P charts
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P charts
Hi,I am sure everyone is familiar with the old performance graphs. Just wondering how I could convert the graphs to equations, so I could bung them in my laptop.Then input temp, pressure,slope,weight etc and the TODR would be spat out. Please dont comment on why I would even want to do this.
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yeah this is something me and some buddies attempted once at uni. couldn't really figure it out though...went to the bar instead.
there would be so many variables for each aircraft. i would be interested to know if somebody has done it though.
there would be so many variables for each aircraft. i would be interested to know if somebody has done it though.
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Each line on the p-chart is a maths equation (dur) so youd just work out those (or something like that).
the thick line is the line youd find on the pchar. all youd do is multiply the last answer by 2/2.1 (in this case).
havnt tried it though, let me know how you go.
the thick line is the line youd find on the pchar. all youd do is multiply the last answer by 2/2.1 (in this case).
havnt tried it though, let me know how you go.
Last edited by steinycans; 15th Mar 2006 at 04:19.
Grandpa Aerotart
That's all well and good but how many lines on a P Chart?
Factored or unfactored?
I would suggest about the best you could manage would be an excel spreadsheet with %s added for each 1000' above MSL, each 1 degree of slope, each 5 kts of HWC etc. and then a final buffer % added at the end.
But you would have to sit down with the actual charts and calculate all exactly what % each of these things adds to the basic zero wind, level, short dry grass MSL strip.
Personally I believe the variation in airfields within Australia is so small you'd be better placed simply working out a MTOW distance for several sets of circumstances and just eyeball it after that.
Unless a purely accedemic excercise I think you're on a flogging to nowhere
Factored or unfactored?
I would suggest about the best you could manage would be an excel spreadsheet with %s added for each 1000' above MSL, each 1 degree of slope, each 5 kts of HWC etc. and then a final buffer % added at the end.
But you would have to sit down with the actual charts and calculate all exactly what % each of these things adds to the basic zero wind, level, short dry grass MSL strip.
Personally I believe the variation in airfields within Australia is so small you'd be better placed simply working out a MTOW distance for several sets of circumstances and just eyeball it after that.
Unless a purely accedemic excercise I think you're on a flogging to nowhere
Also some charts I've used have curvy lines, so you'd have to be working out parabolas and all that kind of poop too.
Probably could be done, very time consuming but, I'd say.
Probably could be done, very time consuming but, I'd say.
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it totally could be done. let's face it, the people who made the charts have the data to make the lines and curves and everything.
the curvy lines are the hardest obviously. if you really wanted to do it, i think you'd have to do a number of examples (trial and error style) to ascertain the formulas for each line. this would be a big job. and it would only work for one aircraft.
the curvy lines are the hardest obviously. if you really wanted to do it, i think you'd have to do a number of examples (trial and error style) to ascertain the formulas for each line. this would be a big job. and it would only work for one aircraft.
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P Factors
If you search the CAA rules, you will find out the performance factors for wind, slope, surface - in part 135 if I remember. Take into account the altitude and temperature factor which you will know. Then you insert the correct aircraft Performance and voila! One P-Chart
Did you want to put it onto your palm pilot for rapid calculations?
ECT?
Did you want to put it onto your palm pilot for rapid calculations?
ECT?
Know a couple of people who have done this allready (mainly with W/B) and they reckon the biggest hurdle is convincing CASA thats it a safe alternative to the paper version.
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How to...
This is the hard way, doing it all yourself with none of the fancy auto-factorising software out there. Those with MathCad need not apply! In a couple of places I say to use a series of linear regressions over a range of values to approximate a curve. If you can find the equation of the curve (e.g. parabola), it's more elegant, but usually won't make a noticeable difference to the end result.
Take MTOW, sea level PA at ISA, zero wind, zero slope, nil surface factor (dry bitumen). Convert weight to TODR with a multiplication factor (for example, weight x 0.6 = TODR).
Take minimum practical TOW, convert to TODR with another multiplication factor (for example, weight x 0.73 = TODR).
Linearly regress the factor for all weights between minimum practical TOW and MTOW (for example, factor varies linearly between 0.73 at min TOW and 0.6 at MTOW). Check by converting an intermediate TOW to a TODR and comparing with the real P-Chart. If the weight lines on the P-chart are evenly spaced, it will work, but if not, you will need to go non-linear to get an accurate answer. Go non-linear only if you have to, by plotting actual multiplication factors at a range of weights, and linearly regressing between each factor over a narrow range. A curve is approximated quite well by a large number of short straight lines, if you follow me...
Congratulations! You've factored TOW.
Now factor for slope - use the commercial factors such as 5% change in TODR for each 1% slope, or whatever CASA says is true. That's actually an easy one, nice and linear.
Now factor for surface. Again, commercial CASA-based or manufacturer-generated data should be available, such as +15% for grass, etc.
Now the home straight - factor for Pressure Alt, holding temperature at ISA. It will be approximately linear from SL to about 5000', but if you have to go above that, allow for non-linearity by using a different factor for 5000-7000', 7000-9000' etc.
Factor for ISA deviation in the same way. Almost certainly non-linear, use one factor for ISA±5, another for ISA+5 to ISA+10, etc.
