Interpolating

[boogs82]

Hey everybody,

I'm just wondering if there's an easy way to figure this out when it comes to cruise performance? Unfortunately interpolating is something I struggle with quite a bit. I'm sure it's straight forward on the written PPL but it's something we have to know nonetheless. Any tips/advice would be great.

Thanks.

[Colonel Sanders]

I'm sure it's straight forward on the written PPL

Uh, no. You must learn to interpolate the horrible Cessna
performance charts. Other manufacturers have much
easier-to-use charts, and I suspect the engineers at Cessna
(long since retired) would be horrified if they knew what
had been perpetrated in their name.

Any of those engineers would tell you to use the worst number,
because the probability of you being able to duplicate the factory
performance numbers is a big fat zero.

You have a worn engine, worn prop, bugs on the scarred leading
edges and you are NOT a factory test pilot who flies very accurately.

Anyways, that is not the world you live in. Remember my
immortal words to my instructor candidates, when they start
to argue with me about stuff like this that doesn't make any
sense:

We eat this sh1t with a spoon

[ross1]

another good t-shirt...

[jschnurr]

It's easy if it is exactly half way (which is a high probability on the test) but for the FTU it won't always be that simple.
Say you have these numbers (for takeoff distance, 172M, 2300lbs):

Code: Select all

Pressure Alt              10C         20C            
1000                     915ft       980ft
2000                    1000ft      1070ft

Say your pressure altitude is 1150, and your temperature is 13.5... what to do?
First you have to realize that 1150 is .150 of the way between 1000 and 2000. Ok?

Code: Select all

Pressure Alt              10C         13.5C         20C            
1000                     915ft                     980ft
1150                     ???          ???          ???
2000                    1000ft                    1070ft

Now you want to find out what is .150 of the way between 915 and 1000 in the 10C column.
So you take the difference between the two: 1000-915 = 85. Multiply that by 0.15... =12.75, or round to 13. Add that to the lower chart value, in this
case, 915, and you get 928. So far so good?

Fill in the spaces on your chart with the remaining calculations:

Code: Select all

Pressure Alt              10C         13.5C         20C            
1000                     915ft                     980ft
1150                     928ft        ???          994ft
2000                    1000ft                    1070ft

Now you interpolate for the temperature (13.5 is 0.35 of the way between 10 and 20):

Code: Select all

Pressure Alt              10C         13.5C         20C            
1000                     915ft                     980ft
1150                     928ft        951ft        994ft
2000                    1000ft                    1070ft

The final result is your 172 will take off in exactly 951ft.

edited because apparently I can't do grade 2 math

[Shiny Side Up]

Hey everybody,

I'm just wondering if there's an easy way to figure this out when it comes to cruise performance?

[boogs82]

Thanks guys. I realize that you'll likely never have to do this in real life. I'm alright when it comes to math but for some reason I'm having difficulty grasping the concepts. I should have paid more attention to this in high school lol.

[Colonel Sanders]

The final result is your 172 will take off in exactly 958ft

It would have been a lot easier (and safer) to just
have taken the biggest number: 1070 feet

But that's not what they want you to do.

I have a theory about why the TC written test questions
are so completely bizarre. I've posted it here before, but
let me know if enough time has gone by that what's old
is new again.

[boogs82]

Well one thing I've figured out from reading everything here as well as from flying in general is that it's safer to overestimate distances than to underestimate. But of course that's common sense; which unfortunately isn't so common.

[MIQ]

Same thing with the fuel burn btw. If the POH states 8.1 gal / hour at 4.000ft and 8.4 gal / hour at 6.000ft and you're flying at 5, I'd just calculate with 9 gal / hour. Shouldn't do that on a written exam but in 'real life' I find this to be working out a lot better. I'd rather land with too much fuel in my tanks than with too little.
I know that you should calculate for reserve and contingency fuel anyway but I still feel better using the bigger number for my calculations.

[Shiny Side Up]

It would have been a lot easier (and safer) to just
have taken the biggest number: 1070 feet

At the end of the day though, all the written test is asking is two things: a) Do you have the ability to read a performance chart, and b) can you interpolate between numbers on that chart. In other words, can you read and follow directions, and can you do some grade six level math if you need to. Some charts are easier to use than the Cessna's some are worse. Cessna's really have been made to make the pilot's job easier if you look at them. After all, you don't have to do something hard like make a density altitude calculation, or use a Koch chart.

Personally I don't think its a bad thing if we disqualify people from being pilots who can't do grade six level math, but I'm sure the more egalitarian out there would disagree.

[sakism]

Now you want to find out what is .150 of the way between 915 and 1000 in the 10C column.
So you take the difference between the two: 1000-915 = 85. Multiply that by 0.15... =12.75, or round to 13. Add that to the lower chart value, in this
case, 915, and you get 938. So far so good?

