Hi Bod,

Recently, I'm studying P charts in Part9--Basic Aeroplane Performance in the Book if RPL. I understand the content of how to use those charts, but I have a question that concerned me lot. How are those chart made? How dose those charts come out?

For example, for chart of Airfield Pressure height, is it square box? why is temperature line slant? How to decide the gap between each temperature? the vertical line represents the pressure height; what about horizontal line?

As far as the take-off distance chart, why do both of vertical and horizontal line represent distance & the gab between each are getting narrow? how to decide? a small chart next to it(sorry, don't how to define the shade of it), why does it look like that?

I consulted other books, finding different charts. could you give me an explanation to those please or recommend some books&website I could look up?

Thanks,

Chao

I don't have Bob's books so I can only speak generically unless you post a picture of the chart(s) of interest.

How are those chart made?

The general equations which make up performance charts are fairly straightforward and can be found in most basic books on flight dynamics. Base flight test points are obtained for takeoff and landing and then the equations are used to generate intermediate and extrapolated data.

How dose those charts come out?

In terms of accuracy, the majority of charts are pretty good, providing that they have been generated sensibly. However, the charts include assumptions as to various factors .. if the real world factors differ from the assumptions in the P-charts, then all bets are off to a greater or lesser extent. Sometimes, you will see strange things and variations .. for instance, a few old P-charts were generated on the basis of constant takeoff (MTOW) or landing (MLW) speeds to save money for the customer in developing them .. and the charts get a tad strange in details, eg landing distance increasing with reducing weight (due to the higher speed flare involving a distance where the aircraft floats prior to being able to be put on the ground. Why DCA permitted them to be scheduled in such a manner is somewhat beyond me ..

chart of Airfield Pressure height, is it square box?

Generally, for the class of aircraft you are looking at here, pressure height plus OAT is used to generate density height which is more useful for piston-engined aircraft. The chart may look to be square, and may well be, but that is only incidental to the need to generate the density height output.

why is temperature line slant?

A necessary requirement to generate density heights from pressure heights across the region of interest..

How to decide the gap between each temperature?

Entirely up to the person generating the chart. The usual approach is to use intervals which give a reasonably easy to use chart while not looking a bit "strange".

the vertical line represents the pressure height; what about horizontal line?

Presuming you are referring to the old DCA format P-Charts, the altitude grid horizontal scale should be density height.

why do both of vertical and horizontal line represent distance[/b]

Again, presuming you are talking about the old DCA charts - a trick of drawing. The vertical scale is distance and just wraps around to the lower horizontal where the lower part of the chart is truncated.

gap between each are getting narrow?

Just a consequence of the chart equations.

a small chart next to it(sorry, don't how to define the shade of it), why does it look like that?

Again, presuming DCA P-charts. The grid is for surface correction. It applies a variation depending on what surface mu value you choose. The lines plotted are for the standard surface mu values DCA used.

some books & website

Books, mainly undergraduate level flight mechanics and similar, as well as flight test manuals (eg AGARD). Websites - a google search should locate places such as the US flight test schools which usually have some documents available for download

Hi John,

Thanks for your explanation. I just upload photos of those chart so that you could have a look. Maybe explain little bit according to photos. I just could not understand why those look like that. they are different from the charts that I learned in school, studying Math which more make sense to me. I mean that vertical and horizontal have different values which could make a shape come out. I also check out some other books where charts are different from those, so now I confused...

As a polit, does it need to know how to make those charts?or just need to how to use them?

Thanks,

Chao

Chao,

Thanks for that .. we are, indeed, dealing with the old DCA (antecedent of CASA) P-chart presentation, as I had guessed from your post. These go back a long ways, certainly to the early 60s and perhaps a few years prior to then .. back when DCA HO was in Melbourne and the performance gurus (which included weight control) were Icko Tenenbaum and John Fincher (both lovely chaps with whom to work). Unfortunately, Icko died a few years ago but John, last I heard, is enjoying his retirement in Gippsland.

The style of charts was introduced with the now defunct DCA style of light aircraft flight manual to meet the need for takeoff and landing distance data. This was associated with the domestic fleet's moving on from Austers and Tigers, etc. (which generally managed OK with just a CofA and simplistic distance requirements). They (just) predate my involvement in the Industry and I am not sure just who was responsible for their introduction ..although my guess would be Icko.

