help with speeds plz!

[SuperTed]

Im stuck with the following problems.

An aircraft climbs at constant TAS through an inversion, what happens to the RAS and Mach number?

Im I right in thinking that RAS will decrease while Mach will increase?

And also if the aircraft descends through an isothermal layer with constant TAS what happens to the RAS and Mach??

Many thanks,

ST

[Genghis the Engineer]

Sounds like an exam question to me...

As you climb through an inversion, the temperature increases

So pressure has dropped slightly, and temperature has increased. Overall, the density has gone down. TAS = RAS (I call it CAS myself) divided by root sigma. Sigma is relative density, so in this case it's increased.

This means that at constant TAS, CAS / RAS will go-down. In practice however you fly at CAS, which is directly related to IAS, so if you keep the same number on the dial, you'll go faster.

Local speed of sound is proportional to the square root of absolute temperature, so when it gets warmer, the local speed of sound will go up, and at constant TAS, the Mach number will consequently go down. Not by very much mind you.


Descending through an isothermal layer at constant TAS (again you wouldn't, you'd fly at constant CAS) Mach number will remain constant because it's a function of temperature, not density. Because density is increasing, CAS / RAS will reduce at constant TAS.

Which exam was that out of? And who thinks you fly at a TAS rather than a CAS / RAS / IAS ?

G

[SuperTed]

Thanks Genghis :)

Yes it is an exam question.

Ive learnt these graphs from a book that show the 4 main speeds in the order of E R T M, where E= EAS, R= RAS etc.

For instance the graph that shows constant TAS (by having the TAS line on the graph as a vertical line) show that the Mach speed increases and RAS to decrease.

Hence this is what I put for my answer to the first question which I now know is wrong.

Its quite hard to describe these graphs without producing the actual graph, although they are very simple. Are these not valid then for entering an isotherm or inversion?

Many thanks again,

ST

[Keith.Williams.]

Superted,

Those graphs you refer to are pretty good but you must remember their limitations.
The thing to remember is that they are for the Interantional Standard Atmosphere where there are no inversions and no isothermal layers (below 36000 ft).

If a question asks about climbing or descending through an isothermal layer just use the graph indicating flight above the tropopause (Where in the ISA is all one big isothermal layer).

If it asks about an inversion just remember that the effects of changing pressure with changing altitude are the ones that affect the density most. So climbing through an inversion still causes density to decrease. Whenever density decreases the ratio of TAS to (CAS,RAS,IAS,or EAS) increases. An inversion does not change this effect.

The trick with an inversion is to remember that it is temperature that controls the TAS : mach number relationship. An inversion revereses the normal temperature lapse rate so you must reverse the effets on the TAS : mach number relationship. So (in an exam question) climbing through an inversion at any given TAS causes mach number decrease. when descending through one at constant TAS the mach number increases.

[Keith.Williams.]

Anyone studying for the POF exam might like to try these additional examples of inversion/isothermal type questions. You will not get 10 questions of this type in an exam but you might well get one or two. Answers and full explanations are available from [email protected]

INVERSION 1.
When descending through an inversion at constant TAS?

a. Mach number increases.
b. Mach number decreases.
c. Mach number remains constant.
d. CAS decreases.

INVERSION 2.
When climbing through an inversion at constant TAS?

a. Mach number increases.
b. Mach number decreases.
c. Mach number remains constant.
d. CAS increases.

INVERSION 3.
When descending through an inversion at constant CAS?

a. TAS increases.
b. Mach number increases.
c. Mach number remains constant.
d. TAS decreases.

INVERSION 4.
When climbing through an inversion at constant CAS?

a. TAS increases.
b. Mach number increases.
c. Mach number remains constant.
d. TAS decreases.

INVERSION 5.
When climbing through an inversion at constant mach number?

a. CAS increases.
b. TAS decreases.
c. TAS remains constant.
d. TAS increases.

INVERSION 6.
When descending through an inversion at constant mach number?

a. TAS increases.
b. TAS decreases.
c. TAS remains constant.
d. CAS increases.

INVERSION 7.
When climbing through an inversion at constant mach number?

a. CAS decreases.
b. LSS decreases.
c. TAS remains constant.
d. TAS increases.

INVERSION 8.
When descending through an inversion at constant mach number?

a. CAS increases.
b. LSS increases.
c. LSS remains constant.
d. TAS decreases.

INVERSION 9.
When climbing through an inversion at constant CAS?

a. TAS increases.
b. TAS decreases.
c. TAS remains constant.
d. Mach number increases.

