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Old 15th Mar 2006, 09:16
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Oktas8
 
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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

Last edited by Oktas8; 15th Mar 2006 at 09:31.
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