Chart presentation in performance work can take all sorts of twists and turns. There is nothing terribly clever about this particular style of presentation .. just a case that the originators in the early days developed this style. Although it looks quite different from, say, the typical GAMA POH style of chart, the information is much the same and can be plotted either way (and, indeed, other ways as well). You refer back to (Cartesian) work in school .. all the same sort of thing .. just a matter of plotting Xs and Ys although it can get a bit fancier if you need to plot in multiple dimensions to reduce the physical number of charts to tell the story.

For all charts, one starts with some sort of basic data, eg distances applicable to particular elevation and temperature but for nominated other parameters (wind, slope, etc). Then the other parameters are addressed by specific equations which look at how the particular parameter causes the basic data to vary .. this then is plotted as a modifying chart (often called carpets, grids, etc). This style is no different in that regard to others.

I see you are concerned by the grid which has the distances wrapped around to the horizontal axis. It might help you come to terms with this if you ..

(a) extrapolate the lower lines so that they all intersect along an extension of the vertical scale.
(b) move the distance scale numbers down to the extended vertical scale.

It then should be evident that all that is happening is that the bottom of the chart has been "cut off", if you like, and the numbers moved up along with the lines. It is not a case of both axes being distance scales .. indeed, the horizontal scale is density height, carried up from the lower grid involving pressure height and OAT. I guess one of the confusing bits is that we tend not to identify a lot of scales where that knowledge is of little use to the practical application of the charts.

Don't worry too much about the fact that this sort of information can be presented in a range of ways .. even just numeric tables. Just a fact of life and dependent on the preferences of the OEM aerodynamicists (the aerody section in a design office normally gets to look after flight manuals for their sins) or Industry engineering consultants who did the work originally.

For the pilot side of things, it might be nice to know how the charts are drawn but you certainly don't need to know that level of detail information. You do, however, need to know how to use the charts to extract information relevant to your flying operations.

If you need, do ask more questions and we can endeavour to answer them for you.

Hi John,

Thanks for your explanation. I got a few more questions about those chats to ask. I hope you could help me out.

As for as the density height chart, I read some other books and fully understand it now. You could see an attachment of coloured pic of density height, which I found from another book that made me understand better.

Now I got a few new questions. You can have a look at other two pictures first. One is from Bob, another is from FTA. First question is about the take-off distance chart. Why does the spacing between each line get narrowed? In one of chars from FTA, the lines look not straight, they look like curves. Should they be straight or curve? All those lines are plotted diagonally. Could they be plotted horizontally?

Secondly, for the slope chart, in picture of Bob's(Figure3), why is the level line close to up-slope rather than a diagonal line which divide the chart into two same parts? the spacing between 2%up and level is bigger than 2%down, why? In the FTA's chart(Cessna type take-off chart), the level line is the diagonal line, but why is the spacing between each other getting narrow from top to bottom? which of them is more accurate?

Thirdly, as far as the wing chart, why is not the line of zero wind a diagonal line? why is it on the left of diagonal line? how to define the tilt rate of each lines? they look like not 45 degree.

As you said before, 'for the pilot side of things, it might be nice to know how the charts are drawn but you certainly don't need to know that level of detail information. You do, however, need to know how to use the charts to extract information relevant to your flying operations.' I wanna ask that where they are from, those charts? coming with manuals of aircraft or from airport or some where? If there are not charts, does pilot need to draw them himself?

Thanks for your time.

Chao,

Let's play some more with these charts, shall we ?

You can have a look at other two pictures ..

First off, a generic comment. Both charts look to be the old DCA format. However, the specific equations which went into them are not disclosed so there is the possibility that they are neither quite the same nor, even, the same as the equations in the DCA Report. That makes it a little difficult to be very specific for the particular charts.

the take-off distance chart. Why does the spacing between each line get narrowed?

The upper left region of the distance grid is associated with higher density heights and higher AUWs .. ie the thrust/weight ratio decreases and overall performance decreases. As a consequence, the variation of TODR with increasing density height (or weight) is more rapid and the lines start to bunch up.

To see this a bit clearer, take a look at a few notional examples -

(a) a low AUW (say at nil wind, nil slope, short dry grass) comes into the distance grid as a horizontal line towards the bottom of the grid. Moving to the left (ie increasing density height) has the distance lines bunching up as the thrust decreases with increasing density height ie the degraded performance shows up as a more rapidly increasing distance requirement.

