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## Interpolation accuracy in PEXO Performance exam

• Posts: 13

### SJM created the topic: Interpolation accuracy in PEXO Performance exam

Hi,
I have a question on exam accuracy, particuarly if the question is 'enter the value' as opposed to multi-choice.

Consider:
Exercise 4.4 (Page 82 , answers page 125 on the Performance e-text)

What TAS could be expected in an Echo when cruising at 5000ft with an OAT of plus 15 degrees Celsius, if gross weight is 2500kg and 75% power is used

My approach was (different to the Answer approach, but hopefully valid)
Pressure Height = 5000 feet
ISA Temperature = 15 - 2(5000/1000) = 15 - 10 = +5 degrees Celsius
ISA Deviation = OAT - ISA Temperature = 15 - 5 = plus 10
Density Height = Pressure Height + 120(ISA Deviation) = 5000 + 120(10) = 6200 feet
Since we have Density Height use the ISA Chart on the supplement - using 6200 feet values
• TAS(ISA; 5,000 feet; 2,500kg, 75% Power) = 192 kts
• TAS(ISA; 10,000 feet; 2,500kg, 75% Power) = 200 kts

This is 8 kts increase over 5000 feet; or 1.6kts/1000 feet;
So for 6200 feet TAS = 192kts (at 5000 feet) + [1.6x1.2] (for the extra 1200 feet) = 192+(1.6*1.2) = 193.9 kts
The Answer on page 125 takes a different (and valid) approach by interpolating the TAS at Pressure Height 5000 at ISA, and Pressure Height 10,000 at ISA+20 to get the TAS at Pressure Height of 5000 at ISA +10. All of this is at 2,500kg, 75% Power. The answer here is 193.5kts

MY Query:
Which approach is correct in an exam situation? The second approach worked well as ISA + 10 is in the middle between ISA and ISA+20.
If it was multi-choice I could select the right one, but I'm not sure how PEXO would mark me for 193.9 (my method) vs 193.5 (other method)... or is there an error in my calcs?

Cheers
SJM

• John.Heddles
• Offline
• ATPL/consulting aero engineer
• Posts: 331

### John.Heddles replied the topic: Interpolation accuracy in PEXO Performance exam

I'll leave it for Bob/Stuart to comment on what the examiner wants these days. Obviously, if he wants to see interpolations to 5 decimals, then give him what he wants.

However, there is a more general concern with your question. The tables etc., from which you get your basic figures for interpolation are developed by the aerodynamics guys/gals, and then refined by the flight test folk. If you are very lucky, the table accuracy might be 2-3 kts. Then consider how accurately you can fly/set/read your ASI. Interpolation to decimals, for any practical purpose, is a bit optimistic.

Give the examiner what he wants, obviously, but please don't think that there is any real world point in trying to interpolate better than to the nearer knot .. and then try and fly to somewhere near that figure.

Engineering specialist in aircraft performance and weight control.

• Posts: 13

### SJM replied the topic: Interpolation accuracy in PEXO Performance exam

Hi John - I totally agree from a practical flight ops stand point, hence the title of my post refers directly to the PEXO exam and not practical operations.

I've probably over-through this too much - I've always wondered how the PEXO exam deals with rounding etc (if there's valid range of answers) behind the scenes when marking.

• Posts: 1901

### bobtait replied the topic: Interpolation accuracy in PEXO Performance exam

The good news is that the examiner has given up on interpolations. A question that requires a TAS, for example, will simply give you a TAS to be used in your calculation of such things as fuel required etc.

I have included the TAS and other such tables in the supplement because the CASA syllabus requires that you should be able to extract operational information from tables or graphs, but CASA don't even give you the tables in the exam. They include such information in the text of the question.

Take heart my friend. We are all in constant danger of taking this sort of thing too seriously!!

• John.Heddles
• Offline
• ATPL/consulting aero engineer
• Posts: 331

### John.Heddles replied the topic: Interpolation accuracy in PEXO Performance exam

I have included the TAS and other such tables in the supplement because the CASA syllabus requires that you should be able to extract operational information from tables or graphs,

One would never see this go away so long as we have paper-based data - interpolation is a necessary skill for flight crew. One needs to note, though, that extrapolation has some traps and we generally avoid that exercise.

I must say I am reassured by Bob's comment that silly levels of arithmetic, for no benefit, are being culled. The nearer knot, certainly, is the best that one should try for with this sort of data.

Engineering specialist in aircraft performance and weight control.