Your extremely detailed explanation would carry a lot more weight if you had not added 915 and 13 and arrived at 938.

Remember: garbage in, garbage out.

[Colonel Sanders]

Personally I don't think its a bad thing if we disqualify people from being pilots who can't do grade six level math, but I'm sure the more egalitarian out there would disagree

It would be nice if pilots could also solve 2nd order
ordinary differential equations (eg RLC circuits) with
solutions of the form e to the i theta, so they would
understand my very lame joke about why Polish pilots
should not fly formation in right echelon.

The above is about as useful as the silly interpolation
business.

Poles in the right hand plane. Get it?

http://www.physicsforums.com/archive/in ... 13062.html

[boogs82]

Personally I don't think its a bad thing if we disqualify people from being pilots who can't do grade six level math, but I'm sure the more egalitarian out there would disagree.

I guess I'll quit while I'm ahead since I have a bit of difficulty grasping concepts that aren't used beyond the flight exams.

[Shiny Side Up]

The above is about as useful as the silly interpolation
business.

Its important to make the distiction that interpolating the Cessna charts is silly business, but having the ability to interpolate is not. After all if you can't interpolate numbers it shows a lack of knowledge of a very basic kind. Its an extrapolation of basic division skills, the ability to think in fractions, or what mean and median numbers are. I believe it was you who was lamenting a little while ago how people aren't taught to estimate anymore? The ability to estimate is based upon one's ability to think in terms of the above, a somewhat useful skill in every day life, for example I used my math powers to figure out how many bags of insulation I needed for my garage today.

Poles in the right hand plane. Get it?

Boooo.

[Colonel Sanders]

Estimation is an incredibly important skill, and comes with
experience, and a feel for the proportions of a system. For
example, if you're driving your car or motorcycle, and you
don't want to run out of gas, you can better be able to
estimate pretty well, where you're going to buy gas if you
are travelling someplace you have never been before.

However I will honestly admit that I am a math bigot and
a physics geek - . Lorre owes me money, frankly -
but I realize that not everyone shares my interest and
enthusiasm for understanding how things work - they
only want to be able to use it, and that's ok. Not everyone
that plays a fiddle wants to build a better one.

People like Steve Wolf

http://www.wolfpitts.com/steve.html

humble the rest of us.

[boogs82]

The problem for me wasn't dividing the numbers. The problem for me was identifying the relationships between the numbers when compared to standard rates identified in the performance charts and which numbers to use in order to figure out where to interpolate. Now that it was explained to me properly, I'm good to go. I must say. I completed the online training through Harv's Air and there wasn't much done to explain interpolating. At 30 years old I haven't done this math in quite a few years. The refresher helped quite a bit and when it was broken down it's simple to see. It's got nothing to do with not being able to grasp grade six math or not following instructions properly. It's got more to do with not having done something in many years.

[sidestick stirrer]

What I have been waiting for is a more-knowledgable contributor to mention that the differences between the altitudes and temperatures might not be linear but rather somewhat logarithmic, making interpolation less accurate than it at first appears.
In the real world ( of heavier iron), the performance charts are entered at the next higher values of weight, altitude and temperature but the next lower one for wind.
This takes but a few seconds and if the resultant runway required is less than the runway available, you're done.
If it exceeds the runway available, then initially just one value gets interpolated and the result compared, and so on...

[Colonel Sanders]

I don't think this crowd is up for

y = mx + b

let alone real-world non-linearities.

Also, the irony of the "precision" calculations, right
down to the last foot, is probably lost.

Meanwhile, the Cessnas are approaching 20 mph
too fast, and landing on the nosewheels first ...

Kind of funny, actually.

[sidestick stirrer]

"Meanwhile, the Cessnas are approaching 20 mph
too fast, and landing on the nosewheels first ..."

Couldn't agree more, AB. At the airport where I instruct, the runway is the shortest in the entire area, by far.
While it does take a little longer to get a student to solo as the energy tolerances at the threshold are necessarily tighter, there's no doubt that they are better pilots for it.

[Shiny Side Up]

Well there you've just exposed the whole paradox which is flight training where precision counts the most where it matters the least.

[Big Pistons Forever]

In the real world ( of heavier iron), the performance charts are entered at the next higher values of weight, altitude and temperature but the next lower one for wind.
This takes but a few seconds and if the resultant runway required is less than the runway available, you're done.
If it exceeds the runway available, then initially just one value gets interpolated and the result compared, and so on...

Excellent advice for the real world operation of any aircraft. Unfortunately we are not talking about the real world we are talking about the TC fantasy land that is the written exam. Here the powers that be have decided that interpolating to a such a high level of accuracy that the result is completely meaningless is an important skill for pilots