(b) if you repeat the exercise for a high AUW (for the same conditions), you see a similar effect with increasing density height but, due to the increased weight (further reducing t/w) the effect is more pronounced than for the lower weight.

(c) similarly, entering with low/high density heights, as you move vertically up the distance grid, you see much the same sort of effect as the weight increases.

In one of charts from FTA, the lines look not straight, they look like curves. Should they be straight or curve?

Generally, I would expect curves. The other chart appears to have been linearised .. and not terribly well. This is not the school’s fault or concern at all .. just what was done by the person who drew the chart originally.

All those lines are plotted diagonally. Could they be plotted horizontally?

Not quite sure what your point is here .. you can use drafting tricks to make the charts look whatever .. but at the expense of complicating their use needlessly and for no useful gain.

Secondly, for the slope chart, in picture of Bob's(Figure3), why is the level line close to up-slope rather than a diagonal line which divide the chart into two same parts?

The positioning of the nil slope line comes from the equation numbers and has nothing to do with dividing the grid into two halves. That is just an artefact of the way the grid was drawn by the originator.

the spacing between 2%up and level is bigger than 2%down, why?

If you come up from the weight grid, 2% down will give you a lower TODR than 2% up. An easy way to figure this out is

(a) for the acceleration, the downslope puts a gravity component of weight on your side and the net acceleration is higher than for the upslope where the gravity component of weight reduces your acceleration. As a result you get to the liftoff speed much quicker (and in a shorter distance) on a downslope than an upslope

(b) for the climb to 50ft, an upslope (assumed to be constant for the whole takeoff) means you take a longer air distance to get to 50 ft above the upsloping ground. Alternatively, for a downslope, you get there much quicker .. ie a geometric consideration.

(c) End result is that the downslope gives a significantly shorter TODR. I note that the effect is different between the two charts .. it would take knowledge of the specific equations to sort that out.

In the FTA's chart(Cessna type take-off chart), the level line is the diagonal line

Forget the diagonal line’s bisecting the grid .. that’s just a co-incidental artefact of the drafting. No reason why it should or shouldn't

but why is the spacing between each other getting narrow from top to bottom? which of them is more accurate?

I would need the equations for both charts to see exactly what is going on for this question.

Thirdly, as far as the wind chart, why is not the line of zero wind a diagonal line? why is it on the left of diagonal line?

Again, the lines do not divide the grid into two halves .. just an artefact of the drafting layout

how to define the tilt rate of each lines? they look like not 45 degree.

The slope follows from the specific equations and how the grid drafting work is done. I would need the specific equations to be much more informative.

where they are from, those charts? coming with manuals of aircraft or from airport or some where?

Takeoff and landing charts are developed either by the OEM’s flight test/aerodynamics sections, Regulators (DCA used to produce most of this format P-chart for the old flight manuals), or Industry engineering consultants who used to do this progressively more in the latter part of the period as DCA (and its descendants) devolved increasing amounts of work to Industry. I don’t remember just how many I would have designed .. probably several dozen, I guess .. the only ones which come to mind at the moment are the Commander singles after the 112A (that was done by Rudi Paspa as I recall). All involve the development of flight mechanics equations (examples can be found in the engineering and flight test texts) and flight test data to baseline the equations. Put the two together and you end up with a bunch of numbers which are either tabulated or plotted for flight crew use.

The data (as tables or graphs) either will be in a flight manual or a pilot operating handbook for most newer aircraft. If you go back a LONG way to the old machines, there may just be a single strip length requirement in the Certificate of Airworthiness. Going back to the early 50s and prior, there was very, very little in the way of real data. For the heavy aircraft civil world, the regulatory approach changed when ICAO issued their Provisional Means of Compliance document for performance in the early 50’s. Not many copies floating around these days .. although I have one on the bookshelf, courtesy of a retired CASA test pilot mate.

If there are not charts, does pilot need to draw them himself?

Can’t see the pilot ever having to do that .. you can presume reasonably that you will always have some appropriate and usable data available in the aircraft documentation.

Just want to pipe in and say "Wow". Thanks very much for the interesting and very detailed responses, John.
Cheers,
Rich

Very impressive, very detailed! Help me lot, much appreciate, John!!!