Tell your program how to convert OAT into ISA deviation so the user doesn't have to, and you have the software you need.
Now go back to using P-charts, because as someone else said, CASA probably won't accept your sterling work...
NB - someone above commented you'd have to repeat for each different aircraft. Not as bad as it sounds - as you will have worked out for yourself by this time, the only aircraft-specific variable is the weight-to-TODR factor which you worked out first. All the rest is a function of what grass does to tires, or what energy it takes to climb a hill, which does not change between aircraft types.
You could go one step further, recognising that P-charts are useless unless one uses the correct rotate & threshold speeds, and get the software to spit out nominal Vr and Vts along with TODR and LDR.
O8
Take MTOW, sea level PA at ISA, zero wind, zero slope, nil surface factor (dry bitumen). Convert weight to TODR with a multiplication factor (for example, weight x 0.6 = TODR).
Take minimum practical TOW, convert to TODR with another multiplication factor (for example, weight x 0.73 = TODR).
Linearly regress the factor for all weights between minimum practical TOW and MTOW (for example, factor varies linearly between 0.73 at min TOW and 0.6 at MTOW). Check by converting an intermediate TOW to a TODR and comparing with the real P-Chart. If the weight lines on the P-chart are evenly spaced, it will work, but if not, you will need to go non-linear to get an accurate answer. Go non-linear only if you have to, by plotting actual multiplication factors at a range of weights, and linearly regressing between each factor over a narrow range. A curve is approximated quite well by a large number of short straight lines, if you follow me...
Congratulations! You've factored TOW.
Now factor for slope - use the commercial factors such as 5% change in TODR for each 1% slope, or whatever CASA says is true. That's actually an easy one, nice and linear.
Now factor for surface. Again, commercial CASA-based or manufacturer-generated data should be available, such as +15% for grass, etc.
Now the home straight - factor for Pressure Alt, holding temperature at ISA. It will be approximately linear from SL to about 5000', but if you have to go above that, allow for non-linearity by using a different factor for 5000-7000', 7000-9000' etc.
Factor for ISA deviation in the same way. Almost certainly non-linear, use one factor for ISA±5, another for ISA+5 to ISA+10, etc.
Tell your program how to convert OAT into ISA deviation so the user doesn't have to, and you have the software you need.
Now go back to using P-charts, because as someone else said, CASA probably won't accept your sterling work...
NB - someone above commented you'd have to repeat for each different aircraft. Not as bad as it sounds - as you will have worked out for yourself by this time, the only aircraft-specific variable is the weight-to-TODR factor which you worked out first. All the rest is a function of what grass does to tires, or what energy it takes to climb a hill, which does not change between aircraft types.
You could go one step further, recognising that P-charts are useless unless one uses the correct rotate & threshold speeds, and get the software to spit out nominal Vr and Vts along with TODR and LDR.
O8
Last edited by Oktas8; 15th Mar 2006 at 09:31.
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Three simple ways to approach the problem
(a) use the original (and fairly simple equations) which were used to generate the majority of the P-charts. For the older charts there were two CASA-antecedent tech memos which gave the derivations from simplistic first principles. For some of the later examples which were produced prior to CASA opting out of local flight manuals, you might find charts based on the later (and much more rigorously complex) memo developed by JCF.
I don't have the books to hand but they are in my archives .. when I next spot them I will revisit this thread and put the older equations in for instance.
Alternatively, use some of the similarly derived equations from one of the standard references .. if I recall correctly the AGARD manuals had a reasonably useful set.
(b) do regressions on the charts as printed and generate a set of polynomials to suit
(c) similar to (b) but set up a set of look-up tables to do much the same sort of thing
Pretty simple non-rocket-science stuff ..
(a) use the original (and fairly simple equations) which were used to generate the majority of the P-charts. For the older charts there were two CASA-antecedent tech memos which gave the derivations from simplistic first principles. For some of the later examples which were produced prior to CASA opting out of local flight manuals, you might find charts based on the later (and much more rigorously complex) memo developed by JCF.
I don't have the books to hand but they are in my archives .. when I next spot them I will revisit this thread and put the older equations in for instance.
Alternatively, use some of the similarly derived equations from one of the standard references .. if I recall correctly the AGARD manuals had a reasonably useful set.
(b) do regressions on the charts as printed and generate a set of polynomials to suit
(c) similar to (b) but set up a set of look-up tables to do much the same sort of thing
Pretty simple non-rocket-science stuff ..
Bugsmasherdriverandjediknite
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hey John, try that out with a weight and balance on the B206 long ranger. Not quiet a "P" chart but a tricky exercise I reckon.
I saw a "P" chart once..............I think it was during an exam somewhere.
I saw a "P" chart once..............I think it was during an exam somewhere.
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A while since I have played with the LongRanger but the W&B charts are pretty straightforward from my recollection. Simplest setup for the PC is to set the thing up in Excel (or your favourite alternative). If you want to do that please do email me with where you are at and a copy of your present progress and I will give you a helping hand.
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I did a number of weight & balance charts for a range of a/c in a previous company. All you had to do was key in the variables and it would calculate and plot the results.
P charts? might take a tad longer
P charts? might take a tad longer