INVERSION 1.
When descending through an inversion at constant CAS?

a. TAS increases.
b. TAS decreases.
c. TAS remains constant.
d. Mach number increases.

ISOTHERMAL 1.
When descending through an isothermal layer at constant TAS?

a. Mach number increases.
b. Mach number decreases.
c. Mach number remains constant.
d. CAS decreases.

ISOTHERMAL 2.
When climbing through an isothermal layer at constant TAS?

a. Mach number increases.
b. Mach number decreases.
c. Mach number remains constant.
d. CAS increases.

ISOTHERMAL 3.
When descending through an isothermal layer at constant CAS?

a. Mach number increases.
b. Mach number decreases.
c. Mach number remains constant.
d. TAS increases.

ISOTHERMAL 4.
When climbing through an isothermal layer at constant CAS?

a. Mach number increases.
b. Mach number decreases.
c. Mach number remains constant.
d. TAS decreases.

ISOTHERMAL 5.
When climbing through an isothermal layer at constant mach number?

a. TAS increases.
b. TAS decreases.
c. TAS remains constant.
d. CAS increases.

ISOTHERMAL 6.
When descending through an isothermal layer at constant mach number?

a. TAS increases.
b. TAS decreases.
c. TAS remains constant.
d. CAS decreases.

ISOTHERMAL 7.
When climbing through an isothermal layer at constant mach number?

a. CAS increases.
b. CAS decreases.
c. CAS remains constant.
d. TAS decreases.

ISOTHERMAL 8.
When descending through an isothermal layer at constant CAS?

a. LSS increases.
b. LSS increases.
c. LSS remains constant.
d. TAS increases.

ISOTHERMAL 9.
When climbing through an isothermal layer at constant CAS?

a. TAS increases.
b. TAS decreases.
c. TAS remains constant.
d. Mach number decreases.

ISOTHERMAL 10.
When descending through an isothermal layer at constant CAS?

a. TAS increases.
b. TAS decreases.
c. TAS remains constant.
d. Mach number increases.

[Genghis the Engineer]

I'd recommend disregarding the graphs for the moment and just learning the relationship: -

(1) Pressure drops as you climb
(2) Below the tropopause at 36,069 ft, temperature drops as you climb. Except for an inversion, where the relationship inverts, or an isothermal layer, where it does nothing.

Density = sea level density * relative pressure / relative density.

Local speed of sound is proportional to the square root of local absolute temperature. So, if you take speed of sound at sea level, and multiply it by SQRT [ (S/L OAT in °C + 273.15) / (local OAT in °C + 273.15) ] you'll have your local speed of sound.


Now to the actual speeds...

(1) IAS = what you see on the dial

(2) CAS or RAS = IAS corrected for system pressure errors. There's a graph in the POH to show you the errors, and in any case it should not be more than 5 knots different on a certified aeroplane.

(3) EAS = CAS corrected for compressibility. Below FL100 and M=0.7 you can assume EAS=CAS with no correction needed.

(4) TAS = EAS corrected for altitude. The correction is TAS = EAS divided by the square root of relative density.

(5) Mach number = TAS divided by local speed of sound.


Personally I don't use graphs in working such stuff out (and as you'll guess from the fact that I've just written all this from memory) I use ISA tables, or if I'm being very accurate, the basic ISA equations.

G

[Keith.Williams.]

Genghis,

I suspect we are talking about different graphs. I do not mean the rather complicted curves ones found in aerodynamic/engineering manuals. These are okay for the heavy stuff but are too much for students doing the JAR ATPL POF exams.

The ones I mean are simply straight lines indicating the general efects of climbing and descending.

The one for use below the tropopause in the ISA uses three straight lines spreading out in a fan shape fom the same point at the bottom. These are marked C (for CAS), T (for TAS) and M (for Mach number) from left to right. The speed scale increases from right to left, and the altitude vertically upwards.

To find the effect of climbing at constant CAS, TAS or Mach, simply rotate the fan so that your constant value is vertical. The other lines then indicate how the other two variables change. Climbing at constant TAS for example causes CAS to decrease and Mach to increase.

The graph for use above the tropopause is even more simple. Because temp and LSS are constant, the mach number at any TAS is constant. This means that TAS and Mach are indicated by a single line. Climbing above the tropopause at constant CAS for example, causes TAS and mach number to increase.

To determine the effects when descending simply move down the graph and observe how the lines converge.

