerate. Therefore, we can reduce the thrust to match that reduced drag. The issue is whether the speed value for max range reduces as weight reduces. Airbus says it does, in that earlier reference I gave.

http://i521.photobucket.com/albums/w334/capnbloggs/IMG_20120515_221412.jpg

Where does the curve go as weight reduces? That is the crux of the issue (with thanks to DP Davies :D) because that will determine where the tangent line is, speedwise.

Do you have a reference for the AoA not being constant at the Max Range Speed for various weights? I was always under the impression that Max Range speed at any weight was at the same AoA.

Found a Boeing document that talks about the subject:

Aero 12 - Angle of Attack (http://www.boeing.com/commercial/aeromagazine/aero_12/attack_story.html#figure7)

What I don't get is that "It can be seen that the optimal long-range cruise Mach number does not vary significantly as gross weight (hence, lift and AOA) changes." seems to be counter to those Airbus figures which show a max-range speed change of .67 to .73 over a 40t weight change. I would have thought that that was significant (although a 40 tonne burn is almost more than my aeroplane weighs!). :E

[hawk37]

Bloggs, I agree with what you have just posted.

You ask "Do you have a reference for the AoA not being constant at the Max Range Speed for various weights?"

No I don't, probably because no one has made an technical argument that it should be, for a jet. However, figure 7 from the boeing doc you linked to appears to suggest that the heavier situation is indeed at a higher aoa, for max range, although one has to extrapolate a bit. Additionally, the boeing doc makes no reference at all to a jet's max range speed being at constant aoa. Now, having said that, for a piston aircraft that may be true, though I'd have to brush up on my aerodynamics before I made that assertion.

You say you don't get that "optimal long-range cruise Mach number does not vary significantly as gross weight (hence, lift and AOA) changes"

I have to agree with you on that. I consider it significant, everyone has their opinion on what constitutes "significant", I guess.

[Natstrackalpha]

I see on your question in question, that this is a teaser question ( I clicked on the Link) there is also a quick solution to the answer (which I make to be between the last option and the second to last multi-choice thang. I have got a horrible feeling that the . . .establishment in question has a nice juicy formula for calculating the FL under the given conditions of weight . . . I mean, do look at what all the other guys have said/suggested - and, while I am here thank you guy(s) for your input on my little bit of . . . input before, also.

Referring to the formula - for example, there was a formula for the A330 which I have since forgotten - hopefully an A330 Captain will chime in but it was an approximate referring to a specific type something like for optimum level take 256 (hell, it could have been 567, I forgot . . !) . so take 256-GW=Opt FL. So, therefore; 256-230=26
Using the other figure of 567 gives another flight level. 560 - 230 = 330, yup, that looks like it.

So, I think maybe they (the advert) are just trying to get you hooked into joining the course.