These graphs can also be used to deternmine how flight through an inversion or isothermal layer affects speeds, provided you remember what we have both said about these phenomena. (temp lapse is reversed in an inversion and temp is constant in an isothermal). This means that as far as the
ratios of speeds goes, flight in an isothermal is like flight above the tropopause (only two lines on the graph) and for flight in an inversion just go in the opposite direction on the three line graph.

Your equation for mach number/LSS is probably a bit too much for the exams. In most cases it is enough to remember that the LSS is 38.94 x the square root of the absolute temperature.

The questions I provided in my previous post are intended to help students to develop skills in analysing these factors. Some of them (like many real exam questions) might appear to be lacking in information, but are in fact quite complete. In all cases there is only one best option. With the aid of the graphs I described above, each of the questions can be answered within a couple of minutes or less.

[SuperTed]

Can I just thank both you gentlemen for taking the time to answer my question(s) in full. It is people like yourselfs that make this site worthwhile. Thankyou.

Keith could you perhaps post the answers to the questions on here. It would make it much easier.

Thankyou again.

ST

[Keith.Williams.]

Superted,

The full explanations of these questions, together with more than 1000 others, are contained in a book that I have produced. Unfortunately direct advertising in these posts is not permitted.

My purpose in asking memebers to e-mail me is simply to enable me to offer the book for sale. It is more effective to make the offer to people who are studying for these exams, rather than simply sending e-mails to all members. Anyone receiving my offer is of course free to decline it. Receiving the answers to these questions is not conditional upon buying anything.

As I have already offered you the book and you have not responded, I will send you the answers by e-mail.

The second reason for not posting the answers directly in this forum is that the whole text is rather long. You can see from my previous posts just how long twenty questions are when posted in this forum. Each of the answers is about three times as long as the related question. The pprune system is often already tediously slow without my adding to this problem.

[PETERJ]

Keith..........I'm not even a wannabe......but could I say as a sort of compliment to all sorts of guys on this site.........ta.......you show a generosity of spirit and a willingnes to share knowlege and respect for others less forunate than you ....THANKS IN SPADES

[PETERJ]

Superted

Hang in mate............remember .........it's not the 99% that's gonna fail me ....It;s dat one oper cent.........good luck mate !!!!!!!!!!!!!!!!

[SuperTed]

Can I just say the people on this site are top banana! :D :D

Thankyou PeterJ.

Keith how much is your book out of interest? Does it contain all ATPL subjects??

This surely is not advertising, rather educating! :p

[Keith.Williams.]

Superted,

I have made several attempts to send you the answers using your pprune e-mail address, but this appears to have been closed down due to inactivity. Please send me a usable address and I will try again.

I suspect the moderators will not agree with your assessment of what is and is not advertising. But.........

During my time as a JAR instructor it quickly became apparent to me that although all of the FTOs provide lists of feedback questions (which are of course handed on from student to student), none provides full written explanations of why any particular answer to a question is correct. This problem is compounded by the fact that different schools select different answers, the overall effect being confusion for students struggling to master the subjects.

I therefore concluded that what was needed was a book containing a large number of questions, together with easily understood explanations of how to answer them. Having expended several thousand hours of effort, I have produced just such a book for the subject of POF. It currently contains approximately 1060 questions, answers and explanations (the number keeps increasing each time I get new feedback).

The book costs £35, which includes postage to anywhere in Europe (the actual cost I pay for packing and postage is a little over £6 so the real price I get for the book is less than £29).

The purpose of the book is to provide students with an exhaustive coverage of the type of questions that have been used in past POF exams. It covers those areas of the POF syllabus that students report having been tested on. In effect this is the vast majority of the syllabus. The material is broken down into subject areas in order to enable users to concentrate on any weak areas in their knowledge. For those who feel they already have a good knowledge of the syllabus but need to prepare for resits, the same material is available in the form of a book of 20 practice examination papers.

I am currently working on a similar book dealing with Aircraft Performance. I have more than 1000 questions and am now getting down to the more time consuming task of composing the explanations.

I'm not entirely sure how to interpret the comments by peterj. If the message is that all things in life should be free, then I look forward to hearing from his airline.
Free flights around the world sound like a splendid idea.

I would merely repeat that the answers to the questions in this string are freely available, simply by e-mailing me at [email protected] I will of course include an add (for my book), which recipients are free to ignore.

I also provide a free telephone consultation service covering the subjects of POF, Engines and Engine Instruments. All I ask is that you ring me, rather than me ringing you. Receipt of the answers to the questions in this string and advice by telephone are free.

[Checkboard]

Hmmmmmmm ...... ;)